Metrics for ln(1 + x)

analyze3.0ms (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
0%	0%	100%	0%	0%	0%	0%	2
33.3%	25%	50%	0%	0%	25%	0%	3
66.7%	50%	25%	0%	0%	25%	0%	4
83.3%	62.5%	12.5%	0%	0%	25%	0%	5
91.7%	68.7%	6.2%	0%	0%	25%	0%	6
95.8%	71.8%	3.1%	0%	0%	25%	0%	7
97.9%	73.4%	1.6%	0%	0%	25%	0%	8
99%	74.2%	0.8%	0%	0%	25%	0%	9
99.5%	74.6%	0.4%	0%	0%	25%	0%	10
99.7%	74.8%	0.2%	0%	0%	25%	0%	11
99.9%	74.9%	0.1%	0%	0%	25%	0%	12

Compiler

Compiled 6 to 5 computations (16.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 1.0ms

ival-log: 1.0ms (106.8% of total)

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

const: 0.0ms (0% of total)

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

sample1.8s (16.7%)

Results

975.0ms	4075×	1	valid
416.0ms	1248×	2	valid
156.0ms	2933×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 962.0ms

ival-log: 736.0ms (76.5% of total)

ival-add: 108.0ms (11.2% of total)

backward-pass: 99.0ms (10.3% of total)

const: 19.0ms (2% of total)

Bogosity

preprocess16.0ms (0.2%)

Algorithm

2×	egg-herbie

Rules

52×	`sum3-define`
20×	`sub-neg`
16×	`fma-define`
16×	`fmsub-define`
14×	`+-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	9
1	20	9
2	28	9
3	38	9
4	57	9
5	77	9
6	98	9
7	118	9
8	120	9
0	4	2
1	8	2
0	8	2

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(log (+ 1 x))

Outputs
(log (+ 1 x))
(log1p.f64 x)

Call 2

Inputs
(log (+ 1 x))
(log (+ 1 (neg x)))
(neg (log (+ 1 (neg x))))

Outputs
(log (+ 1 x))
(log1p x)
(log (+ 1 (neg x)))
(log1p (neg x))
(neg (log (+ 1 (neg x))))
(neg (log1p (neg x)))

explain150.0ms (1.4%)

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
175	-	-	`(log.f64 (+.f64 #s(literal 1 binary64) x))`
0	-	-	`x`
0	-	-	`#s(literal 1 binary64)`
0	-	-	`(+.f64 #s(literal 1 binary64) x)`

Results

64.0ms	260×	1	valid
48.0ms	82×	2	valid
11.0ms	170×	0	valid

Compiler

Compiled 27 to 14 computations (48.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 68.0ms

ival-log: 53.0ms (78% of total)

ival-add: 7.0ms (10.3% of total)

backward-pass: 7.0ms (10.3% of total)

const: 1.0ms (1.5% of total)

eval0.0ms (0%)

Compiler: Compiled 3 to 2 computations (33.3% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(log1p.f64 x)
▶	36.7%	(log.f64 (+.f64 #s(literal 1 binary64) x))

Compiler

Compiled 8 to 6 computations (25% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(log1p.f64 x)
✓	cost-diff	0	(+.f64 #s(literal 1 binary64) x)
✓	cost-diff	128	(log.f64 (+.f64 #s(literal 1 binary64) x))

Rules

4×	`+-lowering-+.f64`
4×	`+-lowering-+.f32`
2×	`log1p-lowering-log1p.f32`
2×	`log-lowering-log.f64`
2×	`log1p-lowering-log1p.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	10
1	8	10
0	8	10

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(log (+ 1 x))
(+ 1 x)
1
x
(log (+ 1 x))
x

Outputs
(log (+ 1 x))
(log1p.f64 x)
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
1
#s(literal 1 binary64)
x
(log (+ 1 x))
(log1p.f64 x)
x

localize311.0ms (2.9%)

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(log1p.f64 x)
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) x)
✓	accuracy	99.6%	(log.f64 (+.f64 #s(literal 1 binary64) x))

Results

292.0ms	171×	5	exit
8.0ms	85×	0	valid

Compiler

Compiled 14 to 6 computations (57.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 251.0ms

ival-log: 225.0ms (89.5% of total)

backward-pass: 14.0ms (5.6% of total)

ival-add: 6.0ms (2.4% of total)

compiled-spec: 5.0ms (2% of total)

const: 1.0ms (0.4% of total)

series2.0ms (0%)

Counts

3 → 36

Calls

Call 1

Inputs
#<alt (log (+ 1 x))>
#<alt (+ 1 x)>
#<alt (log (+ 1 x))>

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

Calls

9 calls:

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

rewrite309.0ms (2.9%)

Algorithm

1×	batch-egg-rewrite

Rules

3862×	`/-lowering-/.f32`
3862×	`/-lowering-/.f64`
3086×	`-lowering-.f32`
3086×	`-lowering-.f64`
1778×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	7
1	21	7
2	141	7
3	1093	7
0	8377	7

Stop Event

1×	iter limit
1×	node limit

Counts

3 → 311

Calls

Call 1

Inputs
(log (+ 1 x))
(+ 1 x)
(log (+ 1 x))

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

simplify318.0ms (3%)

Algorithm

1×	egg-herbie

Rules

1994×	`fma-lowering-fma.f32`
1994×	`fma-lowering-fma.f64`
1970×	`fmsub-define`
1908×	`sum3-define`
1776×	`fmm-def`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	62	296
1	188	252
2	458	240
3	1230	236
4	3932	236
0	8232	236

Stop Event

1×	iter limit
1×	node limit

Counts

36 → 36

Calls

Call 1

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

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

eval81.0ms (0.8%)

Compiler: Compiled 10185 to 919 computations (91% saved)

prune32.0ms (0.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	343	4	347
Fresh	0	0	0
Picked	0	2	2
Done	0	0	0
Total	343	6	349

Accuracy

100.0%

Counts

349 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	68.7%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))))))
▶	69.6%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64))))))
▶	68.4%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))))
✓	100.0%	(log1p.f64 x)
✓	36.7%	(log.f64 (+.f64 #s(literal 1 binary64) x))
▶	69.3%	x

Compiler

Compiled 46 to 34 computations (26.1% saved)

simplify70.0ms (0.7%)

Algorithm

1×	egg-herbie

Localize:

Found 11 expressions of interest:

New	Metric	Program
✓	cost-diff	(+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64)))))
✓	cost-diff	(.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal -1/4 binary64))))))
✓	cost-diff	(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal -1/4 binary64)))))))
✓	cost-diff	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))))))
✓	cost-diff	(+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64)))
✓	cost-diff	(.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))))
✓	cost-diff	(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64)))))
✓	cost-diff	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64))))))
✓	cost-diff	(*.f64 x #s(literal -1/2 binary64))
✓	cost-diff	(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal -1/2 binary64)))
✓	cost-diff	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))))

Rules

1430×	`fma-define`
1068×	`fma-lowering-fma.f32`
1068×	`fma-lowering-fma.f64`
336×	`-lowering-.f32`
336×	`-lowering-.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	20	126
1	66	106
2	184	103
3	457	103
4	967	103
5	1391	103
6	1552	103
7	1554	103
0	1554	103

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize109.0ms (1%)

Localize:

Found 11 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal -1/4 binary64)))
✓	accuracy	100.0%	(.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal -1/4 binary64))))))
✓	accuracy	99.9%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))))))
✓	accuracy	99.7%	(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))
✓	accuracy	100.0%	(+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64)))
✓	accuracy	99.9%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64))))))
✓	accuracy	99.9%	(.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))))
✓	accuracy	99.5%	(*.f64 x #s(literal 1/3 binary64))
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal -1/2 binary64)))
✓	accuracy	100.0%	(*.f64 x #s(literal -1/2 binary64))
✓	accuracy	100.0%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))))

Results

77.0ms	255×	0	valid
1.0ms	1×	2	valid

Compiler

Compiled 128 to 21 computations (83.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 31.0ms

ival-mult: 17.0ms (55.4% of total)

ival-add: 9.0ms (29.3% of total)

...c/correct-round.rkt:119:19: 4.0ms (13% of total)

const: 1.0ms (3.3% of total)

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

series11.0ms (0.1%)

Counts

14 → 168

Calls

Call 1

Inputs
#<alt (* x (+ 1 (* x -1/2)))>
#<alt (+ 1 (* x -1/2))>
#<alt (* x -1/2)>
#<alt (* x (+ 1 (* x (+ -1/2 (* x 1/3)))))>
#<alt (+ 1 (* x (+ -1/2 (* x 1/3))))>
#<alt (* x (+ -1/2 (* x 1/3)))>
#<alt (+ -1/2 (* x 1/3))>
#<alt (* x (+ 1 (* x (+ -1/2 (* x (+ 1/3 (* x -1/4)))))))>
#<alt (+ 1 (* x (+ -1/2 (* x (+ 1/3 (* x -1/4))))))>
#<alt (* x (+ -1/2 (* x (+ 1/3 (* x -1/4)))))>
#<alt (+ -1/2 (* x (+ 1/3 (* x -1/4))))>
#<alt (* x 1/3)>
#<alt (* x (+ 1/3 (* x -1/4)))>
#<alt (+ 1/3 (* x -1/4))>

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

Calls

42 calls:

Time	Variable		Point	Expression
2.0ms	x	@	0	(* x (+ 1 (* x -1/2)))
1.0ms	x	@	inf	(* x 1/3)
1.0ms	x	@	0	(* x (+ 1 (* x (+ -1/2 (* x 1/3)))))
0.0ms	x	@	inf	(* x (+ 1 (* x -1/2)))
0.0ms	x	@	-inf	(* x (+ 1 (* x -1/2)))

rewrite401.0ms (3.7%)

Algorithm

1×	batch-egg-rewrite

Rules

3810×	`-lowering-.f32`
3810×	`-lowering-.f64`
3484×	`/-lowering-/.f32`
3484×	`/-lowering-/.f64`
1980×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	20	110
1	137	90
2	1288	87
0	8126	87

Stop Event

1×	iter limit
1×	node limit

Counts

14 → 510

Calls

Call 1

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

Outputs
(+.f64 x (.f64 x (.f64 x #s(literal -1/2 binary64))))
(+.f64 (.f64 x (.f64 x #s(literal -1/2 binary64))) x)
(-.f64 (/.f64 (.f64 x x) (-.f64 x (.f64 x (.f64 x #s(literal -1/2 binary64))))) (/.f64 (.f64 (.f64 x (.f64 x #s(literal -1/2 binary64))) (.f64 x (.f64 x #s(literal -1/2 binary64)))) (-.f64 x (.f64 x (.f64 x #s(literal -1/2 binary64))))))
(fma.f64 x #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64))))
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) x)
(fma.f64 #s(literal 1 binary64) x (.f64 x (.f64 x #s(literal -1/2 binary64))))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) x)
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) x x)
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) x)
(/.f64 x (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal -1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 x x) (-.f64 (.f64 (.f64 x (.f64 x #s(literal -1/2 binary64))) (.f64 x (.f64 x #s(literal -1/2 binary64)))) (.f64 x (.f64 x (.f64 x #s(literal -1/2 binary64)))))) (+.f64 (.f64 x (.f64 x x)) (.f64 (.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x x))) (.f64 x (*.f64 x x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (.f64 x (.f64 x #s(literal -1/2 binary64)))) (-.f64 (.f64 x x) (.f64 (.f64 x (.f64 x #s(literal -1/2 binary64))) (.f64 x (.f64 x #s(literal -1/2 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64)))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/8 binary64) (.f64 x (*.f64 x x)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))) (.f64 x (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 x x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64)))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/8 binary64) (.f64 x (*.f64 x x)))) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))) (.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 x x))) x)))
(/.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 (.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x x))) (.f64 x (.f64 x x)))) (+.f64 (.f64 x x) (-.f64 (.f64 (.f64 x (.f64 x #s(literal -1/2 binary64))) (.f64 x (.f64 x #s(literal -1/2 binary64)))) (.f64 x (.f64 x (*.f64 x #s(literal -1/2 binary64)))))))
(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x (.f64 x #s(literal -1/2 binary64))) (.f64 x (.f64 x #s(literal -1/2 binary64))))) (-.f64 x (.f64 x (.f64 x #s(literal -1/2 binary64)))))
(/.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x x))))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 (*.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64)))))
(/.f64 (.f64 x (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 x x)))) (-.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))))
(/.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x x)))) x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 (*.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64)))))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 x x))) x) (-.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))))
(/.f64 (neg.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 (.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x x))) (.f64 x (.f64 x x))))) (neg.f64 (+.f64 (.f64 x x) (-.f64 (.f64 (.f64 x (.f64 x #s(literal -1/2 binary64))) (.f64 x (.f64 x #s(literal -1/2 binary64)))) (.f64 x (.f64 x (*.f64 x #s(literal -1/2 binary64))))))))
(/.f64 (neg.f64 (-.f64 (.f64 x x) (.f64 (.f64 x (.f64 x #s(literal -1/2 binary64))) (.f64 x (.f64 x #s(literal -1/2 binary64)))))) (neg.f64 (-.f64 x (.f64 x (.f64 x #s(literal -1/2 binary64))))))
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(/.f64 (neg.f64 (.f64 x (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 x x))))) (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64)))))
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(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 x #s(literal 1/3 binary64)) (.f64 x (.f64 x #s(literal -1/4 binary64)))) (-.f64 (.f64 #s(literal 1/9 binary64) (.f64 x x)) (.f64 (.f64 x (.f64 x #s(literal -1/4 binary64))) (.f64 x (.f64 x #s(literal -1/4 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x #s(literal -1/4 binary64)) (+.f64 (.f64 x #s(literal -1/4 binary64)) #s(literal -1/3 binary64)))) (.f64 x (+.f64 #s(literal 1/27 binary64) (.f64 (.f64 x (*.f64 x x)) #s(literal -1/64 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))) (.f64 x (-.f64 #s(literal 1/9 binary64) (.f64 #s(literal 1/16 binary64) (.f64 x x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x #s(literal -1/4 binary64)) (+.f64 (.f64 x #s(literal -1/4 binary64)) #s(literal -1/3 binary64)))) (.f64 (+.f64 #s(literal 1/27 binary64) (.f64 (.f64 x (*.f64 x x)) #s(literal -1/64 binary64))) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))) (.f64 (-.f64 #s(literal 1/9 binary64) (.f64 #s(literal 1/16 binary64) (.f64 x x))) x)))
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(+.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal -1/4 binary64)))
(+.f64 (*.f64 x #s(literal -1/4 binary64)) #s(literal 1/3 binary64))
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(-.f64 (/.f64 #s(literal 1/9 binary64) (-.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64)))) (/.f64 (.f64 #s(literal 1/16 binary64) (.f64 x x)) (-.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64)))))
(-.f64 (/.f64 (.f64 #s(literal 1/16 binary64) (.f64 x x)) (+.f64 (.f64 x #s(literal -1/4 binary64)) #s(literal -1/3 binary64))) (/.f64 #s(literal 1/9 binary64) (+.f64 (.f64 x #s(literal -1/4 binary64)) #s(literal -1/3 binary64))))
(fma.f64 x #s(literal -1/4 binary64) #s(literal 1/3 binary64))
(fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal -1/4 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal -1/4 binary64)))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 #s(literal 1/16 binary64) (.f64 x x)) (-.f64 #s(literal 1/9 binary64) (.f64 #s(literal -1/12 binary64) x))) (+.f64 #s(literal 1/27 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal -1/64 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 x #s(literal -1/4 binary64)) #s(literal -1/3 binary64)) (+.f64 (.f64 #s(literal 1/16 binary64) (*.f64 x x)) #s(literal -1/9 binary64))))
(/.f64 (+.f64 #s(literal 1/27 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal -1/64 binary64))) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x #s(literal -1/4 binary64)) (+.f64 (.f64 x #s(literal -1/4 binary64)) #s(literal -1/3 binary64)))))
(/.f64 (+.f64 #s(literal 1/27 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal -1/64 binary64))) (+.f64 (.f64 #s(literal 1/16 binary64) (.f64 x x)) (-.f64 #s(literal 1/9 binary64) (.f64 #s(literal -1/12 binary64) x))))
(/.f64 (-.f64 #s(literal 1/9 binary64) (.f64 #s(literal 1/16 binary64) (.f64 x x))) (-.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal -1/4 binary64))))
(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/27 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal -1/64 binary64)))) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x #s(literal -1/4 binary64)) (+.f64 (.f64 x #s(literal -1/4 binary64)) #s(literal -1/3 binary64))))))
(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/27 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal -1/64 binary64)))) (neg.f64 (+.f64 (.f64 #s(literal 1/16 binary64) (.f64 x x)) (-.f64 #s(literal 1/9 binary64) (.f64 #s(literal -1/12 binary64) x)))))
(/.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1/9 binary64) (.f64 #s(literal 1/16 binary64) (.f64 x x)))) (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal -1/4 binary64)))))
(/.f64 (+.f64 (.f64 #s(literal 1/16 binary64) (.f64 x x)) #s(literal -1/9 binary64)) (+.f64 (*.f64 x #s(literal -1/4 binary64)) #s(literal -1/3 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal -1/4 binary64))))))
(/.f64 (-.f64 (.f64 #s(literal 1/9 binary64) (-.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64)))) (.f64 (-.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))) (.f64 #s(literal 1/16 binary64) (.f64 x x)))) (.f64 (-.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))) (-.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal -1/4 binary64)))))
(/.f64 (.f64 (+.f64 #s(literal 1/19683 binary64) (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -1/64 binary64)) (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -1/64 binary64)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/64 binary64))))) #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 1/729 binary64) (-.f64 (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -1/64 binary64)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/64 binary64))) (.f64 #s(literal -1/1728 binary64) (.f64 x (.f64 x x))))) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x #s(literal -1/4 binary64)) (+.f64 (.f64 x #s(literal -1/4 binary64)) #s(literal -1/3 binary64))))))
(/.f64 (.f64 (-.f64 #s(literal 1/729 binary64) (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -1/64 binary64)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/64 binary64)))) #s(literal 1 binary64)) (.f64 (-.f64 #s(literal 1/27 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal -1/64 binary64))) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x #s(literal -1/4 binary64)) (+.f64 (*.f64 x #s(literal -1/4 binary64)) #s(literal -1/3 binary64))))))
(/.f64 (.f64 (-.f64 #s(literal 1/729 binary64) (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -1/64 binary64)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/64 binary64)))) #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 1/81 binary64) (+.f64 (.f64 (.f64 #s(literal 1/16 binary64) (.f64 x x)) (.f64 #s(literal 1/16 binary64) (.f64 x x))) (.f64 #s(literal 1/9 binary64) (.f64 #s(literal 1/16 binary64) (.f64 x x))))) (-.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64)))))
(/.f64 (.f64 (-.f64 #s(literal 1/81 binary64) (.f64 (.f64 #s(literal 1/16 binary64) (.f64 x x)) (.f64 #s(literal 1/16 binary64) (.f64 x x)))) #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 1/9 binary64) (.f64 #s(literal 1/16 binary64) (.f64 x x))) (-.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64)))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/27 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal -1/64 binary64))))) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x #s(literal -1/4 binary64)) (+.f64 (.f64 x #s(literal -1/4 binary64)) #s(literal -1/3 binary64)))))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1/9 binary64) (.f64 #s(literal 1/16 binary64) (.f64 x x))))) (neg.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal -1/4 binary64))))))
(/.f64 (neg.f64 (+.f64 (.f64 #s(literal 1/16 binary64) (.f64 x x)) #s(literal -1/9 binary64))) (neg.f64 (+.f64 (*.f64 x #s(literal -1/4 binary64)) #s(literal -1/3 binary64))))
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(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal -1/4 binary64)))) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))
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(.f64 (-.f64 #s(literal 1/9 binary64) (.f64 #s(literal 1/16 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64)))))
(.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/27 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal -1/64 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x #s(literal -1/4 binary64)) (+.f64 (*.f64 x #s(literal -1/4 binary64)) #s(literal -1/3 binary64)))))))
(.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1/9 binary64) (.f64 #s(literal 1/16 binary64) (.f64 x x)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))))
(.f64 (+.f64 (.f64 #s(literal 1/16 binary64) (.f64 x x)) #s(literal -1/9 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x #s(literal -1/4 binary64)) #s(literal -1/3 binary64))))

