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 (103.1% of total)

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

const: 0.0ms (0% of total)

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

sample1.7s (24.3%)

Results

940.0ms	4123×	1	valid
420.0ms	1317×	2	valid
128.0ms	2816×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 1.1s

ival-log: 761.0ms (69.4% of total)

ival-add: 240.0ms (21.9% of total)

backward-pass: 77.0ms (7% of total)

const: 18.0ms (1.6% of total)

Bogosity

preprocess20.0ms (0.3%)

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)))

explain112.0ms (1.6%)

FPErrors

Click to see full error table

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

Results

45.0ms	240×	1	valid
35.0ms	96×	2	valid
10.0ms	176×	0	valid

Compiler

Compiled 27 to 14 computations (48.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 59.0ms

ival-log: 46.0ms (78.2% of total)

ival-add: 7.0ms (11.9% of total)

backward-pass: 5.0ms (8.5% of total)

const: 1.0ms (1.7% 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)

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Localize:

Found 1 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(log1p.f64 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	3
1	8	3
0	8	3

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(log (+ 1 x))
x

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

localize39.0ms (0.6%)

Localize:

Found 1 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(log1p.f64 x)

Results

28.0ms	168×	5	exit
5.0ms	88×	0	valid

Compiler

Compiled 5 to 3 computations (40% saved)

Precisions

Click to see histograms. Total time spent on operations: 28.0ms

compiled-spec: 13.0ms (46.5% of total)

ival-add: 8.0ms (28.6% of total)

ival-log: 4.0ms (14.3% of total)

backward-pass: 3.0ms (10.7% of total)

const: 0.0ms (0% of total)

series1.0ms (0%)

Counts

1 → 12

Calls

Call 1

Inputs
#<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))))>

Calls

3 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))

rewrite467.0ms (6.7%)

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	2
1	21	2
2	141	2
3	1093	2
0	8377	2

Stop Event

1×	iter limit
1×	node limit

Counts

1 → 69

Calls

Call 1

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

simplify156.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

1970×	`fmsub-define`
1904×	`sum3-define`
1846×	`fma-lowering-fma.f32`
1846×	`fma-lowering-fma.f64`
1776×	`fmm-def`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	59	133
1	178	111
2	443	105
3	1210	103
4	3925	96
0	8245	96

Stop Event

1×	iter limit
1×	node limit

Counts

12 → 12

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))))

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

eval9.0ms (0.1%)

Compiler: Compiled 2272 to 351 computations (84.6% saved)

prune25.0ms (0.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	77	4	81
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	77	5	82

Accuracy

100.0%

Counts

82 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	66.6%	(.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))))))))
▶	67.6%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64))))))
▶	66.4%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))))
✓	100.0%	(log1p.f64 x)
▶	67.7%	x

Compiler

Compiled 41 to 30 computations (26.8% saved)

simplify47.0ms (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)

localize216.0ms (3.1%)

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	99.9%	(.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	99.6%	(.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	99.4%	(*.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

187.0ms

256×

valid

Compiler

Compiled 128 to 21 computations (83.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 43.0ms

ival-mult: 30.0ms (70% of total)

ival-add: 8.0ms (18.7% of total)

...c/correct-round.rkt:119:19: 4.0ms (9.3% of total)

const: 1.0ms (2.3% of total)

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

series30.0ms (0.4%)

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
21.0ms	x	@	inf	(* x (+ 1 (* x -1/2)))
1.0ms	x	@	inf	(* x 1/3)
1.0ms	x	@	0	(* x (+ 1 (* x (+ -1/2 (* x 1/3)))))
1.0ms	x	@	0	(* x (+ 1 (* x -1/2)))
0.0ms	x	@	-inf	(* x (+ 1 (* x -1/2)))

rewrite581.0ms (8.3%)

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))))))
(/.f64 (neg.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x x)))))) (-.f64 #s(literal 0 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 (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)))))
(/.f64 (neg.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x x)))) x)) (-.f64 #s(literal 0 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 (neg.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 x x))) x)) (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64)))))
(/.f64 (+.f64 (.f64 (.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x x))) (.f64 x (.f64 x x))) (.f64 x (.f64 x x))) (+.f64 (.f64 (.f64 x (.f64 x #s(literal -1/2 binary64))) (.f64 x (.f64 x #s(literal -1/2 binary64)))) (-.f64 (.f64 x x) (.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 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))) 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 #s(literal 1 binary64) (+.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 #s(literal 1 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 #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 #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 #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 #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)))) (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 (/.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 1/4 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))
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(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))))
(/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/9 binary64) (-.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64)))) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 #s(literal 1/16 binary64) (.f64 x x)) (-.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64)))) #s(literal 3 binary64))) (+.f64 (.f64 (/.f64 #s(literal 1/9 binary64) (-.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64)))) (/.f64 #s(literal 1/9 binary64) (-.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))) (+.f64 (.f64 (/.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 #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 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))))))))
(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))))
(.f64 (+.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 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 #s(literal 1 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 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))))

simplify220.0ms (3.2%)

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)))

eval98.0ms (1.4%)

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

prune67.0ms (1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	673	5	678
Fresh	0	0	0
Picked	3	1	4
Done	0	1	1
Total	676	7	683

Accuracy

100.0%

Counts

683 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	35.4%	(/.f64 (-.f64 (.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 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 x x)))) (-.f64 x (.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))))
▶	66.6%	(+.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 x)) x)
▶	67.6%	(+.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64))))) x)
▶	66.4%	(+.f64 (.f64 x (.f64 x #s(literal -1/2 binary64))) x)
▶	67.6%	(.f64 x (+.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))) (.f64 #s(literal 1/3 binary64) (.f64 x x))))
✓	100.0%	(log1p.f64 x)
✓	67.7%	x

Compiler

Compiled 201 to 99 computations (50.7% saved)

simplify213.0ms (3.1%)

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(.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 x)) (.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	0	(*.f64 x x)
✓	cost-diff	128	(-.f64 (.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 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 x x))))
✓	cost-diff	2048	(/.f64 (-.f64 (.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 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 x x)))) (-.f64 x (.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	0	(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))
✓	cost-diff	0	(+.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 (+.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	0	(+.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 x)) x)
✓	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 #s(literal 1/3 binary64) (*.f64 x x)))
✓	cost-diff	128	(.f64 x (+.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))) (.f64 #s(literal 1/3 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

2120×	`-lowering-.f32`
2120×	`-lowering-.f64`
1644×	`fma-lowering-fma.f32`
1644×	`fma-lowering-fma.f64`
1508×	`sum3-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	28	241
1	100	209
2	304	207
3	1303	207
4	4525	207
0	8058	207

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

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

localize146.0ms (2.1%)

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(.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 x)) (.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	99.6%	(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))
✓	accuracy	85.5%	(-.f64 (.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 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 x x))))
✓	accuracy	42.0%	(/.f64 (-.f64 (.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 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 x x)))) (-.f64 x (.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	100.0%	(*.f64 x #s(literal -1/4 binary64))
✓	accuracy	100.0%	(+.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal -1/4 binary64)))
✓	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	99.6%	(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))
✓	accuracy	100.0%	(*.f64 x #s(literal -1/2 binary64))
✓	accuracy	100.0%	(+.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))) (.f64 #s(literal 1/3 binary64) (*.f64 x x)))
✓	accuracy	99.9%	(.f64 x (+.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))) (.f64 #s(literal 1/3 binary64) (.f64 x x))))
✓	accuracy	99.7%	(.f64 #s(literal 1/3 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	99.9%	(.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	99.4%	(*.f64 x #s(literal 1/3 binary64))

Results

84.0ms

256×

valid

Compiler

Compiled 324 to 29 computations (91% saved)

Precisions

Click to see histograms. Total time spent on operations: 40.0ms

ival-mult: 20.0ms (50.5% of total)

ival-add: 10.0ms (25.2% of total)

...c/correct-round.rkt:119:19: 4.0ms (10.1% of total)

ival-sub: 2.0ms (5% of total)

ival-div: 2.0ms (5% of total)

const: 1.0ms (2.5% of total)

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

series8.0ms (0.1%)

Counts

22 → 264

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

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 (- (* 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>
#<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 (* -1/2 (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))>
#<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 (* 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 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 (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* -1/4 (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (* (pow x 2) (- (* 1/3 x) 1/4))))>
#<alt (* (pow x 2) (+ 1 (* (pow x 2) (- (* x (+ 1/3 (* -13/36 x))) 1/4))))>
#<alt (* -1/16 (pow x 8))>
#<alt (* (pow x 8) (- (* 1/6 (/ 1 x)) 1/16))>
#<alt (* (pow x 8) (- (* 1/6 (/ 1 x)) (+ 1/16 (/ 13/36 (pow x 2)))))>
#<alt (* (pow x 8) (- (+ (* 1/6 (/ 1 x)) (* 1/3 (/ 1 (pow x 3)))) (+ 1/16 (/ 13/36 (pow x 2)))))>
#<alt (* -1/16 (pow x 8))>
#<alt (* (pow x 8) (- (* 1/6 (/ 1 x)) 1/16))>
#<alt (* (pow x 8) (- (* -1 (/ (- (* 13/36 (/ 1 x)) 1/6) x)) 1/16))>
#<alt (* (pow x 8) (- (* -1 (/ (- (* -1 (/ (- (* 1/3 (/ 1 x)) 13/36) x)) 1/6) x)) 1/16))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (* 1/4 (pow x 4))>
#<alt (* (pow x 4) (+ 1/4 (* -1/3 x)))>
#<alt (* (pow x 4) (+ 1/4 (* x (- (* 13/36 x) 1/3))))>
#<alt (* (pow x 4) (+ 1/4 (* x (- (* x (+ 13/36 (* -1/6 x))) 1/3))))>
#<alt (* 1/16 (pow x 8))>
#<alt (* (pow x 8) (- 1/16 (* 1/6 (/ 1 x))))>
#<alt (* (pow x 8) (- (+ 1/16 (/ 13/36 (pow x 2))) (* 1/6 (/ 1 x))))>
#<alt (* (pow x 8) (- (+ 1/16 (/ 13/36 (pow x 2))) (+ (* 1/6 (/ 1 x)) (* 1/3 (/ 1 (pow x 3))))))>
#<alt (* 1/16 (pow x 8))>
#<alt (* (pow x 8) (- 1/16 (* 1/6 (/ 1 x))))>
#<alt (* (pow x 8) (+ 1/16 (* -1 (/ (- 1/6 (* 13/36 (/ 1 x))) x))))>
#<alt (* (pow x 8) (+ 1/16 (* -1 (/ (+ 1/6 (* -1 (/ (- 13/36 (* 1/3 (/ 1 x))) x))) 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 (* 1/3 (pow x 2))>
#<alt (* 1/3 (pow x 2))>
#<alt (* 1/3 (pow x 2))>
#<alt (* 1/3 (pow x 2))>
#<alt (* 1/3 (pow x 2))>
#<alt (* 1/3 (pow x 2))>
#<alt (* 1/3 (pow x 2))>
#<alt (* 1/3 (pow x 2))>
#<alt (* 1/3 (pow x 2))>
#<alt (* 1/3 (pow x 2))>
#<alt (* 1/3 (pow x 2))>
#<alt (* 1/3 (pow x 2))>
#<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 (* -1/4 x)>
#<alt (* -1/4 x)>
#<alt (* -1/4 x)>
#<alt (* -1/4 x)>
#<alt (* -1/4 x)>
#<alt (* -1/4 x)>
#<alt (* -1/4 x)>
#<alt (* -1/4 x)>
#<alt (* -1/4 x)>
#<alt (* -1/4 x)>
#<alt (* -1/4 x)>
#<alt (* -1/4 x)>

Calls

66 calls:

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

rewrite520.0ms (7.5%)

Algorithm

1×	batch-egg-rewrite

Rules

4396×	`/-lowering-/.f32`
4396×	`/-lowering-/.f64`
4226×	`-lowering-.f32`
4226×	`-lowering-.f64`
2318×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	28	167
1	223	143
2	2175	142
0	9511	142

