Metrics for exp2 (problem 3.3.7)

analyze0.0ms (0%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	50.4%	49.6%	0%	0%	0%	0
100%	50.4%	0%	49.6%	0%	0%	0%	1

Compiler

Compiled 13 to 10 computations (23.1% 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-add: 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)

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

sample4.0s (36.7%)

Results

3.0s	5763×	2	valid
410.0ms	2319×	1	valid
77.0ms	174×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 2.8s

ival-exp: 2.0s (70% of total)

backward-pass: 268.0ms (9.5% of total)

ival-sub: 205.0ms (7.2% of total)

ival-neg: 127.0ms (4.5% of total)

ival-add: 125.0ms (4.4% of total)

ival-fabs: 66.0ms (2.3% of total)

ival-<=: 42.0ms (1.5% of total)

const: 18.0ms (0.6% of total)

Bogosity

preprocess65.0ms (0.6%)

Algorithm

2×	egg-herbie

Rules

296×	`fnmadd-define`
294×	`fmsub-define`
290×	`fnmsub-define`
290×	`fnmadd-define`
282×	`sum3-define`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	25
1	40	22
2	101	22
3	258	22
4	633	22
5	1128	22
6	1355	22
7	1404	22
0	7	8
1	19	7
2	37	7
3	62	7
4	116	7
5	214	7
6	498	7
7	950	7
8	1161	7
9	1232	7
10	1246	7
0	1246	7

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(+ (- (exp x) 2) (exp (neg x)))

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

Call 2

Inputs
(+ (- (exp x) 2) (exp (neg x)))
(+ (- (exp (neg x)) 2) (exp (neg (neg x))))
(neg (+ (- (exp (neg x)) 2) (exp (neg (neg x)))))

Outputs
(+ (- (exp x) 2) (exp (neg x)))
(sum3 (exp x) (recip (exp x)) -2)
(+ (- (exp (neg x)) 2) (exp (neg (neg x))))
(sum3 (exp x) (recip (exp x)) -2)
(neg (+ (- (exp (neg x)) 2) (exp (neg (neg x)))))
(- (- 2 (recip (exp x))) (exp x))

Symmetry

(abs x)

explain327.0ms (3%)

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
138	-	-	`(+.f64 (-.f64 (exp.f64 x) #s(literal 2 binary64)) (exp.f64 (neg.f64 x)))`
0	-	-	`x`
0	-	-	`(exp.f64 (neg.f64 x))`
0	-	-	`(neg.f64 x)`
0	-	-	`(exp.f64 x)`
0	-	-	`(-.f64 (exp.f64 x) #s(literal 2 binary64))`
0	-	-	`#s(literal 2 binary64)`

Results

245.0ms	358×	2	valid
40.0ms	148×	1	valid
1.0ms	6×	0	valid

Compiler

Compiled 55 to 23 computations (58.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 154.0ms

ival-exp: 104.0ms (67.5% of total)

backward-pass: 23.0ms (14.9% of total)

ival-sub: 10.0ms (6.5% of total)

ival-add: 9.0ms (5.8% of total)

ival-neg: 6.0ms (3.9% of total)

const: 1.0ms (0.6% of total)

eval0.0ms (0%)

Compiler: Compiled 10 to 7 computations (30% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	50.9%	(+.f64 (-.f64 (exp.f64 x) #s(literal 2 binary64)) (exp.f64 (neg.f64 x)))
▶	50.9%	(+.f64 (exp.f64 x) (+.f64 (/.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -2 binary64)))

Compiler

Compiled 19 to 14 computations (26.3% saved)

simplify39.0ms (0.4%)

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

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

Rules

296×	`fnmadd-define`
270×	`sum3-define`
252×	`fmsub-define`
244×	`fma-lowering-fma.f32`
244×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	42
1	28	40
2	46	40
3	67	40
4	117	40
5	214	40
6	497	40
7	948	40
8	1159	40
9	1230	40
10	1244	40
0	1244	40

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(+ (exp x) (+ (/ 1 (exp x)) -2))
(exp x)
x
(+ (/ 1 (exp x)) -2)
(/ 1 (exp x))
1
-2
(+ (- (exp x) 2) (exp (neg x)))
(- (exp x) 2)
(exp x)
x
2
(exp (neg x))
(neg x)

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

localize234.0ms (2.2%)

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(exp.f64 (neg.f64 x))
✓	accuracy	100.0%	(exp.f64 x)
✓	accuracy	100.0%	(-.f64 (exp.f64 x) #s(literal 2 binary64))
✓	accuracy	50.9%	(+.f64 (-.f64 (exp.f64 x) #s(literal 2 binary64)) (exp.f64 (neg.f64 x)))
✓	accuracy	100.0%	(exp.f64 x)
✓	accuracy	100.0%	(+.f64 (/.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -2 binary64))
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) (exp.f64 x))
✓	accuracy	50.9%	(+.f64 (exp.f64 x) (+.f64 (/.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -2 binary64)))

Results

153.0ms	179×	2	valid
53.0ms	74×	1	valid
0.0ms	3×	0	valid

Compiler

Compiled 47 to 13 computations (72.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 112.0ms

ival-exp: 69.0ms (61.8% of total)

backward-pass: 17.0ms (15.2% of total)

ival-add: 10.0ms (9% of total)

ival-div: 7.0ms (6.3% of total)

ival-sub: 4.0ms (3.6% of total)

ival-neg: 3.0ms (2.7% of total)

const: 1.0ms (0.9% of total)

series3.0ms (0%)

Counts

7 → 84

Calls

Call 1

Inputs
#<alt (+ (exp x) (+ (/ 1 (exp x)) -2))>
#<alt (exp x)>
#<alt (+ (/ 1 (exp x)) -2)>
#<alt (/ 1 (exp x))>
#<alt (+ (- (exp x) 2) (exp (neg x)))>
#<alt (- (exp x) 2)>
#<alt (exp (neg x))>

