Metrics for x / (x^2 + 1)

analyze1.0ms (0%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
100%	100%	0%	0%	0%	0%	0%	2

Compiler

Compiled 9 to 6 computations (33.3% 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)

sample551.0ms (9.1%)

Results

388.0ms

8256×

valid

Precisions

Click to see histograms. Total time spent on operations: 206.0ms

ival-mult: 86.0ms (41.8% of total)

ival-div: 63.0ms (30.6% of total)

ival-add: 43.0ms (20.9% of total)

const: 11.0ms (5.3% of total)

backward-pass: 3.0ms (1.5% of total)

Bogosity

preprocess43.0ms (0.7%)

Algorithm

2×	egg-herbie

Rules

280×	`fnmadd-define`
254×	`sum3-define`
246×	`fma-define`
144×	`fmsub-define`
134×	`fnmsub-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	19
1	32	19
2	70	18
3	148	18
4	306	18
5	550	18
6	873	18
7	875	18
8	899	18
9	915	18
0	5	6
1	10	6
0	10	6

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(/ x (+ (* x x) 1))

Outputs
(/ x (+ (* x x) 1))
(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))

Call 2

Inputs
(/ x (+ (* x x) 1))
(/ (neg x) (+ (* (neg x) (neg x)) 1))
(neg (/ (neg x) (+ (* (neg x) (neg x)) 1)))

Outputs
(/ x (+ (* x x) 1))
(/ x (fmsub x x -1))
(/ (neg x) (+ (* (neg x) (neg x)) 1))
(/ x (fnmsub x x 1))
(neg (/ (neg x) (+ (* (neg x) (neg x)) 1)))
(/ x (fmsub x x -1))

Symmetry

(negabs x)

explain52.0ms (0.8%)

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
66	-	-	`(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))`
0	-	-	`x`
0	-	-	`(+.f64 (*.f64 x x) #s(literal 1 binary64))`
0	-	-	`(*.f64 x x)`
0	-	-	`#s(literal 1 binary64)`

Results

27.0ms

512×

valid

Compiler

Compiled 46 to 17 computations (63% saved)

Precisions

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

ival-mult: 5.0ms (41.5% of total)

ival-div: 4.0ms (33.2% of total)

ival-add: 3.0ms (24.9% of total)

const: 1.0ms (8.3% of total)

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

eval0.0ms (0%)

Compiler: Compiled 8 to 5 computations (37.5% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	75.9%	(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))

Compiler

Compiled 8 to 5 computations (37.5% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Program
✓	cost-diff	(*.f64 x x)
✓	cost-diff	(+.f64 (*.f64 x x) #s(literal 1 binary64))
✓	cost-diff	(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	14
1	10	14
0	10	14

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(/ x (+ (* x x) 1))
x
(+ (* x x) 1)
(* x x)
1

Outputs
(/ x (+ (* x x) 1))
(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))
x
(+ (* x x) 1)
(+.f64 (*.f64 x x) #s(literal 1 binary64))
(* x x)
(*.f64 x x)
1
#s(literal 1 binary64)

localize23.0ms (0.4%)

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(+.f64 (*.f64 x x) #s(literal 1 binary64))
✓	accuracy	75.9%	(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))

Results

14.0ms

256×

valid

Compiler

Compiled 19 to 6 computations (68.4% saved)

Precisions

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

ival-div: 2.0ms (33.4% of total)

ival-mult: 2.0ms (33.4% of total)

ival-add: 1.0ms (16.7% of total)

const: 0.0ms (0% of total)

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

series2.0ms (0%)

Counts

3 → 36

Calls

Call 1

Inputs
#<alt (/ x (+ (* x x) 1))>
#<alt (+ (* x x) 1)>
#<alt (* x x)>

Outputs
#<alt x>
#<alt (* x (+ 1 (* -1 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))>
#<alt (/ 1 x)>
#<alt (/ (- 1 (/ 1 (pow x 2))) x)>
#<alt (/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)>
#<alt (/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)>
#<alt (/ 1 x)>
#<alt (* -1 (/ (- (/ 1 (pow x 2)) 1) x))>
#<alt (* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))>
#<alt (* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))>
#<alt 1>
#<alt (+ 1 (pow x 2))>
#<alt (+ 1 (pow x 2))>
#<alt (+ 1 (pow x 2))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ 1 (pow x 2))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ 1 (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)>

Calls

9 calls:

Time	Variable		Point	Expression
0.0ms	x	@	inf	(/ x (+ (* x x) 1))
0.0ms	x	@	0	(/ x (+ (* x x) 1))
0.0ms	x	@	-inf	(/ x (+ (* x x) 1))
0.0ms	x	@	inf	(+ (* x x) 1)
0.0ms	x	@	0	(+ (* x x) 1)

rewrite301.0ms (5%)

Algorithm

1×	batch-egg-rewrite

Rules

3352×	`/-lowering-/.f32`
3352×	`/-lowering-/.f64`
2528×	`-lowering-.f32`
2528×	`-lowering-.f64`
1738×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	12
1	32	12
2	209	12
3	1928	12
0	8654	12

Stop Event

1×	iter limit
1×	node limit

Counts

3 → 322

Calls

Call 1

Inputs
(/ x (+ (* x x) 1))
(+ (* x x) 1)
(* x x)

Outputs
(+.f64 (.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (.f64 x (.f64 x (.f64 x x)))) (.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (-.f64 #s(literal 1 binary64) (.f64 x x))))
(+.f64 (.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (-.f64 #s(literal 1 binary64) (.f64 x x))) (.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (.f64 x (.f64 x (.f64 x x)))))
(+.f64 (.f64 (/.f64 x (+.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64))) (.f64 x x)) (.f64 (/.f64 x (+.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal -1 binary64))) #s(literal -1 binary64)))
(+.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (/.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))))
(+.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) (.f64 (.f64 x (.f64 x (.f64 x x))) (/.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))))
(+.f64 (.f64 (.f64 x x) (/.f64 x (+.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64)))) (.f64 #s(literal -1 binary64) (/.f64 x (+.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal -1 binary64)))))
(exp.f64 (.f64 (log.f64 (/.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)) x)) #s(literal -1 binary64)))
(exp.f64 (+.f64 (log.f64 x) (.f64 (log1p.f64 (.f64 x x)) #s(literal -1 binary64))))
(exp.f64 (+.f64 (.f64 (log1p.f64 (.f64 x x)) #s(literal -1 binary64)) (log.f64 x)))
(-.f64 #s(literal 0 binary64) (/.f64 x (-.f64 #s(literal -1 binary64) (*.f64 x x))))
(-.f64 (/.f64 #s(literal 0 binary64) (+.f64 (.f64 x x) #s(literal 1 binary64))) (/.f64 x (-.f64 #s(literal -1 binary64) (.f64 x x))))
(-.f64 (/.f64 (/.f64 (.f64 x x) (+.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) x)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) x)))
(-.f64 (/.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) x)) (/.f64 (/.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) x)))
(fma.f64 (.f64 x x) (/.f64 x (+.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64))) (.f64 #s(literal -1 binary64) (/.f64 x (+.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64)))))
(fma.f64 (.f64 x (.f64 x (.f64 x x))) (/.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x)))))))
(fma.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (.f64 (.f64 x (.f64 x (.f64 x x))) (/.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x)))))))
(fma.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (.f64 x (.f64 x (.f64 x x))) (.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (-.f64 #s(literal 1 binary64) (*.f64 x x))))
(fma.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (-.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (.f64 x (.f64 x (*.f64 x x)))))
(fma.f64 (/.f64 x (+.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64))) (.f64 x x) (.f64 (/.f64 x (+.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64))) #s(literal -1 binary64)))
(neg.f64 (/.f64 x (-.f64 #s(literal -1 binary64) (*.f64 x x))))
(neg.f64 (.f64 #s(literal 1 binary64) (/.f64 x (-.f64 #s(literal -1 binary64) (.f64 x x)))))
(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)) x))
(/.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal -1 binary64) (*.f64 x x)))
(/.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal -1 binary64) (*.f64 x x)) x))
(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) x))
(/.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (*.f64 x x))) (neg.f64 (/.f64 #s(literal 1 binary64) x)))
(/.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 (.f64 x x) #s(literal -1 binary64)))))))
(/.f64 (/.f64 x (+.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) #s(literal -1 binary64))))
(/.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 (.f64 x x) #s(literal -1 binary64)))))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x)))))
(/.f64 (.f64 x (+.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (.f64 x x)))))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 x (.f64 x (.f64 x x))))))))
(/.f64 (.f64 x (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 (.f64 x x) #s(literal -1 binary64))))) (-.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 #s(literal 1 binary64) (.f64 x x))))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (-.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 #s(literal 1 binary64) (*.f64 x x)))))
(/.f64 (.f64 x (+.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64))) (.f64 (+.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64)) (+.f64 (*.f64 x x) #s(literal 1 binary64))))
(/.f64 (.f64 x (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1 binary64))) (.f64 (+.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64)) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 (*.f64 x x) #s(literal 1 binary64))))))
(/.f64 (neg.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 (.f64 x x) #s(literal -1 binary64))))))) (+.f64 #s(literal -1 binary64) (neg.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x))))))
(/.f64 (neg.f64 (.f64 x (+.f64 (.f64 x x) #s(literal -1 binary64)))) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal -1 binary64))))
(/.f64 (/.f64 x #s(literal 1 binary64)) (+.f64 (*.f64 x x) #s(literal 1 binary64)))
(/.f64 (.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x)) (-.f64 #s(literal -1 binary64) (.f64 x x)))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) (.f64 x x)))
(/.f64 (.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (+.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (.f64 x x)))))) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 x (.f64 x (*.f64 x x)))))))
(/.f64 (.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 (.f64 x x) #s(literal -1 binary64))))) (-.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 #s(literal 1 binary64) (.f64 x x))))) (-.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 #s(literal 1 binary64) (.f64 x x))))
(/.f64 (.f64 (/.f64 x (+.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64))) (+.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64))) (+.f64 (.f64 x x) #s(literal 1 binary64)))
(/.f64 (.f64 (/.f64 x (+.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64))) (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1 binary64))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 (.f64 x x) #s(literal 1 binary64)))))
(/.f64 (.f64 x (+.f64 (.f64 x x) #s(literal -1 binary64))) (+.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal -1 binary64)))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (-.f64 #s(literal -1 binary64) (.f64 x x))) (.f64 (-.f64 #s(literal -1 binary64) (.f64 x x)) x)) (.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)) (+.f64 (*.f64 x x) #s(literal 1 binary64))))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (/.f64 (-.f64 #s(literal -1 binary64) (.f64 x x)) x)) (.f64 (-.f64 #s(literal -1 binary64) (.f64 x x)) #s(literal 1 binary64))) (.f64 (-.f64 #s(literal -1 binary64) (.f64 x x)) (/.f64 (-.f64 #s(literal -1 binary64) (*.f64 x x)) x)))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (+.f64 (.f64 x x) #s(literal 1 binary64))) (.f64 (-.f64 #s(literal -1 binary64) (.f64 x x)) (-.f64 #s(literal 0 binary64) x))) (.f64 (-.f64 #s(literal -1 binary64) (.f64 x x)) (+.f64 (*.f64 x x) #s(literal 1 binary64))))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (+.f64 (.f64 x x) #s(literal 1 binary64))) (.f64 (-.f64 #s(literal -1 binary64) (.f64 x x)) (/.f64 x #s(literal -1 binary64)))) (.f64 (-.f64 #s(literal -1 binary64) (.f64 x x)) (+.f64 (*.f64 x x) #s(literal 1 binary64))))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 (.f64 x x) #s(literal -1 binary64))))))) (.f64 (-.f64 #s(literal -1 binary64) (.f64 x x)) (/.f64 x (+.f64 #s(literal -1 binary64) (neg.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))))) (.f64 (-.f64 #s(literal -1 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 (.f64 x x) #s(literal -1 binary64))))))))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) #s(literal -1 binary64)))) (.f64 (-.f64 #s(literal -1 binary64) (.f64 x x)) (/.f64 x (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64)))))) (.f64 (-.f64 #s(literal -1 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) #s(literal -1 binary64)))))
(/.f64 (neg.f64 (/.f64 x (+.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64)))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) #s(literal -1 binary64)))))
(/.f64 (neg.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 (.f64 x x) #s(literal -1 binary64))))))))
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(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 (.f64 x x) #s(literal -1 binary64))))) (-.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 #s(literal 1 binary64) (.f64 x x))))) (-.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 #s(literal 1 binary64) (.f64 x x))))
(.f64 (/.f64 (+.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64)) (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1 binary64))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 (.f64 x x) #s(literal 1 binary64)))))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 (.f64 x x) #s(literal 1 binary64)))))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 (*.f64 x x) #s(literal -1 binary64)))))))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) #s(literal -1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 (*.f64 x x) #s(literal -1 binary64))))))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) #s(literal -1 binary64))))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64))) #s(literal -1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) #s(literal -1 binary64)))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 (.f64 x x) #s(literal 1 binary64))) #s(literal -1 binary64)) (pow.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 (*.f64 x x) #s(literal -1 binary64))) #s(literal -1 binary64)))
(.f64 (pow.f64 (pow.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)) #s(literal -1/2 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)) #s(literal -1/2 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal -1 binary64))) (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64)) (pow.f64 (+.f64 x #s(literal -1 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (+.f64 (.f64 x x) #s(literal -1 binary64)) (+.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x)))))))
(.f64 (pow.f64 (/.f64 (+.f64 (.f64 x x) #s(literal -1 binary64)) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x))))))
(.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 (*.f64 x x) #s(literal -1 binary64))))))))
(.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (+.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x x))))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x x))))
(.f64 (pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 (.f64 x x) #s(literal -1 binary64))))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x)))))))
(.f64 (pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 (.f64 x x) #s(literal -1 binary64))))) (+.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1 binary64))))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)))
(exp.f64 (.f64 (.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 1 binary64)))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(*.f64 x x)
(.f64 (.f64 x x) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (.f64 x x))
(*.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 2 binary64)))
(*.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal 0 binary64) x))

simplify346.0ms (5.7%)

Algorithm

1×	egg-herbie

Rules

2026×	`sum4-define`
1714×	`sum3-define`
1512×	`-lowering-.f32`
1512×	`-lowering-.f64`
1410×	`+-lowering-+.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	45	211
1	137	172
2	356	167
3	1076	166
4	3300	166
0	8302	166

