Metrics for expm1 (example 3.7)

analyze0.0ms (0%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	50%	50%	0%	0%	0%	0
100%	50%	0%	50%	0%	0%	0%	1

Compiler

Compiled 9 to 6 computations (33.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 0.0ms

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

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

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

const: 0.0ms (0% of total)

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

ival-<=: 0.0ms (0% of total)

sample1.6s (31.9%)

Results

1.4s	8073×	1	valid
9.0ms	183×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 1000.0ms

ival-exp: 543.0ms (54.3% of total)

ival-sub: 199.0ms (19.9% of total)

backward-pass: 121.0ms (12.1% of total)

ival-<=: 68.0ms (6.8% of total)

ival-fabs: 57.0ms (5.7% of total)

const: 12.0ms (1.2% of total)

Bogosity

preprocess22.0ms (0.4%)

Algorithm

2×	egg-herbie

Rules

60×	`sum3-define`
58×	`fmsub-define`
30×	`fmm-def`
28×	`fma-define`
28×	`sub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	9
1	21	9
2	41	9
3	62	9
4	96	9
5	134	9
6	161	9
7	199	9
8	225	9
9	238	9
10	250	9
11	251	9
0	4	2
1	10	2
2	11	2
0	11	2

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(- (exp x) 1)

Outputs
(- (exp x) 1)
(expm1.f64 x)

Call 2

Inputs
(- (exp x) 1)
(- (exp (neg x)) 1)
(neg (- (exp (neg x)) 1))

Outputs
(- (exp x) 1)
(expm1 x)
(- (exp (neg x)) 1)
(expm1 (neg x))
(neg (- (exp (neg x)) 1))
(neg (expm1 (neg x)))

explain129.0ms (2.5%)

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
256	-	-	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`
0	-	-	`x`
0	-	-	`(exp.f64 x)`
0	-	-	`#s(literal 1 binary64)`

Results

94.0ms	504×	1	valid
0.0ms	8×	0	valid

Compiler

Compiled 25 to 14 computations (44% saved)

Precisions

Click to see histograms. Total time spent on operations: 56.0ms

ival-exp: 40.0ms (71.3% of total)

backward-pass: 8.0ms (14.3% of total)

ival-sub: 6.0ms (10.7% of total)

const: 1.0ms (1.8% 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%	(expm1.f64 x)

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 1 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(expm1.f64 x)

Rules

4×	`+-lowering-+.f64`
4×	`+-lowering-+.f32`
2×	`exp-lowering-exp.f32`
2×	`expm1-lowering-expm1.f32`
2×	`1-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	3
1	10	3
2	11	3
0	11	3

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(- (exp x) 1)
x

Outputs
(- (exp x) 1)
(expm1.f64 x)
x

localize53.0ms (1%)

Localize:

Found 1 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(expm1.f64 x)

Results

46.0ms	252×	5	exit
0.0ms	4×	0	valid

Compiler

Compiled 5 to 3 computations (40% saved)

Precisions

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

backward-pass: 6.0ms (42.1% of total)

compiled-spec: 4.0ms (28% of total)

ival-exp: 2.0ms (14% of total)

ival-sub: 2.0ms (14% of total)

const: 0.0ms (0% of total)

series1.0ms (0%)

Counts

1 → 12

Calls

Call 1

Inputs
#<alt (- (exp x) 1)>

Outputs
#<alt x>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))>
#<alt (* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>

Calls

3 calls:

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

rewrite29.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

4×	`+-lowering-+.f64`
4×	`+-lowering-+.f32`
2×	`exp-lowering-exp.f32`
2×	`--lowering--.f32`
2×	`expm1-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	2
1	10	2
2	11	2
0	11	2

Stop Event

1×	iter limit
1×	saturated

Counts

1 → 4

Calls

Call 1

Inputs
(- (exp x) 1)

Outputs
(+.f64 (exp.f64 x) #s(literal -1 binary64))
(+.f64 #s(literal -1 binary64) (exp.f64 x))
(-.f64 (exp.f64 x) #s(literal 1 binary64))
(expm1.f64 x)

simplify67.0ms (1.3%)

Algorithm

1×	egg-herbie

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	22	50
1	72	44
2	190	41
3	465	41
4	976	41
5	1402	41
6	1563	41
7	1565	41
0	1565	41

Stop Event

1×	iter limit
1×	saturated

Counts

12 → 12

Calls

Call 1

Inputs
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)

Outputs
x
(* x (+ 1 (* 1/2 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))))))
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)

eval2.0ms (0%)

Compiler: Compiled 65 to 26 computations (60% saved)

prune4.0ms (0.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	12	4	16
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	12	5	17

Accuracy

100.0%

Counts

17 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.9%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))))))
▶	99.8%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
▶	99.4%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))
✓	100.0%	(expm1.f64 x)
▶	98.7%	x

Compiler

Compiled 41 to 30 computations (26.8% saved)

simplify50.0ms (1%)

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 1/6 binary64) (.f64 x #s(literal 1/24 binary64)))))
✓	cost-diff	(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64))))))
✓	cost-diff	(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64)))))))
✓	cost-diff	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))))))
✓	cost-diff	(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))
✓	cost-diff	(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
✓	cost-diff	(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))
✓	cost-diff	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 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	969	103
5	1396	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 1/6)))))
x
(+ 1 (* x (+ 1/2 (* x 1/6))))
1
(* x (+ 1/2 (* x 1/6)))
(+ 1/2 (* x 1/6))
1/2
(* x 1/6)
1/6
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* x 1/24)))))))
x
(+ 1 (* x (+ 1/2 (* x (+ 1/6 (* x 1/24))))))
1
(* x (+ 1/2 (* x (+ 1/6 (* x 1/24)))))
(+ 1/2 (* x (+ 1/6 (* x 1/24))))
1/2
(* x (+ 1/6 (* x 1/24)))
(+ 1/6 (* x 1/24))
1/6
(* x 1/24)
1/24

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 1/6)))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
x
(+ 1 (* x (+ 1/2 (* x 1/6))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))
1
#s(literal 1 binary64)
(* x (+ 1/2 (* x 1/6)))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(+ 1/2 (* x 1/6))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))
1/2
#s(literal 1/2 binary64)
(* x 1/6)
(*.f64 x #s(literal 1/6 binary64))
1/6
#s(literal 1/6 binary64)
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* x 1/24)))))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))))))
x
(+ 1 (* x (+ 1/2 (* x (+ 1/6 (* x 1/24))))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64)))))))
1
#s(literal 1 binary64)
(* x (+ 1/2 (* x (+ 1/6 (* x 1/24)))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64))))))
(+ 1/2 (* x (+ 1/6 (* x 1/24))))
(+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64)))))
1/2
#s(literal 1/2 binary64)
(* x (+ 1/6 (* x 1/24)))
(.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))
(+ 1/6 (* x 1/24))
(+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64)))
1/6
#s(literal 1/6 binary64)
(* x 1/24)
(*.f64 x #s(literal 1/24 binary64))
1/24
#s(literal 1/24 binary64)

localize113.0ms (2.2%)

Localize:

Found 11 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64)))
✓	accuracy	100.0%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))))))
✓	accuracy	99.5%	(.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))
✓	accuracy	99.5%	(*.f64 x #s(literal 1/24 binary64))
✓	accuracy	100.0%	(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))
✓	accuracy	100.0%	(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
✓	accuracy	100.0%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
✓	accuracy	99.5%	(*.f64 x #s(literal 1/6 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

82.0ms

256×

valid

Compiler

Compiled 128 to 21 computations (83.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 30.0ms

ival-mult: 15.0ms (49.4% of total)

ival-add: 7.0ms (23.1% of total)

...c/correct-round.rkt:119:19: 7.0ms (23.1% of total)

const: 1.0ms (3.3% of total)

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

series10.0ms (0.2%)

Counts

15 → 180

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 1/6)))))>
#<alt (+ 1 (* x (+ 1/2 (* x 1/6))))>
#<alt (* x (+ 1/2 (* x 1/6)))>
#<alt (+ 1/2 (* x 1/6))>
#<alt (* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* x 1/24)))))))>
#<alt (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* x 1/24))))))>
#<alt (* x (+ 1/2 (* x (+ 1/6 (* x 1/24)))))>
#<alt (+ 1/2 (* x (+ 1/6 (* x 1/24))))>
#<alt (* x 1/6)>
#<alt (* x 1/24)>
#<alt (* x (+ 1/6 (* x 1/24)))>
#<alt (+ 1/6 (* x 1/24))>

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) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* 1/2 x))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt x>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))>
#<alt (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))>
#<alt 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* x (+ 1/2 (* 1/6 x))))>
#<alt (+ 1 (* x (+ 1/2 (* 1/6 x))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* 1/6 x)))>
#<alt (* x (+ 1/2 (* 1/6 x)))>
#<alt (* x (+ 1/2 (* 1/6 x)))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/6 x))>
#<alt (+ 1/2 (* 1/6 x))>
#<alt (+ 1/2 (* 1/6 x))>
#<alt (* 1/6 x)>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* 1/6 x)>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))>
#<alt (* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))>
#<alt (* 1/24 (pow x 4))>
#<alt (* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))>
#<alt (* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (+ (* 1/6 (/ 1 x)) (/ 1 (pow x 3))))))>
#<alt (* 1/24 (pow x 4))>
#<alt (* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))>
#<alt (* (pow x 4) (+ 1/24 (* -1 (/ (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6) x))))>
#<alt 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* x (+ 1/2 (* 1/6 x))))>
#<alt (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x))))))>
#<alt (* 1/24 (pow x 3))>
#<alt (* (pow x 3) (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* (pow x 3) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))>
#<alt (* (pow x 3) (+ 1/24 (+ (/ 1/2 (pow x 2)) (+ (* 1/6 (/ 1 x)) (/ 1 (pow x 3))))))>
#<alt (* 1/24 (pow x 3))>
#<alt (* (pow x 3) (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/6 (* 1/2 (/ 1 x))) x)) 1/24)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))) x)) 1/24)))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* 1/6 x)))>
#<alt (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))>
#<alt (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))>
#<alt (* 1/24 (pow x 3))>
#<alt (* (pow x 3) (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* (pow x 3) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))>
#<alt (* (pow x 3) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))>
#<alt (* 1/24 (pow x 3))>
#<alt (* (pow x 3) (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/6 (* 1/2 (/ 1 x))) x)) 1/24)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/6 (* 1/2 (/ 1 x))) x)) 1/24)))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/6 x))>
#<alt (+ 1/2 (* x (+ 1/6 (* 1/24 x))))>
#<alt (+ 1/2 (* x (+ 1/6 (* 1/24 x))))>
#<alt (* 1/24 (pow x 2))>
#<alt (* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))>
#<alt (* (pow x 2) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))>
#<alt (* 1/24 (pow x 2))>
#<alt (* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))>
#<alt (* (pow x 2) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/6 x)>
#<alt (* x (+ 1/6 (* 1/24 x)))>
#<alt (* x (+ 1/6 (* 1/24 x)))>
#<alt (* x (+ 1/6 (* 1/24 x)))>
#<alt (* 1/24 (pow x 2))>
#<alt (* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* 1/24 (pow x 2))>
#<alt (* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt 1/6>
#<alt (+ 1/6 (* 1/24 x))>
#<alt (+ 1/6 (* 1/24 x))>
#<alt (+ 1/6 (* 1/24 x))>
#<alt (* 1/24 x)>
#<alt (* x (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* x (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* x (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* 1/24 x)>
#<alt (* x (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* x (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* x (+ 1/24 (* 1/6 (/ 1 x))))>

Calls

45 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(* x 1/24)
1.0ms	x	@	inf	(* x (+ 1 (* x (+ 1/2 (* x 1/6)))))
1.0ms	x	@	-inf	(* x (+ 1 (* x 1/2)))
0.0ms	x	@	inf	(* x (+ 1 (* x 1/2)))
0.0ms	x	@	-inf	(* x (+ 1 (* x (+ 1/2 (* x 1/6)))))

rewrite92.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

1464×	`fma-define`
1096×	`fma-lowering-fma.f32`
1096×	`fma-lowering-fma.f64`
354×	`-lowering-.f32`
354×	`-lowering-.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	20	113
1	66	93
2	184	90
3	459	90
4	973	90
5	1409	90
6	1607	90
7	1654	90
8	1767	90
9	1828	90
0	1828	90