Outputs
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* 1/12 (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (* (pow x 2) (+ 1/12 (* 1/360 (pow x 2))))))>
#<alt (* (pow x 2) (+ 1 (* (pow x 2) (+ 1/12 (* (pow x 2) (+ 1/360 (* 1/20160 (pow x 2))))))))>
#<alt (- (+ (exp x) (/ 1 (exp x))) 2)>
#<alt (- (+ (exp x) (/ 1 (exp x))) 2)>
#<alt (- (+ (exp x) (/ 1 (exp x))) 2)>
#<alt (- (+ (exp x) (/ 1 (exp x))) 2)>
#<alt (- (+ (exp x) (/ 1 (exp x))) 2)>
#<alt (- (+ (exp x) (/ 1 (exp x))) 2)>
#<alt (- (+ (exp x) (/ 1 (exp x))) 2)>
#<alt (- (+ (exp x) (/ 1 (exp x))) 2)>
#<alt 1>
#<alt (+ 1 x)>
#<alt (+ 1 (* x (+ 1 (* 1/2 x))))>
#<alt (+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt -1>
#<alt (- (* -1 x) 1)>
#<alt (- (* x (- (* 1/2 x) 1)) 1)>
#<alt (- (* x (- (* x (+ 1/2 (* -1/6 x))) 1)) 1)>
#<alt (- (/ 1 (exp x)) 2)>
#<alt (- (/ 1 (exp x)) 2)>
#<alt (- (/ 1 (exp x)) 2)>
#<alt (- (/ 1 (exp x)) 2)>
#<alt (- (/ 1 (exp x)) 2)>
#<alt (- (/ 1 (exp x)) 2)>
#<alt (- (/ 1 (exp x)) 2)>
#<alt (- (/ 1 (exp x)) 2)>
#<alt 1>
#<alt (+ 1 (* -1 x))>
#<alt (+ 1 (* x (- (* 1/2 x) 1)))>
#<alt (+ 1 (* x (- (* x (+ 1/2 (* -1/6 x))) 1)))>
#<alt (/ 1 (exp x))>
#<alt (/ 1 (exp x))>
#<alt (/ 1 (exp x))>
#<alt (/ 1 (exp x))>
#<alt (/ 1 (exp x))>
#<alt (/ 1 (exp x))>
#<alt (/ 1 (exp x))>
#<alt (/ 1 (exp x))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* 1/12 (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (* (pow x 2) (+ 1/12 (* 1/360 (pow x 2))))))>
#<alt (* (pow x 2) (+ 1 (* (pow x 2) (+ 1/12 (* (pow x 2) (+ 1/360 (* 1/20160 (pow x 2))))))))>
#<alt (- (+ (exp x) (exp (neg x))) 2)>
#<alt (- (+ (exp x) (exp (neg x))) 2)>
#<alt (- (+ (exp x) (exp (neg x))) 2)>
#<alt (- (+ (exp x) (exp (neg x))) 2)>
#<alt (- (+ (exp x) (exp (* -1 x))) 2)>
#<alt (- (+ (exp x) (exp (* -1 x))) 2)>
#<alt (- (+ (exp x) (exp (* -1 x))) 2)>
#<alt (- (+ (exp x) (exp (* -1 x))) 2)>
#<alt -1>
#<alt (- x 1)>
#<alt (- (* x (+ 1 (* 1/2 x))) 1)>
#<alt (- (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))) 1)>
#<alt (- (exp x) 2)>
#<alt (- (exp x) 2)>
#<alt (- (exp x) 2)>
#<alt (- (exp x) 2)>
#<alt (- (exp x) 2)>
#<alt (- (exp x) 2)>
#<alt (- (exp x) 2)>
#<alt (- (exp x) 2)>
#<alt 1>
#<alt (+ 1 (* -1 x))>
#<alt (+ 1 (* x (- (* 1/2 x) 1)))>
#<alt (+ 1 (* x (- (* x (+ 1/2 (* -1/6 x))) 1)))>
#<alt (exp (neg x))>
#<alt (exp (neg x))>
#<alt (exp (neg x))>
#<alt (exp (neg x))>
#<alt (exp (* -1 x))>
#<alt (exp (* -1 x))>
#<alt (exp (* -1 x))>
#<alt (exp (* -1 x))>

Calls

21 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(+ (exp x) (+ (/ 1 (exp x)) -2))
1.0ms	x	@	0	(+ (exp x) (+ (/ 1 (exp x)) -2))
0.0ms	x	@	inf	(+ (exp x) (+ (/ 1 (exp x)) -2))
0.0ms	x	@	-inf	(+ (- (exp x) 2) (exp (neg x)))
0.0ms	x	@	0	(+ (- (exp x) 2) (exp (neg x)))

rewrite226.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

2280×	`/-lowering-/.f32`
2280×	`/-lowering-/.f64`
1592×	`-lowering-.f32`
1592×	`-lowering-.f64`
1466×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	33
1	35	29
2	86	27
3	257	27
4	906	27
5	3695	27
0	8486	27

Stop Event

1×	iter limit
1×	node limit

Counts

7 → 259

Calls

Call 1

Inputs
(+ (exp x) (+ (/ 1 (exp x)) -2))
(exp x)
(+ (/ 1 (exp x)) -2)
(/ 1 (exp x))
(+ (- (exp x) 2) (exp (neg x)))
(- (exp x) 2)
(exp (neg x))

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

simplify188.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

1978×	`+-lowering-+.f64`
1978×	`+-lowering-+.f32`
1744×	`sum3-define`
1528×	`-lowering-.f32`
1528×	`-lowering-.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	67	495
1	193	430
2	534	423
3	1516	423
4	2671	423
5	6037	423
6	7680	423
0	8142	423

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 84

Calls

Call 1

Inputs
(pow x 2)
(* (pow x 2) (+ 1 (* 1/12 (pow x 2))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 1/12 (* 1/360 (pow x 2))))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 1/12 (* (pow x 2) (+ 1/360 (* 1/20160 (pow x 2))))))))
(- (+ (exp x) (/ 1 (exp x))) 2)
(- (+ (exp x) (/ 1 (exp x))) 2)
(- (+ (exp x) (/ 1 (exp x))) 2)
(- (+ (exp x) (/ 1 (exp x))) 2)
(- (+ (exp x) (/ 1 (exp x))) 2)
(- (+ (exp x) (/ 1 (exp x))) 2)
(- (+ (exp x) (/ 1 (exp x))) 2)
(- (+ (exp x) (/ 1 (exp x))) 2)
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
-1
(- (* -1 x) 1)
(- (* x (- (* 1/2 x) 1)) 1)
(- (* x (- (* x (+ 1/2 (* -1/6 x))) 1)) 1)
(- (/ 1 (exp x)) 2)
(- (/ 1 (exp x)) 2)
(- (/ 1 (exp x)) 2)
(- (/ 1 (exp x)) 2)
(- (/ 1 (exp x)) 2)
(- (/ 1 (exp x)) 2)
(- (/ 1 (exp x)) 2)
(- (/ 1 (exp x)) 2)
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* x (+ 1/2 (* -1/6 x))) 1)))
(/ 1 (exp x))
(/ 1 (exp x))
(/ 1 (exp x))
(/ 1 (exp x))
(/ 1 (exp x))
(/ 1 (exp x))
(/ 1 (exp x))
(/ 1 (exp x))
(pow x 2)
(* (pow x 2) (+ 1 (* 1/12 (pow x 2))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 1/12 (* 1/360 (pow x 2))))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 1/12 (* (pow x 2) (+ 1/360 (* 1/20160 (pow x 2))))))))
(- (+ (exp x) (exp (neg x))) 2)
(- (+ (exp x) (exp (neg x))) 2)
(- (+ (exp x) (exp (neg x))) 2)
(- (+ (exp x) (exp (neg x))) 2)
(- (+ (exp x) (exp (* -1 x))) 2)
(- (+ (exp x) (exp (* -1 x))) 2)
(- (+ (exp x) (exp (* -1 x))) 2)
(- (+ (exp x) (exp (* -1 x))) 2)
-1
(- x 1)
(- (* x (+ 1 (* 1/2 x))) 1)
(- (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))) 1)
(- (exp x) 2)
(- (exp x) 2)
(- (exp x) 2)
(- (exp x) 2)
(- (exp x) 2)
(- (exp x) 2)
(- (exp x) 2)
(- (exp x) 2)
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* x (+ 1/2 (* -1/6 x))) 1)))
(exp (neg x))
(exp (neg x))
(exp (neg x))
(exp (neg x))
(exp (* -1 x))
(exp (* -1 x))
(exp (* -1 x))
(exp (* -1 x))