simplify195.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

2658×	`-lowering-.f32`
2658×	`-lowering-.f64`
1632×	`+-lowering-+.f64`
1632×	`+-lowering-+.f32`
1110×	`/-lowering-/.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	107	1108
1	322	992
2	1068	913
3	3973	879
0	8307	879

Stop Event

1×	iter limit
1×	node limit

Counts

168 → 168

Calls

Call 1

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

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

eval95.0ms (0.9%)

Compiler: Compiled 19647 to 2186 computations (88.9% saved)

prune101.0ms (0.9%)

Pruning

10 alts after pruning (5 fresh and 5 done)

	Pruned	Kept	Total
New	673	5	678
Fresh	0	0	0
Picked	1	3	4
Done	0	2	2
Total	674	10	684

Accuracy

100.0%

Counts

684 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	68.7%	(/.f64 x (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal -1/4 binary64)))))))))
▶	69.6%	(+.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64))))) x)
▶	68.4%	(+.f64 (.f64 x (.f64 x #s(literal -1/2 binary64))) x)
▶	68.5%	(.f64 x (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (.f64 x x))) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (.f64 x x))))) #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (.f64 x x)))) (-.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))))))))
▶	68.7%	(.f64 x (+.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))) (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))) (*.f64 x x))))
✓	68.7%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))))))
✓	68.4%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))))
✓	100.0%	(log1p.f64 x)
✓	36.7%	(log.f64 (+.f64 #s(literal 1 binary64) x))
✓	69.3%	x

Compiler

Compiled 334 to 145 computations (56.6% saved)

simplify256.0ms (2.4%)

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(-.f64 #s(literal 1 binary64) (.f64 (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (.f64 x x))) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (*.f64 x x)))))
✓	cost-diff	128	(.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (.f64 x x))) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (.f64 x x))))) #s(literal 1 binary64))
✓	cost-diff	128	(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (.f64 x x))) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (.f64 x x))))) #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (.f64 x x)))) (-.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal -1/4 binary64)))))))))
✓	cost-diff	128	(.f64 x (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (.f64 x x))) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (.f64 x x))))) #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (.f64 x x)))) (-.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))))))))
✓	cost-diff	0	(.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal -1/4 binary64))))))
✓	cost-diff	0	(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal -1/4 binary64)))))))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal -1/4 binary64))))))))
✓	cost-diff	128	(/.f64 x (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal -1/4 binary64)))))))))
✓	cost-diff	0	(*.f64 x #s(literal -1/2 binary64))
✓	cost-diff	0	(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal -1/2 binary64)))
✓	cost-diff	128	(+.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))) (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))) (.f64 x x)))
✓	cost-diff	128	(.f64 x (+.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))) (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))) (*.f64 x x))))
✓	cost-diff	0	(*.f64 x #s(literal -1/2 binary64))
✓	cost-diff	0	(.f64 x (.f64 x #s(literal -1/2 binary64)))
✓	cost-diff	0	(+.f64 (.f64 x (.f64 x #s(literal -1/2 binary64))) x)
✓	cost-diff	0	(+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64)))
✓	cost-diff	0	(.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))))
✓	cost-diff	0	(.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64)))))
✓	cost-diff	0	(+.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64))))) x)

Rules

4344×	`-lowering-.f32`
4344×	`-lowering-.f64`
2550×	`+-lowering-+.f64`
2550×	`+-lowering-+.f32`
1706×	`fma-define`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	36	546
1	128	386
2	463	374
3	2566	373
0	8409	373

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize286.0ms (2.7%)

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.9%	(.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (.f64 x x))
✓	accuracy	99.9%	(.f64 (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (.f64 x x))) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (*.f64 x x))))
✓	accuracy	99.7%	(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))
✓	accuracy	70.7%	(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (.f64 x x))) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (.f64 x x))))) #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (.f64 x x)))) (-.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal -1/4 binary64)))))))))
✓	accuracy	100.0%	(.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal -1/4 binary64))))))
✓	accuracy	99.9%	(/.f64 x (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal -1/4 binary64)))))))))
✓	accuracy	99.7%	(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))
✓	accuracy	99.3%	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal -1/4 binary64))))))))
✓	accuracy	100.0%	(+.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))) (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))) (.f64 x x)))
✓	accuracy	100.0%	(+.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal -1/4 binary64)))
✓	accuracy	99.9%	(.f64 x (+.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))) (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))) (*.f64 x x))))
✓	accuracy	99.8%	(.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))) (*.f64 x x))
✓	accuracy	100.0%	(.f64 x (.f64 x #s(literal -1/2 binary64)))
✓	accuracy	100.0%	(*.f64 x #s(literal -1/2 binary64))
✓	accuracy	100.0%	(+.f64 (.f64 x (.f64 x #s(literal -1/2 binary64))) x)
✓	accuracy	100.0%	(+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64)))
✓	accuracy	100.0%	(.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64)))))
✓	accuracy	99.9%	(.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))))
✓	accuracy	99.5%	(*.f64 x #s(literal 1/3 binary64))

Results

193.0ms	255×	0	valid
2.0ms	1×	2	valid

Compiler

Compiled 694 to 37 computations (94.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 55.0ms

ival-mult: 30.0ms (54.1% of total)

ival-add: 11.0ms (19.8% of total)

...c/correct-round.rkt:119:19: 6.0ms (10.8% of total)

ival-div: 5.0ms (9% of total)

ival-sub: 2.0ms (3.6% of total)

const: 1.0ms (1.8% of total)

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

series10.0ms (0.1%)

Counts

24 → 288

Calls

Call 1

Inputs
#<alt (+ (* x (* x (+ -1/2 (* x 1/3)))) x)>
#<alt (* x (* x (+ -1/2 (* x 1/3))))>
#<alt (* x (+ -1/2 (* x 1/3)))>
#<alt (+ -1/2 (* x 1/3))>
#<alt (+ (* x (* x -1/2)) x)>
#<alt (* x (* x -1/2))>
#<alt (* x -1/2)>
#<alt (* x (+ (+ 1 (* x -1/2)) (* (+ 1/3 (* x -1/4)) (* x x))))>
#<alt (+ (+ 1 (* x -1/2)) (* (+ 1/3 (* x -1/4)) (* x x)))>
#<alt (+ 1 (* x -1/2))>
#<alt (/ x (/ 1 (+ 1 (* x (+ -1/2 (* x (+ 1/3 (* x -1/4))))))))>
#<alt (/ 1 (+ 1 (* x (+ -1/2 (* x (+ 1/3 (* x -1/4)))))))>
#<alt (+ 1 (* x (+ -1/2 (* x (+ 1/3 (* x -1/4))))))>
#<alt (* x (+ -1/2 (* x (+ 1/3 (* x -1/4)))))>
#<alt (* x (/ (* (- 1 (* (* (+ -1/2 (* x (+ 1/3 (* x -1/4)))) (* (+ -1/2 (* x (+ 1/3 (* x -1/4)))) (* x x))) (* (+ -1/2 (* x (+ 1/3 (* x -1/4)))) (* (+ -1/2 (* x (+ 1/3 (* x -1/4)))) (* x x))))) 1) (* (+ 1 (* (+ -1/2 (* x (+ 1/3 (* x -1/4)))) (* (+ -1/2 (* x (+ 1/3 (* x -1/4)))) (* x x)))) (- 1 (* x (+ -1/2 (* x (+ 1/3 (* x -1/4)))))))))>
#<alt (/ (* (- 1 (* (* (+ -1/2 (* x (+ 1/3 (* x -1/4)))) (* (+ -1/2 (* x (+ 1/3 (* x -1/4)))) (* x x))) (* (+ -1/2 (* x (+ 1/3 (* x -1/4)))) (* (+ -1/2 (* x (+ 1/3 (* x -1/4)))) (* x x))))) 1) (* (+ 1 (* (+ -1/2 (* x (+ 1/3 (* x -1/4)))) (* (+ -1/2 (* x (+ 1/3 (* x -1/4)))) (* x x)))) (- 1 (* x (+ -1/2 (* x (+ 1/3 (* x -1/4))))))))>
#<alt (* (- 1 (* (* (+ -1/2 (* x (+ 1/3 (* x -1/4)))) (* (+ -1/2 (* x (+ 1/3 (* x -1/4)))) (* x x))) (* (+ -1/2 (* x (+ 1/3 (* x -1/4)))) (* (+ -1/2 (* x (+ 1/3 (* x -1/4)))) (* x x))))) 1)>
#<alt (- 1 (* (* (+ -1/2 (* x (+ 1/3 (* x -1/4)))) (* (+ -1/2 (* x (+ 1/3 (* x -1/4)))) (* x x))) (* (+ -1/2 (* x (+ 1/3 (* x -1/4)))) (* (+ -1/2 (* x (+ 1/3 (* x -1/4)))) (* x x)))))>
#<alt (* x 1/3)>
#<alt (* (+ 1/3 (* x -1/4)) (* x x))>
#<alt (+ 1/3 (* x -1/4))>
#<alt (* x (+ 1/3 (* x -1/4)))>
#<alt (* (* (+ -1/2 (* x (+ 1/3 (* x -1/4)))) (* (+ -1/2 (* x (+ 1/3 (* x -1/4)))) (* x x))) (* (+ -1/2 (* x (+ 1/3 (* x -1/4)))) (* (+ -1/2 (* x (+ 1/3 (* x -1/4)))) (* x x))))>
#<alt (* (+ -1/2 (* x (+ 1/3 (* x -1/4)))) (* x x))>