Stop Event

1×	iter limit
1×	node limit

Counts

36 → 36

Calls

Call 1

Inputs
x
(* x (+ 1 (* -1 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))
(/ 1 x)
(/ (- 1 (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)
(/ 1 x)
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))
(* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))
1
(+ 1 (pow x 2))
(+ 1 (pow x 2))
(+ 1 (pow x 2))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (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)

Outputs
x
(* x (+ 1 (* -1 (pow x 2))))
(.f64 x (-.f64 #s(literal 1 binary64) (.f64 x x)))
(* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1 binary64) (.f64 x x)))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))
(.f64 x (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (-.f64 #s(literal 1 binary64) (.f64 x x))))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (- 1 (/ 1 (pow x 2))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)
(/.f64 (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x))))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)
(/.f64 (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (.f64 x x))) (-.f64 (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal -1 binary64) (.f64 x (.f64 x (.f64 x x)))))) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))) x)
(* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))
(/.f64 (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x))))) x)
(* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))
(/.f64 (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (.f64 x x))) (-.f64 (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal -1 binary64) (.f64 x (.f64 x (.f64 x x)))))) x)
1
#s(literal 1 binary64)
(+ 1 (pow x 2))
(+.f64 #s(literal 1 binary64) (*.f64 x x))
(+ 1 (pow x 2))
(+.f64 #s(literal 1 binary64) (*.f64 x x))
(+ 1 (pow x 2))
(+.f64 #s(literal 1 binary64) (*.f64 x x))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(+.f64 #s(literal 1 binary64) (*.f64 x x))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(+.f64 #s(literal 1 binary64) (*.f64 x x))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(+.f64 #s(literal 1 binary64) (*.f64 x x))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(+.f64 #s(literal 1 binary64) (*.f64 x x))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(+.f64 #s(literal 1 binary64) (*.f64 x x))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(+.f64 #s(literal 1 binary64) (*.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)
(pow x 2)
(*.f64 x x)

eval47.0ms (0.8%)

Compiler: Compiled 11877 to 1048 computations (91.2% saved)

prune41.0ms (0.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	353	5	358
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	353	6	359

Accuracy

100.0%

Counts

359 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	75.6%	(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) x))
▶	55.6%	(/.f64 x (/.f64 (.f64 (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) #s(literal -1 binary64)))) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x))))))
✓	75.9%	(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))
▶	51.0%	(/.f64 #s(literal 1 binary64) x)
▶	51.3%	(.f64 x (-.f64 #s(literal 1 binary64) (.f64 x x)))
▶	52.3%	x

Compiler

Compiled 136 to 67 computations (50.7% saved)

simplify208.0ms (3.4%)

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(+.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x)))) #s(literal -1 binary64))
✓	cost-diff	640	(.f64 (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) #s(literal -1 binary64))))
✓	cost-diff	1920	(/.f64 (.f64 (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) #s(literal -1 binary64)))) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))))
✓	cost-diff	1920	(/.f64 x (/.f64 (.f64 (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) #s(literal -1 binary64)))) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x))))))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(-.f64 #s(literal 1 binary64) (*.f64 x x))
✓	cost-diff	0	(.f64 x (-.f64 #s(literal 1 binary64) (.f64 x x)))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) x)
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(+.f64 (*.f64 x x) #s(literal 1 binary64))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) #s(literal 1 binary64)))
✓	cost-diff	256	(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) x))

Rules

2898×	`-lowering-.f32`
2898×	`-lowering-.f64`
2004×	`/-lowering-/.f32`
2004×	`/-lowering-/.f64`
1606×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	21	116
1	71	101
2	186	96
3	539	93
4	2930	93
5	7158	93
0	8555	93

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(/ (/ 1 (+ (* x x) 1)) (/ 1 x))
(/ 1 (+ (* x x) 1))
1
(+ (* x x) 1)
(* x x)
x
(/ 1 x)
x
(/ 1 x)
1
x
(* x (- 1 (* x x)))
x
(- 1 (* x x))
1
(* x x)
(/ x (/ (* (+ (* (* x x) (* (* x (* x x)) (* x (* x x)))) -1) (/ 1 (+ (* x x) -1))) (+ 1 (* x (* x (* x x))))))
x
(/ (* (+ (* (* x x) (* (* x (* x x)) (* x (* x x)))) -1) (/ 1 (+ (* x x) -1))) (+ 1 (* x (* x (* x x)))))
(* (+ (* (* x x) (* (* x (* x x)) (* x (* x x)))) -1) (/ 1 (+ (* x x) -1)))
(+ (* (* x x) (* (* x (* x x)) (* x (* x x)))) -1)
(* (* x x) (* (* x (* x x)) (* x (* x x))))
(* x x)
(* (* x (* x x)) (* x (* x x)))
(* x (* x x))
-1
(/ 1 (+ (* x x) -1))
1
(+ (* x x) -1)
(+ 1 (* x (* x (* x x))))
(* x (* x (* x x)))

Outputs
(/ (/ 1 (+ (* x x) 1)) (/ 1 x))
(/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x)))
(/ 1 (+ (* x x) 1))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x x)))
1
#s(literal 1 binary64)
(+ (* x x) 1)
(+.f64 #s(literal 1 binary64) (*.f64 x x))
(* x x)
(*.f64 x x)
x
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
x
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
1
#s(literal 1 binary64)
x
(* x (- 1 (* x x)))
(.f64 x (-.f64 #s(literal 1 binary64) (.f64 x x)))
x
(- 1 (* x x))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
1
#s(literal 1 binary64)
(* x x)
(*.f64 x x)
(/ x (/ (* (+ (* (* x x) (* (* x (* x x)) (* x (* x x)))) -1) (/ 1 (+ (* x x) -1))) (+ 1 (* x (* x (* x x))))))
(/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x)))
x
(/ (* (+ (* (* x x) (* (* x (* x x)) (* x (* x x)))) -1) (/ 1 (+ (* x x) -1))) (+ 1 (* x (* x (* x x)))))
(+.f64 #s(literal 1 binary64) (*.f64 x x))
(* (+ (* (* x x) (* (* x (* x x)) (* x (* x x)))) -1) (/ 1 (+ (* x x) -1)))
(.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x x))) (+.f64 #s(literal 1 binary64) (*.f64 x x)))
(+ (* (* x x) (* (* x (* x x)) (* x (* x x)))) -1)
(+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 x x) (*.f64 x x)))) #s(literal -1 binary64))
(* (* x x) (* (* x (* x x)) (* x (* x x))))
(.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 x x) (*.f64 x x))))
(* x x)
(*.f64 x x)
(* (* x (* x x)) (* x (* x x)))
(.f64 (.f64 x x) (.f64 (.f64 x x) (*.f64 x x)))
(* x (* x x))
(.f64 x (.f64 x x))
-1
#s(literal -1 binary64)
(/ 1 (+ (* x x) -1))
(/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) #s(literal -1 binary64)))
1
#s(literal 1 binary64)
(+ (* x x) -1)
(+.f64 (*.f64 x x) #s(literal -1 binary64))
(+ 1 (* x (* x (* x x))))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (*.f64 x x)))
(* x (* x (* x x)))
(.f64 (.f64 x x) (*.f64 x x))

localize114.0ms (1.9%)

Localize:

Found 12 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) #s(literal -1 binary64)))
✓	accuracy	77.2%	(.f64 (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) #s(literal -1 binary64))))
✓	accuracy	75.9%	(/.f64 x (/.f64 (.f64 (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) #s(literal -1 binary64)))) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x))))))
✓	accuracy	64.7%	(/.f64 (.f64 (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) #s(literal -1 binary64)))) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))))
✓	accuracy	100.0%	(-.f64 #s(literal 1 binary64) (*.f64 x x))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	99.9%	(.f64 x (-.f64 #s(literal 1 binary64) (.f64 x x)))
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) x)
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(+.f64 (*.f64 x x) #s(literal 1 binary64))
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) #s(literal 1 binary64)))
✓	accuracy	76.1%	(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) x))

Results

76.0ms

256×

valid

Compiler

Compiled 235 to 22 computations (90.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 38.0ms

ival-mult: 22.0ms (57.2% of total)

ival-div: 10.0ms (26% of total)

ival-add: 5.0ms (13% of total)

ival-sub: 1.0ms (2.6% of total)

const: 0.0ms (0% of total)

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

series12.0ms (0.2%)

Counts

12 → 144

Calls

Call 1

Inputs
#<alt (/ (/ 1 (+ (* x x) 1)) (/ 1 x))>
#<alt (/ 1 (+ (* x x) 1))>
#<alt (+ (* x x) 1)>
#<alt (* x x)>
#<alt (/ 1 x)>
#<alt (* x (- 1 (* x x)))>
#<alt (- 1 (* x x))>
#<alt (/ x (/ (* (+ (* (* x x) (* (* x (* x x)) (* x (* x x)))) -1) (/ 1 (+ (* x x) -1))) (+ 1 (* x (* x (* x x))))))>
#<alt (/ (* (+ (* (* x x) (* (* x (* x x)) (* x (* x x)))) -1) (/ 1 (+ (* x x) -1))) (+ 1 (* x (* x (* x x)))))>
#<alt (* (+ (* (* x x) (* (* x (* x x)) (* x (* x x)))) -1) (/ 1 (+ (* x x) -1)))>
#<alt (+ (* (* x x) (* (* x (* x x)) (* x (* x x)))) -1)>
#<alt (/ 1 (+ (* x x) -1))>

Outputs
#<alt x>
#<alt (* x (+ 1 (* -1 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))>
#<alt (/ 1 x)>
#<alt (/ (- 1 (/ 1 (pow x 2))) x)>
#<alt (/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)>
#<alt (/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)>
#<alt (/ 1 x)>
#<alt (* -1 (/ (- (/ 1 (pow x 2)) 1) x))>
#<alt (* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))>
#<alt (* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))>
#<alt 1>
#<alt (+ 1 (* -1 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (pow x 2) 1)))>
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1)))>
#<alt (/ 1 (pow x 2))>
#<alt (/ (- 1 (/ 1 (pow x 2))) (pow x 2))>
#<alt (/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) (pow x 2))>
#<alt (/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ (- 1 (/ 1 (pow x 2))) (pow x 2))>
#<alt (/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) (pow x 2))>
#<alt (/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) (pow x 2))>
#<alt 1>
#<alt (+ 1 (pow x 2))>
#<alt (+ 1 (pow x 2))>
#<alt (+ 1 (pow x 2))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ 1 (pow x 2))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ 1 (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 (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt x>
#<alt (* x (+ 1 (* -1 (pow x 2))))>
#<alt (* x (+ 1 (* -1 (pow x 2))))>
#<alt (* x (+ 1 (* -1 (pow x 2))))>
#<alt (* -1 (pow x 3))>
#<alt (* (pow x 3) (- (/ 1 (pow x 2)) 1))>
#<alt (* (pow x 3) (- (/ 1 (pow x 2)) 1))>
#<alt (* (pow x 3) (- (/ 1 (pow x 2)) 1))>
#<alt (* -1 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- 1 (/ 1 (pow x 2)))))>
#<alt (* -1 (* (pow x 3) (- 1 (/ 1 (pow x 2)))))>
#<alt (* -1 (* (pow x 3) (- 1 (/ 1 (pow x 2)))))>
#<alt 1>
#<alt (+ 1 (* -1 (pow x 2)))>
#<alt (+ 1 (* -1 (pow x 2)))>
#<alt (+ 1 (* -1 (pow x 2)))>
#<alt (* -1 (pow x 2))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1))>
#<alt (* -1 (pow x 2))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1))>
#<alt x>
#<alt (* x (+ 1 (* -1 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))>
#<alt (/ 1 x)>
#<alt (/ (- 1 (/ 1 (pow x 2))) x)>
#<alt (/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)>
#<alt (/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)>
#<alt (/ 1 x)>
#<alt (* -1 (/ (- (/ 1 (pow x 2)) 1) x))>
#<alt (* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))>
#<alt (* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))>
#<alt 1>
#<alt (+ 1 (pow x 2))>
#<alt (+ 1 (pow x 2))>
#<alt (+ 1 (pow x 2))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ 1 (pow x 2))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ 1 (pow x 2))))>
#<alt 1>
#<alt (+ 1 (pow x 2))>
#<alt (+ 1 (* (pow x 2) (+ 1 (pow x 2))))>
#<alt (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 1 (pow x 2))))))>
#<alt (pow x 6)>
#<alt (* (pow x 6) (+ 1 (/ 1 (pow x 2))))>
#<alt (* (pow x 6) (+ 1 (+ (/ 1 (pow x 2)) (/ 1 (pow x 4)))))>
#<alt (* (pow x 6) (+ 1 (+ (/ 1 (pow x 2)) (+ (/ 1 (pow x 4)) (/ 1 (pow x 6))))))>
#<alt (pow x 6)>
#<alt (* (pow x 6) (+ 1 (/ 1 (pow x 2))))>
#<alt (* (pow x 6) (+ 1 (+ (/ 1 (pow x 2)) (/ 1 (pow x 4)))))>
#<alt (* (pow x 6) (+ 1 (+ (/ 1 (pow x 2)) (+ (/ 1 (pow x 4)) (/ 1 (pow x 6))))))>
#<alt -1>
#<alt -1>
#<alt (- (pow x 8) 1)>
#<alt (- (pow x 8) 1)>
#<alt (pow x 8)>
#<alt (pow x 8)>
#<alt (* (pow x 8) (- 1 (/ 1 (pow x 8))))>
#<alt (* (pow x 8) (- 1 (/ 1 (pow x 8))))>
#<alt (pow x 8)>
#<alt (pow x 8)>
#<alt (* (pow x 8) (- 1 (/ 1 (pow x 8))))>
#<alt (* (pow x 8) (- 1 (/ 1 (pow x 8))))>
#<alt -1>
#<alt (- (* -1 (pow x 2)) 1)>
#<alt (- (* (pow x 2) (- (* -1 (pow x 2)) 1)) 1)>
#<alt (- (* (pow x 2) (- (* (pow x 2) (- (* -1 (pow x 2)) 1)) 1)) 1)>
#<alt (/ 1 (pow x 2))>
#<alt (/ (+ 1 (/ 1 (pow x 2))) (pow x 2))>
#<alt (/ (+ 1 (+ (/ 1 (pow x 2)) (/ 1 (pow x 4)))) (pow x 2))>
#<alt (/ (+ 1 (+ (/ 1 (pow x 2)) (+ (/ 1 (pow x 4)) (/ 1 (pow x 6))))) (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ (+ 1 (/ 1 (pow x 2))) (pow x 2))>
#<alt (/ (+ 1 (+ (/ 1 (pow x 2)) (/ 1 (pow x 4)))) (pow x 2))>
#<alt (/ (+ 1 (+ (/ 1 (pow x 2)) (+ (/ 1 (pow x 4)) (/ 1 (pow x 6))))) (pow x 2))>