Stop Event

1×	iter limit
1×	saturated

Counts

15 → 374

Calls

Call 1

Inputs
(* x (+ 1 (* x 1/2)))
(+ 1 (* x 1/2))
(* x 1/2)
(* x (+ 1 (* x (+ 1/2 (* x 1/6)))))
(+ 1 (* x (+ 1/2 (* x 1/6))))
(* x (+ 1/2 (* x 1/6)))
(+ 1/2 (* x 1/6))
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* x 1/24)))))))
(+ 1 (* x (+ 1/2 (* x (+ 1/6 (* x 1/24))))))
(* x (+ 1/2 (* x (+ 1/6 (* x 1/24)))))
(+ 1/2 (* x (+ 1/6 (* x 1/24))))
(* x 1/6)
(* x 1/24)
(* x (+ 1/6 (* x 1/24)))
(+ 1/6 (* x 1/24))

Outputs
(+.f64 x (.f64 #s(literal 1/2 binary64) (.f64 x x)))
(+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) x)
(fma.f64 x #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (.f64 x x)))
(fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x)
(fma.f64 #s(literal 1 binary64) x (.f64 #s(literal 1/2 binary64) (.f64 x x)))
(fma.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (.f64 x x)) x)
(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 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 1 binary64) x)
(fma.f64 (*.f64 x x) #s(literal 1/2 binary64) x)
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))
(.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))))
(.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))) x)
(.f64 (.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))) #s(literal 1 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))
(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))
(.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))
(.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))) #s(literal 1 binary64))
(*.f64 x #s(literal 1/2 binary64))
(.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)))
(*.f64 #s(literal 1/2 binary64) x)
(.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))
(+.f64 x (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))) (*.f64 x x)))
(+.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)))) (.f64 #s(literal 1/6 binary64) (.f64 x (*.f64 x x))))
(+.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))) (*.f64 x x)) x)
(+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal 1/6 binary64))))))
(+.f64 (.f64 #s(literal 1/6 binary64) (.f64 x (.f64 x x))) (.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))))
(+.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))) (.f64 #s(literal 1/2 binary64) (*.f64 x x)))
(fma.f64 x #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))) (*.f64 x x)))
(fma.f64 x (.f64 x #s(literal 1/2 binary64)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))))
(fma.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))) (.f64 #s(literal 1/6 binary64) (.f64 x (.f64 x x))))
(fma.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))) x)
(fma.f64 x (.f64 x (.f64 x #s(literal 1/6 binary64))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)))))
(fma.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64)))) (.f64 #s(literal 1/2 binary64) (.f64 x x)))
(fma.f64 #s(literal 1 binary64) x (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))) (*.f64 x x)))
(fma.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)))) (.f64 #s(literal 1/6 binary64) (.f64 x (*.f64 x x))))
(fma.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))) (*.f64 x x)) x)
(fma.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal 1/6 binary64))))))
(fma.f64 #s(literal 1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 x (.f64 x x))) (.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))))
(fma.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))) (.f64 #s(literal 1/2 binary64) (*.f64 x x)))
(fma.f64 #s(literal 1/2 binary64) (.f64 x x) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))))
(fma.f64 (.f64 x #s(literal 1/2 binary64)) x (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))))
(fma.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))) x (.f64 #s(literal 1/6 binary64) (.f64 x (.f64 x x))))
(fma.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)))) #s(literal 1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 x (*.f64 x x))))
(fma.f64 #s(literal 1/6 binary64) (.f64 x (.f64 x x)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)))))
(fma.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 x x) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)))))
(fma.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))) (.f64 x x) x)
(fma.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))) x x)
(fma.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))) (*.f64 x x)) #s(literal 1 binary64) x)
(fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal 1/6 binary64))))))
(fma.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) x (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)))))
(fma.f64 (.f64 #s(literal 1/6 binary64) (.f64 x (.f64 x x))) #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))))
(fma.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64)))) x (.f64 #s(literal 1/2 binary64) (.f64 x x)))
(fma.f64 (.f64 x x) #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))))
(fma.f64 (.f64 x x) (.f64 x #s(literal 1/6 binary64)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)))))
(fma.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))) x)
(fma.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))) #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (*.f64 x x)))
(fma.f64 (.f64 x (.f64 x x)) #s(literal 1/6 binary64) (.f64 x (+.f64 #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 #s(literal 1/6 binary64))))))
(.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))))
(.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))) x)
(.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))
(+.f64 (.f64 x #s(literal 1/2 binary64)) (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal 1/6 binary64)))))
(+.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))) (.f64 x (*.f64 x #s(literal 1/6 binary64))))
(+.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))) #s(literal 1 binary64))
(+.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))))
(+.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64)))) (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 x #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64)))))
(fma.f64 x (.f64 x #s(literal 1/6 binary64)) (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))
(fma.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)) (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal 1/6 binary64)))))
(fma.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))) (.f64 x (*.f64 x #s(literal 1/6 binary64))))
(fma.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))))
(fma.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64)))) (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64)))))
(fma.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal 1/6 binary64)))))
(fma.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))) #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal 1/6 binary64))))
(fma.f64 #s(literal 1/6 binary64) (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))
(fma.f64 (.f64 x #s(literal 1/6 binary64)) x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))
(fma.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))) x #s(literal 1 binary64))
(fma.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))) #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))))
(fma.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64)))) #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 (.f64 x x) #s(literal 1/6 binary64) (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))
(.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))) #s(literal 1 binary64))
(+.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x (*.f64 x #s(literal 1/6 binary64))))
(+.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 x #s(literal 1/2 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))
(fma.f64 x (.f64 x #s(literal 1/6 binary64)) (.f64 x #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)) (.f64 x (*.f64 x #s(literal 1/6 binary64))))
(fma.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))) (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) x (.f64 x (.f64 x #s(literal 1/6 binary64))))
(fma.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal 1/6 binary64))))
(fma.f64 #s(literal 1/6 binary64) (.f64 x x) (.f64 x #s(literal 1/2 binary64)))
(fma.f64 (.f64 x #s(literal 1/6 binary64)) x (.f64 x #s(literal 1/2 binary64)))
(fma.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 (.f64 x x) #s(literal 1/6 binary64) (.f64 x #s(literal 1/2 binary64)))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))
(.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))) x)
(.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) #s(literal 1 binary64))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))
(+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1 binary64) #s(literal 1/2 binary64))
(.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal 1 binary64))
(+.f64 x (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x)))
(+.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)))) (.f64 (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))) (.f64 x (.f64 x x))))
(+.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))) (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x (*.f64 x x)))))
(+.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))) (.f64 x x)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x #s(literal 1/24 binary64)))))))
(+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))))))
(+.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x)) x)
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(fma.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x #s(literal 1/24 binary64)))) #s(literal 1 binary64) (*.f64 x #s(literal 1/6 binary64)))
(fma.f64 (.f64 x x) #s(literal 1/24 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64))))))
(.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64))))) #s(literal 1 binary64))
(*.f64 x #s(literal 1/6 binary64))
(.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/6 binary64)))
(*.f64 #s(literal 1/6 binary64) x)
(.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1 binary64))
(*.f64 x #s(literal 1/24 binary64))
(.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/24 binary64)))
(*.f64 #s(literal 1/24 binary64) x)
(.f64 (.f64 x #s(literal 1/24 binary64)) #s(literal 1 binary64))
(+.f64 (.f64 x #s(literal 1/6 binary64)) (.f64 x (*.f64 x #s(literal 1/24 binary64))))
(+.f64 (.f64 x (.f64 x #s(literal 1/24 binary64))) (*.f64 x #s(literal 1/6 binary64)))
(fma.f64 x #s(literal 1/6 binary64) (.f64 x (.f64 x #s(literal 1/24 binary64))))
(fma.f64 x (.f64 x #s(literal 1/24 binary64)) (.f64 x #s(literal 1/6 binary64)))
(fma.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/6 binary64)) (.f64 x (*.f64 x #s(literal 1/24 binary64))))
(fma.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/24 binary64))) (*.f64 x #s(literal 1/6 binary64)))
(fma.f64 #s(literal 1/6 binary64) x (.f64 x (.f64 x #s(literal 1/24 binary64))))
(fma.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal 1/24 binary64))))
(fma.f64 #s(literal 1/24 binary64) (.f64 x x) (.f64 x #s(literal 1/6 binary64)))
(fma.f64 (.f64 x #s(literal 1/24 binary64)) x (.f64 x #s(literal 1/6 binary64)))
(fma.f64 (.f64 x (.f64 x #s(literal 1/24 binary64))) #s(literal 1 binary64) (*.f64 x #s(literal 1/6 binary64)))
(fma.f64 (.f64 x x) #s(literal 1/24 binary64) (.f64 x #s(literal 1/6 binary64)))
(.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))
(.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64)))))
(.f64 (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))) x)
(.f64 (.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64)))) #s(literal 1 binary64))
(+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64)))
(+.f64 (*.f64 x #s(literal 1/24 binary64)) #s(literal 1/6 binary64))
(fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64))
(fma.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/24 binary64)) #s(literal 1/6 binary64))
(fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64))
(fma.f64 (*.f64 x #s(literal 1/24 binary64)) #s(literal 1 binary64) #s(literal 1/6 binary64))
(.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))
(.f64 (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))) #s(literal 1 binary64))

simplify217.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

3028×	`-lowering-.f32`
3028×	`-lowering-.f64`
2026×	`+-lowering-+.f64`
2026×	`+-lowering-+.f32`
1870×	`sum3-define`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	84	1189
1	313	981
2	1004	948
3	3990	938
4	6989	935
0	8192	935