Outputs
#<alt x>
#<alt (* x (+ 1 (* -1/2 x)))>
#<alt (* x (+ 1 (* x (- (* 1/3 x) 1/2))))>
#<alt (* x (+ 1 (* x (- (* 1/3 x) 1/2))))>
#<alt (* 1/3 (pow x 3))>
#<alt (* (pow x 3) (- 1/3 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (- (+ 1/3 (/ 1 (pow x 2))) (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (- (+ 1/3 (/ 1 (pow x 2))) (* 1/2 (/ 1 x))))>
#<alt (* 1/3 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- (* 1/2 (/ 1 x)) 1/3)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (- (/ 1 x) 1/2) x)) 1/3)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (- (/ 1 x) 1/2) x)) 1/3)))>
#<alt (* -1/2 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/3 x) 1/2))>
#<alt (* (pow x 2) (- (* 1/3 x) 1/2))>
#<alt (* (pow x 2) (- (* 1/3 x) 1/2))>
#<alt (* 1/3 (pow x 3))>
#<alt (* (pow x 3) (- 1/3 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (- 1/3 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (- 1/3 (* 1/2 (/ 1 x))))>
#<alt (* 1/3 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- (* 1/2 (/ 1 x)) 1/3)))>
#<alt (* -1 (* (pow x 3) (- (* 1/2 (/ 1 x)) 1/3)))>
#<alt (* -1 (* (pow x 3) (- (* 1/2 (/ 1 x)) 1/3)))>
#<alt (* -1/2 x)>
#<alt (* x (- (* 1/3 x) 1/2))>
#<alt (* x (- (* 1/3 x) 1/2))>
#<alt (* x (- (* 1/3 x) 1/2))>
#<alt (* 1/3 (pow x 2))>
#<alt (* (pow x 2) (- 1/3 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (- 1/3 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (- 1/3 (* 1/2 (/ 1 x))))>
#<alt (* 1/3 (pow x 2))>
#<alt (* (pow x 2) (- 1/3 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (- 1/3 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (- 1/3 (* 1/2 (/ 1 x))))>
#<alt -1/2>
#<alt (- (* 1/3 x) 1/2)>
#<alt (- (* 1/3 x) 1/2)>
#<alt (- (* 1/3 x) 1/2)>
#<alt (* 1/3 x)>
#<alt (* x (- 1/3 (* 1/2 (/ 1 x))))>
#<alt (* x (- 1/3 (* 1/2 (/ 1 x))))>
#<alt (* x (- 1/3 (* 1/2 (/ 1 x))))>
#<alt (* 1/3 x)>
#<alt (* -1 (* x (- (* 1/2 (/ 1 x)) 1/3)))>
#<alt (* -1 (* x (- (* 1/2 (/ 1 x)) 1/3)))>
#<alt (* -1 (* x (- (* 1/2 (/ 1 x)) 1/3)))>
#<alt x>
#<alt (* x (+ 1 (* -1/2 x)))>
#<alt (* x (+ 1 (* -1/2 x)))>
#<alt (* x (+ 1 (* -1/2 x)))>
#<alt (* -1/2 (pow x 2))>
#<alt (* (pow x 2) (- (/ 1 x) 1/2))>
#<alt (* (pow x 2) (- (/ 1 x) 1/2))>
#<alt (* (pow x 2) (- (/ 1 x) 1/2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* (pow x 2) (- (/ 1 x) 1/2))>
#<alt (* (pow x 2) (- (/ 1 x) 1/2))>
#<alt (* (pow x 2) (- (/ 1 x) 1/2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt x>
#<alt (* x (+ 1 (* -1/2 x)))>
#<alt (* x (+ 1 (* x (- (* 1/3 x) 1/2))))>
#<alt (* x (+ 1 (* x (- (* x (+ 1/3 (* -1/4 x))) 1/2))))>
#<alt (* -1/4 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/3 (/ 1 x)) 1/4))>
#<alt (* (pow x 4) (- (* 1/3 (/ 1 x)) (+ 1/4 (/ 1/2 (pow x 2)))))>
#<alt (* (pow x 4) (- (+ (* 1/3 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/4 (/ 1/2 (pow x 2)))))>
#<alt (* -1/4 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/3 (/ 1 x)) 1/4))>
#<alt (* (pow x 4) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/3) x)) 1/4))>
#<alt (* (pow x 4) (- (* -1 (/ (- (* -1 (/ (- (/ 1 x) 1/2) x)) 1/3) x)) 1/4))>
#<alt 1>
#<alt (+ 1 (* -1/2 x))>
#<alt (+ 1 (* x (- (* 1/3 x) 1/2)))>
#<alt (+ 1 (* x (- (* x (+ 1/3 (* -1/4 x))) 1/2)))>
#<alt (* -1/4 (pow x 3))>
#<alt (* (pow x 3) (- (* 1/3 (/ 1 x)) 1/4))>
#<alt (* (pow x 3) (- (* 1/3 (/ 1 x)) (+ 1/4 (/ 1/2 (pow x 2)))))>
#<alt (* (pow x 3) (- (+ (* 1/3 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/4 (/ 1/2 (pow x 2)))))>
#<alt (* -1/4 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- 1/4 (* 1/3 (/ 1 x)))))>
#<alt (* -1 (* (pow x 3) (+ 1/4 (* -1 (/ (- 1/3 (* 1/2 (/ 1 x))) x)))))>
#<alt (* -1 (* (pow x 3) (+ 1/4 (* -1 (/ (+ 1/3 (* -1 (/ (- 1/2 (/ 1 x)) x))) x)))))>
#<alt 1>
#<alt (+ 1 (* -1/2 x))>
#<alt (+ 1 (* -1/2 x))>
#<alt (+ 1 (* -1/2 x))>
#<alt (* -1/2 x)>
#<alt (* x (- (/ 1 x) 1/2))>
#<alt (* x (- (/ 1 x) 1/2))>
#<alt (* x (- (/ 1 x) 1/2))>
#<alt (* -1/2 x)>
#<alt (* -1 (* x (- 1/2 (/ 1 x))))>
#<alt (* -1 (* x (- 1/2 (/ 1 x))))>
#<alt (* -1 (* x (- 1/2 (/ 1 x))))>
#<alt x>
#<alt (* x (+ 1 (* -1/2 x)))>
#<alt (* x (+ 1 (* x (- (* 1/3 x) 1/2))))>
#<alt (* x (+ 1 (* x (- (* x (+ 1/3 (* -1/4 x))) 1/2))))>
#<alt (* -1/4 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/3 (/ 1 x)) 1/4))>
#<alt (* (pow x 4) (- (* 1/3 (/ 1 x)) (+ 1/4 (/ 1/2 (pow x 2)))))>
#<alt (* (pow x 4) (- (+ (* 1/3 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/4 (/ 1/2 (pow x 2)))))>
#<alt (* -1/4 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/3 (/ 1 x)) 1/4))>
#<alt (* (pow x 4) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/3) x)) 1/4))>
#<alt (* (pow x 4) (- (* -1 (/ (- (* -1 (/ (- (/ 1 x) 1/2) x)) 1/3) x)) 1/4))>
#<alt 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* x (+ 1/2 (* -1/12 x))))>
#<alt (+ 1 (* x (+ 1/2 (* x (- (* 1/24 x) 1/12)))))>
#<alt (/ -4 (pow x 3))>
#<alt (* -1 (/ (+ 4 (* 16/3 (/ 1 x))) (pow x 3)))>
#<alt (/ (- (/ 8/9 (pow x 2)) (+ 4 (* 16/3 (/ 1 x)))) (pow x 3))>
#<alt (/ (- (/ 8/9 (pow x 2)) (+ 4 (+ (* 16/3 (/ 1 x)) (* 112/27 (/ 1 (pow x 3)))))) (pow x 3))>
#<alt (/ -4 (pow x 3))>
#<alt (* -1 (/ (+ 4 (* 16/3 (/ 1 x))) (pow x 3)))>
#<alt (* -1 (/ (+ 4 (* -1 (/ (- (* 8/9 (/ 1 x)) 16/3) x))) (pow x 3)))>
#<alt (* -1 (/ (+ 4 (* -1 (/ (- (* -1 (/ (- (* 112/27 (/ 1 x)) 8/9) x)) 16/3) x))) (pow x 3)))>
#<alt 1>
#<alt (+ 1 (* -1/2 x))>
#<alt (+ 1 (* x (- (* 1/3 x) 1/2)))>
#<alt (+ 1 (* x (- (* x (+ 1/3 (* -1/4 x))) 1/2)))>
#<alt (* -1/4 (pow x 3))>
#<alt (* (pow x 3) (- (* 1/3 (/ 1 x)) 1/4))>
#<alt (* (pow x 3) (- (* 1/3 (/ 1 x)) (+ 1/4 (/ 1/2 (pow x 2)))))>
#<alt (* (pow x 3) (- (+ (* 1/3 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/4 (/ 1/2 (pow x 2)))))>
#<alt (* -1/4 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- 1/4 (* 1/3 (/ 1 x)))))>
#<alt (* -1 (* (pow x 3) (+ 1/4 (* -1 (/ (- 1/3 (* 1/2 (/ 1 x))) x)))))>
#<alt (* -1 (* (pow x 3) (+ 1/4 (* -1 (/ (+ 1/3 (* -1 (/ (- 1/2 (/ 1 x)) x))) x)))))>
#<alt (* -1/2 x)>
#<alt (* x (- (* 1/3 x) 1/2))>
#<alt (* x (- (* x (+ 1/3 (* -1/4 x))) 1/2))>
#<alt (* x (- (* x (+ 1/3 (* -1/4 x))) 1/2))>
#<alt (* -1/4 (pow x 3))>
#<alt (* (pow x 3) (- (* 1/3 (/ 1 x)) 1/4))>
#<alt (* (pow x 3) (- (* 1/3 (/ 1 x)) (+ 1/4 (/ 1/2 (pow x 2)))))>
#<alt (* (pow x 3) (- (* 1/3 (/ 1 x)) (+ 1/4 (/ 1/2 (pow x 2)))))>
#<alt (* -1/4 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- 1/4 (* 1/3 (/ 1 x)))))>
#<alt (* -1 (* (pow x 3) (+ 1/4 (* -1 (/ (- 1/3 (* 1/2 (/ 1 x))) x)))))>
#<alt (* -1 (* (pow x 3) (+ 1/4 (* -1 (/ (- 1/3 (* 1/2 (/ 1 x))) x)))))>
#<alt x>
#<alt (* x (+ 1 (* -1/2 x)))>
#<alt (* x (+ 1 (* x (- (* 1/3 x) 1/2))))>
#<alt (* x (+ 1 (* x (- (* x (+ 1/3 (* -1/4 x))) 1/2))))>
#<alt (* -1/4 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/3 (/ 1 x)) 1/4))>
#<alt (* (pow x 4) (- (* 1/3 (/ 1 x)) (+ 1/4 (/ 1/2 (pow x 2)))))>
#<alt (* (pow x 4) (- (+ (* 1/3 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/4 (/ 1/2 (pow x 2)))))>
#<alt (* -1/4 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/3 (/ 1 x)) 1/4))>
#<alt (* (pow x 4) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/3) x)) 1/4))>
#<alt (* (pow x 4) (- (* -1 (/ (- (* -1 (/ (- (/ 1 x) 1/2) x)) 1/3) x)) 1/4))>
#<alt 1>
#<alt (+ 1 (* -1/2 x))>
#<alt (+ 1 (* x (- (* 1/3 x) 1/2)))>
#<alt (+ 1 (* x (- (* x (+ 1/3 (* -1/4 x))) 1/2)))>
#<alt (* -1/4 (pow x 3))>
#<alt (* (pow x 3) (- (* 1/3 (/ 1 x)) 1/4))>
#<alt (* (pow x 3) (- (* 1/3 (/ 1 x)) (+ 1/4 (/ 1/2 (pow x 2)))))>
#<alt (* (pow x 3) (- (+ (* 1/3 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/4 (/ 1/2 (pow x 2)))))>
#<alt (* -1/4 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- 1/4 (* 1/3 (/ 1 x)))))>
#<alt (* -1 (* (pow x 3) (+ 1/4 (* -1 (/ (- 1/3 (* 1/2 (/ 1 x))) x)))))>
#<alt (* -1 (* (pow x 3) (+ 1/4 (* -1 (/ (+ 1/3 (* -1 (/ (- 1/2 (/ 1 x)) x))) x)))))>
#<alt 1>
#<alt (+ 1 (* -1/16 (pow x 4)))>
#<alt (+ 1 (* (pow x 4) (- (* 1/6 x) 1/16)))>
#<alt (+ 1 (* (pow x 4) (- (* x (+ 1/6 (* -7/24 x))) 1/16)))>
#<alt (* -1/256 (pow x 12))>
#<alt (* (pow x 12) (- (* 1/48 (/ 1 x)) 1/256))>
#<alt (* (pow x 12) (- (* 1/48 (/ 1 x)) (+ 1/256 (/ 7/96 (pow x 2)))))>
#<alt (* (pow x 12) (- (+ (* 1/48 (/ 1 x)) (* 35/216 (/ 1 (pow x 3)))) (+ 1/256 (/ 7/96 (pow x 2)))))>
#<alt (* -1/256 (pow x 12))>
#<alt (* (pow x 12) (- (* 1/48 (/ 1 x)) 1/256))>
#<alt (* (pow x 12) (- (* -1 (/ (- (* 7/96 (/ 1 x)) 1/48) x)) 1/256))>
#<alt (* (pow x 12) (- (* -1 (/ (- (* -1 (/ (- (* 35/216 (/ 1 x)) 7/96) x)) 1/48) x)) 1/256))>
#<alt 1>
#<alt (+ 1 (* -1/16 (pow x 4)))>
#<alt (+ 1 (* (pow x 4) (- (* 1/6 x) 1/16)))>
#<alt (+ 1 (* (pow x 4) (- (* x (+ 1/6 (* -7/24 x))) 1/16)))>
#<alt (* -1/256 (pow x 12))>
#<alt (* (pow x 12) (- (* 1/48 (/ 1 x)) 1/256))>
#<alt (* (pow x 12) (- (* 1/48 (/ 1 x)) (+ 1/256 (/ 7/96 (pow x 2)))))>
#<alt (* (pow x 12) (- (+ (* 1/48 (/ 1 x)) (* 35/216 (/ 1 (pow x 3)))) (+ 1/256 (/ 7/96 (pow x 2)))))>
#<alt (* -1/256 (pow x 12))>
#<alt (* (pow x 12) (- (* 1/48 (/ 1 x)) 1/256))>
#<alt (* (pow x 12) (- (* -1 (/ (- (* 7/96 (/ 1 x)) 1/48) x)) 1/256))>
#<alt (* (pow x 12) (- (* -1 (/ (- (* -1 (/ (- (* 35/216 (/ 1 x)) 7/96) x)) 1/48) x)) 1/256))>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 (pow x 2))>
#<alt (* (pow x 2) (+ 1/3 (* -1/4 x)))>
#<alt (* (pow x 2) (+ 1/3 (* -1/4 x)))>
#<alt (* (pow x 2) (+ 1/3 (* -1/4 x)))>
#<alt (* -1/4 (pow x 3))>
#<alt (* (pow x 3) (- (* 1/3 (/ 1 x)) 1/4))>
#<alt (* (pow x 3) (- (* 1/3 (/ 1 x)) 1/4))>
#<alt (* (pow x 3) (- (* 1/3 (/ 1 x)) 1/4))>
#<alt (* -1/4 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- 1/4 (* 1/3 (/ 1 x)))))>
#<alt (* -1 (* (pow x 3) (- 1/4 (* 1/3 (/ 1 x)))))>
#<alt (* -1 (* (pow x 3) (- 1/4 (* 1/3 (/ 1 x)))))>
#<alt 1/3>
#<alt (+ 1/3 (* -1/4 x))>
#<alt (+ 1/3 (* -1/4 x))>
#<alt (+ 1/3 (* -1/4 x))>
#<alt (* -1/4 x)>
#<alt (* x (- (* 1/3 (/ 1 x)) 1/4))>
#<alt (* x (- (* 1/3 (/ 1 x)) 1/4))>
#<alt (* x (- (* 1/3 (/ 1 x)) 1/4))>
#<alt (* -1/4 x)>
#<alt (* -1 (* x (- 1/4 (* 1/3 (/ 1 x)))))>
#<alt (* -1 (* x (- 1/4 (* 1/3 (/ 1 x)))))>
#<alt (* -1 (* x (- 1/4 (* 1/3 (/ 1 x)))))>
#<alt (* 1/3 x)>
#<alt (* x (+ 1/3 (* -1/4 x)))>
#<alt (* x (+ 1/3 (* -1/4 x)))>
#<alt (* x (+ 1/3 (* -1/4 x)))>
#<alt (* -1/4 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/3 (/ 1 x)) 1/4))>
#<alt (* (pow x 2) (- (* 1/3 (/ 1 x)) 1/4))>
#<alt (* (pow x 2) (- (* 1/3 (/ 1 x)) 1/4))>
#<alt (* -1/4 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/3 (/ 1 x)) 1/4))>
#<alt (* (pow x 2) (- (* 1/3 (/ 1 x)) 1/4))>
#<alt (* (pow x 2) (- (* 1/3 (/ 1 x)) 1/4))>
#<alt (* 1/16 (pow x 4))>
#<alt (* (pow x 4) (+ 1/16 (* -1/6 x)))>
#<alt (* (pow x 4) (+ 1/16 (* x (- (* 7/24 x) 1/6))))>
#<alt (* (pow x 4) (+ 1/16 (* x (- (* x (+ 7/24 (* -35/108 x))) 1/6))))>
#<alt (* 1/256 (pow x 12))>
#<alt (* (pow x 12) (- 1/256 (* 1/48 (/ 1 x))))>
#<alt (* (pow x 12) (- (+ 1/256 (/ 7/96 (pow x 2))) (* 1/48 (/ 1 x))))>
#<alt (* (pow x 12) (- (+ 1/256 (/ 7/96 (pow x 2))) (+ (* 1/48 (/ 1 x)) (* 35/216 (/ 1 (pow x 3))))))>
#<alt (* 1/256 (pow x 12))>
#<alt (* (pow x 12) (- 1/256 (* 1/48 (/ 1 x))))>
#<alt (* (pow x 12) (+ 1/256 (* -1 (/ (- 1/48 (* 7/96 (/ 1 x))) x))))>
#<alt (* (pow x 12) (+ 1/256 (* -1 (/ (+ 1/48 (* -1 (/ (- 7/96 (* 35/216 (/ 1 x))) x))) x))))>
#<alt (* -1/2 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/3 x) 1/2))>
#<alt (* (pow x 2) (- (* x (+ 1/3 (* -1/4 x))) 1/2))>
#<alt (* (pow x 2) (- (* x (+ 1/3 (* -1/4 x))) 1/2))>
#<alt (* -1/4 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/3 (/ 1 x)) 1/4))>
#<alt (* (pow x 4) (- (* 1/3 (/ 1 x)) (+ 1/4 (/ 1/2 (pow x 2)))))>
#<alt (* (pow x 4) (- (* 1/3 (/ 1 x)) (+ 1/4 (/ 1/2 (pow x 2)))))>
#<alt (* -1/4 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/3 (/ 1 x)) 1/4))>
#<alt (* (pow x 4) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/3) x)) 1/4))>
#<alt (* (pow x 4) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/3) x)) 1/4))>

Calls

72 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(* x (/ (* (- 1 (* (* (+ -1/2 (* x (+ 1/3 (* x -1/4)))) (* (+ -1/2 (* x (+ 1/3 (* x -1/4)))) (* x x))) (* (+ -1/2 (* x (+ 1/3 (* x -1/4)))) (* (+ -1/2 (* x (+ 1/3 (* x -1/4)))) (* x x))))) 1) (* (+ 1 (* (+ -1/2 (* x (+ 1/3 (* x -1/4)))) (* (+ -1/2 (* x (+ 1/3 (* x -1/4)))) (* x x)))) (- 1 (* x (+ -1/2 (* x (+ 1/3 (* x -1/4)))))))))
0.0ms	x	@	-inf	(* x (/ (* (- 1 (* (* (+ -1/2 (* x (+ 1/3 (* x -1/4)))) (* (+ -1/2 (* x (+ 1/3 (* x -1/4)))) (* x x))) (* (+ -1/2 (* x (+ 1/3 (* x -1/4)))) (* (+ -1/2 (* x (+ 1/3 (* x -1/4)))) (* x x))))) 1) (* (+ 1 (* (+ -1/2 (* x (+ 1/3 (* x -1/4)))) (* (+ -1/2 (* x (+ 1/3 (* x -1/4)))) (* x x)))) (- 1 (* x (+ -1/2 (* x (+ 1/3 (* x -1/4)))))))))
0.0ms	x	@	0	(* x (/ (* (- 1 (* (* (+ -1/2 (* x (+ 1/3 (* x -1/4)))) (* (+ -1/2 (* x (+ 1/3 (* x -1/4)))) (* x x))) (* (+ -1/2 (* x (+ 1/3 (* x -1/4)))) (* (+ -1/2 (* x (+ 1/3 (* x -1/4)))) (* x x))))) 1) (* (+ 1 (* (+ -1/2 (* x (+ 1/3 (* x -1/4)))) (* (+ -1/2 (* x (+ 1/3 (* x -1/4)))) (* x x)))) (- 1 (* x (+ -1/2 (* x (+ 1/3 (* x -1/4)))))))))
0.0ms	x	@	-inf	(/ 1 (+ 1 (* x (+ -1/2 (* x (+ 1/3 (* x -1/4)))))))
0.0ms	x	@	inf	(+ (* x (* x (+ -1/2 (* x 1/3)))) x)

rewrite803.0ms (7.5%)

Algorithm

1×	batch-egg-rewrite

Rules

3908×	`-lowering-.f32`
3908×	`-lowering-.f64`
2416×	`fma-lowering-fma.f32`
2416×	`fma-lowering-fma.f64`
1822×	`/-lowering-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	36	265
1	268	194
2	2599	191
0	8217	191