Stop Event

1×	iter limit
1×	node limit

Counts

22 → 821

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

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 x (.f64 x (.f64 x #s(literal 1/3 binary64)))) (.f64 x (+.f64 (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
(+.f64 (.f64 x (+.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) (.f64 x (.f64 x (*.f64 x #s(literal 1/3 binary64)))))
(+.f64 (.f64 x #s(literal 1 binary64)) (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))))))
(+.f64 (.f64 #s(literal 1 binary64) x) (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))))))
(-.f64 (/.f64 (.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))))) (.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 x x) (-.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 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) (.f64 x (+.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))) (-.f64 (.f64 x (+.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) (.f64 x (.f64 x (.f64 x #s(literal 1/3 binary64)))))) (/.f64 (.f64 (.f64 x (.f64 x (.f64 x #s(literal 1/3 binary64)))) (.f64 x (.f64 x (.f64 x #s(literal 1/3 binary64))))) (-.f64 (.f64 x (+.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) (.f64 x (.f64 x (.f64 x #s(literal 1/3 binary64)))))))
(-.f64 (/.f64 (.f64 x x) (-.f64 x (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))))))) (/.f64 (.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))))) (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64)))))) (-.f64 x (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))))))))
(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 x (+.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (.f64 x (.f64 x (.f64 x #s(literal 1/3 binary64)))))
(fma.f64 x (.f64 x (.f64 x #s(literal 1/3 binary64))) (.f64 x (+.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
(fma.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x x)) (.f64 x (+.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
(fma.f64 (.f64 x #s(literal 1/3 binary64)) (.f64 x x) (.f64 x (+.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 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 #s(literal 1 binary64) x (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64))))))
(fma.f64 (+.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) x (.f64 x (.f64 x (.f64 x #s(literal 1/3 binary64)))))
(fma.f64 (.f64 x x) (.f64 x #s(literal 1/3 binary64)) (.f64 x (+.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
(fma.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))) x)
(fma.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) x (.f64 x (+.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
(fma.f64 (.f64 x (.f64 x x)) #s(literal 1/3 binary64) (.f64 x (+.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
(fma.f64 (+.f64 (.f64 #s(literal -1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (.f64 x (-.f64 x (.f64 #s(literal -1/2 binary64) (.f64 x x)))))) (.f64 x (.f64 x (.f64 x #s(literal 1/3 binary64)))))
(fma.f64 (.f64 (.f64 x (+.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))) (-.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) x)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) x)) (.f64 x (.f64 x (.f64 x #s(literal 1/3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))))) (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64)))))) (.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 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))))) (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))))) x) (.f64 (.f64 x (+.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64)))) #s(literal 1 binary64))) (-.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))))) x))))
(/.f64 (+.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 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))))) (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64)))))))) (+.f64 (.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))))) (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64)))))) (.f64 x (-.f64 x (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64)))))))))
(/.f64 (+.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 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))))) (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64)))))))) (+.f64 (.f64 x x) (-.f64 (.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))))) (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64)))))) (.f64 x (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64)))))))))
(/.f64 (.f64 (.f64 x (+.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64)))) #s(literal 1 binary64))) (-.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))))) x)) (-.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))))) x))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 (.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))))) (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64)))))) (.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 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))))) (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64)))))))))))
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(.f64 (.f64 (.f64 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))))))) (+.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 #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))))))) x)
(.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 (.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 (exp.f64 (log.f64 (.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)))))))) (exp.f64 (log.f64 (.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 x #s(literal 1/3 binary64))
(*.f64 #s(literal 1/3 binary64) x)
(.f64 x (.f64 x #s(literal 1/3 binary64)))
(.f64 #s(literal 1/3 binary64) (.f64 x x))
(.f64 (.f64 x #s(literal 1/3 binary64)) x)
(.f64 (.f64 x x) #s(literal 1/3 binary64))
(+.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))
(-.f64 (/.f64 #s(literal 1/9 binary64) (-.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64)))) (/.f64 (.f64 (.f64 x x) #s(literal 1/16 binary64)) (-.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64)))))
(-.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/16 binary64)) (-.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 (+.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 #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 #s(literal 1/9 binary64) (.f64 (*.f64 x x) #s(literal 1/16 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 (.f64 x x) #s(literal 1/16 binary64)) (-.f64 #s(literal 1/9 binary64) (.f64 #s(literal -1/12 binary64) x))))
(/.f64 (-.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) #s(literal 1/16 binary64))) (-.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal -1/4 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.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 #s(literal 1/27 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal -1/64 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))) (-.f64 #s(literal 1/9 binary64) (.f64 (*.f64 x x) #s(literal 1/16 binary64))))))
(/.f64 (neg.f64 (+.f64 #s(literal 1/27 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal -1/64 binary64)))) (neg.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 (neg.f64 (+.f64 #s(literal 1/27 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal -1/64 binary64)))) (neg.f64 (+.f64 (.f64 (.f64 x x) #s(literal 1/16 binary64)) (-.f64 #s(literal 1/9 binary64) (.f64 #s(literal -1/12 binary64) x)))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) #s(literal 1/16 binary64)))) (neg.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal -1/4 binary64)))))
(/.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/16 binary64)) #s(literal 1/9 binary64)) (-.f64 (*.f64 x #s(literal -1/4 binary64)) #s(literal 1/3 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 (.f64 x x) #s(literal 1/16 binary64)))) (.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 (neg.f64 (neg.f64 (+.f64 #s(literal 1/27 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal -1/64 binary64))))) (neg.f64 (neg.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 (neg.f64 (neg.f64 (-.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) #s(literal 1/16 binary64))))) (neg.f64 (neg.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal -1/4 binary64))))))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/16 binary64)) #s(literal 1/9 binary64))) (neg.f64 (-.f64 (*.f64 x #s(literal -1/4 binary64)) #s(literal 1/3 binary64))))
(pow.f64 (/.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 #s(literal 1/27 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal -1/64 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))) (-.f64 #s(literal 1/9 binary64) (.f64 (*.f64 x x) #s(literal 1/16 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 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 1/9 binary64) (.f64 (.f64 x x) #s(literal 1/16 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64)))))
(*.f64 x #s(literal -1/4 binary64))
(*.f64 #s(literal -1/4 binary64) x)

simplify215.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

2508×	`-lowering-.f32`
2508×	`-lowering-.f64`
1662×	`fnmadd-define`
1450×	`+-lowering-+.f64`
1450×	`+-lowering-+.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	177	1793
1	554	1621
2	1558	1511
3	4905	1507
0	8209	1507

Stop Event

1×	iter limit
1×	node limit

Counts

264 → 264

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 (- (* 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
(+ 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))
(* -1/2 (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))
-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)
(* 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))
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))
(pow x 2)
(* (pow x 2) (+ 1 (* -1/4 (pow x 2))))
(* (pow x 2) (+ 1 (* (pow x 2) (- (* 1/3 x) 1/4))))
(* (pow x 2) (+ 1 (* (pow x 2) (- (* x (+ 1/3 (* -13/36 x))) 1/4))))
(* -1/16 (pow x 8))
(* (pow x 8) (- (* 1/6 (/ 1 x)) 1/16))
(* (pow x 8) (- (* 1/6 (/ 1 x)) (+ 1/16 (/ 13/36 (pow x 2)))))
(* (pow x 8) (- (+ (* 1/6 (/ 1 x)) (* 1/3 (/ 1 (pow x 3)))) (+ 1/16 (/ 13/36 (pow x 2)))))
(* -1/16 (pow x 8))
(* (pow x 8) (- (* 1/6 (/ 1 x)) 1/16))
(* (pow x 8) (- (* -1 (/ (- (* 13/36 (/ 1 x)) 1/6) x)) 1/16))
(* (pow x 8) (- (* -1 (/ (- (* -1 (/ (- (* 1/3 (/ 1 x)) 13/36) x)) 1/6) x)) 1/16))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 1/4 (pow x 4))
(* (pow x 4) (+ 1/4 (* -1/3 x)))
(* (pow x 4) (+ 1/4 (* x (- (* 13/36 x) 1/3))))
(* (pow x 4) (+ 1/4 (* x (- (* x (+ 13/36 (* -1/6 x))) 1/3))))
(* 1/16 (pow x 8))
(* (pow x 8) (- 1/16 (* 1/6 (/ 1 x))))
(* (pow x 8) (- (+ 1/16 (/ 13/36 (pow x 2))) (* 1/6 (/ 1 x))))
(* (pow x 8) (- (+ 1/16 (/ 13/36 (pow x 2))) (+ (* 1/6 (/ 1 x)) (* 1/3 (/ 1 (pow x 3))))))
(* 1/16 (pow x 8))
(* (pow x 8) (- 1/16 (* 1/6 (/ 1 x))))
(* (pow x 8) (+ 1/16 (* -1 (/ (- 1/6 (* 13/36 (/ 1 x))) x))))
(* (pow x 8) (+ 1/16 (* -1 (/ (+ 1/6 (* -1 (/ (- 13/36 (* 1/3 (/ 1 x))) x))) 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)
(* 1/3 (pow x 2))
(* 1/3 (pow x 2))
(* 1/3 (pow x 2))
(* 1/3 (pow x 2))
(* 1/3 (pow x 2))
(* 1/3 (pow x 2))
(* 1/3 (pow x 2))
(* 1/3 (pow x 2))
(* 1/3 (pow x 2))
(* 1/3 (pow x 2))
(* 1/3 (pow x 2))
(* 1/3 (pow x 2))
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)))))
(* -1/4 x)
(* -1/4 x)
(* -1/4 x)
(* -1/4 x)
(* -1/4 x)
(* -1/4 x)
(* -1/4 x)
(* -1/4 x)
(* -1/4 x)
(* -1/4 x)
(* -1/4 x)
(* -1/4 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 (- (* 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 #s(literal 1/3 binary64) (.f64 x (*.f64 x x)))
(* (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 #s(literal 1/3 binary64) (.f64 x (*.f64 x x)))
(* -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))))))
(* -1/2 (pow x 2))
(.f64 #s(literal -1/2 binary64) (.f64 x x))
(* (pow x 2) (- (* 1/3 x) 1/2))
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(.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 x (.f64 x (.f64 (.f64 x x) #s(literal -1/4 binary64))))
(* (pow x 4) (- (* 1/3 (/ 1 x)) 1/4))
(.f64 (.f64 x (.f64 x (.f64 x x))) (+.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 (.f64 x (.f64 x (.f64 x x))) (-.f64 #s(literal -1/4 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal -1/3 binary64)) x)))
(* (pow x 4) (- (+ (* 1/3 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/4 (/ 1/2 (pow x 2)))))
(.f64 (.f64 x (.f64 x (.f64 x x))) (+.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 x (.f64 x (.f64 (.f64 x x) #s(literal -1/4 binary64))))
(* (pow x 4) (- (* 1/3 (/ 1 x)) 1/4))
(.f64 (.f64 x (.f64 x (.f64 x x))) (+.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 (.f64 x (.f64 x (.f64 x x))) (-.f64 #s(literal -1/4 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal -1/3 binary64)) x)))
(* (pow x 4) (- (* -1 (/ (- (* -1 (/ (- (/ 1 x) 1/2) x)) 1/3) x)) 1/4))
(.f64 (.f64 x (.f64 x (.f64 x x))) (+.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)))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -1/4 (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -1/4 binary64))))
(* (pow x 2) (+ 1 (* (pow x 2) (- (* 1/3 x) 1/4))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 (*.f64 x #s(literal 1/3 binary64)) #s(literal -1/4 binary64)))))
(* (pow x 2) (+ 1 (* (pow x 2) (- (* x (+ 1/3 (* -13/36 x))) 1/4))))
(.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/4 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -13/36 binary64))))))))))
(* -1/16 (pow x 8))
(*.f64 #s(literal -1/16 binary64) (pow.f64 x #s(literal 8 binary64)))
(* (pow x 8) (- (* 1/6 (/ 1 x)) 1/16))
(*.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 #s(literal -1/16 binary64) (/.f64 #s(literal 1/6 binary64) x)))
(* (pow x 8) (- (* 1/6 (/ 1 x)) (+ 1/16 (/ 13/36 (pow x 2)))))
(*.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 #s(literal -1/16 binary64) (/.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -13/36 binary64) x)) x)))
(* (pow x 8) (- (+ (* 1/6 (/ 1 x)) (* 1/3 (/ 1 (pow x 3)))) (+ 1/16 (/ 13/36 (pow x 2)))))
(*.f64 (pow.f64 x #s(literal 8 binary64)) (-.f64 #s(literal -1/16 binary64) (/.f64 (-.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) x) #s(literal -13/36 binary64)) x)) x)))
(* -1/16 (pow x 8))
(*.f64 #s(literal -1/16 binary64) (pow.f64 x #s(literal 8 binary64)))
(* (pow x 8) (- (* 1/6 (/ 1 x)) 1/16))
(*.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 #s(literal -1/16 binary64) (/.f64 #s(literal 1/6 binary64) x)))
(* (pow x 8) (- (* -1 (/ (- (* 13/36 (/ 1 x)) 1/6) x)) 1/16))
(*.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 #s(literal -1/16 binary64) (/.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -13/36 binary64) x)) x)))
(* (pow x 8) (- (* -1 (/ (- (* -1 (/ (- (* 1/3 (/ 1 x)) 13/36) x)) 1/6) x)) 1/16))
(*.f64 (pow.f64 x #s(literal 8 binary64)) (-.f64 #s(literal -1/16 binary64) (/.f64 (-.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) x) #s(literal -13/36 binary64)) x)) x)))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* 1/4 (pow x 4))
(.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/4 binary64))
(* (pow x 4) (+ 1/4 (* -1/3 x)))
(.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/3 binary64))))
(* (pow x 4) (+ 1/4 (* x (- (* 13/36 x) 1/3))))
(.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 #s(literal 1/4 binary64) (.f64 x (+.f64 #s(literal -1/3 binary64) (.f64 x #s(literal 13/36 binary64))))))
(* (pow x 4) (+ 1/4 (* x (- (* x (+ 13/36 (* -1/6 x))) 1/3))))
(.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 #s(literal 1/4 binary64) (.f64 x (+.f64 #s(literal -1/3 binary64) (.f64 x (+.f64 #s(literal 13/36 binary64) (*.f64 x #s(literal -1/6 binary64))))))))
(* 1/16 (pow x 8))
(*.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1/16 binary64))
(* (pow x 8) (- 1/16 (* 1/6 (/ 1 x))))
(*.f64 (pow.f64 x #s(literal 8 binary64)) (-.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/6 binary64) x)))
(* (pow x 8) (- (+ 1/16 (/ 13/36 (pow x 2))) (* 1/6 (/ 1 x))))
(*.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 #s(literal 1/16 binary64) (/.f64 (+.f64 (/.f64 #s(literal 13/36 binary64) x) #s(literal -1/6 binary64)) x)))
(* (pow x 8) (- (+ 1/16 (/ 13/36 (pow x 2))) (+ (* 1/6 (/ 1 x)) (* 1/3 (/ 1 (pow x 3))))))
(*.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 #s(literal 1/16 binary64) (/.f64 (-.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) x) #s(literal -13/36 binary64)) x)) x)))
(* 1/16 (pow x 8))
(*.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1/16 binary64))
(* (pow x 8) (- 1/16 (* 1/6 (/ 1 x))))
(*.f64 (pow.f64 x #s(literal 8 binary64)) (-.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1/6 binary64) x)))
(* (pow x 8) (+ 1/16 (* -1 (/ (- 1/6 (* 13/36 (/ 1 x))) x))))
(*.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 #s(literal 1/16 binary64) (/.f64 (+.f64 (/.f64 #s(literal 13/36 binary64) x) #s(literal -1/6 binary64)) x)))
(* (pow x 8) (+ 1/16 (* -1 (/ (+ 1/6 (* -1 (/ (- 13/36 (* 1/3 (/ 1 x))) x))) x))))
(*.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 #s(literal 1/16 binary64) (/.f64 (-.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/3 binary64) x) #s(literal -13/36 binary64)) x)) x)))
(* 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 (pow x 2))
(.f64 x (.f64 x #s(literal 1/3 binary64)))
(* 1/3 (pow x 2))
(.f64 x (.f64 x #s(literal 1/3 binary64)))
(* 1/3 (pow x 2))
(.f64 x (.f64 x #s(literal 1/3 binary64)))
(* 1/3 (pow x 2))
(.f64 x (.f64 x #s(literal 1/3 binary64)))
(* 1/3 (pow x 2))
(.f64 x (.f64 x #s(literal 1/3 binary64)))
(* 1/3 (pow x 2))
(.f64 x (.f64 x #s(literal 1/3 binary64)))
(* 1/3 (pow x 2))
(.f64 x (.f64 x #s(literal 1/3 binary64)))
(* 1/3 (pow x 2))
(.f64 x (.f64 x #s(literal 1/3 binary64)))
(* 1/3 (pow x 2))
(.f64 x (.f64 x #s(literal 1/3 binary64)))
(* 1/3 (pow x 2))
(.f64 x (.f64 x #s(literal 1/3 binary64)))
(* 1/3 (pow x 2))
(.f64 x (.f64 x #s(literal 1/3 binary64)))
(* 1/3 (pow x 2))
(.f64 x (.f64 x #s(literal 1/3 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)))
(* -1/4 x)
(*.f64 x #s(literal -1/4 binary64))
(* -1/4 x)
(*.f64 x #s(literal -1/4 binary64))
(* -1/4 x)
(*.f64 x #s(literal -1/4 binary64))
(* -1/4 x)
(*.f64 x #s(literal -1/4 binary64))
(* -1/4 x)
(*.f64 x #s(literal -1/4 binary64))
(* -1/4 x)
(*.f64 x #s(literal -1/4 binary64))
(* -1/4 x)
(*.f64 x #s(literal -1/4 binary64))
(* -1/4 x)
(*.f64 x #s(literal -1/4 binary64))
(* -1/4 x)
(*.f64 x #s(literal -1/4 binary64))
(* -1/4 x)
(*.f64 x #s(literal -1/4 binary64))
(* -1/4 x)
(*.f64 x #s(literal -1/4 binary64))
(* -1/4 x)
(*.f64 x #s(literal -1/4 binary64))