Outputs
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 1/12 (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal 1/12 binary64))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 1/12 (* 1/360 (pow x 2))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64))))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 1/12 (* (pow x 2) (+ 1/360 (* 1/20160 (pow x 2))))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64)))))))))
(- (+ (exp x) (/ 1 (exp x))) 2)
(+.f64 (exp.f64 x) (+.f64 (/.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -2 binary64)))
(- (+ (exp x) (/ 1 (exp x))) 2)
(+.f64 (exp.f64 x) (+.f64 (/.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -2 binary64)))
(- (+ (exp x) (/ 1 (exp x))) 2)
(+.f64 (exp.f64 x) (+.f64 (/.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -2 binary64)))
(- (+ (exp x) (/ 1 (exp x))) 2)
(+.f64 (exp.f64 x) (+.f64 (/.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -2 binary64)))
(- (+ (exp x) (/ 1 (exp x))) 2)
(+.f64 (exp.f64 x) (+.f64 (/.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -2 binary64)))
(- (+ (exp x) (/ 1 (exp x))) 2)
(+.f64 (exp.f64 x) (+.f64 (/.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -2 binary64)))
(- (+ (exp x) (/ 1 (exp x))) 2)
(+.f64 (exp.f64 x) (+.f64 (/.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -2 binary64)))
(- (+ (exp x) (/ 1 (exp x))) 2)
(+.f64 (exp.f64 x) (+.f64 (/.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -2 binary64)))
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
(+ 1 (* x (+ 1 (* 1/2 x))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(+.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)))))))
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
-1
#s(literal -1 binary64)
(- (* -1 x) 1)
(-.f64 #s(literal -1 binary64) x)
(- (* x (- (* 1/2 x) 1)) 1)
(+.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))
(- (* x (- (* x (+ 1/2 (* -1/6 x))) 1)) 1)
(-.f64 #s(literal -1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64))))))
(- (/ 1 (exp x)) 2)
(+.f64 (/.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -2 binary64))
(- (/ 1 (exp x)) 2)
(+.f64 (/.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -2 binary64))
(- (/ 1 (exp x)) 2)
(+.f64 (/.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -2 binary64))
(- (/ 1 (exp x)) 2)
(+.f64 (/.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -2 binary64))
(- (/ 1 (exp x)) 2)
(+.f64 (/.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -2 binary64))
(- (/ 1 (exp x)) 2)
(+.f64 (/.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -2 binary64))
(- (/ 1 (exp x)) 2)
(+.f64 (/.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -2 binary64))
(- (/ 1 (exp x)) 2)
(+.f64 (/.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -2 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* x (- (* 1/2 x) 1)))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))
(+ 1 (* x (- (* x (+ 1/2 (* -1/6 x))) 1)))
(-.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64))))))
(/ 1 (exp x))
(/.f64 #s(literal 1 binary64) (exp.f64 x))
(/ 1 (exp x))
(/.f64 #s(literal 1 binary64) (exp.f64 x))
(/ 1 (exp x))
(/.f64 #s(literal 1 binary64) (exp.f64 x))
(/ 1 (exp x))
(/.f64 #s(literal 1 binary64) (exp.f64 x))
(/ 1 (exp x))
(/.f64 #s(literal 1 binary64) (exp.f64 x))
(/ 1 (exp x))
(/.f64 #s(literal 1 binary64) (exp.f64 x))
(/ 1 (exp x))
(/.f64 #s(literal 1 binary64) (exp.f64 x))
(/ 1 (exp x))
(/.f64 #s(literal 1 binary64) (exp.f64 x))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 1/12 (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal 1/12 binary64))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 1/12 (* 1/360 (pow x 2))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64))))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 1/12 (* (pow x 2) (+ 1/360 (* 1/20160 (pow x 2))))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64)))))))))
(- (+ (exp x) (exp (neg x))) 2)
(+.f64 (exp.f64 x) (+.f64 (/.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -2 binary64)))
(- (+ (exp x) (exp (neg x))) 2)
(+.f64 (exp.f64 x) (+.f64 (/.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -2 binary64)))
(- (+ (exp x) (exp (neg x))) 2)
(+.f64 (exp.f64 x) (+.f64 (/.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -2 binary64)))
(- (+ (exp x) (exp (neg x))) 2)
(+.f64 (exp.f64 x) (+.f64 (/.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -2 binary64)))
(- (+ (exp x) (exp (* -1 x))) 2)
(+.f64 (exp.f64 x) (+.f64 (/.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -2 binary64)))
(- (+ (exp x) (exp (* -1 x))) 2)
(+.f64 (exp.f64 x) (+.f64 (/.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -2 binary64)))
(- (+ (exp x) (exp (* -1 x))) 2)
(+.f64 (exp.f64 x) (+.f64 (/.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -2 binary64)))
(- (+ (exp x) (exp (* -1 x))) 2)
(+.f64 (exp.f64 x) (+.f64 (/.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -2 binary64)))
-1
#s(literal -1 binary64)
(- x 1)
(+.f64 x #s(literal -1 binary64))
(- (* x (+ 1 (* 1/2 x))) 1)
(+.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)))) #s(literal -1 binary64))
(- (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))) 1)
(+.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))
(- (exp x) 2)
(+.f64 (exp.f64 x) #s(literal -2 binary64))
(- (exp x) 2)
(+.f64 (exp.f64 x) #s(literal -2 binary64))
(- (exp x) 2)
(+.f64 (exp.f64 x) #s(literal -2 binary64))
(- (exp x) 2)
(+.f64 (exp.f64 x) #s(literal -2 binary64))
(- (exp x) 2)
(+.f64 (exp.f64 x) #s(literal -2 binary64))
(- (exp x) 2)
(+.f64 (exp.f64 x) #s(literal -2 binary64))
(- (exp x) 2)
(+.f64 (exp.f64 x) #s(literal -2 binary64))
(- (exp x) 2)
(+.f64 (exp.f64 x) #s(literal -2 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* x (- (* 1/2 x) 1)))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))))
(+ 1 (* x (- (* x (+ 1/2 (* -1/6 x))) 1)))
(-.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64))))))
(exp (neg x))
(/.f64 #s(literal 1 binary64) (exp.f64 x))
(exp (neg x))
(/.f64 #s(literal 1 binary64) (exp.f64 x))
(exp (neg x))
(/.f64 #s(literal 1 binary64) (exp.f64 x))
(exp (neg x))
(/.f64 #s(literal 1 binary64) (exp.f64 x))
(exp (* -1 x))
(/.f64 #s(literal 1 binary64) (exp.f64 x))
(exp (* -1 x))
(/.f64 #s(literal 1 binary64) (exp.f64 x))
(exp (* -1 x))
(/.f64 #s(literal 1 binary64) (exp.f64 x))
(exp (* -1 x))
(/.f64 #s(literal 1 binary64) (exp.f64 x))

eval41.0ms (0.4%)

Compiler: Compiled 5296 to 713 computations (86.5% saved)

prune52.0ms (0.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	448	7	455
Fresh	0	0	0
Picked	2	0	2
Done	0	0	0
Total	450	7	457