Stop Event

1×	iter limit
1×	node limit

Counts

180 → 180

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) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
1
(+ 1 (* 1/2 x))
(+ 1 (* 1/2 x))
(+ 1 (* 1/2 x))
(* 1/2 x)
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* 1/2 x)
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* 1/2 x)
(* x (+ 1/2 (* 1/6 x)))
(* x (+ 1/2 (* 1/6 x)))
(* x (+ 1/2 (* 1/6 x)))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
1/2
(+ 1/2 (* 1/6 x))
(+ 1/2 (* 1/6 x))
(+ 1/2 (* 1/6 x))
(* 1/6 x)
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* 1/6 x)
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(* 1/24 (pow x 4))
(* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (+ (* 1/6 (/ 1 x)) (/ 1 (pow x 3))))))
(* 1/24 (pow x 4))
(* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(* (pow x 4) (+ 1/24 (* -1 (/ (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6) x))))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x))))))
(* 1/24 (pow x 3))
(* (pow x 3) (+ 1/24 (* 1/6 (/ 1 x))))
(* (pow x 3) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(* (pow x 3) (+ 1/24 (+ (/ 1/2 (pow x 2)) (+ (* 1/6 (/ 1 x)) (/ 1 (pow x 3))))))
(* 1/24 (pow x 3))
(* (pow x 3) (+ 1/24 (* 1/6 (/ 1 x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/6 (* 1/2 (/ 1 x))) x)) 1/24)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))) x)) 1/24)))
(* 1/2 x)
(* x (+ 1/2 (* 1/6 x)))
(* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))
(* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))
(* 1/24 (pow x 3))
(* (pow x 3) (+ 1/24 (* 1/6 (/ 1 x))))
(* (pow x 3) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(* (pow x 3) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(* 1/24 (pow x 3))
(* (pow x 3) (+ 1/24 (* 1/6 (/ 1 x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/6 (* 1/2 (/ 1 x))) x)) 1/24)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/6 (* 1/2 (/ 1 x))) x)) 1/24)))
1/2
(+ 1/2 (* 1/6 x))
(+ 1/2 (* x (+ 1/6 (* 1/24 x))))
(+ 1/2 (* x (+ 1/6 (* 1/24 x))))
(* 1/24 (pow x 2))
(* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))
(* (pow x 2) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(* (pow x 2) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(* 1/24 (pow x 2))
(* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))
(* (pow x 2) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(* (pow x 2) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/6 x)
(* x (+ 1/6 (* 1/24 x)))
(* x (+ 1/6 (* 1/24 x)))
(* x (+ 1/6 (* 1/24 x)))
(* 1/24 (pow x 2))
(* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))
(* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))
(* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))
(* 1/24 (pow x 2))
(* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))
(* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))
(* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))
1/6
(+ 1/6 (* 1/24 x))
(+ 1/6 (* 1/24 x))
(+ 1/6 (* 1/24 x))
(* 1/24 x)
(* x (+ 1/24 (* 1/6 (/ 1 x))))
(* x (+ 1/24 (* 1/6 (/ 1 x))))
(* x (+ 1/24 (* 1/6 (/ 1 x))))
(* 1/24 x)
(* x (+ 1/24 (* 1/6 (/ 1 x))))
(* x (+ 1/24 (* 1/6 (/ 1 x))))
(* x (+ 1/24 (* 1/6 (/ 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 #s(literal 1/2 binary64) (.f64 x x))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(.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 (+ 1/2 (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))
(* x (+ 1/2 (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))
(* x (+ 1/2 (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (+ 1/2 (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))
(* x (+ 1/2 (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))
(* x (+ 1/2 (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
x
(* x (+ 1 (* 1/2 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(* 1/6 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/6 binary64))))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(* 1/6 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/6 binary64))))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(.f64 x (.f64 (*.f64 x x) (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(.f64 x (.f64 (*.f64 x x) (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x))))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))
(* 1/6 (pow x 2))
(.f64 x (.f64 x #s(literal 1/6 binary64)))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))
(* 1/6 (pow x 2))
(.f64 x (.f64 x #s(literal 1/6 binary64)))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (+ 1/2 (* 1/6 x)))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(* x (+ 1/2 (* 1/6 x)))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(* x (+ 1/2 (* 1/6 x)))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(* 1/6 (pow x 2))
(.f64 x (.f64 x #s(literal 1/6 binary64)))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(* 1/6 (pow x 2))
(.f64 x (.f64 x #s(literal 1/6 binary64)))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/6 x))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))
(+ 1/2 (* 1/6 x))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))
(+ 1/2 (* 1/6 x))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))
x
(* x (+ 1 (* 1/2 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))))))
(* 1/24 (pow x 4))
(.f64 #s(literal 1/24 binary64) (.f64 (.f64 x (.f64 x x)) x))
(* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))
(.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(.f64 (.f64 (.f64 x (.f64 x x)) x) (+.f64 #s(literal 1/24 binary64) (*.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 1/2 binary64) x)))))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (+ (* 1/6 (/ 1 x)) (/ 1 (pow x 3))))))
(.f64 (.f64 (.f64 x (.f64 x x)) x) (+.f64 (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/6 binary64) x)) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))))
(* 1/24 (pow x 4))
(.f64 #s(literal 1/24 binary64) (.f64 (.f64 x (.f64 x x)) x))
(* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))
(.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(.f64 (.f64 (.f64 x (.f64 x x)) x) (+.f64 #s(literal 1/24 binary64) (*.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 1/2 binary64) x)))))
(* (pow x 4) (+ 1/24 (* -1 (/ (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6) x))))
(.f64 (.f64 (.f64 x (.f64 x x)) x) (+.f64 #s(literal 1/24 binary64) (/.f64 (+.f64 #s(literal 1/6 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 (+ 1/2 (* 1/6 x))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))
(+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x))))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64)))))))
(* 1/24 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/24 binary64))))
(* (pow x 3) (+ 1/24 (* 1/6 (/ 1 x))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64))))
(* (pow x 3) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64))))))
(* (pow x 3) (+ 1/24 (+ (/ 1/2 (pow x 2)) (+ (* 1/6 (/ 1 x)) (/ 1 (pow x 3))))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64)))))))
(* 1/24 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/24 binary64))))
(* (pow x 3) (+ 1/24 (* 1/6 (/ 1 x))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/6 (* 1/2 (/ 1 x))) x)) 1/24)))
(.f64 (.f64 x x) (+.f64 (*.f64 x #s(literal 1/24 binary64)) (neg.f64 (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal -1/2 binary64) x)))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))) x)) 1/24)))
(-.f64 (.f64 x (.f64 x (.f64 x #s(literal 1/24 binary64)))) (neg.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (+ 1/2 (* 1/6 x)))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64))))))
(* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64))))))
(* 1/24 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/24 binary64))))
(* (pow x 3) (+ 1/24 (* 1/6 (/ 1 x))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64))))
(* (pow x 3) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64))))))
(* (pow x 3) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64))))))
(* 1/24 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/24 binary64))))
(* (pow x 3) (+ 1/24 (* 1/6 (/ 1 x))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/6 (* 1/2 (/ 1 x))) x)) 1/24)))
(.f64 (.f64 x x) (+.f64 (*.f64 x #s(literal 1/24 binary64)) (neg.f64 (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal -1/2 binary64) x)))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/6 (* 1/2 (/ 1 x))) x)) 1/24)))
(.f64 (.f64 x x) (+.f64 (*.f64 x #s(literal 1/24 binary64)) (neg.f64 (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal -1/2 binary64) x)))))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/6 x))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))
(+ 1/2 (* x (+ 1/6 (* 1/24 x))))
(+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64)))))
(+ 1/2 (* x (+ 1/6 (* 1/24 x))))
(+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64)))))
(* 1/24 (pow x 2))
(.f64 x (.f64 x #s(literal 1/24 binary64)))
(* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))
(* (pow x 2) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64)))))
(* (pow x 2) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64)))))
(* 1/24 (pow x 2))
(.f64 x (.f64 x #s(literal 1/24 binary64)))
(* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))
(* (pow x 2) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64)))))
(* (pow x 2) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64)))))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* x (+ 1/6 (* 1/24 x)))
(.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))
(* x (+ 1/6 (* 1/24 x)))
(.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))
(* x (+ 1/6 (* 1/24 x)))
(.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))
(* 1/24 (pow x 2))
(.f64 x (.f64 x #s(literal 1/24 binary64)))
(* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))
(* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))
(* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))
(* 1/24 (pow x 2))
(.f64 x (.f64 x #s(literal 1/24 binary64)))
(* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))
(* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))
(* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))
1/6
#s(literal 1/6 binary64)
(+ 1/6 (* 1/24 x))
(+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64)))
(+ 1/6 (* 1/24 x))
(+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64)))
(+ 1/6 (* 1/24 x))
(+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64)))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* x (+ 1/24 (* 1/6 (/ 1 x))))
(+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64)))
(* x (+ 1/24 (* 1/6 (/ 1 x))))
(+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64)))
(* x (+ 1/24 (* 1/6 (/ 1 x))))
(+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64)))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* x (+ 1/24 (* 1/6 (/ 1 x))))
(+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64)))
(* x (+ 1/24 (* 1/6 (/ 1 x))))
(+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64)))
(* x (+ 1/24 (* 1/6 (/ 1 x))))
(+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64)))

eval63.0ms (1.2%)

Compiler: Compiled 8003 to 883 computations (89% saved)

prune49.0ms (1%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	551	3	554
Fresh	0	0	0
Picked	2	2	4
Done	0	1	1
Total	553	6	559

Accuracy

100.0%

Counts

559 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(+.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x)) x)
▶	99.5%	(+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) x)
▶	26.0%	(.f64 (.f64 (.f64 x (.f64 x x)) x) (+.f64 #s(literal 1/24 binary64) (/.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) x)))
✓	99.8%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
✓	100.0%	(expm1.f64 x)
✓	98.7%	x

Compiler

Compiled 63 to 43 computations (31.7% saved)

simplify186.0ms (3.6%)

Algorithm

1×	egg-herbie

Localize:

Found 11 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))
✓	cost-diff	0	(+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64)))))
✓	cost-diff	0	(.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x))
✓	cost-diff	0	(+.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x)) x)
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(.f64 #s(literal 1/2 binary64) (.f64 x x))
✓	cost-diff	0	(+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) x)
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(.f64 x (.f64 x x))
✓	cost-diff	0	(.f64 (.f64 x (*.f64 x x)) x)
✓	cost-diff	384	(.f64 (.f64 (.f64 x (.f64 x x)) x) (+.f64 #s(literal 1/24 binary64) (/.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) x)))

Rules

2956×	`-lowering-.f32`
2956×	`-lowering-.f64`
1990×	`fma-define`
1820×	`+-lowering-+.f64`
1820×	`+-lowering-+.f32`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	23	148
1	63	136
2	153	136
3	368	136
4	815	136
5	1405	126
6	2344	126
7	5042	126
8	6694	126
9	7374	126
0	8014	126

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(* (* (* x (* x x)) x) (+ 1/24 (/ (+ 1/6 (/ (+ 1/2 (/ 1 x)) x)) x)))
(* (* x (* x x)) x)
(* x (* x x))
x
(* x x)
(+ 1/24 (/ (+ 1/6 (/ (+ 1/2 (/ 1 x)) x)) x))
1/24
(/ (+ 1/6 (/ (+ 1/2 (/ 1 x)) x)) x)
(+ 1/6 (/ (+ 1/2 (/ 1 x)) x))
1/6
(/ (+ 1/2 (/ 1 x)) x)
(+ 1/2 (/ 1 x))
1/2
(/ 1 x)
1
(+ (* 1/2 (* x x)) x)
(* 1/2 (* x x))
1/2
(* x x)
x
(+ (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) x)
(* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x))
(+ 1/2 (* x (+ 1/6 (* x 1/24))))
1/2
(* x (+ 1/6 (* x 1/24)))
x
(+ 1/6 (* x 1/24))
1/6
(* x 1/24)
1/24
(* x x)

Outputs
(* (* (* x (* x x)) x) (+ 1/24 (/ (+ 1/6 (/ (+ 1/2 (/ 1 x)) x)) x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))))))
(* (* x (* x x)) x)
(.f64 x (.f64 x (*.f64 x x)))
(* x (* x x))
(.f64 x (.f64 x x))
x
(* x x)
(*.f64 x x)
(+ 1/24 (/ (+ 1/6 (/ (+ 1/2 (/ 1 x)) x)) x))
(+.f64 #s(literal 1/24 binary64) (/.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) x))
1/24
#s(literal 1/24 binary64)
(/ (+ 1/6 (/ (+ 1/2 (/ 1 x)) x)) x)
(/.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) x)
(+ 1/6 (/ (+ 1/2 (/ 1 x)) x))
(+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x))
1/6
#s(literal 1/6 binary64)
(/ (+ 1/2 (/ 1 x)) x)
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)
(+ 1/2 (/ 1 x))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x))
1/2
#s(literal 1/2 binary64)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
1
#s(literal 1 binary64)
(+ (* 1/2 (* x x)) x)
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))
(* 1/2 (* x x))
(.f64 x (.f64 x #s(literal 1/2 binary64)))
1/2
#s(literal 1/2 binary64)
(* x x)
(*.f64 x x)
x
(+ (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) x)
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))))))
(* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x))
(.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))))
(+ 1/2 (* x (+ 1/6 (* x 1/24))))
(+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64)))))
1/2
#s(literal 1/2 binary64)
(* x (+ 1/6 (* x 1/24)))
(.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))
x
(+ 1/6 (* x 1/24))
(+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64)))
1/6
#s(literal 1/6 binary64)
(* x 1/24)
(*.f64 x #s(literal 1/24 binary64))
1/24
#s(literal 1/24 binary64)
(* x x)
(*.f64 x x)

localize137.0ms (2.7%)

Localize:

Found 11 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64)))
✓	accuracy	100.0%	(.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x))
✓	accuracy	99.5%	(.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))
✓	accuracy	99.5%	(*.f64 x #s(literal 1/24 binary64))
✓	accuracy	100.0%	(+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) x)
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(.f64 #s(literal 1/2 binary64) (.f64 x x))
✓	accuracy	99.8%	(.f64 x (.f64 x x))
✓	accuracy	99.8%	(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)
✓	accuracy	99.8%	(.f64 (.f64 x (*.f64 x x)) x)
✓	accuracy	27.2%	(.f64 (.f64 (.f64 x (.f64 x x)) x) (+.f64 #s(literal 1/24 binary64) (/.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) x)))

Results

96.0ms

256×

valid

Compiler

Compiled 167 to 24 computations (85.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 45.0ms

ival-mult: 20.0ms (44.2% of total)

ival-add: 10.0ms (22.1% of total)

...c/correct-round.rkt:119:19: 8.0ms (17.7% of total)

ival-div: 6.0ms (13.3% of total)

const: 1.0ms (2.2% of total)

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

series6.0ms (0.1%)

Counts

13 → 156

Calls

Call 1

Inputs
#<alt (* (* (* x (* x x)) x) (+ 1/24 (/ (+ 1/6 (/ (+ 1/2 (/ 1 x)) x)) x)))>
#<alt (* (* x (* x x)) x)>
#<alt (* x (* x x))>
#<alt (* x x)>
#<alt (+ (* 1/2 (* x x)) x)>
#<alt (* 1/2 (* x x))>
#<alt (+ (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) x)>
#<alt (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x))>
#<alt (+ 1/2 (* x (+ 1/6 (* x 1/24))))>
#<alt (* x (+ 1/6 (* x 1/24)))>
#<alt (/ (+ 1/2 (/ 1 x)) x)>
#<alt (* x 1/24)>
#<alt (+ 1/6 (* x 1/24))>