eval254.0ms (3.6%)

Compiler: Compiled 91234 to 3233 computations (96.5% saved)

prune138.0ms (2%)

Pruning

9 alts after pruning (4 fresh and 5 done)

	Pruned	Kept	Total
New	1707	4	1711
Fresh	0	0	0
Picked	2	3	5
Done	0	2	2
Total	1709	9	1718

Accuracy

100.0%

Counts

1718 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	35.9%	(/.f64 (-.f64 (.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 x x)) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))) (.f64 x x)))) (-.f64 x (.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))))
▶	36.2%	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/3 binary64))))) (-.f64 x (.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))))
▶	36.2%	(/.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 (.f64 x #s(literal 1/3 binary64)) #s(literal -1/4 binary64))))) (-.f64 x (.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))))
✓	66.6%	(+.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 x)) x)
✓	67.6%	(+.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64))))) x)
✓	66.4%	(+.f64 (.f64 x (.f64 x #s(literal -1/2 binary64))) x)
▶	67.6%	(.f64 x (+.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64)) (.f64 x #s(literal -1/2 binary64))))
✓	100.0%	(log1p.f64 x)
✓	67.7%	x

Compiler

Compiled 165 to 92 computations (44.2% saved)

simplify264.0ms (3.8%)

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

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

Rules

3072×	`-lowering-.f32`
3072×	`-lowering-.f64`
2192×	`fma-lowering-fma.f32`
2192×	`fma-lowering-fma.f64`
1994×	`fmsub-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	37	439
1	140	378
2	514	365
3	2217	365
4	5526	365
0	8081	365

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize239.0ms (3.4%)

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(.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 x)) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))) (.f64 x x)))
✓	accuracy	99.6%	(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))
✓	accuracy	99.4%	(*.f64 x #s(literal 1/3 binary64))
✓	accuracy	46.2%	(/.f64 (-.f64 (.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 x x)) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))) (.f64 x x)))) (-.f64 x (.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 x (.f64 x x))
✓	accuracy	99.6%	(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))
✓	accuracy	99.4%	(*.f64 x #s(literal -1/3 binary64))
✓	accuracy	45.7%	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/3 binary64))))) (-.f64 x (.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 x x) (+.f64 (*.f64 x #s(literal 1/3 binary64)) #s(literal -1/4 binary64)))
✓	accuracy	99.6%	(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64))))
✓	accuracy	99.4%	(*.f64 x #s(literal 1/3 binary64))
✓	accuracy	45.7%	(/.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 (.f64 x #s(literal 1/3 binary64)) #s(literal -1/4 binary64))))) (-.f64 x (.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	100.0%	(+.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64)) (*.f64 x #s(literal -1/2 binary64)))
✓	accuracy	99.9%	(.f64 x (+.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64)) (.f64 x #s(literal -1/2 binary64))))
✓	accuracy	99.8%	(.f64 x (.f64 x #s(literal 1/3 binary64)))
✓	accuracy	99.4%	(*.f64 x #s(literal 1/3 binary64))

Results

108.0ms

256×

valid

Compiler

Compiled 495 to 38 computations (92.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 57.0ms

ival-mult: 26.0ms (45.6% of total)

ival-add: 14.0ms (24.6% of total)

...c/correct-round.rkt:119:19: 8.0ms (14% of total)

ival-div: 5.0ms (8.8% of total)

ival-sub: 4.0ms (7% of total)

const: 1.0ms (1.8% of total)

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

series11.0ms (0.2%)

Counts

19 → 228

Calls

Call 1

Inputs
#<alt (* x (+ (+ (* x (* x 1/3)) 1) (* x -1/2)))>
#<alt (+ (+ (* x (* x 1/3)) 1) (* x -1/2))>
#<alt (+ (* x (* x 1/3)) 1)>
#<alt (* x (* x 1/3))>
#<alt (/ (* (* x x) (+ 1 (* (* x x) (+ (* x 1/3) -1/4)))) (- x (* (+ -1/2 (* x (+ 1/3 (* x -1/4)))) (* x x))))>
#<alt (* (* x x) (+ 1 (* (* x x) (+ (* x 1/3) -1/4))))>
#<alt (* x x)>
#<alt (+ 1 (* (* x x) (+ (* x 1/3) -1/4)))>
#<alt (/ (- (* x x) (* (* x (* x (* x x))) (+ 1/4 (* x -1/3)))) (- x (* (+ -1/2 (* x (+ 1/3 (* x -1/4)))) (* x x))))>
#<alt (- (* x x) (* (* x (* x (* x x))) (+ 1/4 (* x -1/3))))>
#<alt (* (* x (* x (* x x))) (+ 1/4 (* x -1/3)))>
#<alt (/ (- (* x x) (* (* (+ -1/2 (* x (+ 1/3 (* x -1/4)))) (* x x)) (* (+ -1/2 (* x 1/3)) (* x x)))) (- x (* (+ -1/2 (* x (+ 1/3 (* x -1/4)))) (* x x))))>
#<alt (- (* x x) (* (* (+ -1/2 (* x (+ 1/3 (* x -1/4)))) (* x x)) (* (+ -1/2 (* x 1/3)) (* x x))))>
#<alt (* (* (+ -1/2 (* x (+ 1/3 (* x -1/4)))) (* x x)) (* (+ -1/2 (* x 1/3)) (* x x)))>
#<alt (* x 1/3)>
#<alt (* x (+ 1/3 (* x -1/4)))>
#<alt (* (* x x) (+ (* x 1/3) -1/4))>
#<alt (* x -1/3)>
#<alt (* x (* 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>
#<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>
#<alt (+ 1 (* 1/3 (pow x 2)))>
#<alt (+ 1 (* 1/3 (pow x 2)))>
#<alt (+ 1 (* 1/3 (pow x 2)))>
#<alt (* 1/3 (pow x 2))>
#<alt (* (pow x 2) (+ 1/3 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/3 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/3 (/ 1 (pow x 2))))>
#<alt (* 1/3 (pow x 2))>
#<alt (* (pow x 2) (+ 1/3 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/3 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/3 (/ 1 (pow x 2))))>
#<alt (* 1/3 (pow x 2))>
#<alt (* 1/3 (pow x 2))>
#<alt (* 1/3 (pow x 2))>
#<alt (* 1/3 (pow x 2))>
#<alt (* 1/3 (pow x 2))>
#<alt (* 1/3 (pow x 2))>
#<alt (* 1/3 (pow x 2))>
#<alt (* 1/3 (pow x 2))>
#<alt (* 1/3 (pow x 2))>
#<alt (* 1/3 (pow x 2))>
#<alt (* 1/3 (pow x 2))>
#<alt (* 1/3 (pow x 2))>
#<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 (* 4/3 x)>
#<alt (* x (+ 4/3 (* 7/9 (/ 1 x))))>
#<alt (* x (- (+ 4/3 (* 7/9 (/ 1 x))) (/ 44/27 (pow x 2))))>
#<alt (* x (+ 4/3 (+ (* -1 (/ (+ 44/27 (* 410/81 (/ 1 x))) (pow x 2))) (* 7/9 (/ 1 x)))))>
#<alt (* 4/3 x)>
#<alt (* x (+ 4/3 (* 7/9 (/ 1 x))))>
#<alt (* -1 (* x (- (* -1 (/ (- 7/9 (* 44/27 (/ 1 x))) x)) 4/3)))>
#<alt (* -1 (* x (- (* -1 (/ (+ 7/9 (* -1 (/ (+ 44/27 (* 410/81 (/ 1 x))) x))) x)) 4/3)))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* -1/4 (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (* (pow x 2) (- (* 1/3 x) 1/4))))>
#<alt (* (pow x 2) (+ 1 (* (pow x 2) (- (* 1/3 x) 1/4))))>
#<alt (* 1/3 (pow x 5))>
#<alt (* (pow x 5) (- 1/3 (* 1/4 (/ 1 x))))>
#<alt (* (pow x 5) (- (+ 1/3 (/ 1 (pow x 3))) (* 1/4 (/ 1 x))))>
#<alt (* (pow x 5) (- (+ 1/3 (/ 1 (pow x 3))) (* 1/4 (/ 1 x))))>
#<alt (* 1/3 (pow x 5))>
#<alt (* -1 (* (pow x 5) (- (* 1/4 (/ 1 x)) 1/3)))>
#<alt (* -1 (* (pow x 5) (- (* -1 (/ (- (/ 1 (pow x 2)) 1/4) x)) 1/3)))>
#<alt (* -1 (* (pow x 5) (- (* -1 (/ (- (/ 1 (pow x 2)) 1/4) x)) 1/3)))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt 1>
#<alt (+ 1 (* -1/4 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (* 1/3 x) 1/4)))>
#<alt (+ 1 (* (pow x 2) (- (* 1/3 x) 1/4)))>
#<alt (* 1/3 (pow x 3))>
#<alt (* (pow x 3) (- 1/3 (* 1/4 (/ 1 x))))>
#<alt (* (pow x 3) (- (+ 1/3 (/ 1 (pow x 3))) (* 1/4 (/ 1 x))))>
#<alt (* (pow x 3) (- (+ 1/3 (/ 1 (pow x 3))) (* 1/4 (/ 1 x))))>
#<alt (* 1/3 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- (* 1/4 (/ 1 x)) 1/3)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (- (/ 1 (pow x 2)) 1/4) x)) 1/3)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (- (/ 1 (pow x 2)) 1/4) 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 (* 4/3 x)>
#<alt (* x (+ 4/3 (* 7/9 (/ 1 x))))>
#<alt (* x (- (+ 4/3 (* 7/9 (/ 1 x))) (/ 44/27 (pow x 2))))>
#<alt (* x (+ 4/3 (+ (* -1 (/ (+ 44/27 (* 410/81 (/ 1 x))) (pow x 2))) (* 7/9 (/ 1 x)))))>
#<alt (* 4/3 x)>
#<alt (* x (+ 4/3 (* 7/9 (/ 1 x))))>
#<alt (* -1 (* x (- (* -1 (/ (- 7/9 (* 44/27 (/ 1 x))) x)) 4/3)))>
#<alt (* -1 (* x (- (* -1 (/ (+ 7/9 (* -1 (/ (+ 44/27 (* 410/81 (/ 1 x))) x))) x)) 4/3)))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* -1/4 (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (* (pow x 2) (- (* 1/3 x) 1/4))))>
#<alt (* (pow x 2) (+ 1 (* (pow x 2) (- (* 1/3 x) 1/4))))>
#<alt (* 1/3 (pow x 5))>
#<alt (* (pow x 5) (- 1/3 (* 1/4 (/ 1 x))))>
#<alt (* (pow x 5) (- (+ 1/3 (/ 1 (pow x 3))) (* 1/4 (/ 1 x))))>
#<alt (* (pow x 5) (- (+ 1/3 (/ 1 (pow x 3))) (* 1/4 (/ 1 x))))>
#<alt (* 1/3 (pow x 5))>
#<alt (* -1 (* (pow x 5) (- (* 1/4 (/ 1 x)) 1/3)))>
#<alt (* -1 (* (pow x 5) (- (* -1 (/ (- (/ 1 (pow x 2)) 1/4) x)) 1/3)))>
#<alt (* -1 (* (pow x 5) (- (* -1 (/ (- (/ 1 (pow x 2)) 1/4) x)) 1/3)))>
#<alt (* 1/4 (pow x 4))>
#<alt (* (pow x 4) (+ 1/4 (* -1/3 x)))>
#<alt (* (pow x 4) (+ 1/4 (* -1/3 x)))>
#<alt (* (pow x 4) (+ 1/4 (* -1/3 x)))>
#<alt (* -1/3 (pow x 5))>
#<alt (* (pow x 5) (- (* 1/4 (/ 1 x)) 1/3))>
#<alt (* (pow x 5) (- (* 1/4 (/ 1 x)) 1/3))>
#<alt (* (pow x 5) (- (* 1/4 (/ 1 x)) 1/3))>
#<alt (* -1/3 (pow x 5))>
#<alt (* -1 (* (pow x 5) (- 1/3 (* 1/4 (/ 1 x)))))>
#<alt (* -1 (* (pow x 5) (- 1/3 (* 1/4 (/ 1 x)))))>
#<alt (* -1 (* (pow x 5) (- 1/3 (* 1/4 (/ 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 (* 1/3 (pow x 3))>
#<alt (* (pow x 3) (- 1/3 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (+ 1/3 (* -1 (/ (+ 1/2 (* 4/3 (/ 1 (pow x 2)))) x))))>
#<alt (* (pow x 3) (- (+ 1/3 (* 2/9 (/ 1 (pow x 4)))) (+ (* 1/2 (/ 1 x)) (/ 4/3 (pow x 3)))))>
#<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)) (/ 4/3 (pow x 3))) 1/3)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (- (/ 2/9 (pow x 3)) (+ 1/2 (* 4/3 (/ 1 (pow x 2))))) x)) 1/3)))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* -1/4 (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (* (pow x 2) (- (* 1/3 x) 1/4))))>
#<alt (* (pow x 2) (+ 1 (* (pow x 2) (- (* x (+ 1/3 (* -17/72 x))) 1/4))))>
#<alt (* 1/12 (pow x 7))>
#<alt (* (pow x 7) (- 1/12 (* 17/72 (/ 1 x))))>
#<alt (* (pow x 7) (- (+ 1/12 (/ 1/3 (pow x 2))) (* 17/72 (/ 1 x))))>
#<alt (* (pow x 7) (- (+ 1/12 (/ 1/3 (pow x 2))) (+ (* 17/72 (/ 1 x)) (* 1/4 (/ 1 (pow x 3))))))>
#<alt (* 1/12 (pow x 7))>
#<alt (* -1 (* (pow x 7) (- (* 17/72 (/ 1 x)) 1/12)))>
#<alt (* -1 (* (pow x 7) (- (* -1 (/ (- (* 1/3 (/ 1 x)) 17/72) x)) 1/12)))>
#<alt (* -1 (* (pow x 7) (- (* -1 (/ (- (* -1 (/ (- (* 1/4 (/ 1 x)) 1/3) x)) 17/72) x)) 1/12)))>
#<alt (* 1/4 (pow x 4))>
#<alt (* (pow x 4) (+ 1/4 (* -1/3 x)))>
#<alt (* (pow x 4) (+ 1/4 (* x (- (* 17/72 x) 1/3))))>
#<alt (* (pow x 4) (+ 1/4 (* x (- (* x (+ 17/72 (* -1/12 x))) 1/3))))>
#<alt (* -1/12 (pow x 7))>
#<alt (* (pow x 7) (- (* 17/72 (/ 1 x)) 1/12))>
#<alt (* (pow x 7) (- (* 17/72 (/ 1 x)) (+ 1/12 (/ 1/3 (pow x 2)))))>
#<alt (* (pow x 7) (- (+ (* 17/72 (/ 1 x)) (* 1/4 (/ 1 (pow x 3)))) (+ 1/12 (/ 1/3 (pow x 2)))))>
#<alt (* -1/12 (pow x 7))>
#<alt (* -1 (* (pow x 7) (- 1/12 (* 17/72 (/ 1 x)))))>
#<alt (* -1 (* (pow x 7) (+ 1/12 (* -1 (/ (- 17/72 (* 1/3 (/ 1 x))) x)))))>
#<alt (* -1 (* (pow x 7) (+ 1/12 (* -1 (/ (+ 17/72 (* -1 (/ (- 1/3 (* 1/4 (/ 1 x))) x))) 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 (* 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 (* -1/4 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/3 x) 1/4))>
#<alt (* (pow x 2) (- (* 1/3 x) 1/4))>
#<alt (* (pow x 2) (- (* 1/3 x) 1/4))>
#<alt (* 1/3 (pow x 3))>
#<alt (* (pow x 3) (- 1/3 (* 1/4 (/ 1 x))))>
#<alt (* (pow x 3) (- 1/3 (* 1/4 (/ 1 x))))>
#<alt (* (pow x 3) (- 1/3 (* 1/4 (/ 1 x))))>
#<alt (* 1/3 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- (* 1/4 (/ 1 x)) 1/3)))>
#<alt (* -1 (* (pow x 3) (- (* 1/4 (/ 1 x)) 1/3)))>
#<alt (* -1 (* (pow x 3) (- (* 1/4 (/ 1 x)) 1/3)))>
#<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 (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>