Accuracy

100.0%

Counts

457 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
	50.9%	(-.f64 (*.f64 #s(literal 2 binary64) (cosh.f64 x)) #s(literal 2 binary64))
	50.8%	(+.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (E.f64)) (-.f64 #s(literal 0 binary64) x)) #s(literal 2 binary64)) (exp.f64 (neg.f64 x)))
▶	49.8%	(+.f64 (exp.f64 x) #s(literal -1 binary64))
▶	99.4%	(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64))))))
▶	99.4%	(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64)))))))))
▶	99.3%	(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal 1/12 binary64))))
▶	98.8%	(*.f64 x x)

Compiler

Compiled 168 to 108 computations (35.7% saved)

simplify432.0ms (4%)

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

New	Metric	Program
✓	cost-diff	(exp.f64 x)
✓	cost-diff	(+.f64 (exp.f64 x) #s(literal -1 binary64))
✓	cost-diff	(.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64))))
✓	cost-diff	(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64)))))
✓	cost-diff	(*.f64 x x)
✓	cost-diff	(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64))))))
✓	cost-diff	(.f64 (.f64 x x) #s(literal 1/12 binary64))
✓	cost-diff	(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal 1/12 binary64)))
✓	cost-diff	(*.f64 x x)
✓	cost-diff	(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal 1/12 binary64))))
✓	cost-diff	(*.f64 x x)
✓	cost-diff	(.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64)))))))
✓	cost-diff	(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64))))))))
✓	cost-diff	(*.f64 x x)
✓	cost-diff	(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64)))))))))

Rules

3222×	`fma-define`
2750×	`fma-lowering-fma.f32`
2750×	`fma-lowering-fma.f64`
2680×	`sum3-define`
1482×	`distribute-lft-in`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	25	179
1	91	158
2	314	155
3	946	155
4	2237	155
5	3172	155
6	4628	155
7	5680	155
8	6112	155
9	6198	155
10	6241	155
11	6270	155
12	6273	155
13	6273	155
14	7224	155
15	7224	155
0	7224	155

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(* (* x x) (+ 1 (* (* x x) (+ 1/12 (* x (* x (+ 1/360 (* (* x x) 1/20160))))))))
(* x x)
x
(+ 1 (* (* x x) (+ 1/12 (* x (* x (+ 1/360 (* (* x x) 1/20160)))))))
1
(* (* x x) (+ 1/12 (* x (* x (+ 1/360 (* (* x x) 1/20160))))))
(+ 1/12 (* x (* x (+ 1/360 (* (* x x) 1/20160)))))
1/12
(* x (* x (+ 1/360 (* (* x x) 1/20160))))
(* x (+ 1/360 (* (* x x) 1/20160)))
(+ 1/360 (* (* x x) 1/20160))
1/360
(* (* x x) 1/20160)
1/20160
(* x x)
x
(* (* x x) (+ 1 (* (* x x) 1/12)))
(* x x)
x
(+ 1 (* (* x x) 1/12))
1
(* (* x x) 1/12)
1/12
(* (* x x) (+ 1 (* (* x x) (+ 1/12 (* (* x x) 1/360)))))
(* x x)
x
(+ 1 (* (* x x) (+ 1/12 (* (* x x) 1/360))))
1
(* (* x x) (+ 1/12 (* (* x x) 1/360)))
(+ 1/12 (* (* x x) 1/360))
1/12
(* (* x x) 1/360)
1/360
(+ (exp x) -1)
(exp x)
x
-1

Outputs
(* (* x x) (+ 1 (* (* x x) (+ 1/12 (* x (* x (+ 1/360 (* (* x x) 1/20160))))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64)))))))))
(* x x)
(*.f64 x x)
x
(+ 1 (* (* x x) (+ 1/12 (* x (* x (+ 1/360 (* (* x x) 1/20160)))))))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64))))))))
1
#s(literal 1 binary64)
(* (* x x) (+ 1/12 (* x (* x (+ 1/360 (* (* x x) 1/20160))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64)))))))
(+ 1/12 (* x (* x (+ 1/360 (* (* x x) 1/20160)))))
(+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64))))))
1/12
#s(literal 1/12 binary64)
(* x (* x (+ 1/360 (* (* x x) 1/20160))))
(.f64 x (.f64 x (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64)))))
(* x (+ 1/360 (* (* x x) 1/20160)))
(.f64 x (+.f64 #s(literal 1/360 binary64) (.f64 (*.f64 x x) #s(literal 1/20160 binary64))))
(+ 1/360 (* (* x x) 1/20160))
(+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64)))
1/360
#s(literal 1/360 binary64)
(* (* x x) 1/20160)
(.f64 (.f64 x x) #s(literal 1/20160 binary64))
1/20160
#s(literal 1/20160 binary64)
(* x x)
(*.f64 x x)
x
(* (* x x) (+ 1 (* (* x x) 1/12)))
(.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal 1/12 binary64)))))
(* x x)
(*.f64 x x)
x
(+ 1 (* (* x x) 1/12))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal 1/12 binary64)))
1
#s(literal 1 binary64)
(* (* x x) 1/12)
(.f64 (.f64 x x) #s(literal 1/12 binary64))
1/12
#s(literal 1/12 binary64)
(* (* x x) (+ 1 (* (* x x) (+ 1/12 (* (* x x) 1/360)))))
(.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64))))))))
(* x x)
(*.f64 x x)
x
(+ 1 (* (* x x) (+ 1/12 (* (* x x) 1/360))))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64))))))
1
#s(literal 1 binary64)
(* (* x x) (+ 1/12 (* (* x x) 1/360)))
(.f64 x (.f64 x (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64)))))
(+ 1/12 (* (* x x) 1/360))
(+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64)))
1/12
#s(literal 1/12 binary64)
(* (* x x) 1/360)
(.f64 (.f64 x x) #s(literal 1/360 binary64))
1/360
#s(literal 1/360 binary64)
(+ (exp x) -1)
(+.f64 (exp.f64 x) #s(literal -1 binary64))
(exp x)
(exp.f64 x)
x
-1
#s(literal -1 binary64)

localize296.0ms (2.7%)

Localize:

Found 15 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(exp.f64 x)
✓	accuracy	8.2%	(+.f64 (exp.f64 x) #s(literal -1 binary64))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64))))))
✓	accuracy	99.7%	(.f64 (.f64 x x) #s(literal 1/360 binary64))
✓	accuracy	99.7%	(.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64))))
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal 1/12 binary64)))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal 1/12 binary64))))
✓	accuracy	99.7%	(.f64 (.f64 x x) #s(literal 1/12 binary64))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	99.8%	(.f64 (.f64 x x) #s(literal 1/20160 binary64))
✓	accuracy	99.8%	(.f64 x (.f64 x (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64)))))
✓	accuracy	99.7%	(.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64)))))))
✓	accuracy	99.6%	(.f64 x (+.f64 #s(literal 1/360 binary64) (.f64 (*.f64 x x) #s(literal 1/20160 binary64))))

Results

223.0ms	250×	1	valid
2.0ms	6×	0	valid

Compiler

Compiled 215 to 26 computations (87.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 106.0ms

ival-mult: 36.0ms (34% of total)

backward-pass: 22.0ms (20.8% of total)

...c/correct-round.rkt:119:19: 19.0ms (18% of total)

ival-add: 16.0ms (15.1% of total)

ival-exp: 11.0ms (10.4% of total)

const: 1.0ms (0.9% of total)

series9.0ms (0.1%)