Outputs
#<alt x>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))>
#<alt (* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))>
#<alt (* 1/24 (pow x 4))>
#<alt (* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))>
#<alt (* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (+ (* 1/6 (/ 1 x)) (/ 1 (pow x 3))))))>
#<alt (* 1/24 (pow x 4))>
#<alt (* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))>
#<alt (* (pow x 4) (+ 1/24 (* -1 (/ (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6) x))))>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (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 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) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<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 x>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))>
#<alt (* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))>
#<alt (* 1/24 (pow x 4))>
#<alt (* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))>
#<alt (* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (+ (* 1/6 (/ 1 x)) (/ 1 (pow x 3))))))>
#<alt (* 1/24 (pow x 4))>
#<alt (* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))>
#<alt (* (pow x 4) (+ 1/24 (* -1 (/ (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6) x))))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (* 1/6 x)))>
#<alt (* (pow x 2) (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))>
#<alt (* (pow x 2) (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))>
#<alt (* 1/24 (pow x 4))>
#<alt (* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))>
#<alt (* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))>
#<alt (* 1/24 (pow x 4))>
#<alt (* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))>
#<alt (* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/6 x))>
#<alt (+ 1/2 (* x (+ 1/6 (* 1/24 x))))>
#<alt (+ 1/2 (* x (+ 1/6 (* 1/24 x))))>
#<alt (* 1/24 (pow x 2))>
#<alt (* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))>
#<alt (* (pow x 2) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))>
#<alt (* 1/24 (pow x 2))>
#<alt (* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))>
#<alt (* (pow x 2) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))>
#<alt (* 1/6 x)>
#<alt (* x (+ 1/6 (* 1/24 x)))>
#<alt (* x (+ 1/6 (* 1/24 x)))>
#<alt (* x (+ 1/6 (* 1/24 x)))>
#<alt (* 1/24 (pow x 2))>
#<alt (* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* 1/24 (pow x 2))>
#<alt (* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (/ 1 (pow x 2))>
#<alt (/ (+ 1 (* 1/2 x)) (pow x 2))>
#<alt (/ (+ 1 (* 1/2 x)) (pow x 2))>
#<alt (/ (+ 1 (* 1/2 x)) (pow x 2))>
#<alt (/ 1/2 x)>
#<alt (/ (+ 1/2 (/ 1 x)) x)>
#<alt (/ (+ 1/2 (/ 1 x)) x)>
#<alt (/ (+ 1/2 (/ 1 x)) x)>
#<alt (/ 1/2 x)>
#<alt (/ (+ 1/2 (/ 1 x)) x)>
#<alt (/ (+ 1/2 (/ 1 x)) x)>
#<alt (/ (+ 1/2 (/ 1 x)) x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt 1/6>
#<alt (+ 1/6 (* 1/24 x))>
#<alt (+ 1/6 (* 1/24 x))>
#<alt (+ 1/6 (* 1/24 x))>
#<alt (* 1/24 x)>
#<alt (* x (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* x (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* x (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* 1/24 x)>
#<alt (* x (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* x (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* x (+ 1/24 (* 1/6 (/ 1 x))))>

Calls

39 calls:

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

rewrite325.0ms (6.3%)

Algorithm

1×	batch-egg-rewrite

Rules

2572×	`+-lowering-+.f64`
2572×	`+-lowering-+.f32`
2286×	`-lowering-.f32`
2286×	`-lowering-.f64`
1686×	`/-lowering-/.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	23	92
1	83	80
2	280	80
3	1399	79
4	6940	79
0	9209	79

Stop Event

1×	iter limit
1×	node limit

Counts

13 → 927

Calls

Call 1

Inputs
(* (* (* x (* x x)) x) (+ 1/24 (/ (+ 1/6 (/ (+ 1/2 (/ 1 x)) x)) x)))
(* (* x (* x x)) x)
(* x (* x x))
(* x x)
(+ (* 1/2 (* x x)) x)
(* 1/2 (* x x))
(+ (* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x)) x)
(* (+ 1/2 (* x (+ 1/6 (* x 1/24)))) (* x x))
(+ 1/2 (* x (+ 1/6 (* x 1/24))))
(* x (+ 1/6 (* x 1/24)))
(/ (+ 1/2 (/ 1 x)) x)
(* x 1/24)
(+ 1/6 (* x 1/24))

Outputs
(+.f64 (.f64 x (.f64 (.f64 x x) (+.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) (.f64 x #s(literal 1/24 binary64))))) (fma.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) (.f64 x (.f64 x x)) (.f64 (.f64 x (*.f64 x x)) (-.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)))))
(+.f64 (.f64 x (.f64 (.f64 x x) (+.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) (.f64 x #s(literal 1/24 binary64))))) (fma.f64 (/.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) x) (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x x)) (-.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)))))
(+.f64 (.f64 x (.f64 (.f64 x x) (+.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) (.f64 x #s(literal 1/24 binary64))))) (fma.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) (.f64 (neg.f64 (.f64 x (*.f64 x x))) (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)))))
(+.f64 (.f64 x (.f64 (.f64 x x) (+.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) (.f64 x #s(literal 1/24 binary64))))) (fma.f64 (.f64 (.f64 x (.f64 x x)) (-.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x))) #s(literal -1 binary64) (.f64 (.f64 x (.f64 x x)) (-.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)))))
(+.f64 (.f64 x (.f64 (.f64 x x) (+.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) (.f64 x #s(literal 1/24 binary64))))) (fma.f64 (.f64 (.f64 x x) (-.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x))) (-.f64 #s(literal 0 binary64) x) (.f64 (.f64 x (*.f64 x x)) (-.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)))))
(+.f64 (.f64 x (.f64 (.f64 x x) (+.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) (.f64 x #s(literal 1/24 binary64))))) (fma.f64 (neg.f64 (.f64 x (.f64 x x))) (-.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) (.f64 (.f64 x (*.f64 x x)) (-.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)))))
(+.f64 (.f64 x (.f64 (.f64 x x) (+.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) (.f64 x #s(literal 1/24 binary64))))) (fma.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)))) (.f64 (.f64 x (.f64 x x)) (-.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)))))
(+.f64 (.f64 x (.f64 (.f64 x x) (+.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) (.f64 x #s(literal 1/24 binary64))))) (fma.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (-.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)))) (/.f64 #s(literal -1 binary64) x) (.f64 (.f64 x (*.f64 x x)) (-.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)))))
(+.f64 (.f64 x (.f64 (.f64 x x) (+.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) (.f64 x #s(literal 1/24 binary64))))) (fma.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 (-.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) x) (.f64 (.f64 x (.f64 x x)) (-.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)))))
(+.f64 (.f64 x (.f64 (.f64 x x) (+.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) (.f64 x #s(literal 1/24 binary64))))) (fma.f64 x (.f64 x (.f64 x (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)))) (.f64 (.f64 x (*.f64 x x)) (-.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)))))
(+.f64 (.f64 x (.f64 (.f64 x x) (+.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) (.f64 x #s(literal 1/24 binary64))))) (fma.f64 (/.f64 #s(literal 1 binary64) x) (.f64 (.f64 x x) (.f64 x (.f64 x (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x))))) (.f64 (.f64 x (*.f64 x x)) (-.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)))))
(+.f64 (.f64 x (.f64 (.f64 x x) (+.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) (.f64 x #s(literal 1/24 binary64))))) (fma.f64 (-.f64 #s(literal 0 binary64) x) (.f64 (.f64 x x) (-.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x))) (.f64 x (.f64 (*.f64 x x) (-.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x))))))
(+.f64 (.f64 x (.f64 (.f64 x x) (+.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) (.f64 x #s(literal 1/24 binary64))))) (fma.f64 #s(literal -1 binary64) (.f64 (.f64 x (.f64 x x)) (-.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x))) (.f64 #s(literal 1 binary64) (.f64 (.f64 x (*.f64 x x)) (-.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x))))))
(+.f64 (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64))) (.f64 (.f64 x x) (*.f64 x (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)))))
(+.f64 (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)))) (.f64 x (.f64 (.f64 x (*.f64 x x)) #s(literal 1/24 binary64))))
(+.f64 (fma.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64)) (neg.f64 (.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (-.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x))) x) x))) (fma.f64 (.f64 x (.f64 x (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)))) x (.f64 (/.f64 (.f64 (.f64 x (*.f64 x x)) (-.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x))) x) x)))
(+.f64 (fma.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64)) (neg.f64 (.f64 (/.f64 (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)))) (-.f64 #s(literal 0 binary64) x)) x))) (fma.f64 (.f64 x (.f64 x (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)))) x (.f64 (/.f64 (.f64 (.f64 x x) (*.f64 x (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)))) (-.f64 #s(literal 0 binary64) x)) x)))
(+.f64 (fma.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64)) (neg.f64 (.f64 (/.f64 (.f64 (.f64 x x) (-.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x))) x) (.f64 x x)))) (fma.f64 (neg.f64 (/.f64 (.f64 (.f64 x x) (-.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x))) x)) (.f64 x x) (.f64 (/.f64 (.f64 (.f64 x x) (-.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x))) x) (.f64 x x))))
(+.f64 (fma.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/24 binary64)) (neg.f64 (.f64 (/.f64 (.f64 x (.f64 x (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)))) (-.f64 #s(literal 0 binary64) x)) (.f64 x x)))) (fma.f64 (neg.f64 (/.f64 (.f64 x (.f64 x (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)))) (-.f64 #s(literal 0 binary64) x))) (.f64 x x) (.f64 (/.f64 (.f64 x (.f64 x (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)))) (-.f64 #s(literal 0 binary64) x)) (.f64 x x))))
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(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (/.f64 x (+.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1/2 binary64)))) (-.f64 #s(literal 0 binary64) x)) (.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 x (+.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1/2 binary64)))))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) x)) (.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)))) (*.f64 x x))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (/.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)))) x) (.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)))))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) x) (.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1/2 binary64)))) (/.f64 x (/.f64 #s(literal -1 binary64) x)))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 (+.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1/2 binary64)) x))) (-.f64 #s(literal 0 binary64) x))
(pow.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1 binary64))
(pow.f64 (/.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64))
(pow.f64 (exp.f64 (log.f64 (/.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x))))) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x))
(*.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)))
(*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 (+.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1/2 binary64)) x))
(*.f64 (+.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1/2 binary64)) (/.f64 #s(literal -1 binary64) x))
(*.f64 (/.f64 #s(literal -1 binary64) x) (+.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1/2 binary64)))
(*.f64 (/.f64 #s(literal -1 binary64) x) (pow.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)))))
(*.f64 (/.f64 (+.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1/2 binary64)) x) #s(literal -1 binary64))
(*.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) x))
(neg.f64 (/.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1 binary64) x)))
(/.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/24 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/24 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1 binary64) x))))
(/.f64 (*.f64 x #s(literal 1/24 binary64)) #s(literal 1 binary64))
(/.f64 (/.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1 binary64) x)) #s(literal -1 binary64))
(/.f64 #s(literal -1/24 binary64) (/.f64 #s(literal -1 binary64) x))
(*.f64 x #s(literal 1/24 binary64))
(*.f64 #s(literal 1/24 binary64) x)
(.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/24 binary64)))
(.f64 (.f64 x #s(literal 1/24 binary64)) #s(literal 1 binary64))
(*.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -1/24 binary64))
(*.f64 (/.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1 binary64) x)) #s(literal -1 binary64))
(*.f64 #s(literal -1/24 binary64) (-.f64 #s(literal 0 binary64) x))
(+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64)))
(+.f64 (*.f64 x #s(literal 1/24 binary64)) #s(literal 1/6 binary64))
(fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64))
(fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64))
(fma.f64 (*.f64 x #s(literal 1/24 binary64)) #s(literal 1 binary64) #s(literal 1/6 binary64))
(.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))
(.f64 (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))) #s(literal 1 binary64))

simplify201.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

2972×	`-lowering-.f32`
2972×	`-lowering-.f64`
1530×	`fma-define`
1416×	`+-lowering-+.f64`
1416×	`+-lowering-+.f32`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	60	979
1	207	841
2	591	800
3	1511	791
4	3913	755
0	9151	755