Calls

36 calls:

Time	Variable		Point	Expression
6.0ms	x	@	0	(/ (* (+ (* (* x x) (* (* x (* x x)) (* x (* x x)))) -1) (/ 1 (+ (* x x) -1))) (+ 1 (* x (* x (* x x)))))
1.0ms	x	@	inf	(/ (* (+ (* (* x x) (* (* x (* x x)) (* x (* x x)))) -1) (/ 1 (+ (* x x) -1))) (+ 1 (* x (* x (* x x)))))
0.0ms	x	@	-inf	(/ 1 x)
0.0ms	x	@	inf	(/ x (/ (* (+ (* (* x x) (* (* x (* x x)) (* x (* x x)))) -1) (/ 1 (+ (* x x) -1))) (+ 1 (* x (* x (* x x))))))
0.0ms	x	@	0	(/ x (/ (* (+ (* (* x x) (* (* x (* x x)) (* x (* x x)))) -1) (/ 1 (+ (* x x) -1))) (+ 1 (* x (* x (* x x))))))

rewrite547.0ms (9%)

Algorithm

1×	batch-egg-rewrite

Rules

3456×	`/-lowering-/.f32`
3456×	`/-lowering-/.f64`
3360×	`-lowering-.f32`
3360×	`-lowering-.f64`
1190×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	21	69
1	167	61
2	1280	57
0	8747	57

Stop Event

1×	iter limit
1×	node limit

Counts

12 → 943

Calls

Call 1

Inputs
(/ (/ 1 (+ (* x x) 1)) (/ 1 x))
(/ 1 (+ (* x x) 1))
(+ (* x x) 1)
(* x x)
(/ 1 x)
(* x (- 1 (* x x)))
(- 1 (* x x))
(/ x (/ (* (+ (* (* x x) (* (* x (* x x)) (* x (* x x)))) -1) (/ 1 (+ (* x x) -1))) (+ 1 (* x (* x (* x x))))))
(/ (* (+ (* (* x x) (* (* x (* x x)) (* x (* x x)))) -1) (/ 1 (+ (* x x) -1))) (+ 1 (* x (* x (* x x)))))
(* (+ (* (* x x) (* (* x (* x x)) (* x (* x x)))) -1) (/ 1 (+ (* x x) -1)))
(+ (* (* x x) (* (* x (* x x)) (* x (* x x)))) -1)
(/ 1 (+ (* x x) -1))

Outputs
(+.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 x (/.f64 #s(literal 1 binary64) x)))) (.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 x (/.f64 #s(literal 1 binary64) x)))) (.f64 x (.f64 x (.f64 x x)))))
(+.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 x (/.f64 #s(literal 1 binary64) x)))) (/.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x)))) (+.f64 x (/.f64 #s(literal 1 binary64) x)))))
(+.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 x (/.f64 #s(literal 1 binary64) x)))) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 x (/.f64 #s(literal 1 binary64) x)))))
(+.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 x (/.f64 #s(literal 1 binary64) x)))) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x)))) (+.f64 x (/.f64 #s(literal 1 binary64) x)))))
(exp.f64 (*.f64 (log.f64 (+.f64 x (/.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64)))
(exp.f64 (-.f64 (.f64 (log1p.f64 (.f64 x x)) #s(literal -1 binary64)) (*.f64 (log.f64 x) #s(literal -1 binary64))))
(-.f64 #s(literal 0 binary64) (/.f64 x (-.f64 #s(literal -1 binary64) (*.f64 x x))))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal -1 binary64) (.f64 x x))) (/.f64 x (-.f64 #s(literal -1 binary64) (.f64 x x))))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 #s(literal -1 binary64) x)) (/.f64 x (-.f64 #s(literal -1 binary64) (*.f64 x x))))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 x (/.f64 #s(literal 1 binary64) x)))) (/.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x)))) (+.f64 x (/.f64 #s(literal 1 binary64) x)))))
(fma.f64 (.f64 x (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 x (/.f64 #s(literal 1 binary64) x)))) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x)))) (+.f64 x (/.f64 #s(literal 1 binary64) x)))))
(fma.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 x (/.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 x (/.f64 #s(literal 1 binary64) x)))) (.f64 x (.f64 x (.f64 x x)))))
(fma.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 x (/.f64 #s(literal 1 binary64) x)))) (.f64 x (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x)))) (+.f64 x (/.f64 #s(literal 1 binary64) x)))))
(neg.f64 (/.f64 x (-.f64 #s(literal -1 binary64) (*.f64 x x))))
(/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x)))
(/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x)))) (+.f64 x (/.f64 #s(literal 1 binary64) x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 #s(literal 1 binary64) (.f64 x x))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64))))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x (*.f64 x x))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 #s(literal 1 binary64) (.f64 x x))) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x))))) (.f64 x (-.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (*.f64 x x))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64)))) (.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 x (/.f64 #s(literal 1 binary64) x)))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x (*.f64 x x))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 x (/.f64 #s(literal 1 binary64) x)))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (*.f64 x x))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) #s(literal -1 binary64))) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x))))) (/.f64 x (+.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (*.f64 x x)))) #s(literal -1 binary64)))))
(/.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x x)))
(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x x))) (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x))))
(/.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x)))) (+.f64 x (/.f64 #s(literal 1 binary64) x))))
(/.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal -1 binary64) (*.f64 x x)))
(/.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (*.f64 x x))) (/.f64 #s(literal -1 binary64) x))
(/.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 x (/.f64 #s(literal 1 binary64) x)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x))))))
(/.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x (.f64 x x)))))) (.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 #s(literal 1 binary64) (.f64 x x))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal -1 binary64))))))
(/.f64 (.f64 x (-.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))))) (.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 #s(literal 1 binary64) (.f64 x x))) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x))))))
(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))
(/.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 x (/.f64 #s(literal 1 binary64) x)))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x (.f64 x x)))))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal -1 binary64)))))
(/.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 x (/.f64 #s(literal 1 binary64) x)))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))))) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x)))))
(/.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x))))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 #s(literal 1 binary64) (*.f64 x x))))
(/.f64 (/.f64 x (+.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal -1 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) #s(literal -1 binary64))) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x))))))
(/.f64 (neg.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (-.f64 #s(literal -1 binary64) (*.f64 x x))))
(/.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64))
(/.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 x (/.f64 #s(literal 1 binary64) x))))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x)))))))
(/.f64 (neg.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x (.f64 x x))))))) (neg.f64 (.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 #s(literal 1 binary64) (.f64 x x))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal -1 binary64)))))))
(/.f64 (neg.f64 (.f64 x (-.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))))) (neg.f64 (.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 #s(literal 1 binary64) (.f64 x x))) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x)))))))
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(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal -1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x (.f64 x x)))))))))) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x (.f64 x x)))))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (*.f64 x x)))))))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x (.f64 x x)))))) #s(literal -1 binary64)))) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1 binary64)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x (.f64 x x)))))) (+.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1 binary64))) #s(literal 3 binary64))) (+.f64 (.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x (.f64 x x)))))) (+.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1 binary64))) (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x (.f64 x x)))))) (+.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1 binary64)))) (+.f64 (.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1 binary64)))) (.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x (.f64 x x)))))) (+.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (*.f64 x x)))) #s(literal 1 binary64)))))))
(/.f64 (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x (.f64 x x))))))) #s(literal 1 binary64)) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x (.f64 x x)))))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (*.f64 x x)))))))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x (.f64 x x)))))) (+.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1 binary64))) (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x (.f64 x x)))))) (+.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1 binary64)))) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1 binary64))))) (+.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x (.f64 x x)))))) (+.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (*.f64 x x)))) #s(literal 1 binary64)))))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (*.f64 x x)))) #s(literal -1 binary64))) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal -1 binary64)))
(.f64 (+.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal -1 binary64)) #s(literal 1 binary64))
(.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal -1 binary64)))
(.f64 (+.f64 #s(literal -1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x (.f64 x x)))))))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x (.f64 x x)))))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))))))
(.f64 (+.f64 #s(literal -1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x (.f64 x x)))))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x (.f64 x x)))))) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))))))
(.f64 (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x (.f64 x x)))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (*.f64 x x)))) #s(literal 1 binary64))))
(.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal -1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x (.f64 x x))))))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x (.f64 x x)))))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))))))))
(.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x (.f64 x x)))))) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (*.f64 x x)))) #s(literal 1 binary64)))))
(.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x (.f64 x x))))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (*.f64 x x)))))))
(exp.f64 (.f64 (log.f64 (+.f64 (.f64 x x) #s(literal -1 binary64))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x x))))
(-.f64 (/.f64 (.f64 x x) (+.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64))) (/.f64 #s(literal -1 binary64) (+.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal -1 binary64))))
(-.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal -1 binary64))) (/.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (+.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal -1 binary64))))
(-.f64 (/.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 (.f64 x x) #s(literal -1 binary64))) (+.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) #s(literal -1 binary64))) (+.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal -1 binary64))))
(neg.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x x))))
(/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) #s(literal -1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))))
(/.f64 (+.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64)))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x x)))
(/.f64 (-.f64 #s(literal -1 binary64) (.f64 x x)) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (.f64 x x))))
(/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x x)))) (+.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal -1 binary64)))
(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x x))))) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal -1 binary64))))
(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (+.f64 x #s(literal -1 binary64)))
(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x x))))
(/.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) (-.f64 #s(literal 0 binary64) (+.f64 x #s(literal -1 binary64))))
(pow.f64 (+.f64 (*.f64 x x) #s(literal -1 binary64)) #s(literal -1 binary64))
(pow.f64 (.f64 (+.f64 (.f64 x x) #s(literal -1 binary64)) (+.f64 (*.f64 x x) #s(literal -1 binary64))) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 (+.f64 (*.f64 x x) #s(literal -1 binary64)) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 (log.f64 (+.f64 (*.f64 x x) #s(literal -1 binary64)))) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) #s(literal -1 binary64))))
(.f64 (+.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal -1 binary64))))
(.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x x))))
(.f64 (+.f64 (.f64 x x) #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) #s(literal -1 binary64))) (+.f64 (.f64 x x) #s(literal -1 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) #s(literal -1 binary64))) #s(literal 1 binary64))
(.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (*.f64 x x)))) #s(literal -1 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))
(.f64 (pow.f64 (+.f64 (.f64 x x) #s(literal -1 binary64)) #s(literal -1/2 binary64)) (pow.f64 (+.f64 (*.f64 x x) #s(literal -1 binary64)) #s(literal -1/2 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 x x)))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal -1 binary64))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 x x)))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal -1 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 x x))))) #s(literal -1 binary64)))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 #s(literal 1 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) #s(literal -1 binary64))))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (+.f64 #s(literal 1 binary64) (.f64 x x))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 #s(literal 1 binary64) (.f64 x x)))) (+.f64 (.f64 x x) #s(literal -1 binary64))))

simplify213.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

2880×	`-lowering-.f32`
2880×	`-lowering-.f64`
1926×	`/-lowering-/.f32`
1926×	`/-lowering-/.f64`
1754×	`+-lowering-+.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	81	987
1	241	801
2	692	777
3	2322	759
4	7783	759
0	8247	759

Stop Event

1×	iter limit
1×	node limit

Counts

144 → 144

Calls

Call 1

Inputs
x
(* x (+ 1 (* -1 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))
(/ 1 x)
(/ (- 1 (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)
(/ 1 x)
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))
(* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))
1
(+ 1 (* -1 (pow x 2)))
(+ 1 (* (pow x 2) (- (pow x 2) 1)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1)))
(/ 1 (pow x 2))
(/ (- 1 (/ 1 (pow x 2))) (pow x 2))
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) (pow x 2))
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) (pow x 2))
(/ 1 (pow x 2))
(/ (- 1 (/ 1 (pow x 2))) (pow x 2))
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) (pow x 2))
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) (pow x 2))
1
(+ 1 (pow x 2))
(+ 1 (pow x 2))
(+ 1 (pow x 2))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (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)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
x
(* x (+ 1 (* -1 (pow x 2))))
(* x (+ 1 (* -1 (pow x 2))))
(* x (+ 1 (* -1 (pow x 2))))
(* -1 (pow x 3))
(* (pow x 3) (- (/ 1 (pow x 2)) 1))
(* (pow x 3) (- (/ 1 (pow x 2)) 1))
(* (pow x 3) (- (/ 1 (pow x 2)) 1))
(* -1 (pow x 3))
(* -1 (* (pow x 3) (- 1 (/ 1 (pow x 2)))))
(* -1 (* (pow x 3) (- 1 (/ 1 (pow x 2)))))
(* -1 (* (pow x 3) (- 1 (/ 1 (pow x 2)))))
1
(+ 1 (* -1 (pow x 2)))
(+ 1 (* -1 (pow x 2)))
(+ 1 (* -1 (pow x 2)))
(* -1 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* -1 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
x
(* x (+ 1 (* -1 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))
(/ 1 x)
(/ (- 1 (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)
(/ 1 x)
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))
(* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))
1
(+ 1 (pow x 2))
(+ 1 (pow x 2))
(+ 1 (pow x 2))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
1
(+ 1 (pow x 2))
(+ 1 (* (pow x 2) (+ 1 (pow x 2))))
(+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 1 (pow x 2))))))
(pow x 6)
(* (pow x 6) (+ 1 (/ 1 (pow x 2))))
(* (pow x 6) (+ 1 (+ (/ 1 (pow x 2)) (/ 1 (pow x 4)))))
(* (pow x 6) (+ 1 (+ (/ 1 (pow x 2)) (+ (/ 1 (pow x 4)) (/ 1 (pow x 6))))))
(pow x 6)
(* (pow x 6) (+ 1 (/ 1 (pow x 2))))
(* (pow x 6) (+ 1 (+ (/ 1 (pow x 2)) (/ 1 (pow x 4)))))
(* (pow x 6) (+ 1 (+ (/ 1 (pow x 2)) (+ (/ 1 (pow x 4)) (/ 1 (pow x 6))))))
-1
-1
(- (pow x 8) 1)
(- (pow x 8) 1)
(pow x 8)
(pow x 8)
(* (pow x 8) (- 1 (/ 1 (pow x 8))))
(* (pow x 8) (- 1 (/ 1 (pow x 8))))
(pow x 8)
(pow x 8)
(* (pow x 8) (- 1 (/ 1 (pow x 8))))
(* (pow x 8) (- 1 (/ 1 (pow x 8))))
-1
(- (* -1 (pow x 2)) 1)
(- (* (pow x 2) (- (* -1 (pow x 2)) 1)) 1)
(- (* (pow x 2) (- (* (pow x 2) (- (* -1 (pow x 2)) 1)) 1)) 1)
(/ 1 (pow x 2))
(/ (+ 1 (/ 1 (pow x 2))) (pow x 2))
(/ (+ 1 (+ (/ 1 (pow x 2)) (/ 1 (pow x 4)))) (pow x 2))
(/ (+ 1 (+ (/ 1 (pow x 2)) (+ (/ 1 (pow x 4)) (/ 1 (pow x 6))))) (pow x 2))
(/ 1 (pow x 2))
(/ (+ 1 (/ 1 (pow x 2))) (pow x 2))
(/ (+ 1 (+ (/ 1 (pow x 2)) (/ 1 (pow x 4)))) (pow x 2))
(/ (+ 1 (+ (/ 1 (pow x 2)) (+ (/ 1 (pow x 4)) (/ 1 (pow x 6))))) (pow x 2))