Counts

16 → 192

Calls

Call 1

Inputs
#<alt (* (* x x) (+ 1 (* (* x x) (+ 1/12 (* x (* x (+ 1/360 (* (* x x) 1/20160))))))))>
#<alt (* x x)>
#<alt (+ 1 (* (* x x) (+ 1/12 (* x (* x (+ 1/360 (* (* x x) 1/20160)))))))>
#<alt (* (* x x) (+ 1/12 (* x (* x (+ 1/360 (* (* x x) 1/20160))))))>
#<alt (* (* x x) (+ 1 (* (* x x) 1/12)))>
#<alt (+ 1 (* (* x x) 1/12))>
#<alt (* (* x x) 1/12)>
#<alt (* (* x x) (+ 1 (* (* x x) (+ 1/12 (* (* x x) 1/360)))))>
#<alt (+ 1 (* (* x x) (+ 1/12 (* (* x x) 1/360))))>
#<alt (* (* x x) (+ 1/12 (* (* x x) 1/360)))>
#<alt (+ (exp x) -1)>
#<alt (exp x)>
#<alt (* x (+ 1/360 (* (* x x) 1/20160)))>
#<alt (* x (* x (+ 1/360 (* (* x x) 1/20160))))>
#<alt (* (* x x) 1/20160)>
#<alt (* (* x x) 1/360)>

Outputs
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* 1/12 (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (* (pow x 2) (+ 1/12 (* 1/360 (pow x 2))))))>
#<alt (* (pow x 2) (+ 1 (* (pow x 2) (+ 1/12 (* (pow x 2) (+ 1/360 (* 1/20160 (pow x 2))))))))>
#<alt (* 1/20160 (pow x 8))>
#<alt (* (pow x 8) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))>
#<alt (* (pow x 8) (+ 1/20160 (+ (/ 1/12 (pow x 4)) (* 1/360 (/ 1 (pow x 2))))))>
#<alt (* (pow x 8) (+ 1/20160 (+ (/ 1/12 (pow x 4)) (+ (* 1/360 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))>
#<alt (* 1/20160 (pow x 8))>
#<alt (* (pow x 8) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))>
#<alt (* (pow x 8) (+ 1/20160 (+ (/ 1/12 (pow x 4)) (* 1/360 (/ 1 (pow x 2))))))>
#<alt (* (pow x 8) (+ 1/20160 (+ (/ 1/12 (pow x 4)) (+ (* 1/360 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt 1>
#<alt (+ 1 (* 1/12 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (+ 1/12 (* 1/360 (pow x 2)))))>
#<alt (+ 1 (* (pow x 2) (+ 1/12 (* (pow x 2) (+ 1/360 (* 1/20160 (pow x 2)))))))>
#<alt (* 1/20160 (pow x 6))>
#<alt (* (pow x 6) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (+ 1/20160 (+ (/ 1/12 (pow x 4)) (* 1/360 (/ 1 (pow x 2))))))>
#<alt (* (pow x 6) (+ 1/20160 (+ (/ 1/12 (pow x 4)) (+ (* 1/360 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))>
#<alt (* 1/20160 (pow x 6))>
#<alt (* (pow x 6) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (+ 1/20160 (+ (/ 1/12 (pow x 4)) (* 1/360 (/ 1 (pow x 2))))))>
#<alt (* (pow x 6) (+ 1/20160 (+ (/ 1/12 (pow x 4)) (+ (* 1/360 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))>
#<alt (* 1/12 (pow x 2))>
#<alt (* (pow x 2) (+ 1/12 (* 1/360 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/12 (* (pow x 2) (+ 1/360 (* 1/20160 (pow x 2))))))>
#<alt (* (pow x 2) (+ 1/12 (* (pow x 2) (+ 1/360 (* 1/20160 (pow x 2))))))>
#<alt (* 1/20160 (pow x 6))>
#<alt (* (pow x 6) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (+ 1/20160 (+ (/ 1/12 (pow x 4)) (* 1/360 (/ 1 (pow x 2))))))>
#<alt (* (pow x 6) (+ 1/20160 (+ (/ 1/12 (pow x 4)) (* 1/360 (/ 1 (pow x 2))))))>
#<alt (* 1/20160 (pow x 6))>
#<alt (* (pow x 6) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (+ 1/20160 (+ (/ 1/12 (pow x 4)) (* 1/360 (/ 1 (pow x 2))))))>
#<alt (* (pow x 6) (+ 1/20160 (+ (/ 1/12 (pow x 4)) (* 1/360 (/ 1 (pow x 2))))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* 1/12 (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (* 1/12 (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (* 1/12 (pow x 2))))>
#<alt (* 1/12 (pow x 4))>
#<alt (* (pow x 4) (+ 1/12 (/ 1 (pow x 2))))>
#<alt (* (pow x 4) (+ 1/12 (/ 1 (pow x 2))))>
#<alt (* (pow x 4) (+ 1/12 (/ 1 (pow x 2))))>
#<alt (* 1/12 (pow x 4))>
#<alt (* (pow x 4) (+ 1/12 (/ 1 (pow x 2))))>
#<alt (* (pow x 4) (+ 1/12 (/ 1 (pow x 2))))>
#<alt (* (pow x 4) (+ 1/12 (/ 1 (pow x 2))))>
#<alt 1>
#<alt (+ 1 (* 1/12 (pow x 2)))>
#<alt (+ 1 (* 1/12 (pow x 2)))>
#<alt (+ 1 (* 1/12 (pow x 2)))>
#<alt (* 1/12 (pow x 2))>
#<alt (* (pow x 2) (+ 1/12 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/12 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/12 (/ 1 (pow x 2))))>
#<alt (* 1/12 (pow x 2))>
#<alt (* (pow x 2) (+ 1/12 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/12 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/12 (/ 1 (pow x 2))))>
#<alt (* 1/12 (pow x 2))>
#<alt (* 1/12 (pow x 2))>
#<alt (* 1/12 (pow x 2))>
#<alt (* 1/12 (pow x 2))>
#<alt (* 1/12 (pow x 2))>
#<alt (* 1/12 (pow x 2))>
#<alt (* 1/12 (pow x 2))>
#<alt (* 1/12 (pow x 2))>
#<alt (* 1/12 (pow x 2))>
#<alt (* 1/12 (pow x 2))>
#<alt (* 1/12 (pow x 2))>
#<alt (* 1/12 (pow x 2))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* 1/12 (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (* (pow x 2) (+ 1/12 (* 1/360 (pow x 2))))))>
#<alt (* (pow x 2) (+ 1 (* (pow x 2) (+ 1/12 (* 1/360 (pow x 2))))))>
#<alt (* 1/360 (pow x 6))>
#<alt (* (pow x 6) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (+ 1/360 (+ (* 1/12 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))>
#<alt (* (pow x 6) (+ 1/360 (+ (* 1/12 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))>
#<alt (* 1/360 (pow x 6))>
#<alt (* (pow x 6) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (+ 1/360 (+ (* 1/12 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))>
#<alt (* (pow x 6) (+ 1/360 (+ (* 1/12 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))>
#<alt 1>
#<alt (+ 1 (* 1/12 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (+ 1/12 (* 1/360 (pow x 2)))))>
#<alt (+ 1 (* (pow x 2) (+ 1/12 (* 1/360 (pow x 2)))))>
#<alt (* 1/360 (pow x 4))>
#<alt (* (pow x 4) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 1/360 (+ (* 1/12 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))>
#<alt (* (pow x 4) (+ 1/360 (+ (* 1/12 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))>
#<alt (* 1/360 (pow x 4))>
#<alt (* (pow x 4) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 1/360 (+ (* 1/12 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))>
#<alt (* (pow x 4) (+ 1/360 (+ (* 1/12 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))>
#<alt (* 1/12 (pow x 2))>
#<alt (* (pow x 2) (+ 1/12 (* 1/360 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/12 (* 1/360 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/12 (* 1/360 (pow x 2))))>
#<alt (* 1/360 (pow x 4))>
#<alt (* (pow x 4) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))>
#<alt (* 1/360 (pow x 4))>
#<alt (* (pow x 4) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 1/360 (* 1/12 (/ 1 (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 (- (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)>
#<alt 1>
#<alt (+ 1 x)>
#<alt (+ 1 (* x (+ 1 (* 1/2 x))))>
#<alt (+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (* 1/360 x)>
#<alt (* x (+ 1/360 (* 1/20160 (pow x 2))))>
#<alt (* x (+ 1/360 (* 1/20160 (pow x 2))))>
#<alt (* x (+ 1/360 (* 1/20160 (pow x 2))))>
#<alt (* 1/20160 (pow x 3))>
#<alt (* (pow x 3) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))>
#<alt (* 1/20160 (pow x 3))>
#<alt (* (pow x 3) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))>
#<alt (* 1/360 (pow x 2))>
#<alt (* (pow x 2) (+ 1/360 (* 1/20160 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/360 (* 1/20160 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/360 (* 1/20160 (pow x 2))))>
#<alt (* 1/20160 (pow x 4))>
#<alt (* (pow x 4) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))>
#<alt (* 1/20160 (pow x 4))>
#<alt (* (pow x 4) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))>
#<alt (* 1/20160 (pow x 2))>
#<alt (* 1/20160 (pow x 2))>
#<alt (* 1/20160 (pow x 2))>
#<alt (* 1/20160 (pow x 2))>
#<alt (* 1/20160 (pow x 2))>
#<alt (* 1/20160 (pow x 2))>
#<alt (* 1/20160 (pow x 2))>
#<alt (* 1/20160 (pow x 2))>
#<alt (* 1/20160 (pow x 2))>
#<alt (* 1/20160 (pow x 2))>
#<alt (* 1/20160 (pow x 2))>
#<alt (* 1/20160 (pow x 2))>
#<alt (* 1/360 (pow x 2))>
#<alt (* 1/360 (pow x 2))>
#<alt (* 1/360 (pow x 2))>
#<alt (* 1/360 (pow x 2))>
#<alt (* 1/360 (pow x 2))>
#<alt (* 1/360 (pow x 2))>
#<alt (* 1/360 (pow x 2))>
#<alt (* 1/360 (pow x 2))>
#<alt (* 1/360 (pow x 2))>
#<alt (* 1/360 (pow x 2))>
#<alt (* 1/360 (pow x 2))>
#<alt (* 1/360 (pow x 2))>