Calls

57 calls:

Time	Variable		Point	Expression
2.0ms	x	@	0	(* (* (+ -1/2 (* x (+ 1/3 (* x -1/4)))) (* x x)) (* (+ -1/2 (* x 1/3)) (* x x)))
0.0ms	x	@	inf	(/ (- (* x x) (* (* (+ -1/2 (* x (+ 1/3 (* x -1/4)))) (* x x)) (* (+ -1/2 (* x 1/3)) (* x x)))) (- x (* (+ -1/2 (* x (+ 1/3 (* x -1/4)))) (* x x))))
0.0ms	x	@	inf	(* (* (+ -1/2 (* x (+ 1/3 (* x -1/4)))) (* x x)) (* (+ -1/2 (* x 1/3)) (* x x)))
0.0ms	x	@	-inf	(/ (- (* x x) (* (* (+ -1/2 (* x (+ 1/3 (* x -1/4)))) (* x x)) (* (+ -1/2 (* x 1/3)) (* x x)))) (- x (* (+ -1/2 (* x (+ 1/3 (* x -1/4)))) (* x x))))
0.0ms	x	@	-inf	(/ (* (* x x) (+ 1 (* (* x x) (+ (* x 1/3) -1/4)))) (- x (* (+ -1/2 (* x (+ 1/3 (* x -1/4)))) (* x x))))

rewrite371.0ms (5.3%)

Algorithm

1×	batch-egg-rewrite

Rules

3516×	`-lowering-.f32`
3516×	`-lowering-.f64`
2466×	`/-lowering-/.f32`
2466×	`/-lowering-/.f64`
1560×	`pow-lowering-pow.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	37	241
1	304	204
2	2941	197
0	8356	197