Stop Event

1×	iter limit
1×	node limit

Counts

24 → 1284

Calls

Call 1

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

Outputs
(+.f64 x (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64))))))
(+.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64))))) x)
(-.f64 (/.f64 (.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64)))) (.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64)))) (.f64 x x))) (-.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))))) x)) (/.f64 (.f64 x x) (-.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))))) x)))
(fma.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64)))) x)
(fma.f64 x #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64))))))
(fma.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))) (.f64 x x) x)
(fma.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64)))) x x)
(fma.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))) x)
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64)))) (.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64)))) (.f64 x x))) (.f64 x (-.f64 x (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64)))))))) (+.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))))) (.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64)))) (.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64)))) (.f64 x x)))))))
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(exp.f64 (neg.f64 (.f64 (log1p.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))))) #s(literal -1 binary64))))
(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64)))))))) (/.f64 (.f64 (.f64 x x) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))))) (-.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal -1/4 binary64)))))))))
(-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))))))) (-.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64)))))))) (/.f64 (.f64 (.f64 (.f64 x x) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))))) (.f64 (.f64 x x) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64)))))))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64)))))))) (-.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))))))))
(-.f64 (/.f64 (.f64 (+.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (+.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) (-.f64 (+.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))) (.f64 x x)))) (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))) (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (-.f64 (+.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))) (.f64 x x)))))
(fma.f64 x #s(literal -1/2 binary64) (+.f64 (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))) (*.f64 x x)) #s(literal 1 binary64)))
(fma.f64 x #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))) (*.f64 x x))))
(fma.f64 x (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64)))) (+.f64 (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(fma.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) #s(literal 1 binary64))
(fma.f64 #s(literal -1/2 binary64) x (+.f64 (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))) (*.f64 x x)) #s(literal 1 binary64)))
(fma.f64 #s(literal -1/2 binary64) x (+.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))) (*.f64 x x))))
(fma.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64) (+.f64 (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))) (.f64 x x)) #s(literal 1 binary64)))
(fma.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))) (.f64 x x))))
(fma.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64)) (+.f64 (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))) (.f64 x x)) #s(literal 1 binary64)))
(fma.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64)) (+.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))) (.f64 x x))))
(fma.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal -1/4 binary64)))))) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64)))))))) (neg.f64 (/.f64 (.f64 (.f64 x x) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))))) (-.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal -1/4 binary64))))))))))
(fma.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))))))) (-.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64)))))))) (neg.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))))) (.f64 (.f64 x x) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64)))))))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64)))))))) (-.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64)))))))))))
(fma.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))) (.f64 x x) (+.f64 (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(fma.f64 (.f64 x x) (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))) (+.f64 (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(fma.f64 (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64)))) x (+.f64 (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(fma.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) x #s(literal 1 binary64))
(fma.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal -1/4 binary64)))))) #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x #s(literal -1/2 binary64)) (-.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))) (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))) (*.f64 x x)))
(fma.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64)))) (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))) (.f64 x x)))
(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))))))) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))))) (neg.f64 (/.f64 (.f64 (.f64 x x) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))))) (-.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))))))))
(fma.f64 (.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64) (+.f64 (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))) (.f64 x x)) #s(literal 1 binary64)))
(fma.f64 (.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))) (.f64 x x))))
(fma.f64 (.f64 #s(literal 1 binary64) x) (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal -1/4 binary64))))) #s(literal 1 binary64))
(fma.f64 (.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal -1/4 binary64)))))) x #s(literal 1 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64)))))) (.f64 (.f64 x x) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64)))))))))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64)))))) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))))))) (neg.f64 (/.f64 (.f64 (.f64 x x) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))))) (-.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))))))))
(neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x x) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))))) (.f64 (.f64 x x) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))))))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64)))))))) (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64)))))))))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x x) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))))) (.f64 (.f64 x x) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64)))))))))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64)))))))) (-.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal -1/4 binary64)))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64)))))) (-.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64)))))) #s(literal 1 binary64)))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64)))))) (.f64 (.f64 x x) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64)))))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 (+.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (+.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) (.f64 (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))) (.f64 x x)) (-.f64 (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))) (.f64 x x)) (+.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))) (+.f64 (.f64 (+.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (.f64 (+.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (+.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))) (.f64 (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))) (.f64 x x)) (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))) (+.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal -1/4 binary64)))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (+.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))) (.f64 x x))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))))) (-.f64 (+.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))) (.f64 x x))))))
(/.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal -1/4 binary64))))))) #s(literal 1 binary64))
(/.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x x) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))))) (.f64 (.f64 x x) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))))))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64)))))))) (-.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64)))))))))
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(.f64 (pow.f64 (.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))))) #s(literal 2 binary64)) (.f64 (.f64 x x) (.f64 x x)))
(.f64 (pow.f64 (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))))) #s(literal 2 binary64)) (.f64 x x))
(.f64 (pow.f64 (.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))))) #s(literal 2 binary64)) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal -1/4 binary64)))))))
(.f64 (pow.f64 (.f64 (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64)))))) x) #s(literal 2 binary64)) (.f64 x x))
(.f64 (exp.f64 (.f64 #s(literal 2 binary64) (log.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))))))) (exp.f64 (.f64 #s(literal 2 binary64) (log.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal -1/4 binary64))))))))))
(+.f64 (.f64 x (.f64 x #s(literal -1/2 binary64))) (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))) (.f64 x (.f64 x x))))
(+.f64 (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))) (.f64 x (.f64 x x))) (.f64 x (.f64 x #s(literal -1/2 binary64))))
(fma.f64 x (.f64 x #s(literal -1/2 binary64)) (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))) (.f64 x (*.f64 x x))))
(fma.f64 x (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))) (.f64 x x)) (.f64 x (*.f64 x #s(literal -1/2 binary64))))
(fma.f64 #s(literal -1/2 binary64) (.f64 x x) (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))) (.f64 x (*.f64 x x))))
(fma.f64 (.f64 x #s(literal -1/2 binary64)) x (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))) (.f64 x (*.f64 x x))))
(fma.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))) (.f64 x (.f64 x x)) (.f64 x (*.f64 x #s(literal -1/2 binary64))))
(fma.f64 (.f64 x x) #s(literal -1/2 binary64) (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))) (.f64 x (*.f64 x x))))
(fma.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64)))) (.f64 x (*.f64 x #s(literal -1/2 binary64))))
(fma.f64 (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))) (.f64 x x)) x (.f64 x (*.f64 x #s(literal -1/2 binary64))))
(fma.f64 (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64)))) (.f64 x x) (.f64 x (*.f64 x #s(literal -1/2 binary64))))
(fma.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))) (.f64 x (*.f64 x #s(literal -1/2 binary64))))
(/.f64 (.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64)))) (.f64 x (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))))))) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64)))) (-.f64 (.f64 x (+.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal -1/4 binary64)))) #s(literal -1/2 binary64)))))
(/.f64 (.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64)))))))) (-.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal -1/4 binary64))))))
(/.f64 (.f64 (+.f64 #s(literal -1/8 binary64) (.f64 (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64)))) (.f64 x (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64)))))))) (.f64 x x)) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64)))) (-.f64 (.f64 x (+.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal -1/4 binary64)))) #s(literal -1/2 binary64)))))
(/.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 x (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))))) (.f64 x x)) (-.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal -1/4 binary64))))))
(.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64)))))))
(.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))))
(.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (.f64 x x))
(.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64)))))) x)

simplify286.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

3854×	`-lowering-.f32`
3854×	`-lowering-.f64`
2210×	`fma-lowering-fma.f32`
2210×	`fma-lowering-fma.f64`
1670×	`+-lowering-+.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	244	2330
1	753	2121
2	2177	2015
3	6984	2011
0	8371	2011

Stop Event

1×	iter limit
1×	node limit

Counts

288 → 288

Calls

Call 1

Inputs
x
(* x (+ 1 (* -1/2 x)))
(* x (+ 1 (* x (- (* 1/3 x) 1/2))))
(* x (+ 1 (* x (- (* 1/3 x) 1/2))))
(* 1/3 (pow x 3))
(* (pow x 3) (- 1/3 (* 1/2 (/ 1 x))))
(* (pow x 3) (- (+ 1/3 (/ 1 (pow x 2))) (* 1/2 (/ 1 x))))
(* (pow x 3) (- (+ 1/3 (/ 1 (pow x 2))) (* 1/2 (/ 1 x))))
(* 1/3 (pow x 3))
(* -1 (* (pow x 3) (- (* 1/2 (/ 1 x)) 1/3)))
(* -1 (* (pow x 3) (- (* -1 (/ (- (/ 1 x) 1/2) x)) 1/3)))
(* -1 (* (pow x 3) (- (* -1 (/ (- (/ 1 x) 1/2) x)) 1/3)))
(* -1/2 (pow x 2))
(* (pow x 2) (- (* 1/3 x) 1/2))
(* (pow x 2) (- (* 1/3 x) 1/2))
(* (pow x 2) (- (* 1/3 x) 1/2))
(* 1/3 (pow x 3))
(* (pow x 3) (- 1/3 (* 1/2 (/ 1 x))))
(* (pow x 3) (- 1/3 (* 1/2 (/ 1 x))))
(* (pow x 3) (- 1/3 (* 1/2 (/ 1 x))))
(* 1/3 (pow x 3))
(* -1 (* (pow x 3) (- (* 1/2 (/ 1 x)) 1/3)))
(* -1 (* (pow x 3) (- (* 1/2 (/ 1 x)) 1/3)))
(* -1 (* (pow x 3) (- (* 1/2 (/ 1 x)) 1/3)))
(* -1/2 x)
(* x (- (* 1/3 x) 1/2))
(* x (- (* 1/3 x) 1/2))
(* x (- (* 1/3 x) 1/2))
(* 1/3 (pow x 2))
(* (pow x 2) (- 1/3 (* 1/2 (/ 1 x))))
(* (pow x 2) (- 1/3 (* 1/2 (/ 1 x))))
(* (pow x 2) (- 1/3 (* 1/2 (/ 1 x))))
(* 1/3 (pow x 2))
(* (pow x 2) (- 1/3 (* 1/2 (/ 1 x))))
(* (pow x 2) (- 1/3 (* 1/2 (/ 1 x))))
(* (pow x 2) (- 1/3 (* 1/2 (/ 1 x))))
-1/2
(- (* 1/3 x) 1/2)
(- (* 1/3 x) 1/2)
(- (* 1/3 x) 1/2)
(* 1/3 x)
(* x (- 1/3 (* 1/2 (/ 1 x))))
(* x (- 1/3 (* 1/2 (/ 1 x))))
(* x (- 1/3 (* 1/2 (/ 1 x))))
(* 1/3 x)
(* -1 (* x (- (* 1/2 (/ 1 x)) 1/3)))
(* -1 (* x (- (* 1/2 (/ 1 x)) 1/3)))
(* -1 (* x (- (* 1/2 (/ 1 x)) 1/3)))
x
(* x (+ 1 (* -1/2 x)))
(* x (+ 1 (* -1/2 x)))
(* x (+ 1 (* -1/2 x)))
(* -1/2 (pow x 2))
(* (pow x 2) (- (/ 1 x) 1/2))
(* (pow x 2) (- (/ 1 x) 1/2))
(* (pow x 2) (- (/ 1 x) 1/2))
(* -1/2 (pow x 2))
(* (pow x 2) (- (/ 1 x) 1/2))
(* (pow x 2) (- (/ 1 x) 1/2))
(* (pow x 2) (- (/ 1 x) 1/2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
x
(* x (+ 1 (* -1/2 x)))
(* x (+ 1 (* x (- (* 1/3 x) 1/2))))
(* x (+ 1 (* x (- (* x (+ 1/3 (* -1/4 x))) 1/2))))
(* -1/4 (pow x 4))
(* (pow x 4) (- (* 1/3 (/ 1 x)) 1/4))
(* (pow x 4) (- (* 1/3 (/ 1 x)) (+ 1/4 (/ 1/2 (pow x 2)))))
(* (pow x 4) (- (+ (* 1/3 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/4 (/ 1/2 (pow x 2)))))
(* -1/4 (pow x 4))
(* (pow x 4) (- (* 1/3 (/ 1 x)) 1/4))
(* (pow x 4) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/3) x)) 1/4))
(* (pow x 4) (- (* -1 (/ (- (* -1 (/ (- (/ 1 x) 1/2) x)) 1/3) x)) 1/4))
1
(+ 1 (* -1/2 x))
(+ 1 (* x (- (* 1/3 x) 1/2)))
(+ 1 (* x (- (* x (+ 1/3 (* -1/4 x))) 1/2)))
(* -1/4 (pow x 3))
(* (pow x 3) (- (* 1/3 (/ 1 x)) 1/4))
(* (pow x 3) (- (* 1/3 (/ 1 x)) (+ 1/4 (/ 1/2 (pow x 2)))))
(* (pow x 3) (- (+ (* 1/3 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/4 (/ 1/2 (pow x 2)))))
(* -1/4 (pow x 3))
(* -1 (* (pow x 3) (- 1/4 (* 1/3 (/ 1 x)))))
(* -1 (* (pow x 3) (+ 1/4 (* -1 (/ (- 1/3 (* 1/2 (/ 1 x))) x)))))
(* -1 (* (pow x 3) (+ 1/4 (* -1 (/ (+ 1/3 (* -1 (/ (- 1/2 (/ 1 x)) x))) x)))))
1
(+ 1 (* -1/2 x))
(+ 1 (* -1/2 x))
(+ 1 (* -1/2 x))
(* -1/2 x)
(* x (- (/ 1 x) 1/2))
(* x (- (/ 1 x) 1/2))
(* x (- (/ 1 x) 1/2))
(* -1/2 x)
(* -1 (* x (- 1/2 (/ 1 x))))
(* -1 (* x (- 1/2 (/ 1 x))))
(* -1 (* x (- 1/2 (/ 1 x))))
x
(* x (+ 1 (* -1/2 x)))
(* x (+ 1 (* x (- (* 1/3 x) 1/2))))
(* x (+ 1 (* x (- (* x (+ 1/3 (* -1/4 x))) 1/2))))
(* -1/4 (pow x 4))
(* (pow x 4) (- (* 1/3 (/ 1 x)) 1/4))
(* (pow x 4) (- (* 1/3 (/ 1 x)) (+ 1/4 (/ 1/2 (pow x 2)))))
(* (pow x 4) (- (+ (* 1/3 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/4 (/ 1/2 (pow x 2)))))
(* -1/4 (pow x 4))
(* (pow x 4) (- (* 1/3 (/ 1 x)) 1/4))
(* (pow x 4) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/3) x)) 1/4))
(* (pow x 4) (- (* -1 (/ (- (* -1 (/ (- (/ 1 x) 1/2) x)) 1/3) x)) 1/4))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/12 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/24 x) 1/12)))))
(/ -4 (pow x 3))
(* -1 (/ (+ 4 (* 16/3 (/ 1 x))) (pow x 3)))
(/ (- (/ 8/9 (pow x 2)) (+ 4 (* 16/3 (/ 1 x)))) (pow x 3))
(/ (- (/ 8/9 (pow x 2)) (+ 4 (+ (* 16/3 (/ 1 x)) (* 112/27 (/ 1 (pow x 3)))))) (pow x 3))
(/ -4 (pow x 3))
(* -1 (/ (+ 4 (* 16/3 (/ 1 x))) (pow x 3)))
(* -1 (/ (+ 4 (* -1 (/ (- (* 8/9 (/ 1 x)) 16/3) x))) (pow x 3)))
(* -1 (/ (+ 4 (* -1 (/ (- (* -1 (/ (- (* 112/27 (/ 1 x)) 8/9) x)) 16/3) x))) (pow x 3)))
1
(+ 1 (* -1/2 x))
(+ 1 (* x (- (* 1/3 x) 1/2)))
(+ 1 (* x (- (* x (+ 1/3 (* -1/4 x))) 1/2)))
(* -1/4 (pow x 3))
(* (pow x 3) (- (* 1/3 (/ 1 x)) 1/4))
(* (pow x 3) (- (* 1/3 (/ 1 x)) (+ 1/4 (/ 1/2 (pow x 2)))))
(* (pow x 3) (- (+ (* 1/3 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/4 (/ 1/2 (pow x 2)))))
(* -1/4 (pow x 3))
(* -1 (* (pow x 3) (- 1/4 (* 1/3 (/ 1 x)))))
(* -1 (* (pow x 3) (+ 1/4 (* -1 (/ (- 1/3 (* 1/2 (/ 1 x))) x)))))
(* -1 (* (pow x 3) (+ 1/4 (* -1 (/ (+ 1/3 (* -1 (/ (- 1/2 (/ 1 x)) x))) x)))))
(* -1/2 x)
(* x (- (* 1/3 x) 1/2))
(* x (- (* x (+ 1/3 (* -1/4 x))) 1/2))
(* x (- (* x (+ 1/3 (* -1/4 x))) 1/2))
(* -1/4 (pow x 3))
(* (pow x 3) (- (* 1/3 (/ 1 x)) 1/4))
(* (pow x 3) (- (* 1/3 (/ 1 x)) (+ 1/4 (/ 1/2 (pow x 2)))))
(* (pow x 3) (- (* 1/3 (/ 1 x)) (+ 1/4 (/ 1/2 (pow x 2)))))
(* -1/4 (pow x 3))
(* -1 (* (pow x 3) (- 1/4 (* 1/3 (/ 1 x)))))
(* -1 (* (pow x 3) (+ 1/4 (* -1 (/ (- 1/3 (* 1/2 (/ 1 x))) x)))))
(* -1 (* (pow x 3) (+ 1/4 (* -1 (/ (- 1/3 (* 1/2 (/ 1 x))) x)))))
x
(* x (+ 1 (* -1/2 x)))
(* x (+ 1 (* x (- (* 1/3 x) 1/2))))
(* x (+ 1 (* x (- (* x (+ 1/3 (* -1/4 x))) 1/2))))
(* -1/4 (pow x 4))
(* (pow x 4) (- (* 1/3 (/ 1 x)) 1/4))
(* (pow x 4) (- (* 1/3 (/ 1 x)) (+ 1/4 (/ 1/2 (pow x 2)))))
(* (pow x 4) (- (+ (* 1/3 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/4 (/ 1/2 (pow x 2)))))
(* -1/4 (pow x 4))
(* (pow x 4) (- (* 1/3 (/ 1 x)) 1/4))
(* (pow x 4) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/3) x)) 1/4))
(* (pow x 4) (- (* -1 (/ (- (* -1 (/ (- (/ 1 x) 1/2) x)) 1/3) x)) 1/4))
1
(+ 1 (* -1/2 x))
(+ 1 (* x (- (* 1/3 x) 1/2)))
(+ 1 (* x (- (* x (+ 1/3 (* -1/4 x))) 1/2)))
(* -1/4 (pow x 3))
(* (pow x 3) (- (* 1/3 (/ 1 x)) 1/4))
(* (pow x 3) (- (* 1/3 (/ 1 x)) (+ 1/4 (/ 1/2 (pow x 2)))))
(* (pow x 3) (- (+ (* 1/3 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/4 (/ 1/2 (pow x 2)))))
(* -1/4 (pow x 3))
(* -1 (* (pow x 3) (- 1/4 (* 1/3 (/ 1 x)))))
(* -1 (* (pow x 3) (+ 1/4 (* -1 (/ (- 1/3 (* 1/2 (/ 1 x))) x)))))
(* -1 (* (pow x 3) (+ 1/4 (* -1 (/ (+ 1/3 (* -1 (/ (- 1/2 (/ 1 x)) x))) x)))))
1
(+ 1 (* -1/16 (pow x 4)))
(+ 1 (* (pow x 4) (- (* 1/6 x) 1/16)))
(+ 1 (* (pow x 4) (- (* x (+ 1/6 (* -7/24 x))) 1/16)))
(* -1/256 (pow x 12))
(* (pow x 12) (- (* 1/48 (/ 1 x)) 1/256))
(* (pow x 12) (- (* 1/48 (/ 1 x)) (+ 1/256 (/ 7/96 (pow x 2)))))
(* (pow x 12) (- (+ (* 1/48 (/ 1 x)) (* 35/216 (/ 1 (pow x 3)))) (+ 1/256 (/ 7/96 (pow x 2)))))
(* -1/256 (pow x 12))
(* (pow x 12) (- (* 1/48 (/ 1 x)) 1/256))
(* (pow x 12) (- (* -1 (/ (- (* 7/96 (/ 1 x)) 1/48) x)) 1/256))
(* (pow x 12) (- (* -1 (/ (- (* -1 (/ (- (* 35/216 (/ 1 x)) 7/96) x)) 1/48) x)) 1/256))
1
(+ 1 (* -1/16 (pow x 4)))
(+ 1 (* (pow x 4) (- (* 1/6 x) 1/16)))
(+ 1 (* (pow x 4) (- (* x (+ 1/6 (* -7/24 x))) 1/16)))
(* -1/256 (pow x 12))
(* (pow x 12) (- (* 1/48 (/ 1 x)) 1/256))
(* (pow x 12) (- (* 1/48 (/ 1 x)) (+ 1/256 (/ 7/96 (pow x 2)))))
(* (pow x 12) (- (+ (* 1/48 (/ 1 x)) (* 35/216 (/ 1 (pow x 3)))) (+ 1/256 (/ 7/96 (pow x 2)))))
(* -1/256 (pow x 12))
(* (pow x 12) (- (* 1/48 (/ 1 x)) 1/256))
(* (pow x 12) (- (* -1 (/ (- (* 7/96 (/ 1 x)) 1/48) x)) 1/256))
(* (pow x 12) (- (* -1 (/ (- (* -1 (/ (- (* 35/216 (/ 1 x)) 7/96) x)) 1/48) x)) 1/256))
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 (pow x 2))
(* (pow x 2) (+ 1/3 (* -1/4 x)))
(* (pow x 2) (+ 1/3 (* -1/4 x)))
(* (pow x 2) (+ 1/3 (* -1/4 x)))
(* -1/4 (pow x 3))
(* (pow x 3) (- (* 1/3 (/ 1 x)) 1/4))
(* (pow x 3) (- (* 1/3 (/ 1 x)) 1/4))
(* (pow x 3) (- (* 1/3 (/ 1 x)) 1/4))
(* -1/4 (pow x 3))
(* -1 (* (pow x 3) (- 1/4 (* 1/3 (/ 1 x)))))
(* -1 (* (pow x 3) (- 1/4 (* 1/3 (/ 1 x)))))
(* -1 (* (pow x 3) (- 1/4 (* 1/3 (/ 1 x)))))
1/3
(+ 1/3 (* -1/4 x))
(+ 1/3 (* -1/4 x))
(+ 1/3 (* -1/4 x))
(* -1/4 x)
(* x (- (* 1/3 (/ 1 x)) 1/4))
(* x (- (* 1/3 (/ 1 x)) 1/4))
(* x (- (* 1/3 (/ 1 x)) 1/4))
(* -1/4 x)
(* -1 (* x (- 1/4 (* 1/3 (/ 1 x)))))
(* -1 (* x (- 1/4 (* 1/3 (/ 1 x)))))
(* -1 (* x (- 1/4 (* 1/3 (/ 1 x)))))
(* 1/3 x)
(* x (+ 1/3 (* -1/4 x)))
(* x (+ 1/3 (* -1/4 x)))
(* x (+ 1/3 (* -1/4 x)))
(* -1/4 (pow x 2))
(* (pow x 2) (- (* 1/3 (/ 1 x)) 1/4))
(* (pow x 2) (- (* 1/3 (/ 1 x)) 1/4))
(* (pow x 2) (- (* 1/3 (/ 1 x)) 1/4))
(* -1/4 (pow x 2))
(* (pow x 2) (- (* 1/3 (/ 1 x)) 1/4))
(* (pow x 2) (- (* 1/3 (/ 1 x)) 1/4))
(* (pow x 2) (- (* 1/3 (/ 1 x)) 1/4))
(* 1/16 (pow x 4))
(* (pow x 4) (+ 1/16 (* -1/6 x)))
(* (pow x 4) (+ 1/16 (* x (- (* 7/24 x) 1/6))))
(* (pow x 4) (+ 1/16 (* x (- (* x (+ 7/24 (* -35/108 x))) 1/6))))
(* 1/256 (pow x 12))
(* (pow x 12) (- 1/256 (* 1/48 (/ 1 x))))
(* (pow x 12) (- (+ 1/256 (/ 7/96 (pow x 2))) (* 1/48 (/ 1 x))))
(* (pow x 12) (- (+ 1/256 (/ 7/96 (pow x 2))) (+ (* 1/48 (/ 1 x)) (* 35/216 (/ 1 (pow x 3))))))
(* 1/256 (pow x 12))
(* (pow x 12) (- 1/256 (* 1/48 (/ 1 x))))
(* (pow x 12) (+ 1/256 (* -1 (/ (- 1/48 (* 7/96 (/ 1 x))) x))))
(* (pow x 12) (+ 1/256 (* -1 (/ (+ 1/48 (* -1 (/ (- 7/96 (* 35/216 (/ 1 x))) x))) x))))
(* -1/2 (pow x 2))
(* (pow x 2) (- (* 1/3 x) 1/2))
(* (pow x 2) (- (* x (+ 1/3 (* -1/4 x))) 1/2))
(* (pow x 2) (- (* x (+ 1/3 (* -1/4 x))) 1/2))
(* -1/4 (pow x 4))
(* (pow x 4) (- (* 1/3 (/ 1 x)) 1/4))
(* (pow x 4) (- (* 1/3 (/ 1 x)) (+ 1/4 (/ 1/2 (pow x 2)))))
(* (pow x 4) (- (* 1/3 (/ 1 x)) (+ 1/4 (/ 1/2 (pow x 2)))))
(* -1/4 (pow x 4))
(* (pow x 4) (- (* 1/3 (/ 1 x)) 1/4))
(* (pow x 4) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/3) x)) 1/4))
(* (pow x 4) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/3) x)) 1/4))