Outputs
x
(* x (+ 1 (* -1 (pow x 2))))
(.f64 x (-.f64 #s(literal 1 binary64) (.f64 x x)))
(* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x x))))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))
(.f64 x (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x))))))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (- 1 (/ 1 (pow x 2))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))) (.f64 x x))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)
(/.f64 (-.f64 (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))) (.f64 x x)) (+.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (.f64 x (.f64 x x))))) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))) x)
(* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))) (.f64 x x))) x)
(* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))
(/.f64 (-.f64 (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))) (.f64 x x)) (+.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (.f64 x (.f64 x x))))) x)
1
#s(literal 1 binary64)
(+ 1 (* -1 (pow x 2)))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(+ 1 (* (pow x 2) (- (pow x 2) 1)))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x x)))))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1)))
(.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x)))))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ (- 1 (/ 1 (pow x 2))) (pow x 2))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (.f64 x x))) (.f64 x x))
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) (pow x 2))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))) (.f64 x x))) (*.f64 x x))
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) (pow x 2))
(/.f64 (-.f64 (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))) (.f64 x x)) (+.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (.f64 x (.f64 x x))))) (*.f64 x x))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ (- 1 (/ 1 (pow x 2))) (pow x 2))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (.f64 x x))) (.f64 x x))
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) (pow x 2))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))) (.f64 x x))) (*.f64 x x))
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) (pow x 2))
(/.f64 (-.f64 (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))) (.f64 x x)) (+.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (.f64 x (.f64 x x))))) (*.f64 x x))
1
#s(literal 1 binary64)
(+ 1 (pow x 2))
(+.f64 #s(literal 1 binary64) (*.f64 x x))
(+ 1 (pow x 2))
(+.f64 #s(literal 1 binary64) (*.f64 x x))
(+ 1 (pow x 2))
(+.f64 #s(literal 1 binary64) (*.f64 x x))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(+.f64 #s(literal 1 binary64) (*.f64 x x))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(+.f64 #s(literal 1 binary64) (*.f64 x x))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(+.f64 #s(literal 1 binary64) (*.f64 x x))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(+.f64 #s(literal 1 binary64) (*.f64 x x))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(+.f64 #s(literal 1 binary64) (*.f64 x x))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(+.f64 #s(literal 1 binary64) (*.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)
(pow x 2)
(*.f64 x x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
x
(* x (+ 1 (* -1 (pow x 2))))
(.f64 x (-.f64 #s(literal 1 binary64) (.f64 x x)))
(* x (+ 1 (* -1 (pow x 2))))
(.f64 x (-.f64 #s(literal 1 binary64) (.f64 x x)))
(* x (+ 1 (* -1 (pow x 2))))
(.f64 x (-.f64 #s(literal 1 binary64) (.f64 x x)))
(* -1 (pow x 3))
(-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x)))
(* (pow x 3) (- (/ 1 (pow x 2)) 1))
(.f64 x (-.f64 #s(literal 1 binary64) (.f64 x x)))
(* (pow x 3) (- (/ 1 (pow x 2)) 1))
(.f64 x (-.f64 #s(literal 1 binary64) (.f64 x x)))
(* (pow x 3) (- (/ 1 (pow x 2)) 1))
(.f64 x (-.f64 #s(literal 1 binary64) (.f64 x x)))
(* -1 (pow x 3))
(-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x)))
(* -1 (* (pow x 3) (- 1 (/ 1 (pow x 2)))))
(.f64 x (-.f64 #s(literal 1 binary64) (.f64 x x)))
(* -1 (* (pow x 3) (- 1 (/ 1 (pow x 2)))))
(.f64 x (-.f64 #s(literal 1 binary64) (.f64 x x)))
(* -1 (* (pow x 3) (- 1 (/ 1 (pow x 2)))))
(.f64 x (-.f64 #s(literal 1 binary64) (.f64 x x)))
1
#s(literal 1 binary64)
(+ 1 (* -1 (pow x 2)))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(+ 1 (* -1 (pow x 2)))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(+ 1 (* -1 (pow x 2)))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(* -1 (pow x 2))
(-.f64 #s(literal 0 binary64) (*.f64 x x))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(* -1 (pow x 2))
(-.f64 #s(literal 0 binary64) (*.f64 x x))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
x
(* x (+ 1 (* -1 (pow x 2))))
(.f64 x (-.f64 #s(literal 1 binary64) (.f64 x x)))
(* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x x))))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))
(.f64 x (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x))))))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (- 1 (/ 1 (pow x 2))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))) (.f64 x x))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)
(/.f64 (-.f64 (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))) (.f64 x x)) (+.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (.f64 x (.f64 x x))))) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))) x)
(* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))) (.f64 x x))) x)
(* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))
(/.f64 (-.f64 (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))) (.f64 x x)) (+.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (.f64 x (.f64 x x))))) x)
1
#s(literal 1 binary64)
(+ 1 (pow x 2))
(+.f64 #s(literal 1 binary64) (*.f64 x x))
(+ 1 (pow x 2))
(+.f64 #s(literal 1 binary64) (*.f64 x x))
(+ 1 (pow x 2))
(+.f64 #s(literal 1 binary64) (*.f64 x x))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(+.f64 #s(literal 1 binary64) (*.f64 x x))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(+.f64 #s(literal 1 binary64) (*.f64 x x))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(+.f64 #s(literal 1 binary64) (*.f64 x x))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(+.f64 #s(literal 1 binary64) (*.f64 x x))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(+.f64 #s(literal 1 binary64) (*.f64 x x))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(+.f64 #s(literal 1 binary64) (*.f64 x x))
1
#s(literal 1 binary64)
(+ 1 (pow x 2))
(+.f64 #s(literal 1 binary64) (*.f64 x x))
(+ 1 (* (pow x 2) (+ 1 (pow x 2))))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x x)))))
(+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 1 (pow x 2))))))
(.f64 (+.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x)))))
(pow x 6)
(.f64 x (.f64 x (.f64 x (.f64 x (*.f64 x x)))))
(* (pow x 6) (+ 1 (/ 1 (pow x 2))))
(.f64 (.f64 x x) (.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x x)))))
(* (pow x 6) (+ 1 (+ (/ 1 (pow x 2)) (/ 1 (pow x 4)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x x))))))
(* (pow x 6) (+ 1 (+ (/ 1 (pow x 2)) (+ (/ 1 (pow x 4)) (/ 1 (pow x 6))))))
(.f64 (+.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x)))))
(pow x 6)
(.f64 x (.f64 x (.f64 x (.f64 x (*.f64 x x)))))
(* (pow x 6) (+ 1 (/ 1 (pow x 2))))
(.f64 (.f64 x x) (.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x x)))))
(* (pow x 6) (+ 1 (+ (/ 1 (pow x 2)) (/ 1 (pow x 4)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x x))))))
(* (pow x 6) (+ 1 (+ (/ 1 (pow x 2)) (+ (/ 1 (pow x 4)) (/ 1 (pow x 6))))))
(.f64 (+.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x)))))
-1
#s(literal -1 binary64)
-1
#s(literal -1 binary64)
(- (pow x 8) 1)
(+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 8 binary64)))
(- (pow x 8) 1)
(+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 8 binary64)))
(pow x 8)
(pow.f64 x #s(literal 8 binary64))
(pow x 8)
(pow.f64 x #s(literal 8 binary64))
(* (pow x 8) (- 1 (/ 1 (pow x 8))))
(+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 8 binary64)))
(* (pow x 8) (- 1 (/ 1 (pow x 8))))
(+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 8 binary64)))
(pow x 8)
(pow.f64 x #s(literal 8 binary64))
(pow x 8)
(pow.f64 x #s(literal 8 binary64))
(* (pow x 8) (- 1 (/ 1 (pow x 8))))
(+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 8 binary64)))
(* (pow x 8) (- 1 (/ 1 (pow x 8))))
(+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 8 binary64)))
-1
#s(literal -1 binary64)
(- (* -1 (pow x 2)) 1)
(-.f64 #s(literal -1 binary64) (*.f64 x x))
(- (* (pow x 2) (- (* -1 (pow x 2)) 1)) 1)
(-.f64 #s(literal -1 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x x)))))
(- (* (pow x 2) (- (* (pow x 2) (- (* -1 (pow x 2)) 1)) 1)) 1)
(.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (-.f64 #s(literal -1 binary64) (*.f64 x x)))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ (+ 1 (/ 1 (pow x 2))) (pow x 2))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))) (.f64 x x))
(/ (+ 1 (+ (/ 1 (pow x 2)) (/ 1 (pow x 4)))) (pow x 2))
(/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (.f64 x (.f64 x (.f64 x x)))))) (*.f64 x x))
(/ (+ 1 (+ (/ 1 (pow x 2)) (+ (/ 1 (pow x 4)) (/ 1 (pow x 6))))) (pow x 2))
(/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (.f64 x (.f64 x x)))))) (*.f64 x x))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ (+ 1 (/ 1 (pow x 2))) (pow x 2))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))) (.f64 x x))
(/ (+ 1 (+ (/ 1 (pow x 2)) (/ 1 (pow x 4)))) (pow x 2))
(/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (.f64 x (.f64 x (.f64 x x)))))) (*.f64 x x))
(/ (+ 1 (+ (/ 1 (pow x 2)) (+ (/ 1 (pow x 4)) (/ 1 (pow x 6))))) (pow x 2))
(/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (.f64 x (.f64 x x)))))) (*.f64 x x))

eval307.0ms (5.1%)

Compiler: Compiled 50593 to 3048 computations (94% saved)

prune128.0ms (2.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	1287	2	1289
Fresh	0	0	0
Picked	2	3	5
Done	1	0	1
Total	1290	5	1295

Accuracy

100.0%

Counts

1295 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	62.4%	(/.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) x))
▶	99.8%	(/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x)))
✓	51.0%	(/.f64 #s(literal 1 binary64) x)
✓	51.3%	(.f64 x (-.f64 #s(literal 1 binary64) (.f64 x x)))
✓	52.3%	x

Compiler

Compiled 46 to 27 computations (41.3% saved)

simplify478.0ms (7.9%)

Algorithm

1×	egg-herbie

Localize:

Found 7 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(+.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal -1 binary64))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal -1 binary64)))
✓	cost-diff	768	(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) #s(literal -1 binary64))))
✓	cost-diff	1024	(/.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) x))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) x)
✓	cost-diff	0	(+.f64 x (/.f64 #s(literal 1 binary64) x))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x)))

Rules

3800×	`/-lowering-/.f32`
3800×	`/-lowering-/.f64`
2342×	`-lowering-.f32`
2342×	`-lowering-.f64`
1886×	`--lowering--.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	15	79
1	43	70
2	108	68
3	409	57
4	1968	57
5	4738	57
0	8713	57

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(/ 1 (+ x (/ 1 x)))
1
(+ x (/ 1 x))
x
(/ 1 x)
(/ (/ (/ 1 (+ (* x (* x (* x x))) -1)) (/ 1 (+ (* x x) -1))) (/ 1 x))
(/ (/ 1 (+ (* x (* x (* x x))) -1)) (/ 1 (+ (* x x) -1)))
(/ 1 (+ (* x (* x (* x x))) -1))
1
(+ (* x (* x (* x x))) -1)
(* x (* x (* x x)))
x
(* x (* x x))
(* x x)
-1
(/ 1 (+ (* x x) -1))
(+ (* x x) -1)
(/ 1 x)

Outputs
(/ 1 (+ x (/ 1 x)))
(/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x)))
1
#s(literal 1 binary64)
(+ x (/ 1 x))
(+.f64 x (/.f64 #s(literal 1 binary64) x))
x
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (/ (/ 1 (+ (* x (* x (* x x))) -1)) (/ 1 (+ (* x x) -1))) (/ 1 x))
(/.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x x)))
(/ (/ 1 (+ (* x (* x (* x x))) -1)) (/ 1 (+ (* x x) -1)))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x x)))
(/ 1 (+ (* x (* x (* x x))) -1))
(/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal -1 binary64)))
1
#s(literal 1 binary64)
(+ (* x (* x (* x x))) -1)
(+.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal -1 binary64))
(* x (* x (* x x)))
(.f64 x (.f64 x (*.f64 x x)))
x
(* x (* x x))
(.f64 x (.f64 x x))
(* x x)
(*.f64 x x)
-1
#s(literal -1 binary64)
(/ 1 (+ (* x x) -1))
(/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) #s(literal -1 binary64)))
(+ (* x x) -1)
(+.f64 (*.f64 x x) #s(literal -1 binary64))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)

localize74.0ms (1.2%)

Localize:

Found 7 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) #s(literal -1 binary64)))
✓	accuracy	99.2%	(/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal -1 binary64)))
✓	accuracy	76.1%	(/.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) x))
✓	accuracy	64.7%	(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) #s(literal -1 binary64))))
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) x)
✓	accuracy	100.0%	(+.f64 x (/.f64 #s(literal 1 binary64) x))
✓	accuracy	99.9%	(/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x)))