Calls

48 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(* x (+ 1/360 (* (* x x) 1/20160)))
1.0ms	x	@	inf	(* (* x x) (+ 1 (* (* x x) (+ 1/12 (* x (* x (+ 1/360 (* (* x x) 1/20160))))))))
0.0ms	x	@	inf	(* (* x x) (+ 1 (* (* x x) 1/12)))
0.0ms	x	@	inf	(* (* x x) 1/12)
0.0ms	x	@	inf	(* (* x x) (+ 1/12 (* x (* x (+ 1/360 (* (* x x) 1/20160))))))

rewrite192.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

2910×	`sum3-define`
2328×	`sum4-define`
1384×	`distribute-lft-in`
1338×	`-lowering-.f32`
1338×	`-lowering-.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	25	135
1	93	118
2	319	115
3	964	115
4	2268	115
5	3274	115
6	4965	115
7	6569	115
8	7322	115
0	8003	115

Stop Event

1×	iter limit
1×	node limit

Counts

16 → 396

Calls

Call 1

Inputs
(* (* x x) (+ 1 (* (* x x) (+ 1/12 (* x (* x (+ 1/360 (* (* x x) 1/20160))))))))
(* x x)
(+ 1 (* (* x x) (+ 1/12 (* x (* x (+ 1/360 (* (* x x) 1/20160)))))))
(* (* x x) (+ 1/12 (* x (* x (+ 1/360 (* (* x x) 1/20160))))))
(* (* x x) (+ 1 (* (* x x) 1/12)))
(+ 1 (* (* x x) 1/12))
(* (* x x) 1/12)
(* (* x x) (+ 1 (* (* x x) (+ 1/12 (* (* x x) 1/360)))))
(+ 1 (* (* x x) (+ 1/12 (* (* x x) 1/360))))
(* (* x x) (+ 1/12 (* (* x x) 1/360)))
(+ (exp x) -1)
(exp x)
(* x (+ 1/360 (* (* x x) 1/20160)))
(* x (* x (+ 1/360 (* (* x x) 1/20160))))
(* (* x x) 1/20160)
(* (* x x) 1/360)