Outputs
x
(* x (+ 1 (* -1/2 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))))
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(*.f64 (pow.f64 x #s(literal 12 binary64)) (+.f64 #s(literal 1/256 binary64) (/.f64 (+.f64 (/.f64 #s(literal 7/96 binary64) x) #s(literal -1/48 binary64)) x)))
(* (pow x 12) (+ 1/256 (* -1 (/ (+ 1/48 (* -1 (/ (- 7/96 (* 35/216 (/ 1 x))) x))) x))))
(*.f64 (pow.f64 x #s(literal 12 binary64)) (+.f64 #s(literal 1/256 binary64) (/.f64 (+.f64 (/.f64 (+.f64 #s(literal 7/96 binary64) (/.f64 #s(literal -35/216 binary64) x)) x) #s(literal -1/48 binary64)) x)))
(* -1/2 (pow x 2))
(.f64 #s(literal -1/2 binary64) (.f64 x x))
(* (pow x 2) (- (* 1/3 x) 1/2))
(.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))) (*.f64 x x))
(* (pow x 2) (- (* x (+ 1/3 (* -1/4 x))) 1/2))
(.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))))
(* (pow x 2) (- (* x (+ 1/3 (* -1/4 x))) 1/2))
(.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))))
(* -1/4 (pow x 4))
(*.f64 #s(literal -1/4 binary64) (pow.f64 x #s(literal 4 binary64)))
(* (pow x 4) (- (* 1/3 (/ 1 x)) 1/4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 #s(literal -1/4 binary64) (/.f64 #s(literal 1/3 binary64) x)))
(* (pow x 4) (- (* 1/3 (/ 1 x)) (+ 1/4 (/ 1/2 (pow x 2)))))
(*.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 #s(literal -1/4 binary64) (/.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal -1/2 binary64) x)) x)))
(* (pow x 4) (- (* 1/3 (/ 1 x)) (+ 1/4 (/ 1/2 (pow x 2)))))
(*.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 #s(literal -1/4 binary64) (/.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal -1/2 binary64) x)) x)))
(* -1/4 (pow x 4))
(*.f64 #s(literal -1/4 binary64) (pow.f64 x #s(literal 4 binary64)))
(* (pow x 4) (- (* 1/3 (/ 1 x)) 1/4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 #s(literal -1/4 binary64) (/.f64 #s(literal 1/3 binary64) x)))
(* (pow x 4) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/3) x)) 1/4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 #s(literal -1/4 binary64) (/.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal -1/2 binary64) x)) x)))
(* (pow x 4) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/3) x)) 1/4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 #s(literal -1/4 binary64) (/.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal -1/2 binary64) x)) x)))

eval338.0ms (3.2%)

Compiler: Compiled 132797 to 4866 computations (96.3% saved)

prune186.0ms (1.7%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	2125	3	2128
Fresh	0	0	0
Picked	4	1	5
Done	2	3	5
Total	2131	7	2138

Accuracy

100.0%

Counts

2138 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	69.8%	(/.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/12 binary64) (*.f64 x #s(literal 1/24 binary64))))))))
▶	69.3%	(/.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/12 binary64))))))
▶	72.7%	(/.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))))
✓	68.4%	(+.f64 (.f64 x (.f64 x #s(literal -1/2 binary64))) x)
✓	100.0%	(log1p.f64 x)
✓	36.7%	(log.f64 (+.f64 #s(literal 1 binary64) x))
✓	69.3%	x

Compiler

Compiled 54 to 39 computations (27.8% saved)

simplify17.0ms (0.2%)

Algorithm

1×	egg-herbie

Localize:

Found 11 expressions of interest:

New	Metric	Program
✓	cost-diff	(+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/12 binary64) (.f64 x #s(literal 1/24 binary64)))))
✓	cost-diff	(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/12 binary64) (*.f64 x #s(literal 1/24 binary64))))))
✓	cost-diff	(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/12 binary64) (*.f64 x #s(literal 1/24 binary64)))))))
✓	cost-diff	(/.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/12 binary64) (*.f64 x #s(literal 1/24 binary64))))))))
✓	cost-diff	(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/12 binary64)))
✓	cost-diff	(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/12 binary64))))
✓	cost-diff	(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/12 binary64)))))
✓	cost-diff	(/.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/12 binary64))))))
✓	cost-diff	(*.f64 x #s(literal 1/2 binary64))
✓	cost-diff	(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))
✓	cost-diff	(/.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))))

Rules

324×	`fma-define`
264×	`fma-lowering-fma.f32`
264×	`fma-lowering-fma.f64`
146×	`sum3-define`
128×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	125
1	49	105
2	119	105
3	218	105
4	326	105
5	411	105
6	432	105
0	432	105

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(/ x (+ 1 (* x 1/2)))
x
(+ 1 (* x 1/2))
1
(* x 1/2)
1/2
(/ x (+ 1 (* x (+ 1/2 (* x -1/12)))))
x
(+ 1 (* x (+ 1/2 (* x -1/12))))
1
(* x (+ 1/2 (* x -1/12)))
(+ 1/2 (* x -1/12))
1/2
(* x -1/12)
-1/12
(/ x (+ 1 (* x (+ 1/2 (* x (+ -1/12 (* x 1/24)))))))
x
(+ 1 (* x (+ 1/2 (* x (+ -1/12 (* x 1/24))))))
1
(* x (+ 1/2 (* x (+ -1/12 (* x 1/24)))))
(+ 1/2 (* x (+ -1/12 (* x 1/24))))
1/2
(* x (+ -1/12 (* x 1/24)))
(+ -1/12 (* x 1/24))
-1/12
(* x 1/24)
1/24

Outputs
(/ x (+ 1 (* x 1/2)))
(/.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))))
x
(+ 1 (* x 1/2))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))
1
#s(literal 1 binary64)
(* x 1/2)
(*.f64 x #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)
(/ x (+ 1 (* x (+ 1/2 (* x -1/12)))))
(/.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/12 binary64))))))
x
(+ 1 (* x (+ 1/2 (* x -1/12))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/12 binary64)))))
1
#s(literal 1 binary64)
(* x (+ 1/2 (* x -1/12)))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/12 binary64))))
(+ 1/2 (* x -1/12))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/12 binary64)))
1/2
#s(literal 1/2 binary64)
(* x -1/12)
(*.f64 x #s(literal -1/12 binary64))
-1/12
#s(literal -1/12 binary64)
(/ x (+ 1 (* x (+ 1/2 (* x (+ -1/12 (* x 1/24)))))))
(/.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/12 binary64) (*.f64 x #s(literal 1/24 binary64))))))))
x
(+ 1 (* x (+ 1/2 (* x (+ -1/12 (* x 1/24))))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/12 binary64) (*.f64 x #s(literal 1/24 binary64)))))))
1
#s(literal 1 binary64)
(* x (+ 1/2 (* x (+ -1/12 (* x 1/24)))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/12 binary64) (*.f64 x #s(literal 1/24 binary64))))))
(+ 1/2 (* x (+ -1/12 (* x 1/24))))
(+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/12 binary64) (.f64 x #s(literal 1/24 binary64)))))
1/2
#s(literal 1/2 binary64)
(* x (+ -1/12 (* x 1/24)))
(.f64 x (+.f64 #s(literal -1/12 binary64) (.f64 x #s(literal 1/24 binary64))))
(+ -1/12 (* x 1/24))
(+.f64 #s(literal -1/12 binary64) (*.f64 x #s(literal 1/24 binary64)))
-1/12
#s(literal -1/12 binary64)
(* x 1/24)
(*.f64 x #s(literal 1/24 binary64))
1/24
#s(literal 1/24 binary64)

localize113.0ms (1.1%)

Localize:

Found 11 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.9%	(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/12 binary64) (*.f64 x #s(literal 1/24 binary64))))))
✓	accuracy	99.6%	(.f64 x (+.f64 #s(literal -1/12 binary64) (.f64 x #s(literal 1/24 binary64))))
✓	accuracy	99.5%	(*.f64 x #s(literal 1/24 binary64))
✓	accuracy	94.7%	(/.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/12 binary64) (*.f64 x #s(literal 1/24 binary64))))))))
✓	accuracy	100.0%	(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/12 binary64)))
✓	accuracy	99.9%	(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/12 binary64))))
✓	accuracy	99.5%	(*.f64 x #s(literal -1/12 binary64))
✓	accuracy	84.2%	(/.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/12 binary64))))))
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))
✓	accuracy	100.0%	(*.f64 x #s(literal 1/2 binary64))
✓	accuracy	100.0%	(/.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))))

Results

81.0ms	254×	0	valid
2.0ms	1×	5	exit
1.0ms	1×	2	valid

Compiler

Compiled 127 to 21 computations (83.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 35.0ms

ival-mult: 11.0ms (31.4% of total)

...c/correct-round.rkt:119:19: 9.0ms (25.7% of total)

ival-add: 8.0ms (22.9% of total)

ival-div: 6.0ms (17.1% of total)

const: 1.0ms (2.9% of total)

backward-pass: 1.0ms (2.9% of total)

series12.0ms (0.1%)

Counts

14 → 168

Calls

Call 1

Inputs
#<alt (/ x (+ 1 (* x 1/2)))>
#<alt (+ 1 (* x 1/2))>
#<alt (* x 1/2)>
#<alt (/ x (+ 1 (* x (+ 1/2 (* x -1/12)))))>
#<alt (+ 1 (* x (+ 1/2 (* x -1/12))))>
#<alt (* x (+ 1/2 (* x -1/12)))>
#<alt (+ 1/2 (* x -1/12))>
#<alt (/ x (+ 1 (* x (+ 1/2 (* x (+ -1/12 (* x 1/24)))))))>
#<alt (+ 1 (* x (+ 1/2 (* x (+ -1/12 (* x 1/24))))))>
#<alt (* x (+ 1/2 (* x (+ -1/12 (* x 1/24)))))>
#<alt (+ 1/2 (* x (+ -1/12 (* x 1/24))))>
#<alt (* x -1/12)>
#<alt (* x 1/24)>
#<alt (* x (+ -1/12 (* x 1/24)))>