Stop Event

1×	iter limit
1×	node limit

Counts

19 → 486

Calls

Call 1

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

Outputs
(+.f64 (.f64 x (.f64 x #s(literal -1/2 binary64))) (.f64 x (+.f64 (.f64 x (*.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64))))
(+.f64 (.f64 x (.f64 x (.f64 x #s(literal 1/3 binary64)))) (.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal -1/2 binary64)))))
(+.f64 (.f64 x (.f64 x (.f64 x #s(literal 1/3 binary64)))) (.f64 (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal -1/2 binary64))) x))
(+.f64 (.f64 x (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64))) (.f64 x (*.f64 x #s(literal -1/2 binary64))))
(fma.f64 x (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64)) (.f64 x (.f64 x #s(literal -1/2 binary64))))
(fma.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64)) x (.f64 x (.f64 x #s(literal -1/2 binary64))))
(/.f64 (+.f64 (.f64 (.f64 x (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64))) (.f64 (.f64 x (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64))) (.f64 x (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64))))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64)))) (+.f64 (.f64 (.f64 x (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64))) (.f64 x (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64)))) (-.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/4 binary64)) (.f64 (.f64 x (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64))) (.f64 x (.f64 x #s(literal -1/2 binary64)))))))
(/.f64 (-.f64 (.f64 (.f64 x (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64))) (.f64 x (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64)))) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/4 binary64))) (-.f64 (.f64 x (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64))) (.f64 x (.f64 x #s(literal -1/2 binary64)))))
(/.f64 (.f64 x (+.f64 (.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64)) (.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64)) (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64)))) (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64)))) (+.f64 (.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64)) (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64))) (.f64 (.f64 x #s(literal -1/2 binary64)) (-.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64))))))
(/.f64 (.f64 x (-.f64 (.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64)) (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64))) (.f64 (.f64 x x) #s(literal 1/4 binary64)))) (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 x #s(literal -1/2 binary64)))))
(/.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64)) (.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64)) (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64)))) (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64))) x) (+.f64 (.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64)) (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64))) (.f64 (.f64 x #s(literal -1/2 binary64)) (-.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64))))))
(/.f64 (.f64 (-.f64 (.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64)) (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64))) (.f64 (.f64 x x) #s(literal 1/4 binary64))) x) (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 x #s(literal -1/2 binary64)))))
(/.f64 (neg.f64 (+.f64 (.f64 (.f64 x (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64))) (.f64 (.f64 x (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64))) (.f64 x (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64))))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64))))) (neg.f64 (+.f64 (.f64 (.f64 x (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64))) (.f64 x (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64)))) (-.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/4 binary64)) (.f64 (.f64 x (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64))) (.f64 x (.f64 x #s(literal -1/2 binary64))))))))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 x (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64))) (.f64 x (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64)))) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/4 binary64)))) (neg.f64 (-.f64 (.f64 x (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64))) (.f64 x (.f64 x #s(literal -1/2 binary64))))))
(/.f64 (neg.f64 (.f64 x (+.f64 (.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64)) (.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64)) (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64)))) (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64))))) (neg.f64 (+.f64 (.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64)) (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64))) (.f64 (.f64 x #s(literal -1/2 binary64)) (-.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64)))))))
(/.f64 (neg.f64 (.f64 x (-.f64 (.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64)) (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64))) (.f64 (.f64 x x) #s(literal 1/4 binary64))))) (neg.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 x #s(literal -1/2 binary64))))))
(/.f64 (neg.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64)) (.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64)) (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64)))) (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64))) x)) (neg.f64 (+.f64 (.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64)) (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64))) (.f64 (.f64 x #s(literal -1/2 binary64)) (-.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64)))))))
(/.f64 (neg.f64 (.f64 (-.f64 (.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64)) (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64))) (.f64 (.f64 x x) #s(literal 1/4 binary64))) x)) (neg.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 x #s(literal -1/2 binary64))))))
(.f64 x (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64)))))
(.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64)))) x)
(+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal -1/2 binary64))))
(+.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) (*.f64 x #s(literal -1/2 binary64))))
(+.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64)) (*.f64 x #s(literal -1/2 binary64)))
(+.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 (.f64 x (*.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64)))
(+.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))) (.f64 x (*.f64 x #s(literal 1/3 binary64))))
(+.f64 (+.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 x (*.f64 x #s(literal 1/3 binary64)))) #s(literal 1 binary64))
(-.f64 (/.f64 (.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64)) (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64))) (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) (-.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))))) (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 x #s(literal -1/2 binary64))))))
(fma.f64 x (.f64 x #s(literal 1/3 binary64)) (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))))
(fma.f64 x #s(literal -1/2 binary64) (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64)))
(fma.f64 (.f64 x #s(literal 1/3 binary64)) x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))))
(fma.f64 #s(literal -1/2 binary64) x (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64)))
(fma.f64 (.f64 x x) #s(literal 1/3 binary64) (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64)) (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64))) (.f64 (.f64 x #s(literal -1/2 binary64)) (-.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64))))) (+.f64 (.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64)) (.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64)) (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64)))) (.f64 (.f64 x (*.f64 x x)) #s(literal -1/8 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) (-.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64)))) (-.f64 (.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64)) (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64))) (.f64 (.f64 x x) #s(literal 1/4 binary64)))))
(/.f64 (+.f64 (.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64)) (.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64)) (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64)))) (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64))) (+.f64 (.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64)) (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64))) (.f64 (.f64 x #s(literal -1/2 binary64)) (-.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 (.f64 x (*.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64))))))
(/.f64 (+.f64 (.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64)) (.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64)) (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64)))) (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64))) (+.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (-.f64 (.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64)) (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64))) (.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64)) (.f64 x #s(literal -1/2 binary64))))))
(/.f64 (-.f64 (.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64)) (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64))) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) (-.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64)))))
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(+.f64 (.f64 x #s(literal 1/3 binary64)) (.f64 (*.f64 x x) #s(literal -1/4 binary64)))
(+.f64 (.f64 (.f64 x x) #s(literal -1/4 binary64)) (*.f64 x #s(literal 1/3 binary64)))
(fma.f64 x #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/4 binary64)))
(fma.f64 #s(literal 1/3 binary64) x (.f64 (.f64 x x) #s(literal -1/4 binary64)))
(/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/27 binary64)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/64 binary64)))) (+.f64 (.f64 (.f64 x x) #s(literal 1/9 binary64)) (-.f64 (.f64 (.f64 (.f64 x x) #s(literal -1/4 binary64)) (.f64 (.f64 x x) #s(literal -1/4 binary64))) (.f64 (.f64 x #s(literal 1/3 binary64)) (.f64 (.f64 x x) #s(literal -1/4 binary64))))))
(/.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/9 binary64)) (.f64 (.f64 (.f64 x x) #s(literal -1/4 binary64)) (.f64 (.f64 x x) #s(literal -1/4 binary64)))) (-.f64 (.f64 x #s(literal 1/3 binary64)) (.f64 (.f64 x x) #s(literal -1/4 binary64))))
(/.f64 (.f64 x (+.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 x (-.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) #s(literal 1/16 binary64)))) (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/4 binary64) x)))
(/.f64 (.f64 (+.f64 #s(literal 1/27 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal -1/64 binary64))) 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 1/9 binary64) (.f64 (.f64 x x) #s(literal 1/16 binary64))) x) (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/4 binary64) x)))
(/.f64 (neg.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/27 binary64)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/64 binary64))))) (neg.f64 (+.f64 (.f64 (.f64 x x) #s(literal 1/9 binary64)) (-.f64 (.f64 (.f64 (.f64 x x) #s(literal -1/4 binary64)) (.f64 (.f64 x x) #s(literal -1/4 binary64))) (.f64 (.f64 x #s(literal 1/3 binary64)) (.f64 (.f64 x x) #s(literal -1/4 binary64)))))))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/9 binary64)) (.f64 (.f64 (.f64 x x) #s(literal -1/4 binary64)) (.f64 (.f64 x x) #s(literal -1/4 binary64))))) (neg.f64 (-.f64 (.f64 x #s(literal 1/3 binary64)) (.f64 (.f64 x x) #s(literal -1/4 binary64)))))
(/.f64 (neg.f64 (.f64 x (+.f64 #s(literal 1/27 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal -1/64 binary64))))) (neg.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 (neg.f64 (.f64 x (-.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) #s(literal 1/16 binary64))))) (neg.f64 (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/4 binary64) x))))
(/.f64 (neg.f64 (.f64 (+.f64 #s(literal 1/27 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal -1/64 binary64))) x)) (neg.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 (neg.f64 (.f64 (-.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) #s(literal 1/16 binary64))) x)) (neg.f64 (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/4 binary64) x))))
(.f64 x (+.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))) x)
(+.f64 (.f64 (.f64 x x) #s(literal -1/4 binary64)) (.f64 x (.f64 x (*.f64 x #s(literal 1/3 binary64)))))
(+.f64 (.f64 x (.f64 x (.f64 x #s(literal 1/3 binary64)))) (.f64 (*.f64 x x) #s(literal -1/4 binary64)))
(+.f64 (.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x #s(literal 1/3 binary64))))) (.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) #s(literal -1/4 binary64))))
(+.f64 (.f64 (.f64 x (.f64 x (.f64 x #s(literal 1/3 binary64)))) #s(literal 1 binary64)) (.f64 (.f64 (*.f64 x x) #s(literal -1/4 binary64)) #s(literal 1 binary64)))
(fma.f64 (.f64 x #s(literal 1/3 binary64)) (.f64 x x) (.f64 (.f64 x x) #s(literal -1/4 binary64)))
(fma.f64 (.f64 x x) (.f64 x #s(literal 1/3 binary64)) (.f64 (.f64 x x) #s(literal -1/4 binary64)))
(/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/27 binary64)))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/64 binary64)))) (+.f64 (.f64 (.f64 x (.f64 x (.f64 x #s(literal 1/3 binary64)))) (.f64 x (.f64 x (.f64 x #s(literal 1/3 binary64))))) (-.f64 (.f64 (.f64 (.f64 x x) #s(literal -1/4 binary64)) (.f64 (.f64 x x) #s(literal -1/4 binary64))) (.f64 (.f64 x (.f64 x (.f64 x #s(literal 1/3 binary64)))) (.f64 (*.f64 x x) #s(literal -1/4 binary64))))))
(/.f64 (-.f64 (.f64 (.f64 x (.f64 x (.f64 x #s(literal 1/3 binary64)))) (.f64 x (.f64 x (.f64 x #s(literal 1/3 binary64))))) (.f64 (.f64 (.f64 x x) #s(literal -1/4 binary64)) (.f64 (.f64 x x) #s(literal -1/4 binary64)))) (-.f64 (.f64 x (.f64 x (.f64 x #s(literal 1/3 binary64)))) (.f64 (*.f64 x x) #s(literal -1/4 binary64))))
(/.f64 (.f64 (.f64 x x) (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/27 binary64)) #s(literal -1/64 binary64))) (+.f64 (.f64 (.f64 x x) #s(literal 1/9 binary64)) (-.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/12 binary64)))))
(/.f64 (.f64 (.f64 x x) (+.f64 (.f64 (.f64 x x) #s(literal 1/9 binary64)) #s(literal -1/16 binary64))) (+.f64 (*.f64 x #s(literal 1/3 binary64)) #s(literal 1/4 binary64)))
(/.f64 (.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/27 binary64)) #s(literal -1/64 binary64)) (.f64 x x)) (+.f64 (.f64 (.f64 x x) #s(literal 1/9 binary64)) (-.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/12 binary64)))))
(/.f64 (.f64 (+.f64 (.f64 (.f64 x x) #s(literal 1/9 binary64)) #s(literal -1/16 binary64)) (.f64 x x)) (+.f64 (*.f64 x #s(literal 1/3 binary64)) #s(literal 1/4 binary64)))
(/.f64 (neg.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/27 binary64)))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/64 binary64))))) (neg.f64 (+.f64 (.f64 (.f64 x (.f64 x (.f64 x #s(literal 1/3 binary64)))) (.f64 x (.f64 x (.f64 x #s(literal 1/3 binary64))))) (-.f64 (.f64 (.f64 (.f64 x x) #s(literal -1/4 binary64)) (.f64 (.f64 x x) #s(literal -1/4 binary64))) (.f64 (.f64 x (.f64 x (.f64 x #s(literal 1/3 binary64)))) (.f64 (*.f64 x x) #s(literal -1/4 binary64)))))))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 x (.f64 x (.f64 x #s(literal 1/3 binary64)))) (.f64 x (.f64 x (.f64 x #s(literal 1/3 binary64))))) (.f64 (.f64 (.f64 x x) #s(literal -1/4 binary64)) (.f64 (.f64 x x) #s(literal -1/4 binary64))))) (neg.f64 (-.f64 (.f64 x (.f64 x (.f64 x #s(literal 1/3 binary64)))) (.f64 (*.f64 x x) #s(literal -1/4 binary64)))))
(/.f64 (neg.f64 (.f64 (.f64 x x) (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/27 binary64)) #s(literal -1/64 binary64)))) (neg.f64 (+.f64 (.f64 (.f64 x x) #s(literal 1/9 binary64)) (-.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/12 binary64))))))
(/.f64 (neg.f64 (.f64 (.f64 x x) (+.f64 (.f64 (.f64 x x) #s(literal 1/9 binary64)) #s(literal -1/16 binary64)))) (neg.f64 (+.f64 (*.f64 x #s(literal 1/3 binary64)) #s(literal 1/4 binary64))))
(/.f64 (neg.f64 (.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/27 binary64)) #s(literal -1/64 binary64)) (.f64 x x))) (neg.f64 (+.f64 (.f64 (.f64 x x) #s(literal 1/9 binary64)) (-.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/12 binary64))))))
(/.f64 (neg.f64 (.f64 (+.f64 (.f64 (.f64 x x) #s(literal 1/9 binary64)) #s(literal -1/16 binary64)) (.f64 x x))) (neg.f64 (+.f64 (*.f64 x #s(literal 1/3 binary64)) #s(literal 1/4 binary64))))
(.f64 x (.f64 x (+.f64 (*.f64 x #s(literal 1/3 binary64)) #s(literal -1/4 binary64))))
(.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 (.f64 x #s(literal 1/3 binary64)) #s(literal -1/4 binary64)))))
(.f64 (.f64 x x) (+.f64 (*.f64 x #s(literal 1/3 binary64)) #s(literal -1/4 binary64)))
(.f64 (+.f64 (.f64 x #s(literal 1/3 binary64)) #s(literal -1/4 binary64)) (*.f64 x x))
(.f64 (.f64 x (.f64 x (+.f64 (.f64 x #s(literal 1/3 binary64)) #s(literal -1/4 binary64)))) #s(literal 1 binary64))
(.f64 (.f64 x (+.f64 (*.f64 x #s(literal 1/3 binary64)) #s(literal -1/4 binary64))) x)
(.f64 (.f64 #s(literal 1 binary64) x) (.f64 x (+.f64 (.f64 x #s(literal 1/3 binary64)) #s(literal -1/4 binary64))))
(.f64 (.f64 #s(literal 1 binary64) (+.f64 (.f64 x #s(literal 1/3 binary64)) #s(literal -1/4 binary64))) (.f64 x x))
(*.f64 x #s(literal -1/3 binary64))
(*.f64 #s(literal -1/3 binary64) x)
(exp.f64 (*.f64 (log.f64 x) #s(literal 3 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 3/2 binary64)))
(pow.f64 x #s(literal 3 binary64))
(pow.f64 (*.f64 x x) #s(literal 3/2 binary64))
(pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 3 binary64))
(.f64 x (.f64 x x))
(.f64 (.f64 x x) x)
(.f64 (.f64 x (*.f64 x x)) (pow.f64 #s(literal 1 binary64) #s(literal 3/2 binary64)))
(*.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))
(.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 (.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)))
(.f64 (pow.f64 #s(literal 1 binary64) #s(literal 3/2 binary64)) (.f64 x (*.f64 x x)))
(.f64 (pow.f64 (.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))

simplify265.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

3866×	`-lowering-.f32`
3866×	`-lowering-.f64`
1978×	`+-lowering-+.f64`
1978×	`+-lowering-+.f32`
1826×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	230	1802
1	740	1615
2	2275	1548
3	6934	1547
0	8082	1547