Results

40.0ms

256×

valid

Compiler

Compiled 114 to 16 computations (86% saved)

Precisions

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

ival-div: 10.0ms (46.4% of total)

ival-mult: 7.0ms (32.4% of total)

ival-add: 4.0ms (18.5% of total)

const: 0.0ms (0% of total)

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

series3.0ms (0%)

Counts

8 → 96

Calls

Call 1

Inputs
#<alt (/ 1 (+ x (/ 1 x)))>
#<alt (+ x (/ 1 x))>
#<alt (/ 1 x)>
#<alt (/ (/ (/ 1 (+ (* x (* x (* x x))) -1)) (/ 1 (+ (* x x) -1))) (/ 1 x))>
#<alt (/ (/ 1 (+ (* x (* x (* x x))) -1)) (/ 1 (+ (* x x) -1)))>
#<alt (/ 1 (+ (* x (* x (* x x))) -1))>
#<alt (+ (* x (* x (* x x))) -1)>
#<alt (/ 1 (+ (* x x) -1))>

Outputs
#<alt x>
#<alt (* x (+ 1 (* -1 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))>
#<alt (/ 1 x)>
#<alt (/ (- 1 (/ 1 (pow x 2))) x)>
#<alt (/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)>
#<alt (/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)>
#<alt (/ 1 x)>
#<alt (* -1 (/ (- (/ 1 (pow x 2)) 1) x))>
#<alt (* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))>
#<alt (* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))>
#<alt (/ 1 x)>
#<alt (/ (+ 1 (pow x 2)) x)>
#<alt (/ (+ 1 (pow x 2)) x)>
#<alt (/ (+ 1 (pow x 2)) x)>
#<alt x>
#<alt (* x (+ 1 (/ 1 (pow x 2))))>
#<alt (* x (+ 1 (/ 1 (pow x 2))))>
#<alt (* x (+ 1 (/ 1 (pow x 2))))>
#<alt x>
#<alt (* x (+ 1 (/ 1 (pow x 2))))>
#<alt (* x (+ 1 (/ 1 (pow x 2))))>
#<alt (* x (+ 1 (/ 1 (pow x 2))))>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt x>
#<alt (* x (+ 1 (* -1 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))>
#<alt (/ 1 x)>
#<alt (/ (- 1 (/ 1 (pow x 2))) x)>
#<alt (/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)>
#<alt (/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)>
#<alt (/ 1 x)>
#<alt (* -1 (/ (- (/ 1 (pow x 2)) 1) x))>
#<alt (* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))>
#<alt (* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))>
#<alt 1>
#<alt (+ 1 (* -1 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (pow x 2) 1)))>
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1)))>
#<alt (/ 1 (pow x 2))>
#<alt (/ (- 1 (/ 1 (pow x 2))) (pow x 2))>
#<alt (/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) (pow x 2))>
#<alt (/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ (- 1 (/ 1 (pow x 2))) (pow x 2))>
#<alt (/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) (pow x 2))>
#<alt (/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) (pow x 2))>
#<alt -1>
#<alt (- (* -1 (pow x 4)) 1)>
#<alt (- (* (pow x 4) (- (* -1 (pow x 4)) 1)) 1)>
#<alt (- (* (pow x 4) (- (* (pow x 4) (- (* -1 (pow x 4)) 1)) 1)) 1)>
#<alt (/ 1 (pow x 4))>
#<alt (/ (+ 1 (/ 1 (pow x 4))) (pow x 4))>
#<alt (/ (+ 1 (+ (/ 1 (pow x 4)) (/ 1 (pow x 8)))) (pow x 4))>
#<alt (/ (+ 1 (+ (/ 1 (pow x 4)) (+ (/ 1 (pow x 8)) (/ 1 (pow x 12))))) (pow x 4))>
#<alt (/ 1 (pow x 4))>
#<alt (/ (+ 1 (/ 1 (pow x 4))) (pow x 4))>
#<alt (/ (+ 1 (+ (/ 1 (pow x 4)) (/ 1 (pow x 8)))) (pow x 4))>
#<alt (/ (+ 1 (+ (/ 1 (pow x 4)) (+ (/ 1 (pow x 8)) (/ 1 (pow x 12))))) (pow x 4))>
#<alt -1>
#<alt (- (pow x 4) 1)>
#<alt (- (pow x 4) 1)>
#<alt (- (pow x 4) 1)>
#<alt (pow x 4)>
#<alt (* (pow x 4) (- 1 (/ 1 (pow x 4))))>
#<alt (* (pow x 4) (- 1 (/ 1 (pow x 4))))>
#<alt (* (pow x 4) (- 1 (/ 1 (pow x 4))))>
#<alt (pow x 4)>
#<alt (* (pow x 4) (- 1 (/ 1 (pow x 4))))>
#<alt (* (pow x 4) (- 1 (/ 1 (pow x 4))))>
#<alt (* (pow x 4) (- 1 (/ 1 (pow x 4))))>
#<alt -1>
#<alt (- (* -1 (pow x 2)) 1)>
#<alt (- (* (pow x 2) (- (* -1 (pow x 2)) 1)) 1)>
#<alt (- (* (pow x 2) (- (* (pow x 2) (- (* -1 (pow x 2)) 1)) 1)) 1)>
#<alt (/ 1 (pow x 2))>
#<alt (/ (+ 1 (/ 1 (pow x 2))) (pow x 2))>
#<alt (/ (+ 1 (+ (/ 1 (pow x 2)) (/ 1 (pow x 4)))) (pow x 2))>
#<alt (/ (+ 1 (+ (/ 1 (pow x 2)) (+ (/ 1 (pow x 4)) (/ 1 (pow x 6))))) (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ (+ 1 (/ 1 (pow x 2))) (pow x 2))>
#<alt (/ (+ 1 (+ (/ 1 (pow x 2)) (/ 1 (pow x 4)))) (pow x 2))>
#<alt (/ (+ 1 (+ (/ 1 (pow x 2)) (+ (/ 1 (pow x 4)) (/ 1 (pow x 6))))) (pow x 2))>

Calls

24 calls:

Time	Variable		Point	Expression
0.0ms	x	@	inf	(/ 1 (+ (* x (* x (* x x))) -1))
0.0ms	x	@	0	(/ 1 (+ (* x (* x (* x x))) -1))
0.0ms	x	@	inf	(/ (/ (/ 1 (+ (* x (* x (* x x))) -1)) (/ 1 (+ (* x x) -1))) (/ 1 x))
0.0ms	x	@	0	(/ (/ (/ 1 (+ (* x (* x (* x x))) -1)) (/ 1 (+ (* x x) -1))) (/ 1 x))
0.0ms	x	@	inf	(+ (* x (* x (* x x))) -1)

rewrite332.0ms (5.5%)

Algorithm

1×	batch-egg-rewrite

Rules

4454×	`-lowering-.f32`
4454×	`-lowering-.f64`
3650×	`/-lowering-/.f32`
3650×	`/-lowering-/.f64`
1226×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	15	47
1	117	42
2	940	37
0	9020	37

Stop Event

1×	iter limit
1×	node limit

Counts

8 → 846

Calls

Call 1

Inputs
(/ 1 (+ x (/ 1 x)))
(+ x (/ 1 x))
(/ 1 x)
(/ (/ (/ 1 (+ (* x (* x (* x x))) -1)) (/ 1 (+ (* x x) -1))) (/ 1 x))
(/ (/ 1 (+ (* x (* x (* x x))) -1)) (/ 1 (+ (* x x) -1)))
(/ 1 (+ (* x (* x (* x x))) -1))
(+ (* x (* x (* x x))) -1)
(/ 1 (+ (* x x) -1))

Outputs
(+.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 x (/.f64 x (+.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64)))) x))
(+.f64 (.f64 x (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))))) (.f64 x (.f64 x (/.f64 x (+.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal -1 binary64))))))
(+.f64 (.f64 x (.f64 x (/.f64 x (+.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64))))) (.f64 x (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x)))))))
(+.f64 (.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x x)) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (.f64 x x)) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x x)) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal -1 binary64))))
(+.f64 (.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x x)) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal -1 binary64))) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x x)) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (.f64 x x)))
(+.f64 (.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (/.f64 #s(literal -1 binary64) (.f64 x x)))) x) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (/.f64 #s(literal -1 binary64) (.f64 x x)))) (/.f64 #s(literal -1 binary64) x)))
(+.f64 (.f64 (.f64 x (/.f64 x (+.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64)))) x) (/.f64 x (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x))))))
(+.f64 (.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x x)) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))))) (.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x x)) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))))))
(+.f64 (.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x x)) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))))) (.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x x)) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))))))
(+.f64 (.f64 x (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (/.f64 #s(literal -1 binary64) (.f64 x x))))) (.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (/.f64 #s(literal -1 binary64) (.f64 x x))))))
(exp.f64 (*.f64 (log.f64 (+.f64 x (/.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (/.f64 #s(literal -1 binary64) x) x)))
(-.f64 (/.f64 x (+.f64 (.f64 x x) (/.f64 #s(literal -1 binary64) (.f64 x x)))) (/.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 (.f64 x x) (/.f64 #s(literal -1 binary64) (.f64 x x)))))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (-.f64 #s(literal 1 binary64) (.f64 x x))))) (/.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (.f64 x (-.f64 #s(literal 1 binary64) (*.f64 x x))))))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 #s(literal -1 binary64) x)) (/.f64 #s(literal 1 binary64) (-.f64 (/.f64 #s(literal -1 binary64) x) x)))
(-.f64 (/.f64 (+.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (.f64 x x))) (+.f64 (.f64 x (.f64 x x)) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x x)) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))))
(neg.f64 (/.f64 #s(literal 1 binary64) (-.f64 (/.f64 #s(literal -1 binary64) x) x)))
(neg.f64 (/.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (.f64 x (-.f64 #s(literal 1 binary64) (*.f64 x x))))))
(neg.f64 (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (.f64 x (+.f64 (*.f64 x x) #s(literal -1 binary64))))))
(neg.f64 (.f64 x (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (.f64 x x)))))
(/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x x))) (/.f64 x (+.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x x))) (/.f64 x (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))))))
(/.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x x)))
(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (-.f64 (/.f64 #s(literal -1 binary64) x) x))
(/.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (.f64 x (+.f64 (*.f64 x x) #s(literal -1 binary64)))))
(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x x))) (/.f64 #s(literal 1 binary64) x))
(/.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (.f64 x (-.f64 #s(literal 1 binary64) (*.f64 x x)))))
(/.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal -1 binary64) (*.f64 x x)))
(/.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (*.f64 x x))) (/.f64 #s(literal -1 binary64) x))
(/.f64 (+.f64 (.f64 x x) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal -1 binary64))) (+.f64 (.f64 x (.f64 x x)) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))))
(/.f64 (+.f64 x (/.f64 #s(literal -1 binary64) x)) (+.f64 (.f64 x x) (/.f64 #s(literal -1 binary64) (.f64 x x))))
(/.f64 (.f64 x (+.f64 (.f64 x x) #s(literal -1 binary64))) (+.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal -1 binary64)))
(/.f64 (.f64 x (-.f64 #s(literal 1 binary64) (.f64 x x))) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x)))))
(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x x) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal -1 binary64)))) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x (.f64 x x)) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))))
(/.f64 (+.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 #s(literal 1 binary64) x)) (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (.f64 x x))))
(/.f64 (/.f64 #s(literal 1 binary64) (-.f64 (/.f64 #s(literal -1 binary64) x) x)) #s(literal -1 binary64))
(/.f64 (/.f64 x (+.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64))) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x x))))
(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x x)) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal -1 binary64)))))
(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (/.f64 #s(literal -1 binary64) (.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 #s(literal -1 binary64) x))))
(/.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x x))) (pow.f64 x #s(literal -1/2 binary64))) (pow.f64 x #s(literal -1/2 binary64)))
(/.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x x))))
(/.f64 (.f64 x (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (.f64 x x)))) #s(literal -1 binary64))
(/.f64 (.f64 x (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x x))))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) x) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x)))))
(/.f64 (.f64 x (/.f64 (+.f64 #s(literal 1 binary64) (neg.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))))) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x x)))))
(/.f64 (.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x x)) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (+.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal -1 binary64)) (.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal -1 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal -1 binary64)))))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal -1 binary64)) (-.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal -1 binary64)) (.f64 x x)))))
(/.f64 (.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x x)) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal -1 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal -1 binary64))))) (+.f64 (+.f64 (.f64 x x) (/.f64 #s(literal -1 binary64) (*.f64 x x))) #s(literal 1 binary64)))
(/.f64 (.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (/.f64 #s(literal -1 binary64) (.f64 x x)))) (+.f64 (.f64 x x) (/.f64 #s(literal -1 binary64) (*.f64 x x)))) (+.f64 x (/.f64 #s(literal 1 binary64) x)))
(/.f64 (.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (/.f64 #s(literal -1 binary64) (.f64 x x)))) (-.f64 (.f64 x (.f64 x x)) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (+.f64 (.f64 x x) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1 binary64))))
(/.f64 (.f64 (/.f64 (+.f64 #s(literal 1 binary64) (neg.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))))) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x))))) x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x x)))))
(/.f64 (/.f64 (+.f64 x (/.f64 #s(literal -1 binary64) x)) (+.f64 x (/.f64 #s(literal 1 binary64) x))) (+.f64 x (/.f64 #s(literal -1 binary64) x)))
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 x (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x))))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x x))))
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(/.f64 (.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x x)))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 #s(literal -1 binary64) (.f64 x x))))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 #s(literal -1 binary64) (.f64 x x))))
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))
(/.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 #s(literal -1 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))))))
(/.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x))))))
(/.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 #s(literal 1 binary64) (.f64 x x))) (+.f64 (*.f64 x x) #s(literal -1 binary64)))
(pow.f64 (+.f64 (*.f64 x x) #s(literal -1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x x))) #s(literal 1 binary64))
(pow.f64 (pow.f64 (+.f64 (*.f64 x x) #s(literal -1 binary64)) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (.f64 (+.f64 (.f64 x x) #s(literal -1 binary64)) (+.f64 (*.f64 x x) #s(literal -1 binary64))) #s(literal -1/2 binary64))
(pow.f64 (exp.f64 (log.f64 (+.f64 (*.f64 x x) #s(literal -1 binary64)))) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x x))))
(.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x x))))
(.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x))))) (+.f64 #s(literal 1 binary64) (*.f64 x x)))
(.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x x))) #s(literal 1 binary64))
(.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x))))) (-.f64 #s(literal -1 binary64) (*.f64 x x)))
(.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x x))) #s(literal -1 binary64))
(.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x (.f64 x (.f64 x (*.f64 x x))))))))
(.f64 (+.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x))))))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal 1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))
(.f64 (pow.f64 (+.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64)) #s(literal -1/2 binary64)) (.f64 (pow.f64 (+.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64)) #s(literal -1/2 binary64)) (+.f64 #s(literal 1 binary64) (*.f64 x x))))
(.f64 (pow.f64 (+.f64 (.f64 x x) #s(literal -1 binary64)) #s(literal -1/2 binary64)) (pow.f64 (+.f64 (*.f64 x x) #s(literal -1 binary64)) #s(literal -1/2 binary64)))
(.f64 (pow.f64 (+.f64 (.f64 x x) #s(literal -1 binary64)) #s(literal -1/2 binary64)) (.f64 (pow.f64 (+.f64 (.f64 x x) #s(literal -1 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 x x)))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 x x))))) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x x)))) #s(literal 1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))))) (.f64 (+.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x))))) (+.f64 #s(literal 1 binary64) (.f64 x x))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal -1 binary64))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 #s(literal 1 binary64) (*.f64 x x))))
(.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))))) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 x x))))))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x))))) #s(literal -1 binary64))
(.f64 (.f64 #s(literal 1 binary64) (pow.f64 (+.f64 (.f64 x x) #s(literal -1 binary64)) #s(literal -1/2 binary64))) (pow.f64 (+.f64 (.f64 x x) #s(literal -1 binary64)) #s(literal -1/2 binary64)))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 #s(literal -1 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))))) (+.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x))))))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 #s(literal -1 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))))))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal -1 binary64))) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x x)))) (+.f64 (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))) #s(literal -1 binary64))) (-.f64 (+.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1 binary64)) (.f64 (.f64 x x) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x (*.f64 x x)))))))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x x)))) (+.f64 #s(literal -1 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))))) (+.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) #s(literal 1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (neg.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))))) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 x x))))))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))))))) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))))))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal -1 binary64)))) (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x (.f64 x x)))) #s(literal -1 binary64)))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))))) (-.f64 #s(literal -1 binary64) (.f64 x (.f64 x (.f64 x x)))))
(.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (+.f64 (.f64 x (.f64 x x)) #s(literal -1 binary64))) (+.f64 (+.f64 #s(literal 1 binary64) (.f64 x x)) x))
(.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (+.f64 (.f64 x x) #s(literal -1 binary64))) (+.f64 #s(literal 1 binary64) x))