Outputs
#<alt x>
#<alt (* x (+ 1 (* -1/2 x)))>
#<alt (* x (+ 1 (* x (- (* 1/4 x) 1/2))))>
#<alt (* x (+ 1 (* x (- (* x (+ 1/4 (* -1/8 x))) 1/2))))>
#<alt 2>
#<alt (- 2 (* 4 (/ 1 x)))>
#<alt (- (+ 2 (/ 8 (pow x 2))) (* 4 (/ 1 x)))>
#<alt (- (+ 2 (/ 8 (pow x 2))) (+ (* 4 (/ 1 x)) (* 16 (/ 1 (pow x 3)))))>
#<alt 2>
#<alt (- 2 (* 4 (/ 1 x)))>
#<alt (+ 2 (* -1 (/ (- 4 (* 8 (/ 1 x))) x)))>
#<alt (+ 2 (* -1 (/ (+ 4 (* -1 (/ (- 8 (* 16 (/ 1 x))) x))) x)))>
#<alt 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* 1/2 x))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt x>
#<alt (* x (+ 1 (* -1/2 x)))>
#<alt (* x (+ 1 (* x (- (* 1/3 x) 1/2))))>
#<alt (* x (+ 1 (* x (- (* x (+ 1/3 (* -5/24 x))) 1/2))))>
#<alt (/ -12 x)>
#<alt (* -1 (/ (+ 12 (* 72 (/ 1 x))) x))>
#<alt (/ (- (* -1 (/ (+ 72 (* 576 (/ 1 x))) x)) 12) x)>
#<alt (/ (- (* -1 (/ (+ 576 (* 4320 (/ 1 x))) (pow x 2))) (+ 12 (* 72 (/ 1 x)))) x)>
#<alt (/ -12 x)>
#<alt (* -1 (/ (+ 12 (* 72 (/ 1 x))) x))>
#<alt (* -1 (/ (+ 12 (+ (* 72 (/ 1 x)) (/ 576 (pow x 2)))) x))>
#<alt (* -1 (/ (+ 12 (* -1 (/ (- (* -1 (/ (+ 576 (* 4320 (/ 1 x))) x)) 72) x))) x))>
#<alt 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* x (+ 1/2 (* -1/12 x))))>
#<alt (+ 1 (* x (+ 1/2 (* -1/12 x))))>
#<alt (* -1/12 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/2 (/ 1 x)) 1/12))>
#<alt (* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) 1/12))>
#<alt (* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) 1/12))>
#<alt (* -1/12 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/2 (/ 1 x)) 1/12))>
#<alt (* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) 1/12))>
#<alt (* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) 1/12))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* -1/12 x)))>
#<alt (* x (+ 1/2 (* -1/12 x)))>
#<alt (* x (+ 1/2 (* -1/12 x)))>
#<alt (* -1/12 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/2 (/ 1 x)) 1/12))>
#<alt (* (pow x 2) (- (* 1/2 (/ 1 x)) 1/12))>
#<alt (* (pow x 2) (- (* 1/2 (/ 1 x)) 1/12))>
#<alt (* -1/12 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/2 (/ 1 x)) 1/12))>
#<alt (* (pow x 2) (- (* 1/2 (/ 1 x)) 1/12))>
#<alt (* (pow x 2) (- (* 1/2 (/ 1 x)) 1/12))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/12 x))>
#<alt (+ 1/2 (* -1/12 x))>
#<alt (+ 1/2 (* -1/12 x))>
#<alt (* -1/12 x)>
#<alt (* x (- (* 1/2 (/ 1 x)) 1/12))>
#<alt (* x (- (* 1/2 (/ 1 x)) 1/12))>
#<alt (* x (- (* 1/2 (/ 1 x)) 1/12))>
#<alt (* -1/12 x)>
#<alt (* -1 (* x (- 1/12 (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* x (- 1/12 (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* x (- 1/12 (* 1/2 (/ 1 x)))))>
#<alt x>
#<alt (* x (+ 1 (* -1/2 x)))>
#<alt (* x (+ 1 (* x (- (* 1/3 x) 1/2))))>
#<alt (* x (+ 1 (* x (- (* x (+ 1/3 (* -1/4 x))) 1/2))))>
#<alt (/ 24 (pow x 2))>
#<alt (/ (+ 24 (* 48 (/ 1 x))) (pow x 2))>
#<alt (/ (- (+ 24 (* 48 (/ 1 x))) (/ 192 (pow x 2))) (pow x 2))>
#<alt (/ (+ 24 (+ (* -1 (/ (+ 192 (* 1536 (/ 1 x))) (pow x 2))) (* 48 (/ 1 x)))) (pow x 2))>
#<alt (/ 24 (pow x 2))>
#<alt (/ (+ 24 (* 48 (/ 1 x))) (pow x 2))>
#<alt (/ (+ 24 (* -1 (/ (- (* 192 (/ 1 x)) 48) x))) (pow x 2))>
#<alt (/ (+ 24 (* -1 (/ (- (+ (* 192 (/ 1 x)) (/ 1536 (pow x 2))) 48) x))) (pow x 2))>
#<alt 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* x (+ 1/2 (* -1/12 x))))>
#<alt (+ 1 (* x (+ 1/2 (* x (- (* 1/24 x) 1/12)))))>
#<alt (* 1/24 (pow x 3))>
#<alt (* (pow x 3) (- 1/24 (* 1/12 (/ 1 x))))>
#<alt (* (pow x 3) (- (+ 1/24 (/ 1/2 (pow x 2))) (* 1/12 (/ 1 x))))>
#<alt (* (pow x 3) (- (+ 1/24 (+ (/ 1/2 (pow x 2)) (/ 1 (pow x 3)))) (* 1/12 (/ 1 x))))>
#<alt (* 1/24 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- (* 1/12 (/ 1 x)) 1/24)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/12) x)) 1/24)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) 1/12) x)) 1/24)))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* -1/12 x)))>
#<alt (* x (+ 1/2 (* x (- (* 1/24 x) 1/12))))>
#<alt (* x (+ 1/2 (* x (- (* 1/24 x) 1/12))))>
#<alt (* 1/24 (pow x 3))>
#<alt (* (pow x 3) (- 1/24 (* 1/12 (/ 1 x))))>
#<alt (* (pow x 3) (- (+ 1/24 (/ 1/2 (pow x 2))) (* 1/12 (/ 1 x))))>
#<alt (* (pow x 3) (- (+ 1/24 (/ 1/2 (pow x 2))) (* 1/12 (/ 1 x))))>
#<alt (* 1/24 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- (* 1/12 (/ 1 x)) 1/24)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/12) x)) 1/24)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/12) x)) 1/24)))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/12 x))>
#<alt (+ 1/2 (* x (- (* 1/24 x) 1/12)))>
#<alt (+ 1/2 (* x (- (* 1/24 x) 1/12)))>
#<alt (* 1/24 (pow x 2))>
#<alt (* (pow x 2) (- 1/24 (* 1/12 (/ 1 x))))>
#<alt (* (pow x 2) (- (+ 1/24 (/ 1/2 (pow x 2))) (* 1/12 (/ 1 x))))>
#<alt (* (pow x 2) (- (+ 1/24 (/ 1/2 (pow x 2))) (* 1/12 (/ 1 x))))>
#<alt (* 1/24 (pow x 2))>
#<alt (* (pow x 2) (- 1/24 (* 1/12 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/24 (* -1 (/ (- 1/12 (* 1/2 (/ 1 x))) x))))>
#<alt (* (pow x 2) (+ 1/24 (* -1 (/ (- 1/12 (* 1/2 (/ 1 x))) x))))>
#<alt (* -1/12 x)>
#<alt (* -1/12 x)>
#<alt (* -1/12 x)>
#<alt (* -1/12 x)>
#<alt (* -1/12 x)>
#<alt (* -1/12 x)>
#<alt (* -1/12 x)>
#<alt (* -1/12 x)>
#<alt (* -1/12 x)>
#<alt (* -1/12 x)>
#<alt (* -1/12 x)>
#<alt (* -1/12 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* -1/12 x)>
#<alt (* x (- (* 1/24 x) 1/12))>
#<alt (* x (- (* 1/24 x) 1/12))>
#<alt (* x (- (* 1/24 x) 1/12))>
#<alt (* 1/24 (pow x 2))>
#<alt (* (pow x 2) (- 1/24 (* 1/12 (/ 1 x))))>
#<alt (* (pow x 2) (- 1/24 (* 1/12 (/ 1 x))))>
#<alt (* (pow x 2) (- 1/24 (* 1/12 (/ 1 x))))>
#<alt (* 1/24 (pow x 2))>
#<alt (* (pow x 2) (- 1/24 (* 1/12 (/ 1 x))))>
#<alt (* (pow x 2) (- 1/24 (* 1/12 (/ 1 x))))>
#<alt (* (pow x 2) (- 1/24 (* 1/12 (/ 1 x))))>

Calls

42 calls:

Time	Variable		Point	Expression
2.0ms	x	@	0	(* x 1/24)
2.0ms	x	@	-inf	(/ x (+ 1 (* x (+ 1/2 (* x -1/12)))))
0.0ms	x	@	inf	(* x (+ -1/12 (* x 1/24)))
0.0ms	x	@	inf	(/ x (+ 1 (* x (+ 1/2 (* x (+ -1/12 (* x 1/24)))))))
0.0ms	x	@	0	(/ x (+ 1 (* x (+ 1/2 (* x (+ -1/12 (* x 1/24)))))))

rewrite301.0ms (2.8%)

Algorithm

1×	batch-egg-rewrite

Rules

4042×	`-lowering-.f32`
4042×	`-lowering-.f64`
3888×	`/-lowering-/.f32`
3888×	`/-lowering-/.f64`
1732×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	108
1	139	89
2	1286	89
0	8258	89

Stop Event

1×	iter limit
1×	node limit

Counts

14 → 476

Calls

Call 1

Inputs
(/ x (+ 1 (* x 1/2)))
(+ 1 (* x 1/2))
(* x 1/2)
(/ x (+ 1 (* x (+ 1/2 (* x -1/12)))))
(+ 1 (* x (+ 1/2 (* x -1/12))))
(* x (+ 1/2 (* x -1/12)))
(+ 1/2 (* x -1/12))
(/ x (+ 1 (* x (+ 1/2 (* x (+ -1/12 (* x 1/24)))))))
(+ 1 (* x (+ 1/2 (* x (+ -1/12 (* x 1/24))))))
(* x (+ 1/2 (* x (+ -1/12 (* x 1/24)))))
(+ 1/2 (* x (+ -1/12 (* x 1/24))))
(* x -1/12)
(* x 1/24)
(* x (+ -1/12 (* x 1/24)))

Outputs
(exp.f64 (.f64 (log.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))) x)) #s(literal -1 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))) (/.f64 x (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))))
(neg.f64 (/.f64 x (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))))
(/.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))) x))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))) (.f64 x #s(literal 1 binary64))))
(/.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))) x)))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) x)) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))))))
(/.f64 (.f64 x #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))
(/.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x #s(literal 1/2 binary64)) (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))) (.f64 (.f64 (.f64 x #s(literal 1/2 binary64)) (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))) (.f64 (.f64 x #s(literal 1/2 binary64)) (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))))))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x)))) (+.f64 #s(literal 1 binary64) (-.f64 (.f64 (.f64 (.f64 x #s(literal 1/2 binary64)) (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))) (.f64 (.f64 x #s(literal 1/2 binary64)) (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))) (.f64 #s(literal 1 binary64) (.f64 (.f64 x #s(literal 1/2 binary64)) (-.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))))))))
(/.f64 (.f64 x (-.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x #s(literal 1/2 binary64)) (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))) (.f64 (.f64 x #s(literal 1/2 binary64)) (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x)))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x #s(literal 1/2 binary64)) (-.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))))))
(/.f64 (.f64 x (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 x x)))) (.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 x x))) (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))))
(/.f64 (.f64 x (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))))) (.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 x x))) (+.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (.f64 x #s(literal 1/2 binary64))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 0 binary64) x))) (neg.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))))))
(/.f64 (neg.f64 (.f64 x #s(literal 1 binary64))) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)))))
(pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))) x) #s(literal -1 binary64))
(.f64 x (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)))))
(.f64 #s(literal 1 binary64) (/.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)))))
(.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)))) x)
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)))) (pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)))
(.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))) x))))
(.f64 (neg.f64 (-.f64 #s(literal 0 binary64) x)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)))))
(.f64 (.f64 x #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))))
(.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x #s(literal 1/2 binary64)) (-.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))))
(.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x #s(literal 1/2 binary64)) (-.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))))))
(.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 x x)))) (-.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))
(.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 x x)))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))
(+.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))
(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)))) (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)))))
(-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)))) #s(literal 1 binary64)) (/.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)))) #s(literal 1 binary64)))
(-.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(fma.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 (*.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)))) (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) (-.f64 (.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1 binary64))))
(/.f64 (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))) #s(literal 1 binary64))
(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))) #s(literal -1 binary64))
(/.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x)))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x #s(literal 1/2 binary64)) (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))))
(/.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x)))) (+.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)))))
(/.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 x x))) (-.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))))))
(/.f64 (neg.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))))) (neg.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x #s(literal 1/2 binary64)) (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))))))
(/.f64 (neg.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))))) (neg.f64 (+.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 x x)))) (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))))
(/.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) #s(literal 1 binary64)) (-.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)))) (.f64 (-.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))) (.f64 #s(literal 1/4 binary64) (.f64 x x)))) (.f64 (-.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))))
(/.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))) (.f64 (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))) (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x)))))) #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 1 binary64) (-.f64 (.f64 (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))) (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x)))) (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x #s(literal 1/2 binary64)) (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))))))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))) (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))))) #s(literal 1 binary64)) (.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x)))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x #s(literal 1/2 binary64)) (-.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))))))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))) (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))))) #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (.f64 #s(literal 1/4 binary64) (.f64 x x))) (.f64 #s(literal 1/4 binary64) (.f64 x x)))) (-.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (.f64 #s(literal 1/4 binary64) (.f64 x x)))) #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 x x))) (-.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (neg.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x)))))) (neg.f64 (neg.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x #s(literal 1/2 binary64)) (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 x x))))) (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))))))
(/.f64 (neg.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) #s(literal 1 binary64))) (neg.f64 (-.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))))
(/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)))) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)))) #s(literal 3 binary64))) (+.f64 (.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))) (+.f64 (.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)))) (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))) (.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)))) (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))))))))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))
(.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))) #s(literal 1 binary64))
(.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x #s(literal 1/2 binary64)) (-.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))))))
(.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))))))
(.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)))))
(.f64 (neg.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x #s(literal 1/2 binary64)) (-.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))))))
(.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 x x)))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))))
(.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))))
(*.f64 x #s(literal 1/2 binary64))
(.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)))
(*.f64 #s(literal 1/2 binary64) x)
(.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))
(.f64 (.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))
(exp.f64 (.f64 (log.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/12 binary64))))) x)) #s(literal -1 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/12 binary64))))))) (/.f64 x (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/12 binary64))))))))
(neg.f64 (/.f64 x (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/12 binary64))))))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/12 binary64)))))))
(/.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/12 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/12 binary64))))) x))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/12 binary64))))) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/12 binary64))))) (*.f64 x #s(literal 1 binary64))))
(/.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/12 binary64)))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/12 binary64))))) x)))
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(.f64 x (+.f64 #s(literal -1/12 binary64) (.f64 x #s(literal 1/24 binary64))))
(.f64 (+.f64 #s(literal -1/12 binary64) (.f64 x #s(literal 1/24 binary64))) x)
(.f64 (+.f64 (.f64 #s(literal -1/1728 binary64) (.f64 x (.f64 x x))) (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824 binary64)) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 1/144 binary64) (.f64 x x)) (-.f64 (.f64 (.f64 x (.f64 x #s(literal 1/24 binary64))) (.f64 x (.f64 x #s(literal 1/24 binary64)))) (.f64 (.f64 x #s(literal -1/12 binary64)) (.f64 x (*.f64 x #s(literal 1/24 binary64))))))))
(.f64 (-.f64 (.f64 #s(literal 1/144 binary64) (.f64 x x)) (.f64 (.f64 x (.f64 x #s(literal 1/24 binary64))) (.f64 x (.f64 x #s(literal 1/24 binary64))))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x #s(literal -1/12 binary64)) (.f64 x (*.f64 x #s(literal 1/24 binary64))))))
(.f64 (.f64 x (+.f64 #s(literal -1/1728 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/144 binary64) (.f64 (.f64 x #s(literal 1/24 binary64)) (-.f64 (.f64 x #s(literal 1/24 binary64)) #s(literal -1/12 binary64))))))
(.f64 (.f64 x (-.f64 #s(literal 1/144 binary64) (.f64 (.f64 x x) #s(literal 1/576 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/12 binary64) (*.f64 #s(literal -1/24 binary64) x))))
(.f64 (.f64 (+.f64 #s(literal -1/1728 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824 binary64))) x) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/144 binary64) (.f64 (.f64 x #s(literal 1/24 binary64)) (-.f64 (.f64 x #s(literal 1/24 binary64)) #s(literal -1/12 binary64))))))
(.f64 (.f64 (-.f64 #s(literal 1/144 binary64) (.f64 (.f64 x x) #s(literal 1/576 binary64))) x) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/12 binary64) (*.f64 #s(literal -1/24 binary64) x))))

simplify241.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

3662×	`-lowering-.f32`
3662×	`-lowering-.f64`
1690×	`+-lowering-+.f64`
1690×	`+-lowering-+.f32`
1376×	`/-lowering-/.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	201	1180
1	609	1043
2	1634	1000
3	4920	966
0	8205	966