Stop Event

1×	iter limit
1×	node limit

Counts

228 → 228

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
(+ 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
(+ 1 (* 1/3 (pow x 2)))
(+ 1 (* 1/3 (pow x 2)))
(+ 1 (* 1/3 (pow x 2)))
(* 1/3 (pow x 2))
(* (pow x 2) (+ 1/3 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1/3 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1/3 (/ 1 (pow x 2))))
(* 1/3 (pow x 2))
(* (pow x 2) (+ 1/3 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1/3 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1/3 (/ 1 (pow x 2))))
(* 1/3 (pow x 2))
(* 1/3 (pow x 2))
(* 1/3 (pow x 2))
(* 1/3 (pow x 2))
(* 1/3 (pow x 2))
(* 1/3 (pow x 2))
(* 1/3 (pow x 2))
(* 1/3 (pow x 2))
(* 1/3 (pow x 2))
(* 1/3 (pow x 2))
(* 1/3 (pow x 2))
(* 1/3 (pow x 2))
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))))
(* 4/3 x)
(* x (+ 4/3 (* 7/9 (/ 1 x))))
(* x (- (+ 4/3 (* 7/9 (/ 1 x))) (/ 44/27 (pow x 2))))
(* x (+ 4/3 (+ (* -1 (/ (+ 44/27 (* 410/81 (/ 1 x))) (pow x 2))) (* 7/9 (/ 1 x)))))
(* 4/3 x)
(* x (+ 4/3 (* 7/9 (/ 1 x))))
(* -1 (* x (- (* -1 (/ (- 7/9 (* 44/27 (/ 1 x))) x)) 4/3)))
(* -1 (* x (- (* -1 (/ (+ 7/9 (* -1 (/ (+ 44/27 (* 410/81 (/ 1 x))) x))) x)) 4/3)))
(pow x 2)
(* (pow x 2) (+ 1 (* -1/4 (pow x 2))))
(* (pow x 2) (+ 1 (* (pow x 2) (- (* 1/3 x) 1/4))))
(* (pow x 2) (+ 1 (* (pow x 2) (- (* 1/3 x) 1/4))))
(* 1/3 (pow x 5))
(* (pow x 5) (- 1/3 (* 1/4 (/ 1 x))))
(* (pow x 5) (- (+ 1/3 (/ 1 (pow x 3))) (* 1/4 (/ 1 x))))
(* (pow x 5) (- (+ 1/3 (/ 1 (pow x 3))) (* 1/4 (/ 1 x))))
(* 1/3 (pow x 5))
(* -1 (* (pow x 5) (- (* 1/4 (/ 1 x)) 1/3)))
(* -1 (* (pow x 5) (- (* -1 (/ (- (/ 1 (pow x 2)) 1/4) x)) 1/3)))
(* -1 (* (pow x 5) (- (* -1 (/ (- (/ 1 (pow x 2)) 1/4) x)) 1/3)))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
1
(+ 1 (* -1/4 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/3 x) 1/4)))
(+ 1 (* (pow x 2) (- (* 1/3 x) 1/4)))
(* 1/3 (pow x 3))
(* (pow x 3) (- 1/3 (* 1/4 (/ 1 x))))
(* (pow x 3) (- (+ 1/3 (/ 1 (pow x 3))) (* 1/4 (/ 1 x))))
(* (pow x 3) (- (+ 1/3 (/ 1 (pow x 3))) (* 1/4 (/ 1 x))))
(* 1/3 (pow x 3))
(* -1 (* (pow x 3) (- (* 1/4 (/ 1 x)) 1/3)))
(* -1 (* (pow x 3) (- (* -1 (/ (- (/ 1 (pow x 2)) 1/4) x)) 1/3)))
(* -1 (* (pow x 3) (- (* -1 (/ (- (/ 1 (pow x 2)) 1/4) 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))))
(* 4/3 x)
(* x (+ 4/3 (* 7/9 (/ 1 x))))
(* x (- (+ 4/3 (* 7/9 (/ 1 x))) (/ 44/27 (pow x 2))))
(* x (+ 4/3 (+ (* -1 (/ (+ 44/27 (* 410/81 (/ 1 x))) (pow x 2))) (* 7/9 (/ 1 x)))))
(* 4/3 x)
(* x (+ 4/3 (* 7/9 (/ 1 x))))
(* -1 (* x (- (* -1 (/ (- 7/9 (* 44/27 (/ 1 x))) x)) 4/3)))
(* -1 (* x (- (* -1 (/ (+ 7/9 (* -1 (/ (+ 44/27 (* 410/81 (/ 1 x))) x))) x)) 4/3)))
(pow x 2)
(* (pow x 2) (+ 1 (* -1/4 (pow x 2))))
(* (pow x 2) (+ 1 (* (pow x 2) (- (* 1/3 x) 1/4))))
(* (pow x 2) (+ 1 (* (pow x 2) (- (* 1/3 x) 1/4))))
(* 1/3 (pow x 5))
(* (pow x 5) (- 1/3 (* 1/4 (/ 1 x))))
(* (pow x 5) (- (+ 1/3 (/ 1 (pow x 3))) (* 1/4 (/ 1 x))))
(* (pow x 5) (- (+ 1/3 (/ 1 (pow x 3))) (* 1/4 (/ 1 x))))
(* 1/3 (pow x 5))
(* -1 (* (pow x 5) (- (* 1/4 (/ 1 x)) 1/3)))
(* -1 (* (pow x 5) (- (* -1 (/ (- (/ 1 (pow x 2)) 1/4) x)) 1/3)))
(* -1 (* (pow x 5) (- (* -1 (/ (- (/ 1 (pow x 2)) 1/4) x)) 1/3)))
(* 1/4 (pow x 4))
(* (pow x 4) (+ 1/4 (* -1/3 x)))
(* (pow x 4) (+ 1/4 (* -1/3 x)))
(* (pow x 4) (+ 1/4 (* -1/3 x)))
(* -1/3 (pow x 5))
(* (pow x 5) (- (* 1/4 (/ 1 x)) 1/3))
(* (pow x 5) (- (* 1/4 (/ 1 x)) 1/3))
(* (pow x 5) (- (* 1/4 (/ 1 x)) 1/3))
(* -1/3 (pow x 5))
(* -1 (* (pow x 5) (- 1/3 (* 1/4 (/ 1 x)))))
(* -1 (* (pow x 5) (- 1/3 (* 1/4 (/ 1 x)))))
(* -1 (* (pow x 5) (- 1/3 (* 1/4 (/ 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))))
(* 1/3 (pow x 3))
(* (pow x 3) (- 1/3 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/3 (* -1 (/ (+ 1/2 (* 4/3 (/ 1 (pow x 2)))) x))))
(* (pow x 3) (- (+ 1/3 (* 2/9 (/ 1 (pow x 4)))) (+ (* 1/2 (/ 1 x)) (/ 4/3 (pow x 3)))))
(* 1/3 (pow x 3))
(* -1 (* (pow x 3) (- (* 1/2 (/ 1 x)) 1/3)))
(* -1 (* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 4/3 (pow x 3))) 1/3)))
(* -1 (* (pow x 3) (- (* -1 (/ (- (/ 2/9 (pow x 3)) (+ 1/2 (* 4/3 (/ 1 (pow x 2))))) x)) 1/3)))
(pow x 2)
(* (pow x 2) (+ 1 (* -1/4 (pow x 2))))
(* (pow x 2) (+ 1 (* (pow x 2) (- (* 1/3 x) 1/4))))
(* (pow x 2) (+ 1 (* (pow x 2) (- (* x (+ 1/3 (* -17/72 x))) 1/4))))
(* 1/12 (pow x 7))
(* (pow x 7) (- 1/12 (* 17/72 (/ 1 x))))
(* (pow x 7) (- (+ 1/12 (/ 1/3 (pow x 2))) (* 17/72 (/ 1 x))))
(* (pow x 7) (- (+ 1/12 (/ 1/3 (pow x 2))) (+ (* 17/72 (/ 1 x)) (* 1/4 (/ 1 (pow x 3))))))
(* 1/12 (pow x 7))
(* -1 (* (pow x 7) (- (* 17/72 (/ 1 x)) 1/12)))
(* -1 (* (pow x 7) (- (* -1 (/ (- (* 1/3 (/ 1 x)) 17/72) x)) 1/12)))
(* -1 (* (pow x 7) (- (* -1 (/ (- (* -1 (/ (- (* 1/4 (/ 1 x)) 1/3) x)) 17/72) x)) 1/12)))
(* 1/4 (pow x 4))
(* (pow x 4) (+ 1/4 (* -1/3 x)))
(* (pow x 4) (+ 1/4 (* x (- (* 17/72 x) 1/3))))
(* (pow x 4) (+ 1/4 (* x (- (* x (+ 17/72 (* -1/12 x))) 1/3))))
(* -1/12 (pow x 7))
(* (pow x 7) (- (* 17/72 (/ 1 x)) 1/12))
(* (pow x 7) (- (* 17/72 (/ 1 x)) (+ 1/12 (/ 1/3 (pow x 2)))))
(* (pow x 7) (- (+ (* 17/72 (/ 1 x)) (* 1/4 (/ 1 (pow x 3)))) (+ 1/12 (/ 1/3 (pow x 2)))))
(* -1/12 (pow x 7))
(* -1 (* (pow x 7) (- 1/12 (* 17/72 (/ 1 x)))))
(* -1 (* (pow x 7) (+ 1/12 (* -1 (/ (- 17/72 (* 1/3 (/ 1 x))) x)))))
(* -1 (* (pow x 7) (+ 1/12 (* -1 (/ (+ 17/72 (* -1 (/ (- 1/3 (* 1/4 (/ 1 x))) x))) 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)
(* 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))
(* -1/4 (pow x 2))
(* (pow x 2) (- (* 1/3 x) 1/4))
(* (pow x 2) (- (* 1/3 x) 1/4))
(* (pow x 2) (- (* 1/3 x) 1/4))
(* 1/3 (pow x 3))
(* (pow x 3) (- 1/3 (* 1/4 (/ 1 x))))
(* (pow x 3) (- 1/3 (* 1/4 (/ 1 x))))
(* (pow x 3) (- 1/3 (* 1/4 (/ 1 x))))
(* 1/3 (pow x 3))
(* -1 (* (pow x 3) (- (* 1/4 (/ 1 x)) 1/3)))
(* -1 (* (pow x 3) (- (* 1/4 (/ 1 x)) 1/3)))
(* -1 (* (pow x 3) (- (* 1/4 (/ 1 x)) 1/3)))
(* -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)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)