Outputs
(+.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/360 binary64) (.f64 (*.f64 x x) #s(literal 1/20160 binary64)))))))))
(+.f64 (.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal 1/12 binary64))))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x (.f64 x (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64))))))))
(+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/12 binary64))) (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64)))))))))
(+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64)))))))) (*.f64 x x))
(+.f64 (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64)))))) (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 (.f64 x x) (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x x))))))))
(+.f64 (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64)))))) (+.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (.f64 #s(literal 1/20160 binary64) (.f64 x (*.f64 x x)))))))
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(fma.f64 x (.f64 x (+.f64 #s(literal 1/12 binary64) (.f64 (*.f64 x x) #s(literal 1/360 binary64)))) #s(literal 1 binary64))
(fma.f64 x (.f64 #s(literal 1/360 binary64) (.f64 x (.f64 x x))) (+.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) #s(literal 1/12 binary64))))
(fma.f64 (.f64 x x) #s(literal 1/12 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 #s(literal 1/360 binary64) (.f64 x (*.f64 x x))))))
(fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/360 binary64)) (+.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) #s(literal 1/12 binary64))))
(fma.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (*.f64 x x) #s(literal 1/360 binary64))) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal 1/12 binary64)) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 #s(literal 1/360 binary64) (.f64 x (.f64 x x))))))
(fma.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64)))) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (.f64 x (.f64 #s(literal 1/360 binary64) (.f64 x (.f64 x x)))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal 1/12 binary64))))
(fma.f64 #s(literal 1/12 binary64) (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 #s(literal 1/360 binary64) (.f64 x (*.f64 x x))))))
(fma.f64 #s(literal 1/360 binary64) (.f64 x (.f64 x (.f64 x x))) (+.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) #s(literal 1/12 binary64))))
(fma.f64 (.f64 (.f64 x x) #s(literal 1/12 binary64)) #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 #s(literal 1/360 binary64) (.f64 x (.f64 x x))))))
(fma.f64 (.f64 (.f64 x x) #s(literal 1/360 binary64)) (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) #s(literal 1/12 binary64))))
(fma.f64 (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64))) (*.f64 x x) #s(literal 1 binary64))
(fma.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64)))) #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 (.f64 x #s(literal 1/360 binary64)) (.f64 x (.f64 x x)) (+.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) #s(literal 1/12 binary64))))
(fma.f64 (.f64 x (.f64 #s(literal 1/360 binary64) (.f64 x (.f64 x x)))) #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal 1/12 binary64))))
(fma.f64 (.f64 x #s(literal 1/12 binary64)) x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 #s(literal 1/360 binary64) (.f64 x (*.f64 x x))))))
(fma.f64 (.f64 x (+.f64 #s(literal 1/12 binary64) (.f64 (*.f64 x x) #s(literal 1/360 binary64)))) x #s(literal 1 binary64))
(fma.f64 (.f64 #s(literal 1/360 binary64) (.f64 x (.f64 x x))) x (+.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) #s(literal 1/12 binary64))))
(fma.f64 (.f64 x (.f64 x x)) (.f64 x #s(literal 1/360 binary64)) (+.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) #s(literal 1/12 binary64))))
(fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/360 binary64) (+.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) #s(literal 1/12 binary64))))
(.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (*.f64 x x) #s(literal 1/360 binary64))))))
(.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (*.f64 x x) #s(literal 1/360 binary64))))) #s(literal 1 binary64))
(+.f64 (.f64 (.f64 x x) #s(literal 1/12 binary64)) (.f64 x (.f64 #s(literal 1/360 binary64) (.f64 x (.f64 x x)))))
(+.f64 (.f64 x (.f64 #s(literal 1/360 binary64) (.f64 x (.f64 x x)))) (.f64 (.f64 x x) #s(literal 1/12 binary64)))
(fma.f64 x (.f64 x #s(literal 1/12 binary64)) (.f64 x (.f64 #s(literal 1/360 binary64) (.f64 x (*.f64 x x)))))
(fma.f64 x (.f64 #s(literal 1/360 binary64) (.f64 x (.f64 x x))) (.f64 (*.f64 x x) #s(literal 1/12 binary64)))
(fma.f64 (.f64 x x) #s(literal 1/12 binary64) (.f64 x (.f64 #s(literal 1/360 binary64) (.f64 x (*.f64 x x)))))
(fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/360 binary64)) (.f64 (*.f64 x x) #s(literal 1/12 binary64)))
(fma.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal 1/12 binary64)) (.f64 x (.f64 #s(literal 1/360 binary64) (.f64 x (.f64 x x)))))
(fma.f64 #s(literal 1 binary64) (.f64 x (.f64 #s(literal 1/360 binary64) (.f64 x (.f64 x x)))) (.f64 (.f64 x x) #s(literal 1/12 binary64)))
(fma.f64 #s(literal 1/12 binary64) (.f64 x x) (.f64 x (.f64 #s(literal 1/360 binary64) (.f64 x (*.f64 x x)))))
(fma.f64 #s(literal 1/360 binary64) (.f64 x (.f64 x (.f64 x x))) (.f64 (*.f64 x x) #s(literal 1/12 binary64)))
(fma.f64 (.f64 (.f64 x x) #s(literal 1/12 binary64)) #s(literal 1 binary64) (.f64 x (.f64 #s(literal 1/360 binary64) (.f64 x (.f64 x x)))))
(fma.f64 (.f64 (.f64 x x) #s(literal 1/360 binary64)) (.f64 x x) (.f64 (*.f64 x x) #s(literal 1/12 binary64)))
(fma.f64 (.f64 x #s(literal 1/360 binary64)) (.f64 x (.f64 x x)) (.f64 (*.f64 x x) #s(literal 1/12 binary64)))
(fma.f64 (.f64 x (.f64 #s(literal 1/360 binary64) (.f64 x (.f64 x x)))) #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal 1/12 binary64)))
(fma.f64 (.f64 x #s(literal 1/12 binary64)) x (.f64 x (.f64 #s(literal 1/360 binary64) (.f64 x (*.f64 x x)))))
(fma.f64 (.f64 #s(literal 1/360 binary64) (.f64 x (.f64 x x))) x (.f64 (*.f64 x x) #s(literal 1/12 binary64)))
(fma.f64 (.f64 x (.f64 x x)) (.f64 x #s(literal 1/360 binary64)) (.f64 (*.f64 x x) #s(literal 1/12 binary64)))
(fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/360 binary64) (.f64 (*.f64 x x) #s(literal 1/12 binary64)))
(.f64 x (.f64 x (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64))))
(.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (*.f64 x x) #s(literal 1/360 binary64)))))
(.f64 (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64))) (.f64 x x))
(.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (*.f64 x x) #s(literal 1/360 binary64)))) #s(literal 1 binary64))
(.f64 (.f64 x (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64)))) x)
(+.f64 (exp.f64 x) #s(literal -1 binary64))
(+.f64 #s(literal -1 binary64) (exp.f64 x))
(exp.f64 x)
(pow.f64 (exp.f64 x) #s(literal 1 binary64))
(pow.f64 (E.f64) x)
(pow.f64 (*.f64 (E.f64) (E.f64)) (/.f64 x #s(literal 2 binary64)))
(pow.f64 (.f64 (E.f64) (.f64 (E.f64) (E.f64))) (*.f64 #s(literal 1/3 binary64) x))
(pow.f64 (exp.f64 #s(literal 1/3 binary64)) (*.f64 #s(literal 3 binary64) x))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 #s(literal 2 binary64) x))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (+.f64 x x))
(pow.f64 (pow.f64 (E.f64) (/.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))
(*.f64 #s(literal 1 binary64) (exp.f64 x))
(*.f64 (exp.f64 x) #s(literal 1 binary64))
(.f64 (pow.f64 (pow.f64 (E.f64) #s(literal 2/3 binary64)) x) (pow.f64 (E.f64) (.f64 #s(literal 1/3 binary64) x)))
(.f64 (pow.f64 (E.f64) (.f64 #s(literal 1/3 binary64) x)) (pow.f64 (pow.f64 (E.f64) #s(literal 2/3 binary64)) x))
(*.f64 (pow.f64 (E.f64) (/.f64 x #s(literal 2 binary64))) (pow.f64 (E.f64) (/.f64 x #s(literal 2 binary64))))
(+.f64 (.f64 x #s(literal 1/360 binary64)) (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x x))))
(+.f64 (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x x))) (.f64 x #s(literal 1/360 binary64)))
(fma.f64 x #s(literal 1/360 binary64) (.f64 #s(literal 1/20160 binary64) (.f64 x (*.f64 x x))))
(fma.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64)) (*.f64 x #s(literal 1/360 binary64)))
(fma.f64 (.f64 x x) (.f64 x #s(literal 1/20160 binary64)) (*.f64 x #s(literal 1/360 binary64)))
(fma.f64 #s(literal 1 binary64) (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x x))) (.f64 x #s(literal 1/360 binary64)))
(fma.f64 #s(literal 1/360 binary64) x (.f64 #s(literal 1/20160 binary64) (.f64 x (*.f64 x x))))
(fma.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x x)) (*.f64 x #s(literal 1/360 binary64)))
(fma.f64 (.f64 (.f64 x x) #s(literal 1/20160 binary64)) x (*.f64 x #s(literal 1/360 binary64)))
(fma.f64 (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x x))) #s(literal 1 binary64) (.f64 x #s(literal 1/360 binary64)))
(fma.f64 (.f64 x #s(literal 1/20160 binary64)) (.f64 x x) (*.f64 x #s(literal 1/360 binary64)))
(fma.f64 (.f64 x (.f64 x x)) #s(literal 1/20160 binary64) (*.f64 x #s(literal 1/360 binary64)))
(.f64 x (+.f64 #s(literal 1/360 binary64) (.f64 (*.f64 x x) #s(literal 1/20160 binary64))))
(.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64)))))
(.f64 (+.f64 #s(literal 1/360 binary64) (.f64 (*.f64 x x) #s(literal 1/20160 binary64))) x)
(.f64 (.f64 x (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64)))) #s(literal 1 binary64))
(+.f64 (.f64 (.f64 x x) #s(literal 1/360 binary64)) (.f64 x (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x x)))))
(+.f64 (.f64 x (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x x)))) (.f64 (.f64 x x) #s(literal 1/360 binary64)))
(fma.f64 x (.f64 x #s(literal 1/360 binary64)) (.f64 x (.f64 #s(literal 1/20160 binary64) (.f64 x (*.f64 x x)))))
(fma.f64 x (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x x))) (.f64 (*.f64 x x) #s(literal 1/360 binary64)))
(fma.f64 (.f64 x x) #s(literal 1/360 binary64) (.f64 x (.f64 #s(literal 1/20160 binary64) (.f64 x (*.f64 x x)))))
(fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/20160 binary64)) (.f64 (*.f64 x x) #s(literal 1/360 binary64)))
(fma.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64)) (.f64 x (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x x)))))
(fma.f64 #s(literal 1 binary64) (.f64 x (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x x)))) (.f64 (.f64 x x) #s(literal 1/360 binary64)))
(fma.f64 #s(literal 1/360 binary64) (.f64 x x) (.f64 x (.f64 #s(literal 1/20160 binary64) (.f64 x (*.f64 x x)))))
(fma.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x x))) (.f64 (*.f64 x x) #s(literal 1/360 binary64)))
(fma.f64 (.f64 (.f64 x x) #s(literal 1/20160 binary64)) (.f64 x x) (.f64 (*.f64 x x) #s(literal 1/360 binary64)))
(fma.f64 (.f64 (.f64 x x) #s(literal 1/360 binary64)) #s(literal 1 binary64) (.f64 x (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x x)))))
(fma.f64 (.f64 x #s(literal 1/360 binary64)) x (.f64 x (.f64 #s(literal 1/20160 binary64) (.f64 x (*.f64 x x)))))
(fma.f64 (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x x))) x (.f64 (*.f64 x x) #s(literal 1/360 binary64)))
(fma.f64 (.f64 x #s(literal 1/20160 binary64)) (.f64 x (.f64 x x)) (.f64 (*.f64 x x) #s(literal 1/360 binary64)))
(fma.f64 (.f64 x (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x x)))) #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64)))
(fma.f64 (.f64 x (.f64 x x)) (.f64 x #s(literal 1/20160 binary64)) (.f64 (*.f64 x x) #s(literal 1/360 binary64)))
(fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/20160 binary64) (.f64 (*.f64 x x) #s(literal 1/360 binary64)))
(.f64 x (.f64 x (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64))))
(.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/360 binary64) (.f64 (*.f64 x x) #s(literal 1/20160 binary64))))))
(.f64 (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64))) (.f64 x x))
(.f64 (.f64 x (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64)))) x)
(.f64 (.f64 x (.f64 x (+.f64 #s(literal 1/360 binary64) (.f64 (*.f64 x x) #s(literal 1/20160 binary64))))) #s(literal 1 binary64))
(.f64 x (.f64 x #s(literal 1/20160 binary64)))
(.f64 (.f64 x x) #s(literal 1/20160 binary64))
(.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) #s(literal 1/20160 binary64)))
(.f64 #s(literal 1/20160 binary64) (.f64 x x))
(.f64 (.f64 (*.f64 x x) #s(literal 1/20160 binary64)) #s(literal 1 binary64))
(.f64 (.f64 x #s(literal 1/20160 binary64)) x)
(.f64 x (.f64 x #s(literal 1/360 binary64)))
(.f64 (.f64 x x) #s(literal 1/360 binary64))
(.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) #s(literal 1/360 binary64)))
(.f64 #s(literal 1/360 binary64) (.f64 x x))
(.f64 (.f64 (*.f64 x x) #s(literal 1/360 binary64)) #s(literal 1 binary64))
(.f64 (.f64 x #s(literal 1/360 binary64)) x)