Stop Event

1×	iter limit
1×	node limit

Counts

168 → 168

Calls

Call 1

Inputs
x
(* x (+ 1 (* -1/2 x)))
(* x (+ 1 (* x (- (* 1/4 x) 1/2))))
(* x (+ 1 (* x (- (* x (+ 1/4 (* -1/8 x))) 1/2))))
2
(- 2 (* 4 (/ 1 x)))
(- (+ 2 (/ 8 (pow x 2))) (* 4 (/ 1 x)))
(- (+ 2 (/ 8 (pow x 2))) (+ (* 4 (/ 1 x)) (* 16 (/ 1 (pow x 3)))))
2
(- 2 (* 4 (/ 1 x)))
(+ 2 (* -1 (/ (- 4 (* 8 (/ 1 x))) x)))
(+ 2 (* -1 (/ (+ 4 (* -1 (/ (- 8 (* 16 (/ 1 x))) x))) x)))
1
(+ 1 (* 1/2 x))
(+ 1 (* 1/2 x))
(+ 1 (* 1/2 x))
(* 1/2 x)
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* 1/2 x)
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
x
(* x (+ 1 (* -1/2 x)))
(* x (+ 1 (* x (- (* 1/3 x) 1/2))))
(* x (+ 1 (* x (- (* x (+ 1/3 (* -5/24 x))) 1/2))))
(/ -12 x)
(* -1 (/ (+ 12 (* 72 (/ 1 x))) x))
(/ (- (* -1 (/ (+ 72 (* 576 (/ 1 x))) x)) 12) x)
(/ (- (* -1 (/ (+ 576 (* 4320 (/ 1 x))) (pow x 2))) (+ 12 (* 72 (/ 1 x)))) x)
(/ -12 x)
(* -1 (/ (+ 12 (* 72 (/ 1 x))) x))
(* -1 (/ (+ 12 (+ (* 72 (/ 1 x)) (/ 576 (pow x 2)))) x))
(* -1 (/ (+ 12 (* -1 (/ (- (* -1 (/ (+ 576 (* 4320 (/ 1 x))) x)) 72) x))) x))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/12 x))))
(+ 1 (* x (+ 1/2 (* -1/12 x))))
(* -1/12 (pow x 2))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/12))
(* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) 1/12))
(* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) 1/12))
(* -1/12 (pow x 2))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/12))
(* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) 1/12))
(* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) 1/12))
(* 1/2 x)
(* x (+ 1/2 (* -1/12 x)))
(* x (+ 1/2 (* -1/12 x)))
(* x (+ 1/2 (* -1/12 x)))
(* -1/12 (pow x 2))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/12))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/12))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/12))
(* -1/12 (pow x 2))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/12))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/12))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/12))
1/2
(+ 1/2 (* -1/12 x))
(+ 1/2 (* -1/12 x))
(+ 1/2 (* -1/12 x))
(* -1/12 x)
(* x (- (* 1/2 (/ 1 x)) 1/12))
(* x (- (* 1/2 (/ 1 x)) 1/12))
(* x (- (* 1/2 (/ 1 x)) 1/12))
(* -1/12 x)
(* -1 (* x (- 1/12 (* 1/2 (/ 1 x)))))
(* -1 (* x (- 1/12 (* 1/2 (/ 1 x)))))
(* -1 (* x (- 1/12 (* 1/2 (/ 1 x)))))
x
(* x (+ 1 (* -1/2 x)))
(* x (+ 1 (* x (- (* 1/3 x) 1/2))))
(* x (+ 1 (* x (- (* x (+ 1/3 (* -1/4 x))) 1/2))))
(/ 24 (pow x 2))
(/ (+ 24 (* 48 (/ 1 x))) (pow x 2))
(/ (- (+ 24 (* 48 (/ 1 x))) (/ 192 (pow x 2))) (pow x 2))
(/ (+ 24 (+ (* -1 (/ (+ 192 (* 1536 (/ 1 x))) (pow x 2))) (* 48 (/ 1 x)))) (pow x 2))
(/ 24 (pow x 2))
(/ (+ 24 (* 48 (/ 1 x))) (pow x 2))
(/ (+ 24 (* -1 (/ (- (* 192 (/ 1 x)) 48) x))) (pow x 2))
(/ (+ 24 (* -1 (/ (- (+ (* 192 (/ 1 x)) (/ 1536 (pow x 2))) 48) x))) (pow x 2))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/12 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/24 x) 1/12)))))
(* 1/24 (pow x 3))
(* (pow x 3) (- 1/24 (* 1/12 (/ 1 x))))
(* (pow x 3) (- (+ 1/24 (/ 1/2 (pow x 2))) (* 1/12 (/ 1 x))))
(* (pow x 3) (- (+ 1/24 (+ (/ 1/2 (pow x 2)) (/ 1 (pow x 3)))) (* 1/12 (/ 1 x))))
(* 1/24 (pow x 3))
(* -1 (* (pow x 3) (- (* 1/12 (/ 1 x)) 1/24)))
(* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/12) x)) 1/24)))
(* -1 (* (pow x 3) (- (* -1 (/ (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) 1/12) x)) 1/24)))
(* 1/2 x)
(* x (+ 1/2 (* -1/12 x)))
(* x (+ 1/2 (* x (- (* 1/24 x) 1/12))))
(* x (+ 1/2 (* x (- (* 1/24 x) 1/12))))
(* 1/24 (pow x 3))
(* (pow x 3) (- 1/24 (* 1/12 (/ 1 x))))
(* (pow x 3) (- (+ 1/24 (/ 1/2 (pow x 2))) (* 1/12 (/ 1 x))))
(* (pow x 3) (- (+ 1/24 (/ 1/2 (pow x 2))) (* 1/12 (/ 1 x))))
(* 1/24 (pow x 3))
(* -1 (* (pow x 3) (- (* 1/12 (/ 1 x)) 1/24)))
(* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/12) x)) 1/24)))
(* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/12) x)) 1/24)))
1/2
(+ 1/2 (* -1/12 x))
(+ 1/2 (* x (- (* 1/24 x) 1/12)))
(+ 1/2 (* x (- (* 1/24 x) 1/12)))
(* 1/24 (pow x 2))
(* (pow x 2) (- 1/24 (* 1/12 (/ 1 x))))
(* (pow x 2) (- (+ 1/24 (/ 1/2 (pow x 2))) (* 1/12 (/ 1 x))))
(* (pow x 2) (- (+ 1/24 (/ 1/2 (pow x 2))) (* 1/12 (/ 1 x))))
(* 1/24 (pow x 2))
(* (pow x 2) (- 1/24 (* 1/12 (/ 1 x))))
(* (pow x 2) (+ 1/24 (* -1 (/ (- 1/12 (* 1/2 (/ 1 x))) x))))
(* (pow x 2) (+ 1/24 (* -1 (/ (- 1/12 (* 1/2 (/ 1 x))) x))))
(* -1/12 x)
(* -1/12 x)
(* -1/12 x)
(* -1/12 x)
(* -1/12 x)
(* -1/12 x)
(* -1/12 x)
(* -1/12 x)
(* -1/12 x)
(* -1/12 x)
(* -1/12 x)
(* -1/12 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* -1/12 x)
(* x (- (* 1/24 x) 1/12))
(* x (- (* 1/24 x) 1/12))
(* x (- (* 1/24 x) 1/12))
(* 1/24 (pow x 2))
(* (pow x 2) (- 1/24 (* 1/12 (/ 1 x))))
(* (pow x 2) (- 1/24 (* 1/12 (/ 1 x))))
(* (pow x 2) (- 1/24 (* 1/12 (/ 1 x))))
(* 1/24 (pow x 2))
(* (pow x 2) (- 1/24 (* 1/12 (/ 1 x))))
(* (pow x 2) (- 1/24 (* 1/12 (/ 1 x))))
(* (pow x 2) (- 1/24 (* 1/12 (/ 1 x))))

Outputs
x
(* x (+ 1 (* -1/2 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))))
(* x (+ 1 (* x (- (* 1/4 x) 1/2))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/4 binary64))))))
(* x (+ 1 (* x (- (* x (+ 1/4 (* -1/8 x))) 1/2))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/8 binary64))))))))
2
#s(literal 2 binary64)
(- 2 (* 4 (/ 1 x)))
(+.f64 #s(literal 2 binary64) (/.f64 #s(literal -4 binary64) x))
(- (+ 2 (/ 8 (pow x 2))) (* 4 (/ 1 x)))
(+.f64 #s(literal 2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 8 binary64) x) #s(literal -4 binary64)) x))
(- (+ 2 (/ 8 (pow x 2))) (+ (* 4 (/ 1 x)) (* 16 (/ 1 (pow x 3)))))
(+.f64 #s(literal 2 binary64) (+.f64 (/.f64 (/.f64 (-.f64 #s(literal 8 binary64) (/.f64 #s(literal 16 binary64) x)) x) x) (/.f64 #s(literal -4 binary64) x)))
2
#s(literal 2 binary64)
(- 2 (* 4 (/ 1 x)))
(+.f64 #s(literal 2 binary64) (/.f64 #s(literal -4 binary64) x))
(+ 2 (* -1 (/ (- 4 (* 8 (/ 1 x))) x)))
(+.f64 #s(literal 2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 8 binary64) x) #s(literal -4 binary64)) x))
(+ 2 (* -1 (/ (+ 4 (* -1 (/ (- 8 (* 16 (/ 1 x))) x))) x)))
(-.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 4 binary64) (/.f64 (-.f64 #s(literal 8 binary64) (/.f64 #s(literal 16 binary64) x)) x)) x))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))
(+ 1 (* 1/2 x))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))
(+ 1 (* 1/2 x))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (+ 1/2 (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))
(* x (+ 1/2 (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))
(* x (+ 1/2 (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (+ 1/2 (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))
(* x (+ 1/2 (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))
(* x (+ 1/2 (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
x
(* x (+ 1 (* -1/2 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))))
(* x (+ 1 (* x (- (* 1/3 x) 1/2))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64))))))
(* x (+ 1 (* x (- (* x (+ 1/3 (* -5/24 x))) 1/2))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -5/24 binary64))))))))
(/ -12 x)
(/.f64 #s(literal -12 binary64) x)
(* -1 (/ (+ 12 (* 72 (/ 1 x))) x))
(/.f64 (+.f64 #s(literal -12 binary64) (/.f64 #s(literal -72 binary64) x)) x)
(/ (- (* -1 (/ (+ 72 (* 576 (/ 1 x))) x)) 12) x)
(/.f64 (+.f64 #s(literal -12 binary64) (/.f64 (+.f64 #s(literal -72 binary64) (/.f64 #s(literal -576 binary64) x)) x)) x)
(/ (- (* -1 (/ (+ 576 (* 4320 (/ 1 x))) (pow x 2))) (+ 12 (* 72 (/ 1 x)))) x)
(/.f64 (+.f64 #s(literal -12 binary64) (/.f64 (+.f64 (/.f64 (+.f64 #s(literal -576 binary64) (/.f64 #s(literal -4320 binary64) x)) x) #s(literal -72 binary64)) x)) x)
(/ -12 x)
(/.f64 #s(literal -12 binary64) x)
(* -1 (/ (+ 12 (* 72 (/ 1 x))) x))
(/.f64 (+.f64 #s(literal -12 binary64) (/.f64 #s(literal -72 binary64) x)) x)
(* -1 (/ (+ 12 (+ (* 72 (/ 1 x)) (/ 576 (pow x 2)))) x))
(/.f64 (+.f64 #s(literal -12 binary64) (+.f64 (/.f64 #s(literal -72 binary64) x) (/.f64 #s(literal -576 binary64) (*.f64 x x)))) x)
(* -1 (/ (+ 12 (* -1 (/ (- (* -1 (/ (+ 576 (* 4320 (/ 1 x))) x)) 72) x))) x))
(/.f64 (-.f64 #s(literal -12 binary64) (/.f64 (-.f64 #s(literal 72 binary64) (/.f64 (+.f64 #s(literal -576 binary64) (/.f64 #s(literal -4320 binary64) x)) x)) x)) x)
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))
(+ 1 (* x (+ 1/2 (* -1/12 x))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/12 binary64)))))
(+ 1 (* x (+ 1/2 (* -1/12 x))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/12 binary64)))))
(* -1/12 (pow x 2))
(.f64 x (.f64 x #s(literal -1/12 binary64)))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/12))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/12 binary64))))
(* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) 1/12))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/12 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))))))
(* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) 1/12))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/12 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))))))
(* -1/12 (pow x 2))
(.f64 x (.f64 x #s(literal -1/12 binary64)))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/12))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/12 binary64))))
(* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) 1/12))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/12 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))))))
(* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) 1/12))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/12 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))))))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (+ 1/2 (* -1/12 x)))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/12 binary64))))
(* x (+ 1/2 (* -1/12 x)))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/12 binary64))))
(* x (+ 1/2 (* -1/12 x)))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/12 binary64))))
(* -1/12 (pow x 2))
(.f64 x (.f64 x #s(literal -1/12 binary64)))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/12))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/12 binary64))))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/12))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/12 binary64))))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/12))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/12 binary64))))
(* -1/12 (pow x 2))
(.f64 x (.f64 x #s(literal -1/12 binary64)))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/12))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/12 binary64))))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/12))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/12 binary64))))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/12))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/12 binary64))))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/12 x))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/12 binary64)))
(+ 1/2 (* -1/12 x))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/12 binary64)))
(+ 1/2 (* -1/12 x))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/12 binary64)))
(* -1/12 x)
(*.f64 x #s(literal -1/12 binary64))
(* x (- (* 1/2 (/ 1 x)) 1/12))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/12 binary64)))
(* x (- (* 1/2 (/ 1 x)) 1/12))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/12 binary64)))
(* x (- (* 1/2 (/ 1 x)) 1/12))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/12 binary64)))
(* -1/12 x)
(*.f64 x #s(literal -1/12 binary64))
(* -1 (* x (- 1/12 (* 1/2 (/ 1 x)))))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/12 binary64)))
(* -1 (* x (- 1/12 (* 1/2 (/ 1 x)))))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/12 binary64)))
(* -1 (* x (- 1/12 (* 1/2 (/ 1 x)))))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/12 binary64)))
x
(* x (+ 1 (* -1/2 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))))
(* x (+ 1 (* x (- (* 1/3 x) 1/2))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64))))))
(* x (+ 1 (* x (- (* x (+ 1/3 (* -1/4 x))) 1/2))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))))))
(/ 24 (pow x 2))
(/.f64 #s(literal 24 binary64) (*.f64 x x))
(/ (+ 24 (* 48 (/ 1 x))) (pow x 2))
(/.f64 (/.f64 (+.f64 #s(literal 24 binary64) (/.f64 #s(literal 48 binary64) x)) x) x)
(/ (- (+ 24 (* 48 (/ 1 x))) (/ 192 (pow x 2))) (pow x 2))
(/.f64 (+.f64 #s(literal 24 binary64) (/.f64 (+.f64 #s(literal 48 binary64) (/.f64 #s(literal -192 binary64) x)) x)) (*.f64 x x))
(/ (+ 24 (+ (* -1 (/ (+ 192 (* 1536 (/ 1 x))) (pow x 2))) (* 48 (/ 1 x)))) (pow x 2))
(/.f64 (+.f64 (+.f64 #s(literal 24 binary64) (/.f64 #s(literal 48 binary64) x)) (/.f64 (-.f64 #s(literal -192 binary64) (/.f64 #s(literal 1536 binary64) x)) (.f64 x x))) (.f64 x x))
(/ 24 (pow x 2))
(/.f64 #s(literal 24 binary64) (*.f64 x x))
(/ (+ 24 (* 48 (/ 1 x))) (pow x 2))
(/.f64 (/.f64 (+.f64 #s(literal 24 binary64) (/.f64 #s(literal 48 binary64) x)) x) x)
(/ (+ 24 (* -1 (/ (- (* 192 (/ 1 x)) 48) x))) (pow x 2))
(/.f64 (+.f64 #s(literal 24 binary64) (/.f64 (+.f64 #s(literal 48 binary64) (/.f64 #s(literal -192 binary64) x)) x)) (*.f64 x x))
(/ (+ 24 (* -1 (/ (- (+ (* 192 (/ 1 x)) (/ 1536 (pow x 2))) 48) x))) (pow x 2))
(/.f64 (+.f64 #s(literal 24 binary64) (/.f64 (-.f64 #s(literal 48 binary64) (+.f64 (/.f64 #s(literal 192 binary64) x) (/.f64 #s(literal 1536 binary64) (.f64 x x)))) x)) (.f64 x x))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))
(+ 1 (* x (+ 1/2 (* -1/12 x))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/12 binary64)))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/24 x) 1/12)))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/12 binary64) (*.f64 x #s(literal 1/24 binary64)))))))
(* 1/24 (pow x 3))
(.f64 (.f64 x (*.f64 x x)) #s(literal 1/24 binary64))
(* (pow x 3) (- 1/24 (* 1/12 (/ 1 x))))
(.f64 (.f64 x x) (*.f64 x (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1/12 binary64) x))))
(* (pow x 3) (- (+ 1/24 (/ 1/2 (pow x 2))) (* 1/12 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/12 binary64) (*.f64 x #s(literal 1/24 binary64))))))
(* (pow x 3) (- (+ 1/24 (+ (/ 1/2 (pow x 2)) (/ 1 (pow x 3)))) (* 1/12 (/ 1 x))))
(.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/24 binary64) (/.f64 (+.f64 #s(literal -1/12 binary64) (+.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal 1 binary64) (.f64 x x)))) x)))
(* 1/24 (pow x 3))
(.f64 (.f64 x (*.f64 x x)) #s(literal 1/24 binary64))
(* -1 (* (pow x 3) (- (* 1/12 (/ 1 x)) 1/24)))
(.f64 (.f64 x x) (*.f64 x (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1/12 binary64) x))))
(* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/12) x)) 1/24)))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/12 binary64) (*.f64 x #s(literal 1/24 binary64))))))
(* -1 (* (pow x 3) (- (* -1 (/ (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) 1/12) x)) 1/24)))
(.f64 (.f64 x (*.f64 x x)) (-.f64 #s(literal 1/24 binary64) (/.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) x) (+.f64 (/.f64 (/.f64 #s(literal -1 binary64) x) x) #s(literal 1/12 binary64))) x)))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (+ 1/2 (* -1/12 x)))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/12 binary64))))
(* x (+ 1/2 (* x (- (* 1/24 x) 1/12))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/12 binary64) (*.f64 x #s(literal 1/24 binary64))))))
(* x (+ 1/2 (* x (- (* 1/24 x) 1/12))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/12 binary64) (*.f64 x #s(literal 1/24 binary64))))))
(* 1/24 (pow x 3))
(.f64 (.f64 x (*.f64 x x)) #s(literal 1/24 binary64))
(* (pow x 3) (- 1/24 (* 1/12 (/ 1 x))))
(.f64 (.f64 x x) (*.f64 x (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1/12 binary64) x))))
(* (pow x 3) (- (+ 1/24 (/ 1/2 (pow x 2))) (* 1/12 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/12 binary64) (*.f64 x #s(literal 1/24 binary64))))))
(* (pow x 3) (- (+ 1/24 (/ 1/2 (pow x 2))) (* 1/12 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/12 binary64) (*.f64 x #s(literal 1/24 binary64))))))
(* 1/24 (pow x 3))
(.f64 (.f64 x (*.f64 x x)) #s(literal 1/24 binary64))
(* -1 (* (pow x 3) (- (* 1/12 (/ 1 x)) 1/24)))
(.f64 (.f64 x x) (*.f64 x (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1/12 binary64) x))))
(* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/12) x)) 1/24)))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/12 binary64) (*.f64 x #s(literal 1/24 binary64))))))
(* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/12) x)) 1/24)))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/12 binary64) (*.f64 x #s(literal 1/24 binary64))))))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/12 x))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/12 binary64)))
(+ 1/2 (* x (- (* 1/24 x) 1/12)))
(+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/12 binary64) (.f64 x #s(literal 1/24 binary64)))))
(+ 1/2 (* x (- (* 1/24 x) 1/12)))
(+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/12 binary64) (.f64 x #s(literal 1/24 binary64)))))
(* 1/24 (pow x 2))
(.f64 x (.f64 x #s(literal 1/24 binary64)))
(* (pow x 2) (- 1/24 (* 1/12 (/ 1 x))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1/12 binary64) x)))
(* (pow x 2) (- (+ 1/24 (/ 1/2 (pow x 2))) (* 1/12 (/ 1 x))))
(+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/12 binary64) (.f64 x #s(literal 1/24 binary64)))))
(* (pow x 2) (- (+ 1/24 (/ 1/2 (pow x 2))) (* 1/12 (/ 1 x))))
(+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/12 binary64) (.f64 x #s(literal 1/24 binary64)))))
(* 1/24 (pow x 2))
(.f64 x (.f64 x #s(literal 1/24 binary64)))
(* (pow x 2) (- 1/24 (* 1/12 (/ 1 x))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1/12 binary64) x)))
(* (pow x 2) (+ 1/24 (* -1 (/ (- 1/12 (* 1/2 (/ 1 x))) x))))
(+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/12 binary64) (.f64 x #s(literal 1/24 binary64)))))
(* (pow x 2) (+ 1/24 (* -1 (/ (- 1/12 (* 1/2 (/ 1 x))) x))))
(+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/12 binary64) (.f64 x #s(literal 1/24 binary64)))))
(* -1/12 x)
(*.f64 x #s(literal -1/12 binary64))
(* -1/12 x)
(*.f64 x #s(literal -1/12 binary64))
(* -1/12 x)
(*.f64 x #s(literal -1/12 binary64))
(* -1/12 x)
(*.f64 x #s(literal -1/12 binary64))
(* -1/12 x)
(*.f64 x #s(literal -1/12 binary64))
(* -1/12 x)
(*.f64 x #s(literal -1/12 binary64))
(* -1/12 x)
(*.f64 x #s(literal -1/12 binary64))
(* -1/12 x)
(*.f64 x #s(literal -1/12 binary64))
(* -1/12 x)
(*.f64 x #s(literal -1/12 binary64))
(* -1/12 x)
(*.f64 x #s(literal -1/12 binary64))
(* -1/12 x)
(*.f64 x #s(literal -1/12 binary64))
(* -1/12 x)
(*.f64 x #s(literal -1/12 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* -1/12 x)
(*.f64 x #s(literal -1/12 binary64))
(* x (- (* 1/24 x) 1/12))
(.f64 x (+.f64 #s(literal -1/12 binary64) (.f64 x #s(literal 1/24 binary64))))
(* x (- (* 1/24 x) 1/12))
(.f64 x (+.f64 #s(literal -1/12 binary64) (.f64 x #s(literal 1/24 binary64))))
(* x (- (* 1/24 x) 1/12))
(.f64 x (+.f64 #s(literal -1/12 binary64) (.f64 x #s(literal 1/24 binary64))))
(* 1/24 (pow x 2))
(.f64 x (.f64 x #s(literal 1/24 binary64)))
(* (pow x 2) (- 1/24 (* 1/12 (/ 1 x))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1/12 binary64) x)))
(* (pow x 2) (- 1/24 (* 1/12 (/ 1 x))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1/12 binary64) x)))
(* (pow x 2) (- 1/24 (* 1/12 (/ 1 x))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1/12 binary64) x)))
(* 1/24 (pow x 2))
(.f64 x (.f64 x #s(literal 1/24 binary64)))
(* (pow x 2) (- 1/24 (* 1/12 (/ 1 x))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1/12 binary64) x)))
(* (pow x 2) (- 1/24 (* 1/12 (/ 1 x))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1/12 binary64) x)))
(* (pow x 2) (- 1/24 (* 1/12 (/ 1 x))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1/12 binary64) x)))