Outputs
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 #s(literal 1/3 binary64) (*.f64 x x)))
(* (pow x 3) (- 1/3 (* 1/2 (/ 1 x))))
(.f64 x (.f64 x (*.f64 x (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal -1/2 binary64) x)))))
(* (pow x 3) (- (+ 1/3 (/ 1 (pow x 2))) (* 1/2 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal -1/2 binary64) x))))))
(* (pow x 3) (- (+ 1/3 (/ 1 (pow x 2))) (* 1/2 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal -1/2 binary64) x))))))
(* 1/3 (pow x 3))
(.f64 x (.f64 #s(literal 1/3 binary64) (*.f64 x x)))
(* -1 (* (pow x 3) (- (* 1/2 (/ 1 x)) 1/3)))
(.f64 x (.f64 x (*.f64 x (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal -1/2 binary64) x)))))
(* -1 (* (pow x 3) (- (* -1 (/ (- (/ 1 x) 1/2) x)) 1/3)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal -1/2 binary64) x))))))
(* -1 (* (pow x 3) (- (* -1 (/ (- (/ 1 x) 1/2) x)) 1/3)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal -1/2 binary64) 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 (- (* 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 #s(literal 1/3 binary64) (.f64 x x))
(* (pow x 2) (- 1/3 (* 1/2 (/ 1 x))))
(.f64 x (.f64 x (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal -1/2 binary64) x))))
(* (pow x 2) (- (+ 1/3 (/ 1 (pow x 2))) (* 1/2 (/ 1 x))))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal -1/2 binary64) x)))))
(* (pow x 2) (- (+ 1/3 (/ 1 (pow x 2))) (* 1/2 (/ 1 x))))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal -1/2 binary64) x)))))
(* 1/3 (pow x 2))
(.f64 #s(literal 1/3 binary64) (.f64 x x))
(* (pow x 2) (- 1/3 (* 1/2 (/ 1 x))))
(.f64 x (.f64 x (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal -1/2 binary64) x))))
(* (pow x 2) (+ 1/3 (* -1 (/ (- 1/2 (/ 1 x)) x))))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal -1/2 binary64) x)))))
(* (pow x 2) (+ 1/3 (* -1 (/ (- 1/2 (/ 1 x)) x))))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal -1/2 binary64) x)))))
1
#s(literal 1 binary64)
(+ 1 (* 1/3 (pow x 2)))
(+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (.f64 x x)))
(+ 1 (* 1/3 (pow x 2)))
(+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (.f64 x x)))
(+ 1 (* 1/3 (pow x 2)))
(+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (.f64 x x)))
(* 1/3 (pow x 2))
(.f64 #s(literal 1/3 binary64) (.f64 x x))
(* (pow x 2) (+ 1/3 (/ 1 (pow x 2))))
(+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (.f64 x x)))
(* (pow x 2) (+ 1/3 (/ 1 (pow x 2))))
(+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (.f64 x x)))
(* (pow x 2) (+ 1/3 (/ 1 (pow x 2))))
(+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (.f64 x x)))
(* 1/3 (pow x 2))
(.f64 #s(literal 1/3 binary64) (.f64 x x))
(* (pow x 2) (+ 1/3 (/ 1 (pow x 2))))
(+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (.f64 x x)))
(* (pow x 2) (+ 1/3 (/ 1 (pow x 2))))
(+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (.f64 x x)))
(* (pow x 2) (+ 1/3 (/ 1 (pow x 2))))
(+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (.f64 x x)))
(* 1/3 (pow x 2))
(.f64 #s(literal 1/3 binary64) (.f64 x x))
(* 1/3 (pow x 2))
(.f64 #s(literal 1/3 binary64) (.f64 x x))
(* 1/3 (pow x 2))
(.f64 #s(literal 1/3 binary64) (.f64 x x))
(* 1/3 (pow x 2))
(.f64 #s(literal 1/3 binary64) (.f64 x x))
(* 1/3 (pow x 2))
(.f64 #s(literal 1/3 binary64) (.f64 x x))
(* 1/3 (pow x 2))
(.f64 #s(literal 1/3 binary64) (.f64 x x))
(* 1/3 (pow x 2))
(.f64 #s(literal 1/3 binary64) (.f64 x x))
(* 1/3 (pow x 2))
(.f64 #s(literal 1/3 binary64) (.f64 x x))
(* 1/3 (pow x 2))
(.f64 #s(literal 1/3 binary64) (.f64 x x))
(* 1/3 (pow x 2))
(.f64 #s(literal 1/3 binary64) (.f64 x x))
(* 1/3 (pow x 2))
(.f64 #s(literal 1/3 binary64) (.f64 x x))
(* 1/3 (pow x 2))
(.f64 #s(literal 1/3 binary64) (.f64 x x))
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))))))))
(* 4/3 x)
(*.f64 x #s(literal 4/3 binary64))
(* x (+ 4/3 (* 7/9 (/ 1 x))))
(+.f64 (*.f64 x #s(literal 4/3 binary64)) #s(literal 7/9 binary64))
(* x (- (+ 4/3 (* 7/9 (/ 1 x))) (/ 44/27 (pow x 2))))
(*.f64 x (+.f64 #s(literal 4/3 binary64) (/.f64 (+.f64 #s(literal 7/9 binary64) (/.f64 #s(literal -44/27 binary64) x)) x)))
(* x (+ 4/3 (+ (* -1 (/ (+ 44/27 (* 410/81 (/ 1 x))) (pow x 2))) (* 7/9 (/ 1 x)))))
(+.f64 #s(literal 7/9 binary64) (.f64 x (+.f64 #s(literal 4/3 binary64) (/.f64 (+.f64 #s(literal -44/27 binary64) (/.f64 #s(literal -410/81 binary64) x)) (.f64 x x)))))
(* 4/3 x)
(*.f64 x #s(literal 4/3 binary64))
(* x (+ 4/3 (* 7/9 (/ 1 x))))
(+.f64 (*.f64 x #s(literal 4/3 binary64)) #s(literal 7/9 binary64))
(* -1 (* x (- (* -1 (/ (- 7/9 (* 44/27 (/ 1 x))) x)) 4/3)))
(*.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 44/27 binary64) x) #s(literal -7/9 binary64)) x) #s(literal -4/3 binary64)) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (- (* -1 (/ (+ 7/9 (* -1 (/ (+ 44/27 (* 410/81 (/ 1 x))) x))) x)) 4/3)))
(-.f64 #s(literal 0 binary64) (*.f64 x (-.f64 #s(literal -4/3 binary64) (/.f64 (+.f64 #s(literal 7/9 binary64) (/.f64 (+.f64 #s(literal -44/27 binary64) (/.f64 #s(literal -410/81 binary64) x)) x)) x))))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -1/4 (pow x 2))))
(.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -1/4 binary64)))))
(* (pow x 2) (+ 1 (* (pow x 2) (- (* 1/3 x) 1/4))))
(.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 (*.f64 x #s(literal 1/3 binary64)) #s(literal -1/4 binary64))))))
(* (pow x 2) (+ 1 (* (pow x 2) (- (* 1/3 x) 1/4))))
(.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 (*.f64 x #s(literal 1/3 binary64)) #s(literal -1/4 binary64))))))
(* 1/3 (pow x 5))
(.f64 #s(literal 1/3 binary64) (.f64 x (.f64 (.f64 x x) (*.f64 x x))))
(* (pow x 5) (- 1/3 (* 1/4 (/ 1 x))))
(.f64 (.f64 x (.f64 (.f64 x x) (*.f64 x x))) (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal -1/4 binary64) x)))
(* (pow x 5) (- (+ 1/3 (/ 1 (pow x 3))) (* 1/4 (/ 1 x))))
(.f64 (.f64 x (.f64 (.f64 x x) (*.f64 x x))) (+.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) #s(literal -1/4 binary64)) x)))
(* (pow x 5) (- (+ 1/3 (/ 1 (pow x 3))) (* 1/4 (/ 1 x))))
(.f64 (.f64 x (.f64 (.f64 x x) (*.f64 x x))) (+.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) #s(literal -1/4 binary64)) x)))
(* 1/3 (pow x 5))
(.f64 #s(literal 1/3 binary64) (.f64 x (.f64 (.f64 x x) (*.f64 x x))))
(* -1 (* (pow x 5) (- (* 1/4 (/ 1 x)) 1/3)))
(.f64 (.f64 x (.f64 (.f64 x x) (*.f64 x x))) (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal -1/4 binary64) x)))
(* -1 (* (pow x 5) (- (* -1 (/ (- (/ 1 (pow x 2)) 1/4) x)) 1/3)))
(-.f64 #s(literal 0 binary64) (.f64 (.f64 x (.f64 (.f64 x x) (*.f64 x x))) (+.f64 (/.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 (/.f64 #s(literal -1 binary64) x) x)) x) #s(literal -1/3 binary64))))
(* -1 (* (pow x 5) (- (* -1 (/ (- (/ 1 (pow x 2)) 1/4) x)) 1/3)))
(-.f64 #s(literal 0 binary64) (.f64 (.f64 x (.f64 (.f64 x x) (*.f64 x x))) (+.f64 (/.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 (/.f64 #s(literal -1 binary64) x) x)) x) #s(literal -1/3 binary64))))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
1
#s(literal 1 binary64)
(+ 1 (* -1/4 (pow x 2)))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -1/4 binary64)))
(+ 1 (* (pow x 2) (- (* 1/3 x) 1/4)))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 (*.f64 x #s(literal 1/3 binary64)) #s(literal -1/4 binary64))))
(+ 1 (* (pow x 2) (- (* 1/3 x) 1/4)))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 (*.f64 x #s(literal 1/3 binary64)) #s(literal -1/4 binary64))))
(* 1/3 (pow x 3))
(.f64 x (.f64 #s(literal 1/3 binary64) (*.f64 x x)))
(* (pow x 3) (- 1/3 (* 1/4 (/ 1 x))))
(.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal -1/4 binary64) x)))
(* (pow x 3) (- (+ 1/3 (/ 1 (pow x 3))) (* 1/4 (/ 1 x))))
(.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) #s(literal -1/4 binary64)) x)))
(* (pow x 3) (- (+ 1/3 (/ 1 (pow x 3))) (* 1/4 (/ 1 x))))
(.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) #s(literal -1/4 binary64)) x)))
(* 1/3 (pow x 3))
(.f64 x (.f64 #s(literal 1/3 binary64) (*.f64 x x)))
(* -1 (* (pow x 3) (- (* 1/4 (/ 1 x)) 1/3)))
(.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal -1/4 binary64) x)))
(* -1 (* (pow x 3) (- (* -1 (/ (- (/ 1 (pow x 2)) 1/4) x)) 1/3)))
(.f64 (+.f64 (/.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 (/.f64 #s(literal -1 binary64) x) x)) x) #s(literal -1/3 binary64)) (-.f64 #s(literal 0 binary64) (.f64 x (*.f64 x x))))
(* -1 (* (pow x 3) (- (* -1 (/ (- (/ 1 (pow x 2)) 1/4) x)) 1/3)))
(.f64 (+.f64 (/.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 (/.f64 #s(literal -1 binary64) x) x)) x) #s(literal -1/3 binary64)) (-.f64 #s(literal 0 binary64) (.f64 x (*.f64 x x))))
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))))))))
(* 4/3 x)
(*.f64 x #s(literal 4/3 binary64))
(* x (+ 4/3 (* 7/9 (/ 1 x))))
(+.f64 (*.f64 x #s(literal 4/3 binary64)) #s(literal 7/9 binary64))
(* x (- (+ 4/3 (* 7/9 (/ 1 x))) (/ 44/27 (pow x 2))))
(*.f64 x (+.f64 #s(literal 4/3 binary64) (/.f64 (+.f64 #s(literal 7/9 binary64) (/.f64 #s(literal -44/27 binary64) x)) x)))
(* x (+ 4/3 (+ (* -1 (/ (+ 44/27 (* 410/81 (/ 1 x))) (pow x 2))) (* 7/9 (/ 1 x)))))
(+.f64 #s(literal 7/9 binary64) (.f64 x (+.f64 #s(literal 4/3 binary64) (/.f64 (+.f64 #s(literal -44/27 binary64) (/.f64 #s(literal -410/81 binary64) x)) (.f64 x x)))))
(* 4/3 x)
(*.f64 x #s(literal 4/3 binary64))
(* x (+ 4/3 (* 7/9 (/ 1 x))))
(+.f64 (*.f64 x #s(literal 4/3 binary64)) #s(literal 7/9 binary64))
(* -1 (* x (- (* -1 (/ (- 7/9 (* 44/27 (/ 1 x))) x)) 4/3)))
(*.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 44/27 binary64) x) #s(literal -7/9 binary64)) x) #s(literal -4/3 binary64)) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (- (* -1 (/ (+ 7/9 (* -1 (/ (+ 44/27 (* 410/81 (/ 1 x))) x))) x)) 4/3)))
(-.f64 #s(literal 0 binary64) (*.f64 x (-.f64 #s(literal -4/3 binary64) (/.f64 (+.f64 #s(literal 7/9 binary64) (/.f64 (+.f64 #s(literal -44/27 binary64) (/.f64 #s(literal -410/81 binary64) x)) x)) x))))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -1/4 (pow x 2))))
(.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -1/4 binary64)))))
(* (pow x 2) (+ 1 (* (pow x 2) (- (* 1/3 x) 1/4))))
(.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 (*.f64 x #s(literal 1/3 binary64)) #s(literal -1/4 binary64))))))
(* (pow x 2) (+ 1 (* (pow x 2) (- (* 1/3 x) 1/4))))
(.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 (*.f64 x #s(literal 1/3 binary64)) #s(literal -1/4 binary64))))))
(* 1/3 (pow x 5))
(.f64 #s(literal 1/3 binary64) (.f64 x (.f64 (.f64 x x) (*.f64 x x))))
(* (pow x 5) (- 1/3 (* 1/4 (/ 1 x))))
(.f64 (.f64 x (.f64 (.f64 x x) (*.f64 x x))) (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal -1/4 binary64) x)))
(* (pow x 5) (- (+ 1/3 (/ 1 (pow x 3))) (* 1/4 (/ 1 x))))
(.f64 (.f64 x (.f64 (.f64 x x) (*.f64 x x))) (+.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) #s(literal -1/4 binary64)) x)))
(* (pow x 5) (- (+ 1/3 (/ 1 (pow x 3))) (* 1/4 (/ 1 x))))
(.f64 (.f64 x (.f64 (.f64 x x) (*.f64 x x))) (+.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) #s(literal -1/4 binary64)) x)))
(* 1/3 (pow x 5))
(.f64 #s(literal 1/3 binary64) (.f64 x (.f64 (.f64 x x) (*.f64 x x))))
(* -1 (* (pow x 5) (- (* 1/4 (/ 1 x)) 1/3)))
(.f64 (.f64 x (.f64 (.f64 x x) (*.f64 x x))) (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal -1/4 binary64) x)))
(* -1 (* (pow x 5) (- (* -1 (/ (- (/ 1 (pow x 2)) 1/4) x)) 1/3)))
(-.f64 #s(literal 0 binary64) (.f64 (.f64 x (.f64 (.f64 x x) (*.f64 x x))) (+.f64 (/.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 (/.f64 #s(literal -1 binary64) x) x)) x) #s(literal -1/3 binary64))))
(* -1 (* (pow x 5) (- (* -1 (/ (- (/ 1 (pow x 2)) 1/4) x)) 1/3)))
(-.f64 #s(literal 0 binary64) (.f64 (.f64 x (.f64 (.f64 x x) (*.f64 x x))) (+.f64 (/.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 (/.f64 #s(literal -1 binary64) x) x)) x) #s(literal -1/3 binary64))))
(* 1/4 (pow x 4))
(.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 x x)))
(* (pow x 4) (+ 1/4 (* -1/3 x)))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/3 binary64))))
(* (pow x 4) (+ 1/4 (* -1/3 x)))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/3 binary64))))
(* (pow x 4) (+ 1/4 (* -1/3 x)))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/3 binary64))))
(* -1/3 (pow x 5))
(.f64 (.f64 x (.f64 (.f64 x x) (*.f64 x x))) #s(literal -1/3 binary64))
(* (pow x 5) (- (* 1/4 (/ 1 x)) 1/3))
(.f64 (.f64 x (.f64 (.f64 x x) (*.f64 x x))) (+.f64 (/.f64 #s(literal 1/4 binary64) x) #s(literal -1/3 binary64)))
(* (pow x 5) (- (* 1/4 (/ 1 x)) 1/3))
(.f64 (.f64 x (.f64 (.f64 x x) (*.f64 x x))) (+.f64 (/.f64 #s(literal 1/4 binary64) x) #s(literal -1/3 binary64)))
(* (pow x 5) (- (* 1/4 (/ 1 x)) 1/3))
(.f64 (.f64 x (.f64 (.f64 x x) (*.f64 x x))) (+.f64 (/.f64 #s(literal 1/4 binary64) x) #s(literal -1/3 binary64)))
(* -1/3 (pow x 5))
(.f64 (.f64 x (.f64 (.f64 x x) (*.f64 x x))) #s(literal -1/3 binary64))
(* -1 (* (pow x 5) (- 1/3 (* 1/4 (/ 1 x)))))
(.f64 (.f64 x (.f64 (.f64 x x) (*.f64 x x))) (+.f64 (/.f64 #s(literal 1/4 binary64) x) #s(literal -1/3 binary64)))
(* -1 (* (pow x 5) (- 1/3 (* 1/4 (/ 1 x)))))
(.f64 (.f64 x (.f64 (.f64 x x) (*.f64 x x))) (+.f64 (/.f64 #s(literal 1/4 binary64) x) #s(literal -1/3 binary64)))
(* -1 (* (pow x 5) (- 1/3 (* 1/4 (/ 1 x)))))
(.f64 (.f64 x (.f64 (.f64 x x) (*.f64 x x))) (+.f64 (/.f64 #s(literal 1/4 binary64) 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))))))))
(* 1/3 (pow x 3))
(.f64 x (.f64 #s(literal 1/3 binary64) (*.f64 x x)))
(* (pow x 3) (- 1/3 (* 1/2 (/ 1 x))))
(.f64 x (.f64 x (*.f64 x (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal -1/2 binary64) x)))))
(* (pow x 3) (+ 1/3 (* -1 (/ (+ 1/2 (* 4/3 (/ 1 (pow x 2)))) x))))
(.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -4/3 binary64) (.f64 x x))) x)))
(* (pow x 3) (- (+ 1/3 (* 2/9 (/ 1 (pow x 4)))) (+ (* 1/2 (/ 1 x)) (/ 4/3 (pow x 3)))))
(.f64 x (.f64 x (.f64 x (+.f64 #s(literal 1/3 binary64) (/.f64 (+.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 #s(literal -4/3 binary64) (.f64 x x)) (/.f64 #s(literal 2/9 binary64) (.f64 x (.f64 x x))))) x)))))
(* 1/3 (pow x 3))
(.f64 x (.f64 #s(literal 1/3 binary64) (*.f64 x x)))
(* -1 (* (pow x 3) (- (* 1/2 (/ 1 x)) 1/3)))
(.f64 x (.f64 x (*.f64 x (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal -1/2 binary64) x)))))
(* -1 (* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 4/3 (pow x 3))) 1/3)))
(.f64 (.f64 x (.f64 x x)) (+.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal -1/2 binary64) x)) (/.f64 #s(literal -4/3 binary64) (.f64 x (*.f64 x x)))))
(* -1 (* (pow x 3) (- (* -1 (/ (- (/ 2/9 (pow x 3)) (+ 1/2 (* 4/3 (/ 1 (pow x 2))))) x)) 1/3)))
(.f64 (-.f64 #s(literal -1/3 binary64) (/.f64 (+.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 #s(literal -4/3 binary64) (.f64 x x)) (/.f64 #s(literal 2/9 binary64) (.f64 x (.f64 x x))))) x)) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -1/4 (pow x 2))))
(.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -1/4 binary64)))))
(* (pow x 2) (+ 1 (* (pow x 2) (- (* 1/3 x) 1/4))))
(.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 (*.f64 x #s(literal 1/3 binary64)) #s(literal -1/4 binary64))))))
(* (pow x 2) (+ 1 (* (pow x 2) (- (* x (+ 1/3 (* -17/72 x))) 1/4))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/4 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -17/72 binary64))))))))
(* 1/12 (pow x 7))
(*.f64 #s(literal 1/12 binary64) (pow.f64 x #s(literal 7 binary64)))
(* (pow x 7) (- 1/12 (* 17/72 (/ 1 x))))
(*.f64 (pow.f64 x #s(literal 7 binary64)) (-.f64 #s(literal 1/12 binary64) (/.f64 #s(literal 17/72 binary64) x)))
(* (pow x 7) (- (+ 1/12 (/ 1/3 (pow x 2))) (* 17/72 (/ 1 x))))
(*.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 #s(literal 1/12 binary64) (/.f64 (+.f64 #s(literal -17/72 binary64) (/.f64 #s(literal 1/3 binary64) x)) x)))
(* (pow x 7) (- (+ 1/12 (/ 1/3 (pow x 2))) (+ (* 17/72 (/ 1 x)) (* 1/4 (/ 1 (pow x 3))))))
(*.f64 (pow.f64 x #s(literal 7 binary64)) (-.f64 #s(literal 1/12 binary64) (/.f64 (+.f64 #s(literal 17/72 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) x) #s(literal -1/3 binary64)) x)) x)))
(* 1/12 (pow x 7))
(*.f64 #s(literal 1/12 binary64) (pow.f64 x #s(literal 7 binary64)))
(* -1 (* (pow x 7) (- (* 17/72 (/ 1 x)) 1/12)))
(*.f64 (pow.f64 x #s(literal 7 binary64)) (-.f64 #s(literal 1/12 binary64) (/.f64 #s(literal 17/72 binary64) x)))
(* -1 (* (pow x 7) (- (* -1 (/ (- (* 1/3 (/ 1 x)) 17/72) x)) 1/12)))
(*.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 #s(literal 1/12 binary64) (/.f64 (+.f64 #s(literal -17/72 binary64) (/.f64 #s(literal 1/3 binary64) x)) x)))
(* -1 (* (pow x 7) (- (* -1 (/ (- (* -1 (/ (- (* 1/4 (/ 1 x)) 1/3) x)) 17/72) x)) 1/12)))
(*.f64 (pow.f64 x #s(literal 7 binary64)) (-.f64 #s(literal 1/12 binary64) (/.f64 (+.f64 #s(literal 17/72 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) x) #s(literal -1/3 binary64)) x)) x)))
(* 1/4 (pow x 4))
(.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 x x)))
(* (pow x 4) (+ 1/4 (* -1/3 x)))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/3 binary64))))
(* (pow x 4) (+ 1/4 (* x (- (* 17/72 x) 1/3))))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 #s(literal 1/4 binary64) (.f64 x (+.f64 #s(literal -1/3 binary64) (.f64 x #s(literal 17/72 binary64))))))
(* (pow x 4) (+ 1/4 (* x (- (* x (+ 17/72 (* -1/12 x))) 1/3))))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 #s(literal 1/4 binary64) (.f64 x (+.f64 #s(literal -1/3 binary64) (.f64 x (+.f64 #s(literal 17/72 binary64) (*.f64 x #s(literal -1/12 binary64))))))))
(* -1/12 (pow x 7))
(*.f64 (pow.f64 x #s(literal 7 binary64)) #s(literal -1/12 binary64))
(* (pow x 7) (- (* 17/72 (/ 1 x)) 1/12))
(*.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 (/.f64 #s(literal 17/72 binary64) x) #s(literal -1/12 binary64)))
(* (pow x 7) (- (* 17/72 (/ 1 x)) (+ 1/12 (/ 1/3 (pow x 2)))))
(*.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 #s(literal -1/12 binary64) (/.f64 (-.f64 #s(literal 17/72 binary64) (/.f64 #s(literal 1/3 binary64) x)) x)))
(* (pow x 7) (- (+ (* 17/72 (/ 1 x)) (* 1/4 (/ 1 (pow x 3)))) (+ 1/12 (/ 1/3 (pow x 2)))))
(*.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 #s(literal -1/12 binary64) (/.f64 (+.f64 #s(literal 17/72 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) x) #s(literal -1/3 binary64)) x)) x)))
(* -1/12 (pow x 7))
(*.f64 (pow.f64 x #s(literal 7 binary64)) #s(literal -1/12 binary64))
(* -1 (* (pow x 7) (- 1/12 (* 17/72 (/ 1 x)))))
(-.f64 #s(literal 0 binary64) (*.f64 (pow.f64 x #s(literal 7 binary64)) (-.f64 #s(literal 1/12 binary64) (/.f64 #s(literal 17/72 binary64) x))))
(* -1 (* (pow x 7) (+ 1/12 (* -1 (/ (- 17/72 (* 1/3 (/ 1 x))) x)))))
(*.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 #s(literal -1/12 binary64) (/.f64 (-.f64 #s(literal 17/72 binary64) (/.f64 #s(literal 1/3 binary64) x)) x)))
(* -1 (* (pow x 7) (+ 1/12 (* -1 (/ (+ 17/72 (* -1 (/ (- 1/3 (* 1/4 (/ 1 x))) x))) x)))))
(*.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 #s(literal -1/12 binary64) (/.f64 (+.f64 #s(literal 17/72 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) x) #s(literal -1/3 binary64)) x)) x)))
(* 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 x (+.f64 #s(literal -1/4 binary64) (/.f64 #s(literal 1/3 binary64) x))))
(* (pow x 2) (- (* 1/3 (/ 1 x)) 1/4))
(.f64 x (.f64 x (+.f64 #s(literal -1/4 binary64) (/.f64 #s(literal 1/3 binary64) x))))
(* (pow x 2) (- (* 1/3 (/ 1 x)) 1/4))
(.f64 x (.f64 x (+.f64 #s(literal -1/4 binary64) (/.f64 #s(literal 1/3 binary64) x))))
(* -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 x (+.f64 #s(literal -1/4 binary64) (/.f64 #s(literal 1/3 binary64) x))))
(* (pow x 2) (- (* 1/3 (/ 1 x)) 1/4))
(.f64 x (.f64 x (+.f64 #s(literal -1/4 binary64) (/.f64 #s(literal 1/3 binary64) x))))
(* (pow x 2) (- (* 1/3 (/ 1 x)) 1/4))
(.f64 x (.f64 x (+.f64 #s(literal -1/4 binary64) (/.f64 #s(literal 1/3 binary64) x))))
(* -1/4 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/4 binary64))
(* (pow x 2) (- (* 1/3 x) 1/4))
(.f64 (.f64 x x) (+.f64 (*.f64 x #s(literal 1/3 binary64)) #s(literal -1/4 binary64)))
(* (pow x 2) (- (* 1/3 x) 1/4))
(.f64 (.f64 x x) (+.f64 (*.f64 x #s(literal 1/3 binary64)) #s(literal -1/4 binary64)))
(* (pow x 2) (- (* 1/3 x) 1/4))
(.f64 (.f64 x x) (+.f64 (*.f64 x #s(literal 1/3 binary64)) #s(literal -1/4 binary64)))
(* 1/3 (pow x 3))
(.f64 x (.f64 #s(literal 1/3 binary64) (*.f64 x x)))
(* (pow x 3) (- 1/3 (* 1/4 (/ 1 x))))
(.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal -1/4 binary64) x)))
(* (pow x 3) (- 1/3 (* 1/4 (/ 1 x))))
(.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal -1/4 binary64) x)))
(* (pow x 3) (- 1/3 (* 1/4 (/ 1 x))))
(.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal -1/4 binary64) x)))
(* 1/3 (pow x 3))
(.f64 x (.f64 #s(literal 1/3 binary64) (*.f64 x x)))
(* -1 (* (pow x 3) (- (* 1/4 (/ 1 x)) 1/3)))
(.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal -1/4 binary64) x)))
(* -1 (* (pow x 3) (- (* 1/4 (/ 1 x)) 1/3)))
(.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal -1/4 binary64) x)))
(* -1 (* (pow x 3) (- (* 1/4 (/ 1 x)) 1/3)))
(.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal -1/4 binary64) x)))
(* -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))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))