simplify224.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

2410×	`fma-lowering-fma.f32`
2410×	`fma-lowering-fma.f64`
2034×	`fmsub-define`
1760×	`--lowering--.f32`
1760×	`--lowering--.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	85	792
1	229	686
2	593	671
3	1747	648
4	5444	648
0	8897	648

Stop Event

1×	iter limit
1×	node limit

Counts

96 → 96

Calls

Call 1

Inputs
x
(* x (+ 1 (* -1 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))
(/ 1 x)
(/ (- 1 (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)
(/ 1 x)
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))
(* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))
(/ 1 x)
(/ (+ 1 (pow x 2)) x)
(/ (+ 1 (pow x 2)) x)
(/ (+ 1 (pow x 2)) x)
x
(* x (+ 1 (/ 1 (pow x 2))))
(* x (+ 1 (/ 1 (pow x 2))))
(* x (+ 1 (/ 1 (pow x 2))))
x
(* x (+ 1 (/ 1 (pow x 2))))
(* x (+ 1 (/ 1 (pow x 2))))
(* x (+ 1 (/ 1 (pow x 2))))
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
x
(* x (+ 1 (* -1 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))
(/ 1 x)
(/ (- 1 (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)
(/ 1 x)
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))
(* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))
1
(+ 1 (* -1 (pow x 2)))
(+ 1 (* (pow x 2) (- (pow x 2) 1)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1)))
(/ 1 (pow x 2))
(/ (- 1 (/ 1 (pow x 2))) (pow x 2))
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) (pow x 2))
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) (pow x 2))
(/ 1 (pow x 2))
(/ (- 1 (/ 1 (pow x 2))) (pow x 2))
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) (pow x 2))
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) (pow x 2))
-1
(- (* -1 (pow x 4)) 1)
(- (* (pow x 4) (- (* -1 (pow x 4)) 1)) 1)
(- (* (pow x 4) (- (* (pow x 4) (- (* -1 (pow x 4)) 1)) 1)) 1)
(/ 1 (pow x 4))
(/ (+ 1 (/ 1 (pow x 4))) (pow x 4))
(/ (+ 1 (+ (/ 1 (pow x 4)) (/ 1 (pow x 8)))) (pow x 4))
(/ (+ 1 (+ (/ 1 (pow x 4)) (+ (/ 1 (pow x 8)) (/ 1 (pow x 12))))) (pow x 4))
(/ 1 (pow x 4))
(/ (+ 1 (/ 1 (pow x 4))) (pow x 4))
(/ (+ 1 (+ (/ 1 (pow x 4)) (/ 1 (pow x 8)))) (pow x 4))
(/ (+ 1 (+ (/ 1 (pow x 4)) (+ (/ 1 (pow x 8)) (/ 1 (pow x 12))))) (pow x 4))
-1
(- (pow x 4) 1)
(- (pow x 4) 1)
(- (pow x 4) 1)
(pow x 4)
(* (pow x 4) (- 1 (/ 1 (pow x 4))))
(* (pow x 4) (- 1 (/ 1 (pow x 4))))
(* (pow x 4) (- 1 (/ 1 (pow x 4))))
(pow x 4)
(* (pow x 4) (- 1 (/ 1 (pow x 4))))
(* (pow x 4) (- 1 (/ 1 (pow x 4))))
(* (pow x 4) (- 1 (/ 1 (pow x 4))))
-1
(- (* -1 (pow x 2)) 1)
(- (* (pow x 2) (- (* -1 (pow x 2)) 1)) 1)
(- (* (pow x 2) (- (* (pow x 2) (- (* -1 (pow x 2)) 1)) 1)) 1)
(/ 1 (pow x 2))
(/ (+ 1 (/ 1 (pow x 2))) (pow x 2))
(/ (+ 1 (+ (/ 1 (pow x 2)) (/ 1 (pow x 4)))) (pow x 2))
(/ (+ 1 (+ (/ 1 (pow x 2)) (+ (/ 1 (pow x 4)) (/ 1 (pow x 6))))) (pow x 2))
(/ 1 (pow x 2))
(/ (+ 1 (/ 1 (pow x 2))) (pow x 2))
(/ (+ 1 (+ (/ 1 (pow x 2)) (/ 1 (pow x 4)))) (pow x 2))
(/ (+ 1 (+ (/ 1 (pow x 2)) (+ (/ 1 (pow x 4)) (/ 1 (pow x 6))))) (pow x 2))

Outputs
x
(* x (+ 1 (* -1 (pow x 2))))
(.f64 x (-.f64 #s(literal 1 binary64) (.f64 x x)))
(* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x x))))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))
(.f64 x (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (-.f64 #s(literal 1 binary64) (.f64 x x))))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (- 1 (/ 1 (pow x 2))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) x) x)) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))) (.f64 x x))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)
(+.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))) (.f64 x x))) x) (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 7 binary64))))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) x) x)) x)
(* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))) (.f64 x x))) x)
(* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))
(+.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))) (.f64 x x))) x) (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 7 binary64))))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (+ 1 (pow x 2)) x)
(/.f64 (+.f64 #s(literal 1 binary64) (*.f64 x x)) x)
(/ (+ 1 (pow x 2)) x)
(/.f64 (+.f64 #s(literal 1 binary64) (*.f64 x x)) x)
(/ (+ 1 (pow x 2)) x)
(/.f64 (+.f64 #s(literal 1 binary64) (*.f64 x x)) x)
x
(* x (+ 1 (/ 1 (pow x 2))))
(+.f64 x (/.f64 #s(literal 1 binary64) x))
(* x (+ 1 (/ 1 (pow x 2))))
(+.f64 x (/.f64 #s(literal 1 binary64) x))
(* x (+ 1 (/ 1 (pow x 2))))
(+.f64 x (/.f64 #s(literal 1 binary64) x))
x
(* x (+ 1 (/ 1 (pow x 2))))
(+.f64 x (/.f64 #s(literal 1 binary64) x))
(* x (+ 1 (/ 1 (pow x 2))))
(+.f64 x (/.f64 #s(literal 1 binary64) x))
(* x (+ 1 (/ 1 (pow x 2))))
(+.f64 x (/.f64 #s(literal 1 binary64) x))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
x
(* x (+ 1 (* -1 (pow x 2))))
(.f64 x (-.f64 #s(literal 1 binary64) (.f64 x x)))
(* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x x))))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))
(.f64 x (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (-.f64 #s(literal 1 binary64) (.f64 x x))))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (- 1 (/ 1 (pow x 2))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) x) x)) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))) (.f64 x x))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)
(+.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))) (.f64 x x))) x) (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 7 binary64))))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) x) x)) x)
(* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))) (.f64 x x))) x)
(* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))
(+.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))) (.f64 x x))) x) (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 7 binary64))))
1
#s(literal 1 binary64)
(+ 1 (* -1 (pow x 2)))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(+ 1 (* (pow x 2) (- (pow x 2) 1)))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x x)))))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1)))
(.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (-.f64 #s(literal 1 binary64) (*.f64 x x)))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ (- 1 (/ 1 (pow x 2))) (pow x 2))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) x) x)) (*.f64 x x))
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) (pow x 2))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))) (.f64 x x))) (*.f64 x x))
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) (pow x 2))
(/.f64 (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))) (.f64 x x)) (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 6 binary64))))) (*.f64 x x))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ (- 1 (/ 1 (pow x 2))) (pow x 2))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) x) x)) (*.f64 x x))
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) (pow x 2))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))) (.f64 x x))) (*.f64 x x))
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) (pow x 2))
(/.f64 (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))) (.f64 x x)) (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 6 binary64))))) (*.f64 x x))
-1
#s(literal -1 binary64)
(- (* -1 (pow x 4)) 1)
(-.f64 #s(literal -1 binary64) (.f64 x (.f64 x (*.f64 x x))))
(- (* (pow x 4) (- (* -1 (pow x 4)) 1)) 1)
(+.f64 #s(literal -1 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 #s(literal -1 binary64) (.f64 x (.f64 x (*.f64 x x))))))
(- (* (pow x 4) (- (* (pow x 4) (- (* -1 (pow x 4)) 1)) 1)) 1)
(.f64 (+.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) (.f64 x (.f64 x (*.f64 x x)))))
(/ 1 (pow x 4))
(/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x (.f64 x x)))
(/ (+ 1 (/ 1 (pow x 4))) (pow x 4))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x (.f64 x x)))) (.f64 x (.f64 x (*.f64 x x))))
(/ (+ 1 (+ (/ 1 (pow x 4)) (/ 1 (pow x 8)))) (pow x 4))
(/.f64 (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))))) (.f64 x (.f64 x (.f64 x x))))
(/ (+ 1 (+ (/ 1 (pow x 4)) (+ (/ 1 (pow x 8)) (/ 1 (pow x 12))))) (pow x 4))
(/.f64 (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x (.f64 x x)))) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 12 binary64))))) (.f64 x (.f64 x (.f64 x x))))
(/ 1 (pow x 4))
(/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x (.f64 x x)))
(/ (+ 1 (/ 1 (pow x 4))) (pow x 4))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x (.f64 x x)))) (.f64 x (.f64 x (*.f64 x x))))
(/ (+ 1 (+ (/ 1 (pow x 4)) (/ 1 (pow x 8)))) (pow x 4))
(/.f64 (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))))) (.f64 x (.f64 x (.f64 x x))))
(/ (+ 1 (+ (/ 1 (pow x 4)) (+ (/ 1 (pow x 8)) (/ 1 (pow x 12))))) (pow x 4))
(/.f64 (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x (.f64 x x)))) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 12 binary64))))) (.f64 x (.f64 x (.f64 x x))))
-1
#s(literal -1 binary64)
(- (pow x 4) 1)
(+.f64 #s(literal -1 binary64) (.f64 x (.f64 x (*.f64 x x))))
(- (pow x 4) 1)
(+.f64 #s(literal -1 binary64) (.f64 x (.f64 x (*.f64 x x))))
(- (pow x 4) 1)
(+.f64 #s(literal -1 binary64) (.f64 x (.f64 x (*.f64 x x))))
(pow x 4)
(.f64 x (.f64 x (*.f64 x x)))
(* (pow x 4) (- 1 (/ 1 (pow x 4))))
(+.f64 #s(literal -1 binary64) (.f64 x (.f64 x (*.f64 x x))))
(* (pow x 4) (- 1 (/ 1 (pow x 4))))
(+.f64 #s(literal -1 binary64) (.f64 x (.f64 x (*.f64 x x))))
(* (pow x 4) (- 1 (/ 1 (pow x 4))))
(+.f64 #s(literal -1 binary64) (.f64 x (.f64 x (*.f64 x x))))
(pow x 4)
(.f64 x (.f64 x (*.f64 x x)))
(* (pow x 4) (- 1 (/ 1 (pow x 4))))
(+.f64 #s(literal -1 binary64) (.f64 x (.f64 x (*.f64 x x))))
(* (pow x 4) (- 1 (/ 1 (pow x 4))))
(+.f64 #s(literal -1 binary64) (.f64 x (.f64 x (*.f64 x x))))
(* (pow x 4) (- 1 (/ 1 (pow x 4))))
(+.f64 #s(literal -1 binary64) (.f64 x (.f64 x (*.f64 x x))))
-1
#s(literal -1 binary64)
(- (* -1 (pow x 2)) 1)
(-.f64 #s(literal -1 binary64) (*.f64 x x))
(- (* (pow x 2) (- (* -1 (pow x 2)) 1)) 1)
(+.f64 #s(literal -1 binary64) (.f64 x (.f64 x (-.f64 #s(literal -1 binary64) (*.f64 x x)))))
(- (* (pow x 2) (- (* (pow x 2) (- (* -1 (pow x 2)) 1)) 1)) 1)
(.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (-.f64 #s(literal -1 binary64) (*.f64 x x)))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ (+ 1 (/ 1 (pow x 2))) (pow x 2))
(/.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) x) x)
(/ (+ 1 (+ (/ 1 (pow x 2)) (/ 1 (pow x 4)))) (pow x 2))
(/.f64 (+.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x (.f64 x x))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x)))) (.f64 x x))
(/ (+ 1 (+ (/ 1 (pow x 2)) (+ (/ 1 (pow x 4)) (/ 1 (pow x 6))))) (pow x 2))
(/.f64 (+.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x (.f64 x x))) (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))))) (.f64 x x))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ (+ 1 (/ 1 (pow x 2))) (pow x 2))
(/.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) x) x)
(/ (+ 1 (+ (/ 1 (pow x 2)) (/ 1 (pow x 4)))) (pow x 2))
(/.f64 (+.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x (.f64 x x))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x)))) (.f64 x x))
(/ (+ 1 (+ (/ 1 (pow x 2)) (+ (/ 1 (pow x 4)) (/ 1 (pow x 6))))) (pow x 2))
(/.f64 (+.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x (.f64 x x))) (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))))) (.f64 x x))

eval148.0ms (2.4%)