eval85.0ms (0.8%)

Compiler: Compiled 17449 to 2063 computations (88.2% saved)

prune87.0ms (0.8%)

Pruning

17 alts after pruning (10 fresh and 7 done)

	Pruned	Kept	Total
New	634	10	644
Fresh	0	0	0
Picked	0	3	3
Done	0	4	4
Total	634	17	651

Accuracy

100.0%

Counts

651 → 17

Alt Table

Click to see full alt table

Status	Accuracy	Program
	70.9%	(/.f64 x (/.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) #s(literal 1 binary64)) (-.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))))
	69.5%	(/.f64 x (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (.f64 #s(literal 1/4 binary64) (.f64 x x)))) #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 x x))) (-.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))))
	72.7%	(/.f64 x (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))))))
	69.0%	(/.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (*.f64 x (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1/12 binary64) x))))))
✓	69.8%	(/.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/12 binary64) (*.f64 x #s(literal 1/24 binary64))))))))
✓	69.3%	(/.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/12 binary64))))))
✓	72.7%	(/.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))))
	70.9%	(/.f64 x (.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))))
	22.4%	(/.f64 x (.f64 (.f64 x (*.f64 x x)) (-.f64 #s(literal 1/24 binary64) (/.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) x) (+.f64 (/.f64 (/.f64 #s(literal -1 binary64) x) x) #s(literal 1/12 binary64))) x))))
	2.8%	(/.f64 #s(literal 24 binary64) (*.f64 x x))
	69.2%	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/12 binary64))))) x))
✓	68.4%	(+.f64 (.f64 x (.f64 x #s(literal -1/2 binary64))) x)
	6.0%	(+.f64 #s(literal 2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 8 binary64) x) #s(literal -4 binary64)) x))
✓	100.0%	(log1p.f64 x)
✓	36.7%	(log.f64 (+.f64 #s(literal 1 binary64) x))
✓	69.3%	x
	7.2%	#s(literal 2 binary64)

Compiler

Compiled 563 to 246 computations (56.3% saved)

regimes45.0ms (0.4%)

Counts

24 → 1

Calls

Call 1

Inputs
#s(literal 2 binary64)
x
(/.f64 #s(literal 24 binary64) (*.f64 x x))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))))
(+.f64 (.f64 x (.f64 x #s(literal -1/2 binary64))) x)
(/.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))))
(+.f64 #s(literal 2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 8 binary64) x) #s(literal -4 binary64)) x))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64))))))
(+.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64))))) x)
(/.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/12 binary64))))))
(/.f64 x (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/12 binary64))))) x))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))))))
(/.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/12 binary64) (*.f64 x #s(literal 1/24 binary64))))))))
(/.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (*.f64 x (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1/12 binary64) x))))))
(/.f64 x (/.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) #s(literal 1 binary64)) (-.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))))
(.f64 x (+.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))) (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))) (*.f64 x x))))
(/.f64 x (.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))))
(/.f64 x (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal -1/4 binary64)))))))))
(/.f64 x (.f64 (.f64 x (*.f64 x x)) (-.f64 #s(literal 1/24 binary64) (/.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) x) (+.f64 (/.f64 (/.f64 #s(literal -1 binary64) x) x) #s(literal 1/12 binary64))) x))))
(/.f64 x (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (.f64 #s(literal 1/4 binary64) (.f64 x x)))) #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 x x))) (-.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))))
(.f64 x (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (.f64 x x))) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (.f64 x x))))) #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (.f64 x x)))) (-.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))))))))
(log1p.f64 x)
(log.f64 (+.f64 #s(literal 1 binary64) x))

Outputs
(log1p.f64 x)

Calls

3 calls:

30.0ms	(log.f64 (+.f64 #s(literal 1 binary64) x))
7.0ms	x
6.0ms	(+.f64 #s(literal 1 binary64) x)

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(log.f64 (+.f64 #s(literal 1 binary64) x))`
100.0%	1	`(+.f64 #s(literal 1 binary64) x)`

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes8.0ms (0.1%)

Counts

22 → 1

Calls

Call 1

Inputs
#s(literal 2 binary64)
x
(/.f64 #s(literal 24 binary64) (*.f64 x x))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))))
(+.f64 (.f64 x (.f64 x #s(literal -1/2 binary64))) x)
(/.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))))
(+.f64 #s(literal 2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 8 binary64) x) #s(literal -4 binary64)) x))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64))))))
(+.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64))))) x)
(/.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/12 binary64))))))
(/.f64 x (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/12 binary64))))) x))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))))))
(/.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/12 binary64) (*.f64 x #s(literal 1/24 binary64))))))))
(/.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (*.f64 x (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1/12 binary64) x))))))
(/.f64 x (/.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) #s(literal 1 binary64)) (-.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))))
(.f64 x (+.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))) (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))) (*.f64 x x))))
(/.f64 x (.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))))
(/.f64 x (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal -1/4 binary64)))))))))
(/.f64 x (.f64 (.f64 x (*.f64 x x)) (-.f64 #s(literal 1/24 binary64) (/.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) x) (+.f64 (/.f64 (/.f64 #s(literal -1 binary64) x) x) #s(literal 1/12 binary64))) x))))
(/.f64 x (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (.f64 #s(literal 1/4 binary64) (.f64 x x)))) #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 x x))) (-.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))))
(.f64 x (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (.f64 x x))) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (.f64 x x))))) #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (.f64 x x)))) (-.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))))))))

Outputs
(/.f64 x (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))))))

Calls

1 calls:

6.0ms

Results

Accuracy	Segments	Branch
72.7%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes32.0ms (0.3%)

Counts

10 → 1

Calls

Call 1

Inputs
#s(literal 2 binary64)
x
(/.f64 #s(literal 24 binary64) (*.f64 x x))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))))
(+.f64 (.f64 x (.f64 x #s(literal -1/2 binary64))) x)
(/.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))))
(+.f64 #s(literal 2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 8 binary64) x) #s(literal -4 binary64)) x))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64))))))
(+.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64))))) x)
(/.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/12 binary64))))))

Outputs
(/.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))))

Calls

1 calls:

31.0ms

Results

Accuracy	Segments	Branch
72.7%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes3.0ms (0%)

Counts

5 → 2

Calls

Call 1

Inputs
#s(literal 2 binary64)
x
(/.f64 #s(literal 24 binary64) (*.f64 x x))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))))
(+.f64 (.f64 x (.f64 x #s(literal -1/2 binary64))) x)

Outputs
(+.f64 (.f64 x (.f64 x #s(literal -1/2 binary64))) x)
#s(literal 2 binary64)

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
72.7%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0%)

Counts

4 → 2

Calls

Call 1

Inputs
#s(literal 2 binary64)
x
(/.f64 #s(literal 24 binary64) (*.f64 x x))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))))

Outputs
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))))
#s(literal 2 binary64)

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
72.7%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0%)

Counts

3 → 2

Calls

Call 1

Inputs
#s(literal 2 binary64)
x
(/.f64 #s(literal 24 binary64) (*.f64 x x))

Outputs
x
#s(literal 2 binary64)

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
72.2%	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
#s(literal 2 binary64)

Outputs
#s(literal 2 binary64)

Calls

1 calls:

1.0ms

Results

Accuracy	Segments	Branch
7.2%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

bsearch11.0ms (0.1%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
10.0ms	0.00033569682643571426	4.154303496615799

Results

6.0ms

128×

valid

Compiler

Compiled 105 to 79 computations (24.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 2.0ms

ival-add: 1.0ms (42.6% of total)

ival-log: 1.0ms (42.6% of total)

const: 0.0ms (0% of total)

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

bsearch16.0ms (0.1%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
15.0ms	0.00033569682643571426	4.154303496615799

Results

11.0ms

128×

valid

Compiler

Compiled 105 to 87 computations (17.1% saved)

Precisions

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

ival-log: 6.0ms (81.3% of total)

ival-add: 1.0ms (13.5% of total)

const: 0.0ms (0% of total)

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

bsearch11.0ms (0.1%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
10.0ms	0.00033569682643571426	4.154303496615799

Results

6.0ms

128×

valid

Compiler

Compiled 57 to 47 computations (17.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 2.0ms

ival-add: 1.0ms (42% of total)

ival-log: 1.0ms (42% of total)

const: 0.0ms (0% of total)

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

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary64`
6×	`+-commutative_binary64`
2×	`1-exp_binary64`
2×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	51
1	33	51

Stop Event

1×

saturated

Calls

Call 1

Inputs
(log1p.f64 x)
(/.f64 x (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))))))
(/.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))))
(if (<=.f64 x #s(literal 6530219459687219/4503599627370496 binary64)) (+.f64 (.f64 x (.f64 x #s(literal -1/2 binary64))) x) #s(literal 2 binary64))
(if (<=.f64 x #s(literal 6530219459687219/4503599627370496 binary64)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64)))) #s(literal 2 binary64))
(if (<=.f64 x #s(literal 2 binary64)) x #s(literal 2 binary64))
#s(literal 2 binary64)

Outputs
(log1p.f64 x)
(/.f64 x (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))))))
(/.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))))
(if (<=.f64 x #s(literal 6530219459687219/4503599627370496 binary64)) (+.f64 (.f64 x (.f64 x #s(literal -1/2 binary64))) x) #s(literal 2 binary64))
(if (<=.f64 x #s(literal 6530219459687219/4503599627370496 binary64)) (+.f64 x (.f64 x (.f64 x #s(literal -1/2 binary64)))) #s(literal 2 binary64))
(if (<=.f64 x #s(literal 6530219459687219/4503599627370496 binary64)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64)))) #s(literal 2 binary64))
(if (<=.f64 x #s(literal 2 binary64)) x #s(literal 2 binary64))
#s(literal 2 binary64)

soundness3.5s (32.7%)

Rules

4042×	`-lowering-.f32`
4042×	`-lowering-.f64`
3888×	`/-lowering-/.f32`
3888×	`/-lowering-/.f64`
3854×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	108
1	139	89
2	1286	89
0	8258	89
0	4	2
1	8	2
0	8	2
0	62	296
1	188	252
2	458	240
3	1230	236
4	3932	236
0	8232	236
0	244	2330
1	753	2121
2	2177	2015
3	6984	2011
0	8371	2011
0	201	1180
1	609	1043
2	1634	1000
3	4920	966
0	8205	966
0	20	110
1	137	90
2	1288	87
0	8126	87

Stop Event

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

Compiler

Compiled 251 to 173 computations (31.1% saved)

preprocess47.0ms (0.4%)

Compiler: Compiled 154 to 72 computations (53.2% saved)

analyze3.0ms (0%)

sample1.8s (16.7%)

preprocess16.0ms (0.2%)

explain150.0ms (1.4%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify3.0ms (0%)

localize311.0ms (2.9%)

series2.0ms (0%)

rewrite309.0ms (2.9%)

simplify318.0ms (3%)

eval81.0ms (0.8%)

prune32.0ms (0.3%)

simplify70.0ms (0.7%)

localize109.0ms (1%)

series11.0ms (0.1%)

rewrite401.0ms (3.7%)

simplify195.0ms (1.8%)

eval95.0ms (0.9%)

prune101.0ms (0.9%)

simplify256.0ms (2.4%)

localize286.0ms (2.7%)

series10.0ms (0.1%)

rewrite803.0ms (7.5%)

simplify286.0ms (2.7%)

eval338.0ms (3.2%)

prune186.0ms (1.7%)

simplify17.0ms (0.2%)

localize113.0ms (1.1%)

series12.0ms (0.1%)

rewrite301.0ms (2.8%)

simplify241.0ms (2.3%)

eval85.0ms (0.8%)

prune87.0ms (0.8%)

regimes45.0ms (0.4%)

regimes8.0ms (0.1%)

regimes32.0ms (0.3%)

regimes3.0ms (0%)

regimes2.0ms (0%)

regimes2.0ms (0%)

regimes1.0ms (0%)

bsearch11.0ms (0.1%)

bsearch16.0ms (0.1%)

bsearch11.0ms (0.1%)

simplify8.0ms (0.1%)

soundness3.5s (32.7%)

preprocess47.0ms (0.4%)

end0.0ms (0%)

Profiling