Stop Event

1×	iter limit
1×	node limit

Counts

156 → 156

Calls

Call 1

Inputs
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(* 1/24 (pow x 4))
(* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (+ (* 1/6 (/ 1 x)) (/ 1 (pow x 3))))))
(* 1/24 (pow x 4))
(* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(* (pow x 4) (+ 1/24 (* -1 (/ (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6) x))))
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 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)
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* 1/2 x)))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* 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))
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(* 1/24 (pow x 4))
(* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (+ (* 1/6 (/ 1 x)) (/ 1 (pow x 3))))))
(* 1/24 (pow x 4))
(* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(* (pow x 4) (+ 1/24 (* -1 (/ (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6) x))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* 1/6 x)))
(* (pow x 2) (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))
(* (pow x 2) (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))
(* 1/24 (pow x 4))
(* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(* 1/24 (pow x 4))
(* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
1/2
(+ 1/2 (* 1/6 x))
(+ 1/2 (* x (+ 1/6 (* 1/24 x))))
(+ 1/2 (* x (+ 1/6 (* 1/24 x))))
(* 1/24 (pow x 2))
(* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))
(* (pow x 2) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(* (pow x 2) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(* 1/24 (pow x 2))
(* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))
(* (pow x 2) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(* (pow x 2) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(* 1/6 x)
(* x (+ 1/6 (* 1/24 x)))
(* x (+ 1/6 (* 1/24 x)))
(* x (+ 1/6 (* 1/24 x)))
(* 1/24 (pow x 2))
(* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))
(* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))
(* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))
(* 1/24 (pow x 2))
(* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))
(* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))
(* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))
(/ 1 (pow x 2))
(/ (+ 1 (* 1/2 x)) (pow x 2))
(/ (+ 1 (* 1/2 x)) (pow x 2))
(/ (+ 1 (* 1/2 x)) (pow x 2))
(/ 1/2 x)
(/ (+ 1/2 (/ 1 x)) x)
(/ (+ 1/2 (/ 1 x)) x)
(/ (+ 1/2 (/ 1 x)) x)
(/ 1/2 x)
(/ (+ 1/2 (/ 1 x)) x)
(/ (+ 1/2 (/ 1 x)) x)
(/ (+ 1/2 (/ 1 x)) x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
1/6
(+ 1/6 (* 1/24 x))
(+ 1/6 (* 1/24 x))
(+ 1/6 (* 1/24 x))
(* 1/24 x)
(* x (+ 1/24 (* 1/6 (/ 1 x))))
(* x (+ 1/24 (* 1/6 (/ 1 x))))
(* x (+ 1/24 (* 1/6 (/ 1 x))))
(* 1/24 x)
(* x (+ 1/24 (* 1/6 (/ 1 x))))
(* x (+ 1/24 (* 1/6 (/ 1 x))))
(* x (+ 1/24 (* 1/6 (/ 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 (+ 1/2 (* 1/6 x)))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))))))
(* 1/24 (pow x 4))
(.f64 x (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x x))))
(* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))
(.f64 (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))) (.f64 x (.f64 x x)))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64)))))))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (+ (* 1/6 (/ 1 x)) (/ 1 (pow x 3))))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))))))
(* 1/24 (pow x 4))
(.f64 x (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x x))))
(* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))
(.f64 (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))) (.f64 x (.f64 x x)))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64)))))))
(* (pow x 4) (+ 1/24 (* -1 (/ (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6) x))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))))))
(pow x 4)
(.f64 x (.f64 x (*.f64 x x)))
(pow x 4)
(.f64 x (.f64 x (*.f64 x x)))
(pow x 4)
(.f64 x (.f64 x (*.f64 x x)))
(pow x 4)
(.f64 x (.f64 x (*.f64 x x)))
(pow x 4)
(.f64 x (.f64 x (*.f64 x x)))
(pow x 4)
(.f64 x (.f64 x (*.f64 x x)))
(pow x 4)
(.f64 x (.f64 x (*.f64 x x)))
(pow x 4)
(.f64 x (.f64 x (*.f64 x x)))
(pow x 4)
(.f64 x (.f64 x (*.f64 x x)))
(pow x 4)
(.f64 x (.f64 x (*.f64 x x)))
(pow x 4)
(.f64 x (.f64 x (*.f64 x x)))
(pow x 4)
(.f64 x (.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))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
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 #s(literal 1/2 binary64) (.f64 x x))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 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 (+ 1/2 (* 1/6 x)))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))))))
(* 1/24 (pow x 4))
(.f64 x (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x x))))
(* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))
(.f64 (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))) (.f64 x (.f64 x x)))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64)))))))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (+ (* 1/6 (/ 1 x)) (/ 1 (pow x 3))))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))))))
(* 1/24 (pow x 4))
(.f64 x (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x x))))
(* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))
(.f64 (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))) (.f64 x (.f64 x x)))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64)))))))
(* (pow x 4) (+ 1/24 (* -1 (/ (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6) x))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))))))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* (pow x 2) (+ 1/2 (* 1/6 x)))
(.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))
(* (pow x 2) (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))
(.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64)))))))
(* (pow x 2) (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))
(.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64)))))))
(* 1/24 (pow x 4))
(.f64 x (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x x))))
(* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))
(.f64 (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))) (.f64 x (.f64 x x)))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64)))))))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64)))))))
(* 1/24 (pow x 4))
(.f64 x (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x x))))
(* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))
(.f64 (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))) (.f64 x (.f64 x x)))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64)))))))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64)))))))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/6 x))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))
(+ 1/2 (* x (+ 1/6 (* 1/24 x))))
(+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64)))))
(+ 1/2 (* x (+ 1/6 (* 1/24 x))))
(+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64)))))
(* 1/24 (pow x 2))
(.f64 #s(literal 1/24 binary64) (.f64 x x))
(* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))
(* (pow x 2) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64)))))
(* (pow x 2) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64)))))
(* 1/24 (pow x 2))
(.f64 #s(literal 1/24 binary64) (.f64 x x))
(* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))
(* (pow x 2) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64)))))
(* (pow x 2) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64)))))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* x (+ 1/6 (* 1/24 x)))
(.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))
(* x (+ 1/6 (* 1/24 x)))
(.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))
(* x (+ 1/6 (* 1/24 x)))
(.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))
(* 1/24 (pow x 2))
(.f64 #s(literal 1/24 binary64) (.f64 x x))
(* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))
(* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))
(* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))
(* 1/24 (pow x 2))
(.f64 #s(literal 1/24 binary64) (.f64 x x))
(* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))
(* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))
(* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ (+ 1 (* 1/2 x)) (pow x 2))
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)
(/ (+ 1 (* 1/2 x)) (pow x 2))
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)
(/ (+ 1 (* 1/2 x)) (pow x 2))
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ (+ 1/2 (/ 1 x)) x)
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)
(/ (+ 1/2 (/ 1 x)) x)
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)
(/ (+ 1/2 (/ 1 x)) x)
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ (+ 1/2 (/ 1 x)) x)
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)
(/ (+ 1/2 (/ 1 x)) x)
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)
(/ (+ 1/2 (/ 1 x)) x)
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
1/6
#s(literal 1/6 binary64)
(+ 1/6 (* 1/24 x))
(+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64)))
(+ 1/6 (* 1/24 x))
(+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64)))
(+ 1/6 (* 1/24 x))
(+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64)))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* x (+ 1/24 (* 1/6 (/ 1 x))))
(+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64)))
(* x (+ 1/24 (* 1/6 (/ 1 x))))
(+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64)))
(* x (+ 1/24 (* 1/6 (/ 1 x))))
(+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64)))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* x (+ 1/24 (* 1/6 (/ 1 x))))
(+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64)))
(* x (+ 1/24 (* 1/6 (/ 1 x))))
(+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64)))
(* x (+ 1/24 (* 1/6 (/ 1 x))))
(+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64)))

eval142.0ms (2.8%)

Compiler: Compiled 38269 to 2729 computations (92.9% saved)

prune147.0ms (2.9%)

Pruning

9 alts after pruning (3 fresh and 6 done)

	Pruned	Kept	Total
New	1212	3	1215
Fresh	0	0	0
Picked	0	3	3
Done	0	3	3
Total	1212	9	1221

Accuracy

100.0%

Counts

1221 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.2%	(/.f64 (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) x))
✓	100.0%	(+.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x)) x)
✓	99.5%	(+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) x)
▶	25.0%	(.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x))))) (+.f64 #s(literal 1/24 binary64) (/.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) x)))
▶	34.1%	(.f64 (+.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) (.f64 x #s(literal 1/24 binary64))) (.f64 x (.f64 x x)))
✓	26.0%	(.f64 (.f64 (.f64 x (.f64 x x)) x) (+.f64 #s(literal 1/24 binary64) (/.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) x)))
✓	99.8%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
✓	100.0%	(expm1.f64 x)
✓	98.7%	x

Compiler

Compiled 119 to 81 computations (31.9% saved)

simplify213.0ms (4.1%)

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) 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 binary64) x))
✓	cost-diff	0	(.f64 x (.f64 x (*.f64 x x)))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x))))
✓	cost-diff	256	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x)))))
✓	cost-diff	384	(.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x))))) (+.f64 #s(literal 1/24 binary64) (/.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) x)))
✓	cost-diff	0	(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)
✓	cost-diff	0	(+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x))
✓	cost-diff	0	(+.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) (*.f64 x #s(literal 1/24 binary64)))
✓	cost-diff	256	(.f64 (+.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) (.f64 x #s(literal 1/24 binary64))) (.f64 x (.f64 x x)))

Rules

3138×	`-lowering-.f32`
3138×	`-lowering-.f64`
2720×	`sum3-define`
1400×	`/-lowering-/.f32`
1400×	`/-lowering-/.f64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	23	163
1	62	154
2	194	154
3	550	154
4	1451	149
5	2464	149
6	3505	149
7	5652	149
8	6492	149
9	6670	149
10	6900	149
11	7207	149
12	7587	149
0	8827	149

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(* (+ (+ 1/6 (/ (+ 1/2 (/ 1 x)) x)) (* x 1/24)) (* x (* x x)))
(+ (+ 1/6 (/ (+ 1/2 (/ 1 x)) x)) (* x 1/24))
(+ 1/6 (/ (+ 1/2 (/ 1 x)) x))
1/6
(/ (+ 1/2 (/ 1 x)) x)
(+ 1/2 (/ 1 x))
1/2
(/ 1 x)
1
x
(* x 1/24)
1/24
(* x (* x x))
(* x x)
(* (/ 1 (/ 1 (* x (* x (* x x))))) (+ 1/24 (/ (+ 1/6 (/ (+ 1/2 (/ 1 x)) x)) x)))
(/ 1 (/ 1 (* x (* x (* x x)))))
1
(/ 1 (* x (* x (* x x))))
(* x (* x (* x x)))
x
(* x (* x x))
(* x x)
(+ 1/24 (/ (+ 1/6 (/ (+ 1/2 (/ 1 x)) x)) x))
1/24
(/ (+ 1/6 (/ (+ 1/2 (/ 1 x)) x)) x)
(+ 1/6 (/ (+ 1/2 (/ 1 x)) x))
1/6
(/ (+ 1/2 (/ 1 x)) x)
(+ 1/2 (/ 1 x))
1/2
(/ 1 x)
(/ (+ 1 (* x 1/2)) (/ 1 x))
(+ 1 (* x 1/2))
1
(* x 1/2)
x
1/2
(/ 1 x)

Outputs
(* (+ (+ 1/6 (/ (+ 1/2 (/ 1 x)) x)) (* x 1/24)) (* x (* x x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))))))
(+ (+ 1/6 (/ (+ 1/2 (/ 1 x)) x)) (* x 1/24))
(+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x) (+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64))))
(+ 1/6 (/ (+ 1/2 (/ 1 x)) x))
(+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x))
1/6
#s(literal 1/6 binary64)
(/ (+ 1/2 (/ 1 x)) x)
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)
(+ 1/2 (/ 1 x))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x))
1/2
#s(literal 1/2 binary64)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
1
#s(literal 1 binary64)
x
(* x 1/24)
(*.f64 x #s(literal 1/24 binary64))
1/24
#s(literal 1/24 binary64)
(* x (* x x))
(.f64 x (.f64 x x))
(* x x)
(*.f64 x x)
(* (/ 1 (/ 1 (* x (* x (* x x))))) (+ 1/24 (/ (+ 1/6 (/ (+ 1/2 (/ 1 x)) x)) x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))))))
(/ 1 (/ 1 (* x (* x (* x x)))))
(.f64 x (.f64 x (*.f64 x x)))
1
#s(literal 1 binary64)
(/ 1 (* x (* x (* x x))))
(/.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x) x)
(* x (* x (* x x)))
(.f64 x (.f64 x (*.f64 x x)))
x
(* x (* x x))
(.f64 x (.f64 x x))
(* x x)
(*.f64 x x)
(+ 1/24 (/ (+ 1/6 (/ (+ 1/2 (/ 1 x)) x)) x))
(+.f64 #s(literal 1/24 binary64) (/.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) x))
1/24
#s(literal 1/24 binary64)
(/ (+ 1/6 (/ (+ 1/2 (/ 1 x)) x)) x)
(/.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) x)
(+ 1/6 (/ (+ 1/2 (/ 1 x)) x))
(+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x))
1/6
#s(literal 1/6 binary64)
(/ (+ 1/2 (/ 1 x)) x)
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)
(+ 1/2 (/ 1 x))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x))
1/2
#s(literal 1/2 binary64)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (+ 1 (* x 1/2)) (/ 1 x))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)))
(+ 1 (* x 1/2))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
1
#s(literal 1 binary64)
(* x 1/2)
(*.f64 #s(literal 1/2 binary64) x)
x
1/2
#s(literal 1/2 binary64)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)

localize153.0ms (3%)