Compiler: Compiled 31901 to 2371 computations (92.6% saved)

prune101.0ms (1.7%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	971	1	972
Fresh	0	0	0
Picked	1	1	2
Done	0	3	3
Total	972	5	977

Accuracy

100.0%

Counts

977 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	13.4%	(/.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) x))
✓	99.8%	(/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x)))
✓	51.0%	(/.f64 #s(literal 1 binary64) x)
✓	51.3%	(.f64 x (-.f64 #s(literal 1 binary64) (.f64 x x)))
✓	52.3%	x

Compiler

Compiled 44 to 25 computations (43.2% saved)

simplify146.0ms (2.4%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) x)
✓	cost-diff	0	(/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x (.f64 x x)))
✓	cost-diff	384	(/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) #s(literal -1 binary64))))
✓	cost-diff	768	(/.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) x))

Rules

2696×	`-lowering-.f32`
2696×	`-lowering-.f64`
1742×	`/-lowering-/.f32`
1742×	`/-lowering-/.f64`
1162×	`+-lowering-+.f64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	11	52
1	36	43
2	113	43
3	494	39
4	2245	38
5	5159	38
0	8037	38

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(/ (/ (/ (/ 1 x) (* x (* x x))) (/ 1 (+ (* x x) -1))) (/ 1 x))
(/ (/ (/ 1 x) (* x (* x x))) (/ 1 (+ (* x x) -1)))
(/ (/ 1 x) (* x (* x x)))
(/ 1 x)
1
x
(* x (* x x))
(* x x)
(/ 1 (+ (* x x) -1))
(+ (* x x) -1)
-1

Outputs
(/ (/ (/ (/ 1 x) (* x (* x x))) (/ 1 (+ (* x x) -1))) (/ 1 x))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) x) x)) x)
(/ (/ (/ 1 x) (* x (* x x))) (/ 1 (+ (* x x) -1)))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) x) x)) (*.f64 x x))
(/ (/ 1 x) (* x (* x x)))
(/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x))))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
1
#s(literal 1 binary64)
x
(* x (* x x))
(.f64 x (.f64 x x))
(* x x)
(*.f64 x x)
(/ 1 (+ (* x x) -1))
(/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) #s(literal -1 binary64)))
(+ (* x x) -1)
(+.f64 (*.f64 x x) #s(literal -1 binary64))
-1
#s(literal -1 binary64)

localize44.0ms (0.7%)

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(.f64 x (.f64 x x))
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) #s(literal -1 binary64)))
✓	accuracy	72.2%	(/.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) x))
✓	accuracy	64.7%	(/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) #s(literal -1 binary64))))

Results

26.0ms

256×

valid

Compiler

Compiled 75 to 12 computations (84% saved)

Precisions

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

ival-div: 8.0ms (57.6% of total)

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

ival-add: 1.0ms (7.2% of total)

const: 0.0ms (0% of total)

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

series2.0ms (0%)

Counts

6 → 72

Calls

Call 1

Inputs
#<alt (/ (/ (/ (/ 1 x) (* x (* x x))) (/ 1 (+ (* x x) -1))) (/ 1 x))>
#<alt (/ (/ (/ 1 x) (* x (* x x))) (/ 1 (+ (* x x) -1)))>
#<alt (/ (/ 1 x) (* x (* x x)))>
#<alt (/ 1 x)>
#<alt (/ 1 (+ (* x x) -1))>
#<alt (* x (* x x))>

Outputs
#<alt (/ -1 (pow x 3))>
#<alt (/ (- (pow x 2) 1) (pow x 3))>
#<alt (/ (- (pow x 2) 1) (pow x 3))>
#<alt (/ (- (pow x 2) 1) (pow x 3))>
#<alt (/ 1 x)>
#<alt (/ (- 1 (/ 1 (pow x 2))) x)>
#<alt (/ (- 1 (/ 1 (pow x 2))) x)>
#<alt (/ (- 1 (/ 1 (pow x 2))) x)>
#<alt (/ 1 x)>
#<alt (* -1 (/ (- (/ 1 (pow x 2)) 1) x))>
#<alt (* -1 (/ (- (/ 1 (pow x 2)) 1) x))>
#<alt (* -1 (/ (- (/ 1 (pow x 2)) 1) x))>
#<alt (/ -1 (pow x 4))>
#<alt (/ (- (pow x 2) 1) (pow x 4))>
#<alt (/ (- (pow x 2) 1) (pow x 4))>
#<alt (/ (- (pow x 2) 1) (pow x 4))>
#<alt (/ 1 (pow x 2))>
#<alt (/ (- 1 (/ 1 (pow x 2))) (pow x 2))>
#<alt (/ (- 1 (/ 1 (pow x 2))) (pow x 2))>
#<alt (/ (- 1 (/ 1 (pow x 2))) (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ (- 1 (/ 1 (pow x 2))) (pow x 2))>
#<alt (/ (- 1 (/ 1 (pow x 2))) (pow x 2))>
#<alt (/ (- 1 (/ 1 (pow x 2))) (pow x 2))>
#<alt (/ 1 (pow x 4))>
#<alt (/ 1 (pow x 4))>
#<alt (/ 1 (pow x 4))>
#<alt (/ 1 (pow x 4))>
#<alt (/ 1 (pow x 4))>
#<alt (/ 1 (pow x 4))>
#<alt (/ 1 (pow x 4))>
#<alt (/ 1 (pow x 4))>
#<alt (/ 1 (pow x 4))>
#<alt (/ 1 (pow x 4))>
#<alt (/ 1 (pow x 4))>
#<alt (/ 1 (pow x 4))>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt -1>
#<alt (- (* -1 (pow x 2)) 1)>
#<alt (- (* (pow x 2) (- (* -1 (pow x 2)) 1)) 1)>
#<alt (- (* (pow x 2) (- (* (pow x 2) (- (* -1 (pow x 2)) 1)) 1)) 1)>
#<alt (/ 1 (pow x 2))>
#<alt (/ (+ 1 (/ 1 (pow x 2))) (pow x 2))>
#<alt (/ (+ 1 (+ (/ 1 (pow x 2)) (/ 1 (pow x 4)))) (pow x 2))>
#<alt (/ (+ 1 (+ (/ 1 (pow x 2)) (+ (/ 1 (pow x 4)) (/ 1 (pow x 6))))) (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ (+ 1 (/ 1 (pow x 2))) (pow x 2))>
#<alt (/ (+ 1 (+ (/ 1 (pow x 2)) (/ 1 (pow x 4)))) (pow x 2))>
#<alt (/ (+ 1 (+ (/ 1 (pow x 2)) (+ (/ 1 (pow x 4)) (/ 1 (pow x 6))))) (pow x 2))>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>

Calls

18 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(/ (/ (/ (/ 1 x) (* x (* x x))) (/ 1 (+ (* x x) -1))) (/ 1 x))
0.0ms	x	@	-inf	(* x (* x x))
0.0ms	x	@	inf	(* x (* x x))
0.0ms	x	@	0	(/ (/ (/ 1 x) (* x (* x x))) (/ 1 (+ (* x x) -1)))
0.0ms	x	@	-inf	(/ (/ (/ (/ 1 x) (* x (* x x))) (/ 1 (+ (* x x) -1))) (/ 1 x))

rewrite308.0ms (5.1%)

Algorithm

1×	batch-egg-rewrite

Rules

3766×	`-lowering-.f32`
3766×	`-lowering-.f64`
3156×	`/-lowering-/.f32`
3156×	`/-lowering-/.f64`
1810×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	43
1	83	31
2	670	28
3	6552	28
0	8192	28

Stop Event

1×	iter limit
1×	node limit

Counts

6 → 606

Calls

Call 1

Inputs
(/ (/ (/ (/ 1 x) (* x (* x x))) (/ 1 (+ (* x x) -1))) (/ 1 x))
(/ (/ (/ 1 x) (* x (* x x))) (/ 1 (+ (* x x) -1)))
(/ (/ 1 x) (* x (* x x)))
(/ 1 x)
(/ 1 (+ (* x x) -1))
(* x (* x x))

Outputs
(+.f64 (/.f64 #s(literal -1 binary64) (.f64 x (.f64 x x))) (.f64 x (/.f64 #s(literal 1 binary64) (.f64 x x))))
(+.f64 (/.f64 #s(literal -1 binary64) (.f64 x (.f64 x x))) (.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x))
(+.f64 (/.f64 #s(literal -1 binary64) (.f64 x (.f64 x x))) (.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (.f64 x x)))
(+.f64 (/.f64 #s(literal -1 binary64) (.f64 x (.f64 x x))) (.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))))
(+.f64 (.f64 x (/.f64 #s(literal 1 binary64) (.f64 x x))) (/.f64 #s(literal -1 binary64) (.f64 x (.f64 x x))))
(+.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x) (/.f64 #s(literal -1 binary64) (.f64 x (.f64 x x))))
(+.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (.f64 x x)) (/.f64 #s(literal -1 binary64) (.f64 x (.f64 x x))))
(+.f64 (.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal -1 binary64) (.f64 x (.f64 x x))))
(exp.f64 (.f64 (log.f64 (/.f64 (.f64 x (.f64 x x)) (+.f64 (.f64 x x) #s(literal -1 binary64)))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (neg.f64 (/.f64 (+.f64 (.f64 x x) #s(literal -1 binary64)) (.f64 x (*.f64 x x)))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (/.f64 (.f64 x x) (+.f64 (.f64 x x) #s(literal -1 binary64))))) (neg.f64 (/.f64 (+.f64 (.f64 x x) #s(literal -1 binary64)) (.f64 x (*.f64 x x)))))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 #s(literal -1 binary64) x)) (neg.f64 (/.f64 (+.f64 (.f64 x x) #s(literal -1 binary64)) (.f64 x (*.f64 x x)))))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 x x) #s(literal -1 binary64))))) (neg.f64 (/.f64 (+.f64 (.f64 x x) #s(literal -1 binary64)) (.f64 x (*.f64 x x)))))
(neg.f64 (neg.f64 (/.f64 (+.f64 (.f64 x x) #s(literal -1 binary64)) (.f64 x (*.f64 x x)))))
(neg.f64 (.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (+.f64 (*.f64 x x) #s(literal -1 binary64))))))
(neg.f64 (.f64 x (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 x (.f64 x (*.f64 x x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x (.f64 x x)) (+.f64 (*.f64 x x) #s(literal -1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 x x) (.f64 x (+.f64 (.f64 x x) #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (.f64 x x))))
(/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 x x) #s(literal -1 binary64)))) (.f64 x (.f64 x (.f64 x (-.f64 #s(literal 0 binary64) x))))))
(/.f64 x (/.f64 x (/.f64 (+.f64 (.f64 x x) #s(literal -1 binary64)) (.f64 x (*.f64 x x)))))
(/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (.f64 x x) (+.f64 (.f64 x x) #s(literal -1 binary64))))
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(/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) x))
(/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 x x)))
(/.f64 (/.f64 (*.f64 x x) (pow.f64 x #s(literal -1/2 binary64))) (pow.f64 x #s(literal -1/2 binary64)))
(pow.f64 x #s(literal 3 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -3 binary64))
(pow.f64 (*.f64 x x) #s(literal 3/2 binary64))
(pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 3 binary64))
(.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))
(.f64 x (.f64 x x))
(.f64 x (/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))
(.f64 x (/.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal -1 binary64) (.f64 x (*.f64 x x)))))
(.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x (.f64 x (.f64 x x))))
(.f64 (.f64 x x) x)
(.f64 (.f64 x x) (/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (*.f64 x x))))
(.f64 (.f64 x (*.f64 x x)) #s(literal 1 binary64))
(.f64 #s(literal -1 binary64) (.f64 x (*.f64 x (-.f64 #s(literal 0 binary64) x))))
(*.f64 #s(literal -1 binary64) (pow.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 3 binary64)))
(.f64 (.f64 x (*.f64 x (-.f64 #s(literal 0 binary64) x))) #s(literal -1 binary64))
(.f64 (.f64 x (*.f64 x (-.f64 #s(literal 0 binary64) x))) (/.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal 1 binary64) x)))
(.f64 (-.f64 #s(literal 0 binary64) x) (.f64 x (-.f64 #s(literal 0 binary64) x)))
(.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))
(.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1 binary64) (.f64 x (*.f64 x x)))))
(.f64 (.f64 x (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) x))
(.f64 (.f64 x (.f64 x (.f64 x (-.f64 #s(literal 0 binary64) x)))) (/.f64 #s(literal -1 binary64) x))
(.f64 (.f64 x (-.f64 #s(literal 0 binary64) x)) (-.f64 #s(literal 0 binary64) x))
(.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x (*.f64 x x)))))
(*.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))
(*.f64 (pow.f64 x #s(literal 3/2 binary64)) (/.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1 binary64)))
(.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) (.f64 x (.f64 x (.f64 x (-.f64 #s(literal 0 binary64) x)))))
(.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1 binary64) x)) (.f64 x (*.f64 x (-.f64 #s(literal 0 binary64) x))))
(.f64 (/.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (/.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x (*.f64 x x)))))
(.f64 (/.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) x)) (/.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))
(.f64 (/.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x (*.f64 x x)))) (/.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(*.f64 (/.f64 x (pow.f64 x #s(literal -1/2 binary64))) (/.f64 x (pow.f64 x #s(literal -1/2 binary64))))
(.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) x)
(.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (.f64 x x))) (*.f64 x x))
(.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))) (/.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal 1 binary64) (*.f64 x x))))
(.f64 (/.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) (/.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) x)))
(.f64 (/.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal -1 binary64) x)) (/.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal -1 binary64) (.f64 x (*.f64 x x)))))
(.f64 (/.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 x x))) (/.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 x x))))
(.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1 binary64) (.f64 x (*.f64 x x)))) (-.f64 #s(literal 0 binary64) x))
(.f64 (pow.f64 (.f64 x x) #s(literal 3/4 binary64)) (pow.f64 (*.f64 x x) #s(literal 3/4 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 x #s(literal 3/2 binary64)))
(.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1 binary64) (.f64 x x))) (*.f64 x (-.f64 #s(literal 0 binary64) x)))

simplify163.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

2006×	`-lowering-.f32`
2006×	`-lowering-.f64`
1950×	`fma-lowering-fma.f32`
1950×	`fma-lowering-fma.f64`
1934×	`fmsub-define`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	41	424
1	91	375
2	234	366
3	542	364
4	1224	364
5	4217	364
0	8137	364