eval140.0ms (2%)

Compiler: Compiled 50139 to 2300 computations (95.4% saved)

prune107.0ms (1.5%)

Pruning

10 alts after pruning (4 fresh and 6 done)

	Pruned	Kept	Total
New	1026	4	1030
Fresh	0	0	0
Picked	3	1	4
Done	0	5	5
Total	1029	10	1039

Accuracy

100.0%

Counts

1039 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
	35.4%	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))) (.f64 x x)) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))) (.f64 x x)))) (-.f64 x (.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))))
	36.2%	(/.f64 (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 (.f64 x #s(literal 1/3 binary64)) #s(literal -1/4 binary64)))))) x) (-.f64 x (.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))))
	35.4%	(/.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/4 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -17/72 binary64)))))))) (-.f64 x (.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))))
	36.1%	(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 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))))))) (.f64 x (-.f64 x (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/3 binary64))))))))
✓	66.6%	(+.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 x)) x)
✓	67.6%	(+.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 1/3 binary64))))) x)
✓	66.4%	(+.f64 (.f64 x (.f64 x #s(literal -1/2 binary64))) x)
✓	67.6%	(.f64 x (+.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64)) (.f64 x #s(literal -1/2 binary64))))
✓	100.0%	(log1p.f64 x)
✓	67.7%	x

Compiler

Compiled 589 to 201 computations (65.9% saved)

regimes21.0ms (0.3%)

Counts

19 → 1

Calls

Call 1

Inputs
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 (+.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 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))) (.f64 #s(literal 1/3 binary64) (.f64 x x))))
(.f64 x (+.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64)) (.f64 x #s(literal -1/2 binary64))))
(.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 (.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)) x)
(/.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 (.f64 x #s(literal 1/3 binary64)) #s(literal -1/4 binary64))))) (-.f64 x (.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 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 (.f64 x #s(literal 1/3 binary64)) #s(literal -1/4 binary64)))))) x) (-.f64 x (.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 (-.f64 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))))))) (.f64 x (-.f64 x (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/3 binary64))))))))
(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/3 binary64))))) (-.f64 x (.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 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/4 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -17/72 binary64)))))))) (-.f64 x (.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 (.f64 x x) (.f64 (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))) (.f64 x x)) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))) (.f64 x x)))) (-.f64 x (.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 (.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 x x)) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))) (.f64 x x)))) (-.f64 x (.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 (.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 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 x x)))) (-.f64 x (.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))))
(log1p.f64 x)
(log.f64 (+.f64 #s(literal 1 binary64) x))

Outputs
(log1p.f64 x)

Calls

3 calls:

9.0ms	x
5.0ms	(+.f64 #s(literal 1 binary64) x)
5.0ms	(log.f64 (+.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)

regimes6.0ms (0.1%)

Accuracy

Total -21.1b remaining (-101.9%)

Threshold costs -21.1b (-101.9%)

Counts

17 → 1

Calls

Call 1

Inputs
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 (+.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 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/2 binary64))) (.f64 #s(literal 1/3 binary64) (.f64 x x))))
(.f64 x (+.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64)) (.f64 x #s(literal -1/2 binary64))))
(.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 (.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)) x)
(/.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 (.f64 x #s(literal 1/3 binary64)) #s(literal -1/4 binary64))))) (-.f64 x (.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 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 (.f64 x #s(literal 1/3 binary64)) #s(literal -1/4 binary64)))))) x) (-.f64 x (.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 (-.f64 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))))))) (.f64 x (-.f64 x (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/3 binary64))))))))
(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/3 binary64))))) (-.f64 x (.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 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/4 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -17/72 binary64)))))))) (-.f64 x (.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 (.f64 x x) (.f64 (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))) (.f64 x x)) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))) (.f64 x x)))) (-.f64 x (.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 (.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 x x)) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 1/3 binary64))) (.f64 x x)))) (-.f64 x (.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 (.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 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 x x)))) (-.f64 x (.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))))

Outputs
x

Calls

1 calls:

5.0ms

Results

Accuracy	Segments	Branch
67.7%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2	3

Stop Event

1×

saturated

Calls

Call 1

Inputs
(log1p.f64 x)
x

Outputs
(log1p.f64 x)
x

soundness220.0ms (3.2%)

Rules

1970×	`fmsub-define`
1904×	`sum3-define`
1846×	`fma-lowering-fma.f32`
1846×	`fma-lowering-fma.f64`
1776×	`fmm-def`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	133
1	178	111
2	443	105
3	1210	103
4	3925	96
0	8245	96
0	4	2
1	8	2
0	8	2

Stop Event

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

Compiler

Compiled 12 to 7 computations (41.7% saved)

preprocess28.0ms (0.4%)

Compiler: Compiled 58 to 30 computations (48.3% saved)

analyze3.0ms (0%)

sample1.7s (24.3%)

preprocess20.0ms (0.3%)

explain112.0ms (1.6%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify3.0ms (0%)

localize39.0ms (0.6%)

series1.0ms (0%)

rewrite467.0ms (6.7%)

simplify156.0ms (2.2%)

eval9.0ms (0.1%)

prune25.0ms (0.4%)

simplify47.0ms (0.7%)

localize216.0ms (3.1%)

series30.0ms (0.4%)

rewrite581.0ms (8.3%)

simplify220.0ms (3.2%)

eval98.0ms (1.4%)

prune67.0ms (1%)

simplify213.0ms (3.1%)

localize146.0ms (2.1%)

series8.0ms (0.1%)

rewrite520.0ms (7.5%)

simplify215.0ms (3.1%)

eval254.0ms (3.6%)

prune138.0ms (2%)

simplify264.0ms (3.8%)

localize239.0ms (3.4%)

series11.0ms (0.2%)

rewrite371.0ms (5.3%)

simplify265.0ms (3.8%)

eval140.0ms (2%)

prune107.0ms (1.5%)

regimes21.0ms (0.3%)

regimes6.0ms (0.1%)

simplify6.0ms (0.1%)

soundness220.0ms (3.2%)

preprocess28.0ms (0.4%)

end0.0ms (0%)

Profiling