Localize:

Found 12 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) x)
✓	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	99.7%	(/.f64 (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) x))
✓	accuracy	99.8%	(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)
✓	accuracy	99.8%	(.f64 x (.f64 x (*.f64 x x)))
✓	accuracy	99.3%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x)))))
✓	accuracy	27.2%	(.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x))))) (+.f64 #s(literal 1/24 binary64) (/.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) x)))
✓	accuracy	99.8%	(.f64 x (.f64 x x))
✓	accuracy	99.8%	(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)
✓	accuracy	99.5%	(*.f64 x #s(literal 1/24 binary64))
✓	accuracy	35.0%	(.f64 (+.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) (.f64 x #s(literal 1/24 binary64))) (.f64 x (.f64 x x)))

Results

107.0ms

256×

valid

Compiler

Compiled 210 to 24 computations (88.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 41.0ms

ival-div: 11.0ms (26.6% of total)

ival-add: 11.0ms (26.6% of total)

ival-mult: 11.0ms (26.6% of total)

...c/correct-round.rkt:119:19: 7.0ms (16.9% of total)

const: 1.0ms (2.4% of total)

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

series3.0ms (0.1%)

Counts

14 → 168

Calls

Call 1

Inputs
#<alt (* (+ (+ 1/6 (/ (+ 1/2 (/ 1 x)) x)) (* x 1/24)) (* x (* x x)))>
#<alt (+ (+ 1/6 (/ (+ 1/2 (/ 1 x)) x)) (* x 1/24))>
#<alt (+ 1/6 (/ (+ 1/2 (/ 1 x)) x))>
#<alt (/ (+ 1/2 (/ 1 x)) x)>
#<alt (* (/ 1 (/ 1 (* x (* x (* x x))))) (+ 1/24 (/ (+ 1/6 (/ (+ 1/2 (/ 1 x)) x)) x)))>
#<alt (/ 1 (/ 1 (* x (* x (* x x)))))>
#<alt (/ 1 (* x (* x (* x x))))>
#<alt (* x (* x (* x x)))>
#<alt (/ (+ 1 (* x 1/2)) (/ 1 x))>
#<alt (+ 1 (* x 1/2))>
#<alt (* x 1/2)>
#<alt (/ 1 x)>
#<alt (* x 1/24)>
#<alt (* x (* x x))>

Outputs
#<alt x>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))>
#<alt (* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))>
#<alt (* 1/24 (pow x 4))>
#<alt (* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))>
#<alt (* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (+ (* 1/6 (/ 1 x)) (/ 1 (pow x 3))))))>
#<alt (* 1/24 (pow x 4))>
#<alt (* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))>
#<alt (* (pow x 4) (+ 1/24 (* -1 (/ (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6) x))))>
#<alt (/ 1 (pow x 2))>
#<alt (/ (+ 1 (* 1/2 x)) (pow x 2))>
#<alt (/ (+ 1 (* x (+ 1/2 (* 1/6 x)))) (pow x 2))>
#<alt (/ (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))) (pow x 2))>
#<alt (* 1/24 x)>
#<alt (* x (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* x (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))>
#<alt (* x (+ 1/24 (+ (/ 1/2 (pow x 2)) (+ (* 1/6 (/ 1 x)) (/ 1 (pow x 3))))))>
#<alt (* 1/24 x)>
#<alt (* x (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* -1 (* x (- (* -1 (/ (+ 1/6 (* 1/2 (/ 1 x))) x)) 1/24)))>
#<alt (* -1 (* x (- (* -1 (/ (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))) x)) 1/24)))>
#<alt (/ 1 (pow x 2))>
#<alt (/ (+ 1 (* 1/2 x)) (pow x 2))>
#<alt (/ (+ 1 (* x (+ 1/2 (* 1/6 x)))) (pow x 2))>
#<alt (/ (+ 1 (* x (+ 1/2 (* 1/6 x)))) (pow x 2))>
#<alt 1/6>
#<alt (+ 1/6 (* 1/2 (/ 1 x)))>
#<alt (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))))>
#<alt (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))))>
#<alt 1/6>
#<alt (+ 1/6 (* 1/2 (/ 1 x)))>
#<alt (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))))>
#<alt (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))))>
#<alt (/ 1 (pow x 2))>
#<alt (/ (+ 1 (* 1/2 x)) (pow x 2))>
#<alt (/ (+ 1 (* 1/2 x)) (pow x 2))>
#<alt (/ (+ 1 (* 1/2 x)) (pow x 2))>
#<alt (/ 1/2 x)>
#<alt (/ (+ 1/2 (/ 1 x)) x)>
#<alt (/ (+ 1/2 (/ 1 x)) x)>
#<alt (/ (+ 1/2 (/ 1 x)) x)>
#<alt (/ 1/2 x)>
#<alt (/ (+ 1/2 (/ 1 x)) x)>
#<alt (/ (+ 1/2 (/ 1 x)) x)>
#<alt (/ (+ 1/2 (/ 1 x)) x)>
#<alt x>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))>
#<alt (* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))>
#<alt (* 1/24 (pow x 4))>
#<alt (* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))>
#<alt (* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (+ (* 1/6 (/ 1 x)) (/ 1 (pow x 3))))))>
#<alt (* 1/24 (pow x 4))>
#<alt (* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))>
#<alt (* (pow x 4) (+ 1/24 (* -1 (/ (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6) x))))>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (/ 1 (pow x 4))>
#<alt (/ 1 (pow x 4))>
#<alt (/ 1 (pow x 4))>
#<alt (/ 1 (pow x 4))>
#<alt (/ 1 (pow x 4))>
#<alt (/ 1 (pow x 4))>
#<alt (/ 1 (pow x 4))>
#<alt (/ 1 (pow x 4))>
#<alt (/ 1 (pow x 4))>
#<alt (/ 1 (pow x 4))>
#<alt (/ 1 (pow x 4))>
#<alt (/ 1 (pow x 4))>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<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) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* 1/2 x))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (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

42 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(* (+ (+ 1/6 (/ (+ 1/2 (/ 1 x)) x)) (* x 1/24)) (* x (* x x)))
0.0ms	x	@	-inf	(/ 1 x)
0.0ms	x	@	-inf	(* (+ (+ 1/6 (/ (+ 1/2 (/ 1 x)) x)) (* x 1/24)) (* x (* x x)))
0.0ms	x	@	0	(/ 1 x)
0.0ms	x	@	inf	(* (+ (+ 1/6 (/ (+ 1/2 (/ 1 x)) x)) (* x 1/24)) (* x (* x x)))

rewrite288.0ms (5.6%)

Algorithm

1×	batch-egg-rewrite

Rules

2242×	`-lowering-.f32`
2242×	`-lowering-.f64`
2010×	`/-lowering-/.f32`
2010×	`/-lowering-/.f64`
1060×	`fma-define`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	95
1	101	85
2	516	85
3	3633	85
0	8333	85

Stop Event

1×	iter limit
1×	node limit

Counts

14 → 1051

Calls

Call 1

Inputs
(* (+ (+ 1/6 (/ (+ 1/2 (/ 1 x)) x)) (* x 1/24)) (* x (* x x)))
(+ (+ 1/6 (/ (+ 1/2 (/ 1 x)) x)) (* x 1/24))
(+ 1/6 (/ (+ 1/2 (/ 1 x)) x))
(/ (+ 1/2 (/ 1 x)) x)
(* (/ 1 (/ 1 (* x (* x (* x x))))) (+ 1/24 (/ (+ 1/6 (/ (+ 1/2 (/ 1 x)) x)) x)))
(/ 1 (/ 1 (* x (* x (* x x)))))
(/ 1 (* x (* x (* x x))))
(* x (* x (* x x)))
(/ (+ 1 (* x 1/2)) (/ 1 x))
(+ 1 (* x 1/2))
(* x 1/2)
(/ 1 x)
(* x 1/24)
(* x (* x x))