Stop Event

1×	iter limit
1×	node limit

Counts

72 → 72

Calls

Call 1

Inputs
(/ -1 (pow x 3))
(/ (- (pow x 2) 1) (pow x 3))
(/ (- (pow x 2) 1) (pow x 3))
(/ (- (pow x 2) 1) (pow x 3))
(/ 1 x)
(/ (- 1 (/ 1 (pow x 2))) x)
(/ (- 1 (/ 1 (pow x 2))) x)
(/ (- 1 (/ 1 (pow x 2))) x)
(/ 1 x)
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(/ -1 (pow x 4))
(/ (- (pow x 2) 1) (pow x 4))
(/ (- (pow x 2) 1) (pow x 4))
(/ (- (pow x 2) 1) (pow x 4))
(/ 1 (pow x 2))
(/ (- 1 (/ 1 (pow x 2))) (pow x 2))
(/ (- 1 (/ 1 (pow x 2))) (pow x 2))
(/ (- 1 (/ 1 (pow x 2))) (pow x 2))
(/ 1 (pow x 2))
(/ (- 1 (/ 1 (pow x 2))) (pow x 2))
(/ (- 1 (/ 1 (pow x 2))) (pow x 2))
(/ (- 1 (/ 1 (pow x 2))) (pow x 2))
(/ 1 (pow x 4))
(/ 1 (pow x 4))
(/ 1 (pow x 4))
(/ 1 (pow x 4))
(/ 1 (pow x 4))
(/ 1 (pow x 4))
(/ 1 (pow x 4))
(/ 1 (pow x 4))
(/ 1 (pow x 4))
(/ 1 (pow x 4))
(/ 1 (pow x 4))
(/ 1 (pow x 4))
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
-1
(- (* -1 (pow x 2)) 1)
(- (* (pow x 2) (- (* -1 (pow x 2)) 1)) 1)
(- (* (pow x 2) (- (* (pow x 2) (- (* -1 (pow x 2)) 1)) 1)) 1)
(/ 1 (pow x 2))
(/ (+ 1 (/ 1 (pow x 2))) (pow x 2))
(/ (+ 1 (+ (/ 1 (pow x 2)) (/ 1 (pow x 4)))) (pow x 2))
(/ (+ 1 (+ (/ 1 (pow x 2)) (+ (/ 1 (pow x 4)) (/ 1 (pow x 6))))) (pow x 2))
(/ 1 (pow x 2))
(/ (+ 1 (/ 1 (pow x 2))) (pow x 2))
(/ (+ 1 (+ (/ 1 (pow x 2)) (/ 1 (pow x 4)))) (pow x 2))
(/ (+ 1 (+ (/ 1 (pow x 2)) (+ (/ 1 (pow x 4)) (/ 1 (pow x 6))))) (pow x 2))
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)

Outputs
(/ -1 (pow x 3))
(/.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) x)
(/ (- (pow x 2) 1) (pow x 3))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))) x)
(/ (- (pow x 2) 1) (pow x 3))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))) x)
(/ (- (pow x 2) 1) (pow x 3))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (- 1 (/ 1 (pow x 2))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))) x)
(/ (- 1 (/ 1 (pow x 2))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))) x)
(/ (- 1 (/ 1 (pow x 2))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))) x)
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))) x)
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))) x)
(/ -1 (pow x 4))
(/.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) (.f64 x x))
(/ (- (pow x 2) 1) (pow x 4))
(/.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))) x) x)
(/ (- (pow x 2) 1) (pow x 4))
(/.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))) x) x)
(/ (- (pow x 2) 1) (pow x 4))
(/.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))) x) x)
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ (- 1 (/ 1 (pow x 2))) (pow x 2))
(/.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))) x) x)
(/ (- 1 (/ 1 (pow x 2))) (pow x 2))
(/.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))) x) x)
(/ (- 1 (/ 1 (pow x 2))) (pow x 2))
(/.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))) x) x)
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ (- 1 (/ 1 (pow x 2))) (pow x 2))
(/.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))) x) x)
(/ (- 1 (/ 1 (pow x 2))) (pow x 2))
(/.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))) x) x)
(/ (- 1 (/ 1 (pow x 2))) (pow x 2))
(/.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))) x) x)
(/ 1 (pow x 4))
(/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x (.f64 x x)))
(/ 1 (pow x 4))
(/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x (.f64 x x)))
(/ 1 (pow x 4))
(/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x (.f64 x x)))
(/ 1 (pow x 4))
(/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x (.f64 x x)))
(/ 1 (pow x 4))
(/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x (.f64 x x)))
(/ 1 (pow x 4))
(/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x (.f64 x x)))
(/ 1 (pow x 4))
(/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x (.f64 x x)))
(/ 1 (pow x 4))
(/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x (.f64 x x)))
(/ 1 (pow x 4))
(/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x (.f64 x x)))
(/ 1 (pow x 4))
(/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x (.f64 x x)))
(/ 1 (pow x 4))
(/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x (.f64 x x)))
(/ 1 (pow x 4))
(/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x (.f64 x x)))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
-1
#s(literal -1 binary64)
(- (* -1 (pow x 2)) 1)
(-.f64 #s(literal -1 binary64) (*.f64 x x))
(- (* (pow x 2) (- (* -1 (pow x 2)) 1)) 1)
(+.f64 #s(literal -1 binary64) (.f64 x (.f64 x (-.f64 #s(literal -1 binary64) (*.f64 x x)))))
(- (* (pow x 2) (- (* (pow x 2) (- (* -1 (pow x 2)) 1)) 1)) 1)
(.f64 (-.f64 #s(literal -1 binary64) (.f64 x x)) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x)))))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ (+ 1 (/ 1 (pow x 2))) (pow x 2))
(/.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) x) x)
(/ (+ 1 (+ (/ 1 (pow x 2)) (/ 1 (pow x 4)))) (pow x 2))
(/.f64 (+.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))))) (.f64 x x))
(/ (+ 1 (+ (/ 1 (pow x 2)) (+ (/ 1 (pow x 4)) (/ 1 (pow x 6))))) (pow x 2))
(/.f64 (+.f64 #s(literal 1 binary64) (+.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x)))) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x x)))))) (*.f64 x x))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ (+ 1 (/ 1 (pow x 2))) (pow x 2))
(/.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) x) x)
(/ (+ 1 (+ (/ 1 (pow x 2)) (/ 1 (pow x 4)))) (pow x 2))
(/.f64 (+.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))))) (.f64 x x))
(/ (+ 1 (+ (/ 1 (pow x 2)) (+ (/ 1 (pow x 4)) (/ 1 (pow x 6))))) (pow x 2))
(/.f64 (+.f64 #s(literal 1 binary64) (+.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x)))) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x x)))))) (*.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))

eval106.0ms (1.7%)

Compiler: Compiled 17579 to 1847 computations (89.5% saved)

prune82.0ms (1.3%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	709	1	710
Fresh	0	0	0
Picked	1	0	1
Done	0	4	4
Total	710	5	715

Accuracy

100.0%

Counts

715 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
	26.1%	(/.f64 (/.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))) x) x) (/.f64 #s(literal 1 binary64) x))
✓	99.8%	(/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x)))
✓	51.0%	(/.f64 #s(literal 1 binary64) x)
✓	51.3%	(.f64 x (-.f64 #s(literal 1 binary64) (.f64 x x)))
✓	52.3%	x

Compiler

Compiled 171 to 60 computations (64.9% saved)

regimes8.0ms (0.1%)

Counts

10 → 1

Calls

Call 1

Inputs
x
(/.f64 #s(literal 1 binary64) x)
(.f64 x (-.f64 #s(literal 1 binary64) (.f64 x x)))
(/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x)))
(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))
(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) x))
(/.f64 (/.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))) x) x) (/.f64 #s(literal 1 binary64) x))
(/.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) x))
(/.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) x))
(/.f64 x (/.f64 (.f64 (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) #s(literal -1 binary64)))) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x))))))

Outputs
(/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x)))

Calls

2 calls:

4.0ms	x
3.0ms	(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))

Results

Accuracy	Segments	Branch
99.8%	1	`x`
99.8%	1	`(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))`

Compiler

Compiled 10 to 6 computations (40% saved)

regimes3.0ms (0.1%)

Counts

3 → 2

Calls

Call 1

Inputs
x
(/.f64 #s(literal 1 binary64) x)
(.f64 x (-.f64 #s(literal 1 binary64) (.f64 x x)))

Outputs
(.f64 x (-.f64 #s(literal 1 binary64) (.f64 x x)))
(/.f64 #s(literal 1 binary64) x)

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
99.7%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0%)

Counts

2 → 2

Calls

Call 1

Inputs
x
(/.f64 #s(literal 1 binary64) x)

Outputs
x
(/.f64 #s(literal 1 binary64) x)

Calls

1 calls:

1.0ms

Results

Accuracy	Segments	Branch
99.4%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes1.0ms (0%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
x

Outputs
x

Calls

1 calls:

1.0ms

Results

Accuracy	Segments	Branch
52.3%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

bsearch12.0ms (0.2%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
11.0ms	0.0005740468287233434	5126.105924518911

Results

7.0ms

144×

valid

Compiler

Compiled 138 to 98 computations (29% saved)

Precisions

Click to see histograms. Total time spent on operations: 3.0ms

ival-div: 1.0ms (30.2% of total)

ival-add: 1.0ms (30.2% of total)

ival-mult: 1.0ms (30.2% of total)

const: 0.0ms (0% of total)

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

bsearch13.0ms (0.2%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
12.0ms	0.0005740468287233434	5126.105924518911

Results

8.0ms

144×

valid

Compiler

Compiled 84 to 62 computations (26.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 5.0ms

ival-div: 2.0ms (43.2% of total)

ival-add: 1.0ms (21.6% of total)

ival-mult: 1.0ms (21.6% of total)

const: 0.0ms (0% of total)

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

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`+-commutative_binary64`
6×	`*-commutative_binary64`
6×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	30
1	23	30
2	30	30
3	34	30
4	36	30

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x)))
(if (<=.f64 x #s(literal 7656119366529843/9007199254740992 binary64)) (.f64 x (-.f64 #s(literal 1 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) x))
(if (<=.f64 x #s(literal 1 binary64)) x (/.f64 #s(literal 1 binary64) x))
x

Outputs
(/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x)))
(if (<=.f64 x #s(literal 7656119366529843/9007199254740992 binary64)) (.f64 x (-.f64 #s(literal 1 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) x))
(if (<=.f64 x #s(literal 1 binary64)) x (/.f64 #s(literal 1 binary64) x))
x

soundness841.0ms (13.8%)

Rules

3456×	`/-lowering-/.f32`
3456×	`/-lowering-/.f64`
3360×	`-lowering-.f32`
3360×	`-lowering-.f64`
3352×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	211
1	137	172
2	356	167
3	1076	166
4	3300	166
0	8302	166
0	21	69
1	167	61
2	1280	57
0	8747	57
0	5	12
1	32	12
2	209	12
3	1928	12
0	8654	12

Stop Event

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

Compiler

Compiled 71 to 38 computations (46.5% saved)

preprocess38.0ms (0.6%)

Remove: (negabs x)
Compiler: Compiled 110 to 56 computations (49.1% saved)

Iter	Nodes	Cost
0	10	19
1	32	19
2	70	18
3	148	18
4	306	18
5	550	18
6	873	18
7	875	18
8	899	18
9	915	18
0	5	6
1	10	6
0	10	6

Iter	Nodes	Cost
0	10	19
1	32	19
2	70	18
3	148	18
4	306	18
5	550	18
6	873	18
7	875	18
8	899	18
9	915	18
0	5	6
1	10	6
0	10	6

analyze1.0ms (0%)

sample551.0ms (9.1%)

preprocess43.0ms (0.7%)

explain52.0ms (0.8%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify3.0ms (0.1%)

localize23.0ms (0.4%)

series2.0ms (0%)

rewrite301.0ms (5%)

simplify346.0ms (5.7%)

eval47.0ms (0.8%)

prune41.0ms (0.7%)

simplify208.0ms (3.4%)

localize114.0ms (1.9%)

series12.0ms (0.2%)

rewrite547.0ms (9%)

simplify213.0ms (3.5%)

eval307.0ms (5.1%)

prune128.0ms (2.1%)

simplify478.0ms (7.9%)

localize74.0ms (1.2%)

series3.0ms (0%)

rewrite332.0ms (5.5%)

simplify224.0ms (3.7%)

eval148.0ms (2.4%)

prune101.0ms (1.7%)

simplify146.0ms (2.4%)

localize44.0ms (0.7%)

series2.0ms (0%)

rewrite308.0ms (5.1%)

simplify163.0ms (2.7%)

eval106.0ms (1.7%)

prune82.0ms (1.3%)

regimes8.0ms (0.1%)

regimes3.0ms (0.1%)

regimes2.0ms (0%)

regimes1.0ms (0%)

bsearch12.0ms (0.2%)

bsearch13.0ms (0.2%)

simplify7.0ms (0.1%)

soundness841.0ms (13.8%)

preprocess38.0ms (0.6%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	10	19
1	32	19
2	70	18
3	148	18
4	306	18
5	550	18
6	873	18
7	875	18
8	899	18
9	915	18
0	5	6
1	10	6
0	10	6