Outputs
(+.f64 (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x)))) (.f64 x (.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) (*.f64 x x))))
(+.f64 (.f64 x (.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) (.f64 x x))) (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x x)))))
(+.f64 (.f64 #s(literal 1/6 binary64) (.f64 x (.f64 x x))) (.f64 x (.f64 (.f64 x x) (+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x) (*.f64 x #s(literal 1/24 binary64))))))
(+.f64 (.f64 x (.f64 (.f64 x x) (+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x) (.f64 x #s(literal 1/24 binary64))))) (.f64 #s(literal 1/6 binary64) (.f64 x (*.f64 x x))))
(+.f64 (.f64 (.f64 x (.f64 x x)) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64)))))
(+.f64 (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64)))) (.f64 (.f64 x (*.f64 x x)) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)))
(+.f64 (.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x) (.f64 x (.f64 x x))) (.f64 (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))) (.f64 x (*.f64 x x))))
(+.f64 (.f64 (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))) (.f64 x (.f64 x x))) (.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x) (.f64 x (*.f64 x x))))
(exp.f64 (.f64 (log.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 (.f64 x x) (+.f64 #s(literal 1/6 binary64) (+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x) (.f64 x #s(literal 1/24 binary64))))))) #s(literal -1 binary64)))
(-.f64 (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1/2 binary64)) x))))))
(-.f64 (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x)))) (/.f64 (/.f64 (+.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1/2 binary64)) x)) x) (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x (.f64 x x)))))
(-.f64 (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x)))) (.f64 (/.f64 (+.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1/2 binary64)) x)) x) (.f64 x (.f64 x (.f64 x x)))))
(-.f64 (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x)))) (.f64 (.f64 x (.f64 x (.f64 x x))) (/.f64 (+.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1/2 binary64)) x)) x)))
(-.f64 (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x)))) (.f64 (.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) (.f64 x (.f64 x (*.f64 x x)))) (/.f64 #s(literal -1 binary64) x)))
(-.f64 (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x)))) (/.f64 (.f64 x (.f64 x (*.f64 x x))) (/.f64 x (+.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1/2 binary64)) x)))))
(-.f64 (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x)))) (/.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) (/.f64 #s(literal -1 binary64) (.f64 x (.f64 x x)))))
(-.f64 (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x)))) (/.f64 (.f64 x (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1/2 binary64)) x)))) x))
(-.f64 (.f64 x (.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) (.f64 x x))) (.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x (*.f64 x x)))) #s(literal 1/24 binary64)))
(-.f64 (.f64 x (.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) (.f64 x x))) (.f64 #s(literal 1/24 binary64) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x (*.f64 x x))))))
(-.f64 (.f64 x (.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) (.f64 x x))) (/.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1 binary64) (.f64 x (.f64 x (.f64 x x))))))
(fma.f64 #s(literal 1/6 binary64) (.f64 x (.f64 x x)) (.f64 x (.f64 (.f64 x x) (+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x) (.f64 x #s(literal 1/24 binary64))))))
(fma.f64 #s(literal 1 binary64) (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x)))) (.f64 x (.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) (*.f64 x x))))
(fma.f64 #s(literal 1 binary64) (.f64 x (.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) (.f64 x x))) (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x x)))))
(fma.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x))) (.f64 x (.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) (.f64 x x))))
(fma.f64 x (.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) (.f64 x x)) (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x)))))
(fma.f64 x (/.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)))) (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x x)))))
(fma.f64 x (/.f64 (/.f64 (+.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1/2 binary64)) x)) x) (/.f64 #s(literal -1 binary64) (.f64 x (.f64 x x)))) (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x)))))
(fma.f64 x (/.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) (/.f64 #s(literal 1 binary64) (.f64 x x))) (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x x)))))
(fma.f64 x (.f64 (.f64 x x) #s(literal 1/6 binary64)) (.f64 x (.f64 (.f64 x x) (+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x) (.f64 x #s(literal 1/24 binary64))))))
(fma.f64 x (.f64 (.f64 x x) (+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x) (.f64 x #s(literal 1/24 binary64)))) (.f64 #s(literal 1/6 binary64) (.f64 x (.f64 x x))))
(fma.f64 x (.f64 #s(literal 1 binary64) (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x)))) (.f64 x (.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) (*.f64 x x))))
(fma.f64 (/.f64 #s(literal 1 binary64) x) (.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x)))))
(fma.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (.f64 x (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)))) (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x x)))))
(fma.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x) (.f64 x (.f64 x x)) (.f64 (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))) (.f64 x (.f64 x x))))
(fma.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) (.f64 x (.f64 x x)) (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x)))))
(fma.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) (.f64 x x))))
(fma.f64 (.f64 x #s(literal 1/24 binary64)) (.f64 x (.f64 x x)) (.f64 x (.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) (.f64 x x))))
(fma.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 1/24 binary64))) (.f64 x (.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) (.f64 x x))))
(fma.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x))) (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x)))))
(fma.f64 (.f64 x x) (/.f64 x (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)))) (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x x)))))
(fma.f64 (.f64 x x) (/.f64 (/.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) x) (/.f64 #s(literal 1 binary64) (.f64 x x))) (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x)))))
(fma.f64 (.f64 x x) (/.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) (/.f64 #s(literal 1 binary64) x)) (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x x)))))
(fma.f64 (.f64 x x) (.f64 x #s(literal 1/6 binary64)) (.f64 x (.f64 (.f64 x x) (+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x) (.f64 x #s(literal 1/24 binary64))))))
(fma.f64 (.f64 x x) (.f64 x (+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x) (.f64 x #s(literal 1/24 binary64)))) (.f64 #s(literal 1/6 binary64) (.f64 x (.f64 x x))))
(fma.f64 (.f64 x (.f64 x x)) #s(literal 1/6 binary64) (.f64 x (.f64 (.f64 x x) (+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x) (.f64 x #s(literal 1/24 binary64))))))
(fma.f64 (.f64 x (.f64 x x)) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x) (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64)))))
(fma.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x x)))))
(fma.f64 (.f64 x (.f64 x x)) (.f64 x #s(literal 1/24 binary64)) (.f64 x (.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) (.f64 x x))))
(fma.f64 (.f64 x (.f64 x x)) (+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x) (.f64 x #s(literal 1/24 binary64))) (.f64 #s(literal 1/6 binary64) (.f64 x (.f64 x x))))
(fma.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))) (.f64 (.f64 x (.f64 x x)) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)))
(fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/24 binary64) (.f64 x (.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) (.f64 x x))))
(fma.f64 (.f64 x (.f64 x (.f64 x x))) (/.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) x) (.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x x)))))
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(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) x)) (.f64 (/.f64 #s(literal -1 binary64) x) (+.f64 #s(literal -1 binary64) (.f64 x #s(literal -1/2 binary64))))) (/.f64 #s(literal -1 binary64) (.f64 x x)))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 (/.f64 #s(literal -1 binary64) x) (.f64 (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal -1/2 binary64))) x))) (/.f64 #s(literal -1 binary64) x))
(/.f64 (neg.f64 (.f64 #s(literal 1 binary64) (+.f64 #s(literal -1 binary64) (.f64 x #s(literal -1/2 binary64))))) (/.f64 #s(literal 1 binary64) x))
(/.f64 (neg.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x #s(literal -1/2 binary64))))) #s(literal 1 binary64))
(pow.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x))) #s(literal 1 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))) #s(literal -1 binary64))
(pow.f64 (exp.f64 (log.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))))) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)))
(.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)) x)
(.f64 (.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))) #s(literal 1 binary64))
(.f64 #s(literal -1 binary64) (.f64 (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal -1/2 binary64))) x))
(.f64 (-.f64 #s(literal 0 binary64) 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))) (-.f64 #s(literal 0 binary64) x))
(.f64 (.f64 (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal -1/2 binary64))) x) #s(literal -1 binary64))
(.f64 (.f64 #s(literal 1 binary64) (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal -1/2 binary64)))) (-.f64 #s(literal 0 binary64) x))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
(+.f64 #s(literal 1 binary64) (neg.f64 (*.f64 x #s(literal -1/2 binary64))))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64))
(+.f64 (neg.f64 (*.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64))
(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal -1/2 binary64))))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 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) (-.f64 #s(literal 0 binary64) x) #s(literal 1 binary64))
(neg.f64 (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal -1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))))))
(/.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)))))
(/.f64 (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal -1/2 binary64))) #s(literal -1 binary64))
(pow.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)))
(.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)) #s(literal 1 binary64))
(.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (.f64 x #s(literal -1/2 binary64))))
(.f64 (+.f64 #s(literal -1 binary64) (.f64 x #s(literal -1/2 binary64))) #s(literal -1 binary64))
(/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x))
(/.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64))
(/.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1 binary64) x))
(/.f64 (*.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))
(/.f64 (neg.f64 (*.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64))
(*.f64 #s(literal 1/2 binary64) x)
(.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x))
(*.f64 x #s(literal 1/2 binary64))
(.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64))
(.f64 #s(literal -1 binary64) (.f64 x #s(literal -1/2 binary64)))
(*.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) x))
(exp.f64 (log.f64 (/.f64 #s(literal 1 binary64) x)))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
(exp.f64 (+.f64 (*.f64 #s(literal -2 binary64) (log.f64 x)) (log.f64 x)))
(exp.f64 (+.f64 (log.f64 x) (*.f64 #s(literal -2 binary64) (log.f64 x))))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1 binary64) x))
(neg.f64 (/.f64 #s(literal -1 binary64) x))
(/.f64 #s(literal 1 binary64) x)
(/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) x))
(/.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1 binary64))
(pow.f64 x #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))
(pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 x))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))
(.f64 x (/.f64 #s(literal 1 binary64) (.f64 x x)))
(*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) x))
(*.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1 binary64))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x)
(/.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1 binary64) x))
(/.f64 (*.f64 x #s(literal 1/24 binary64)) #s(literal 1 binary64))
(/.f64 #s(literal -1/24 binary64) (/.f64 #s(literal -1 binary64) x))
(/.f64 (*.f64 #s(literal 1/24 binary64) (-.f64 #s(literal 0 binary64) x)) #s(literal -1 binary64))
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 1/24 binary64)) #s(literal -1 binary64))
(/.f64 (neg.f64 (*.f64 x #s(literal 1/24 binary64))) #s(literal -1 binary64))
(/.f64 (neg.f64 (*.f64 #s(literal 1/24 binary64) (-.f64 #s(literal 0 binary64) x))) #s(literal 1 binary64))
(/.f64 (neg.f64 (*.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 1/24 binary64))) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/24 binary64)))
(*.f64 x #s(literal 1/24 binary64))
(*.f64 #s(literal 1/24 binary64) x)
(.f64 (.f64 x #s(literal 1/24 binary64)) #s(literal 1 binary64))
(.f64 #s(literal -1 binary64) (.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 1/24 binary64)))
(*.f64 #s(literal -1/24 binary64) (-.f64 #s(literal 0 binary64) x))
(exp.f64 (*.f64 #s(literal 3 binary64) (log.f64 x)))
(exp.f64 (.f64 (.f64 #s(literal 3 binary64) (log.f64 x)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -3 binary64)))
(exp.f64 (.f64 (.f64 #s(literal -3 binary64) (log.f64 x)) #s(literal -1 binary64)))
(neg.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))
(/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x (.f64 x x))))
(/.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) x))
(/.f64 (.f64 x (.f64 x x)) #s(literal 1 binary64))
(/.f64 (.f64 x (.f64 x (*.f64 x x))) x)
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (.f64 x (.f64 x x))))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x (*.f64 x x)))) (-.f64 #s(literal 0 binary64) x))
(/.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal -1 binary64) (.f64 x (.f64 x (*.f64 x x)))))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) #s(literal -1 binary64))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x)) (/.f64 #s(literal -1 binary64) x))
(/.f64 (.f64 (.f64 x x) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) x))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x))) (/.f64 #s(literal 1 binary64) x))
(/.f64 (neg.f64 (.f64 (.f64 x x) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) x))
(pow.f64 x #s(literal 3 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -3 binary64))
(pow.f64 (.f64 x (.f64 x x)) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) #s(literal -1 binary64))
(pow.f64 (exp.f64 #s(literal 3 binary64)) (log.f64 x))
(.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))
(.f64 x (.f64 x x))
(.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x (.f64 x (.f64 x x))))
(.f64 (.f64 x x) x)
(.f64 (.f64 x (*.f64 x x)) #s(literal 1 binary64))
(.f64 (.f64 x (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) x))
(.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (.f64 x (*.f64 x x))))
(.f64 #s(literal -1 binary64) (pow.f64 (-.f64 #s(literal 0 binary64) (.f64 x (*.f64 x x))) #s(literal 1 binary64)))
(.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal -1 binary64) x))
(*.f64 (-.f64 #s(literal 0 binary64) x) (pow.f64 (/.f64 (/.f64 #s(literal -1 binary64) x) x) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal -1 binary64) x) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x (.f64 x x)))))
(.f64 (-.f64 #s(literal 0 binary64) (.f64 x (*.f64 x x))) #s(literal -1 binary64))
(.f64 (.f64 (*.f64 x x) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) x))
(.f64 (pow.f64 (.f64 (*.f64 x x) #s(literal -1 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 0 binary64) x))

simplify181.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

2582×	`-lowering-.f32`
2582×	`-lowering-.f64`
1756×	`sum3-define`
1552×	`fma-lowering-fma.f32`
1552×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	75	961
1	248	830
2	690	814
3	2661	785
4	6482	785
0	8013	785

Stop Event

1×	iter limit
1×	node limit

Counts

168 → 168

Calls

Call 1

Inputs
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(* 1/24 (pow x 4))
(* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (+ (* 1/6 (/ 1 x)) (/ 1 (pow x 3))))))
(* 1/24 (pow x 4))
(* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(* (pow x 4) (+ 1/24 (* -1 (/ (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6) x))))
(/ 1 (pow x 2))
(/ (+ 1 (* 1/2 x)) (pow x 2))
(/ (+ 1 (* x (+ 1/2 (* 1/6 x)))) (pow x 2))
(/ (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))) (pow x 2))
(* 1/24 x)
(* x (+ 1/24 (* 1/6 (/ 1 x))))
(* x (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(* x (+ 1/24 (+ (/ 1/2 (pow x 2)) (+ (* 1/6 (/ 1 x)) (/ 1 (pow x 3))))))
(* 1/24 x)
(* x (+ 1/24 (* 1/6 (/ 1 x))))
(* -1 (* x (- (* -1 (/ (+ 1/6 (* 1/2 (/ 1 x))) x)) 1/24)))
(* -1 (* x (- (* -1 (/ (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))) x)) 1/24)))
(/ 1 (pow x 2))
(/ (+ 1 (* 1/2 x)) (pow x 2))
(/ (+ 1 (* x (+ 1/2 (* 1/6 x)))) (pow x 2))
(/ (+ 1 (* x (+ 1/2 (* 1/6 x)))) (pow x 2))
1/6
(+ 1/6 (* 1/2 (/ 1 x)))
(+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))))
(+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))))
1/6
(+ 1/6 (* 1/2 (/ 1 x)))
(+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))))
(+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))))
(/ 1 (pow x 2))
(/ (+ 1 (* 1/2 x)) (pow x 2))
(/ (+ 1 (* 1/2 x)) (pow x 2))
(/ (+ 1 (* 1/2 x)) (pow x 2))
(/ 1/2 x)
(/ (+ 1/2 (/ 1 x)) x)
(/ (+ 1/2 (/ 1 x)) x)
(/ (+ 1/2 (/ 1 x)) x)
(/ 1/2 x)
(/ (+ 1/2 (/ 1 x)) x)
(/ (+ 1/2 (/ 1 x)) x)
(/ (+ 1/2 (/ 1 x)) x)
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(* 1/24 (pow x 4))
(* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (+ (* 1/6 (/ 1 x)) (/ 1 (pow x 3))))))
(* 1/24 (pow x 4))
(* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(* (pow x 4) (+ 1/24 (* -1 (/ (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6) x))))
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(/ 1 (pow x 4))
(/ 1 (pow x 4))
(/ 1 (pow x 4))
(/ 1 (pow x 4))
(/ 1 (pow x 4))
(/ 1 (pow x 4))
(/ 1 (pow x 4))
(/ 1 (pow x 4))
(/ 1 (pow x 4))
(/ 1 (pow x 4))
(/ 1 (pow x 4))
(/ 1 (pow x 4))
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* 1/2 x)))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
1
(+ 1 (* 1/2 x))
(+ 1 (* 1/2 x))
(+ 1 (* 1/2 x))
(* 1/2 x)
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* 1/2 x)
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(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 (+ 1/2 (* 1/6 x)))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))))))
(* 1/24 (pow x 4))
(*.f64 #s(literal 1/24 binary64) (pow.f64 x #s(literal 4 binary64)))
(* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))
(*.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/6 binary64) x)))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(*.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 #s(literal 1/24 binary64) (/.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 1/2 binary64) x)) x)))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (+ (* 1/6 (/ 1 x)) (/ 1 (pow x 3))))))
(*.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 #s(literal 1/24 binary64) (/.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) x)))
(* 1/24 (pow x 4))
(*.f64 #s(literal 1/24 binary64) (pow.f64 x #s(literal 4 binary64)))
(* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))
(*.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/6 binary64) x)))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(*.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 #s(literal 1/24 binary64) (/.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 1/2 binary64) x)) x)))
(* (pow x 4) (+ 1/24 (* -1 (/ (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6) x))))
(*.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 #s(literal 1/24 binary64) (/.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) x)))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ (+ 1 (* 1/2 x)) (pow x 2))
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)
(/ (+ 1 (* x (+ 1/2 (* 1/6 x)))) (pow x 2))
(+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x))
(/ (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))) (pow x 2))
(/.f64 (.f64 x (+.f64 (.f64 x #s(literal 1/24 binary64)) (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)))) x)
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* x (+ 1/24 (* 1/6 (/ 1 x))))
(+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64)))
(* x (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(+.f64 (*.f64 x #s(literal 1/24 binary64)) (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 1/2 binary64) x)))
(* x (+ 1/24 (+ (/ 1/2 (pow x 2)) (+ (* 1/6 (/ 1 x)) (/ 1 (pow x 3))))))
(+.f64 (*.f64 x #s(literal 1/24 binary64)) (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* x (+ 1/24 (* 1/6 (/ 1 x))))
(+.f64 #s(literal 1/6 binary64) (*.f64 x #s(literal 1/24 binary64)))
(* -1 (* x (- (* -1 (/ (+ 1/6 (* 1/2 (/ 1 x))) x)) 1/24)))
(+.f64 (*.f64 x #s(literal 1/24 binary64)) (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 1/2 binary64) x)))
(* -1 (* x (- (* -1 (/ (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))) x)) 1/24)))
(+.f64 (*.f64 x #s(literal 1/24 binary64)) (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ (+ 1 (* 1/2 x)) (pow x 2))
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)
(/ (+ 1 (* x (+ 1/2 (* 1/6 x)))) (pow x 2))
(+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x))
(/ (+ 1 (* x (+ 1/2 (* 1/6 x)))) (pow x 2))
(+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x))
1/6
#s(literal 1/6 binary64)
(+ 1/6 (* 1/2 (/ 1 x)))
(+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 1/2 binary64) x))
(+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))))
(+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x))
(+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))))
(+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x))
1/6
#s(literal 1/6 binary64)
(+ 1/6 (* 1/2 (/ 1 x)))
(+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 1/2 binary64) x))
(+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))))
(+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x))
(+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))))
(+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ (+ 1 (* 1/2 x)) (pow x 2))
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)
(/ (+ 1 (* 1/2 x)) (pow x 2))
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)
(/ (+ 1 (* 1/2 x)) (pow x 2))
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ (+ 1/2 (/ 1 x)) x)
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)
(/ (+ 1/2 (/ 1 x)) x)
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)
(/ (+ 1/2 (/ 1 x)) x)
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ (+ 1/2 (/ 1 x)) x)
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)
(/ (+ 1/2 (/ 1 x)) x)
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)
(/ (+ 1/2 (/ 1 x)) x)
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) 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 (+ 1/2 (* 1/6 x)))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))))))
(* 1/24 (pow x 4))
(*.f64 #s(literal 1/24 binary64) (pow.f64 x #s(literal 4 binary64)))
(* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))
(*.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/6 binary64) x)))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(*.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 #s(literal 1/24 binary64) (/.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 1/2 binary64) x)) x)))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (+ (* 1/6 (/ 1 x)) (/ 1 (pow x 3))))))
(*.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 #s(literal 1/24 binary64) (/.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) x)))
(* 1/24 (pow x 4))
(*.f64 #s(literal 1/24 binary64) (pow.f64 x #s(literal 4 binary64)))
(* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))
(*.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/6 binary64) x)))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(*.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 #s(literal 1/24 binary64) (/.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 1/2 binary64) x)) x)))
(* (pow x 4) (+ 1/24 (* -1 (/ (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6) x))))
(*.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 #s(literal 1/24 binary64) (/.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) x)))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(/ 1 (pow x 4))
(/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))
(/ 1 (pow x 4))
(/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))
(/ 1 (pow x 4))
(/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))
(/ 1 (pow x 4))
(/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))
(/ 1 (pow x 4))
(/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))
(/ 1 (pow x 4))
(/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))
(/ 1 (pow x 4))
(/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))
(/ 1 (pow x 4))
(/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))
(/ 1 (pow x 4))
(/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))
(/ 1 (pow x 4))
(/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))
(/ 1 (pow x 4))
(/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))
(/ 1 (pow x 4))
(/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
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) (+ 1/2 (/ 1 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))
(* (pow x 2) (+ 1/2 (/ 1 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) (+ 1/2 (/ 1 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(.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 (+ 1/2 (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))
(* x (+ 1/2 (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))
(* x (+ 1/2 (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (+ 1/2 (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))
(* x (+ 1/2 (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))
(* x (+ 1/2 (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(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))

eval173.0ms (3.4%)

Compiler: Compiled 39132 to 3058 computations (92.2% saved)

prune153.0ms (3%)

Pruning

11 alts after pruning (2 fresh and 9 done)

	Pruned	Kept	Total
New	1514	2	1516
Fresh	0	0	0
Picked	0	3	3
Done	0	6	6
Total	1514	11	1525

Accuracy

100.0%

Counts

1525 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.2%	(/.f64 (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) x))
	99.4%	(/.f64 x (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))))
	98.5%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))
✓	100.0%	(+.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x)) x)
✓	99.5%	(+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) x)
✓	25.0%	(.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x))))) (+.f64 #s(literal 1/24 binary64) (/.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) x)))
✓	34.1%	(.f64 (+.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) (.f64 x #s(literal 1/24 binary64))) (.f64 x (.f64 x x)))
✓	26.0%	(.f64 (.f64 (.f64 x (.f64 x x)) x) (+.f64 #s(literal 1/24 binary64) (/.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) x)))
✓	99.8%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
✓	100.0%	(expm1.f64 x)
✓	98.7%	x

Compiler

Compiled 286 to 141 computations (50.7% saved)

regimes12.0ms (0.2%)

Counts

14 → 1

Calls

Call 1

Inputs
x
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))
(+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) x)
(/.f64 x (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))))
(/.f64 (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) x))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))))))
(+.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x)) x)
(.f64 (+.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) (.f64 x #s(literal 1/24 binary64))) (.f64 x (.f64 x x)))
(.f64 (.f64 (.f64 x (.f64 x x)) x) (+.f64 #s(literal 1/24 binary64) (/.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) x)))
(.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x))))) (+.f64 #s(literal 1/24 binary64) (/.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) x)))
(expm1.f64 x)
(-.f64 (exp.f64 x) #s(literal 1 binary64))

Outputs
(expm1.f64 x)

Calls

3 calls:

4.0ms	x
3.0ms	(exp.f64 x)
3.0ms	(-.f64 (exp.f64 x) #s(literal 1 binary64))

Results

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

Compiler

Compiled 10 to 7 computations (30% saved)

regimes5.0ms (0.1%)

Counts

12 → 1

Calls

Call 1

Inputs
x
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))
(+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) x)
(/.f64 x (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))))
(/.f64 (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) x))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))))))
(+.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x)) x)
(.f64 (+.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) (.f64 x #s(literal 1/24 binary64))) (.f64 x (.f64 x x)))
(.f64 (.f64 (.f64 x (.f64 x x)) x) (+.f64 #s(literal 1/24 binary64) (/.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) x)))
(.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x))))) (+.f64 #s(literal 1/24 binary64) (/.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) x)))

Outputs
(+.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x)) x)

Calls

1 calls:

4.0ms

Results

Accuracy	Segments	Branch
100.0%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes3.0ms (0.1%)

Counts

8 → 1

Calls

Call 1

Inputs
x
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))
(+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) x)
(/.f64 x (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))))
(/.f64 (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) x))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))))))

Outputs
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))))))

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
99.9%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes3.0ms (0.1%)

Counts

7 → 1

Calls

Call 1

Inputs
x
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))
(+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) x)
(/.f64 x (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))))
(/.f64 (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) x))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))

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

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
99.8%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes3.0ms (0.1%)

Counts

6 → 1

Calls

Call 1

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

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

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
99.5%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0%)

Counts

3 → 1

Calls

Call 1

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

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

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
99.4%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes7.0ms (0.1%)

Accuracy

Total -0.1b remaining (-18%)

Threshold costs -0.1b (-18%)

Counts

2 → 1

Calls

Call 1

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

Outputs
x

Calls

1 calls:

7.0ms

Results

Accuracy	Segments	Branch
98.7%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

22×	`*-commutative_binary64`
16×	`+-commutative_binary64`
2×	`1-exp_binary64`
2×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	58
1	48	58

Stop Event

1×

saturated

Calls

Call 1

Inputs
(expm1.f64 x)
(+.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x)) x)
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) x)
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))
x

Outputs
(expm1.f64 x)
(+.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x)) x)
(+.f64 x (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))) (.f64 x x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 binary64))))))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) x)
(+.f64 x (.f64 #s(literal 1/2 binary64) (.f64 x x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))
x

soundness213.0ms (4.1%)

Rules

1464×	`fma-define`
1430×	`fma-define`
1096×	`fma-lowering-fma.f32`
1096×	`fma-lowering-fma.f64`
1068×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	113
1	66	93
2	184	90
3	459	90
4	973	90
5	1409	90
6	1607	90
7	1654	90
8	1767	90
9	1828	90
0	1828	90
0	4	2
1	10	2
2	11	2
0	11	2
0	22	50
1	72	44
2	190	41
3	465	41
4	976	41
5	1402	41
6	1563	41
7	1565	41
0	1565	41

Stop Event

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

Compiler

Compiled 166 to 102 computations (38.6% saved)

preprocess46.0ms (0.9%)

Compiler: Compiled 134 to 64 computations (52.2% saved)

Iter	Nodes	Cost
0	8	9
1	21	9
2	41	9
3	62	9
4	96	9
5	134	9
6	161	9
7	199	9
8	225	9
9	238	9
10	250	9
11	251	9
0	4	2
1	10	2
2	11	2
0	11	2

Iter	Nodes	Cost
0	8	9
1	21	9
2	41	9
3	62	9
4	96	9
5	134	9
6	161	9
7	199	9
8	225	9
9	238	9
10	250	9
11	251	9
0	4	2
1	10	2
2	11	2
0	11	2

analyze0.0ms (0%)

sample1.6s (31.9%)

preprocess22.0ms (0.4%)

explain129.0ms (2.5%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify4.0ms (0.1%)

localize53.0ms (1%)

series1.0ms (0%)

rewrite29.0ms (0.6%)

simplify67.0ms (1.3%)

eval2.0ms (0%)

prune4.0ms (0.1%)

simplify50.0ms (1%)

localize113.0ms (2.2%)

series10.0ms (0.2%)

rewrite92.0ms (1.8%)

simplify217.0ms (4.2%)

eval63.0ms (1.2%)

prune49.0ms (1%)

simplify186.0ms (3.6%)

localize137.0ms (2.7%)

series6.0ms (0.1%)

rewrite325.0ms (6.3%)

simplify201.0ms (3.9%)

eval142.0ms (2.8%)

prune147.0ms (2.9%)

simplify213.0ms (4.1%)

localize153.0ms (3%)

series3.0ms (0.1%)

rewrite288.0ms (5.6%)

simplify181.0ms (3.5%)

eval173.0ms (3.4%)

prune153.0ms (3%)

regimes12.0ms (0.2%)

regimes5.0ms (0.1%)

regimes3.0ms (0.1%)

regimes3.0ms (0.1%)

regimes3.0ms (0.1%)

regimes2.0ms (0%)

regimes7.0ms (0.1%)

simplify7.0ms (0.1%)

soundness213.0ms (4.1%)

preprocess46.0ms (0.9%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	8	9
1	21	9
2	41	9
3	62	9
4	96	9
5	134	9
6	161	9
7	199	9
8	225	9
9	238	9
10	250	9
11	251	9
0	4	2
1	10	2
2	11	2
0	11	2