simplify209.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

2812×	`-lowering-.f32`
2812×	`-lowering-.f64`
2450×	`+-lowering-+.f64`
2450×	`+-lowering-+.f32`
1840×	`sum3-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	92	1542
1	316	1229
2	933	1207
3	2733	1207
4	5962	1207
5	7926	1207
0	8136	1207

Stop Event

1×	iter limit
1×	node limit

Counts

192 → 192

Calls

Call 1

Inputs
(pow x 2)
(* (pow x 2) (+ 1 (* 1/12 (pow x 2))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 1/12 (* 1/360 (pow x 2))))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 1/12 (* (pow x 2) (+ 1/360 (* 1/20160 (pow x 2))))))))
(* 1/20160 (pow x 8))
(* (pow x 8) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))
(* (pow x 8) (+ 1/20160 (+ (/ 1/12 (pow x 4)) (* 1/360 (/ 1 (pow x 2))))))
(* (pow x 8) (+ 1/20160 (+ (/ 1/12 (pow x 4)) (+ (* 1/360 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))
(* 1/20160 (pow x 8))
(* (pow x 8) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))
(* (pow x 8) (+ 1/20160 (+ (/ 1/12 (pow x 4)) (* 1/360 (/ 1 (pow x 2))))))
(* (pow x 8) (+ 1/20160 (+ (/ 1/12 (pow x 4)) (+ (* 1/360 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
1
(+ 1 (* 1/12 (pow x 2)))
(+ 1 (* (pow x 2) (+ 1/12 (* 1/360 (pow x 2)))))
(+ 1 (* (pow x 2) (+ 1/12 (* (pow x 2) (+ 1/360 (* 1/20160 (pow x 2)))))))
(* 1/20160 (pow x 6))
(* (pow x 6) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 1/20160 (+ (/ 1/12 (pow x 4)) (* 1/360 (/ 1 (pow x 2))))))
(* (pow x 6) (+ 1/20160 (+ (/ 1/12 (pow x 4)) (+ (* 1/360 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))
(* 1/20160 (pow x 6))
(* (pow x 6) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 1/20160 (+ (/ 1/12 (pow x 4)) (* 1/360 (/ 1 (pow x 2))))))
(* (pow x 6) (+ 1/20160 (+ (/ 1/12 (pow x 4)) (+ (* 1/360 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))
(* 1/12 (pow x 2))
(* (pow x 2) (+ 1/12 (* 1/360 (pow x 2))))
(* (pow x 2) (+ 1/12 (* (pow x 2) (+ 1/360 (* 1/20160 (pow x 2))))))
(* (pow x 2) (+ 1/12 (* (pow x 2) (+ 1/360 (* 1/20160 (pow x 2))))))
(* 1/20160 (pow x 6))
(* (pow x 6) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 1/20160 (+ (/ 1/12 (pow x 4)) (* 1/360 (/ 1 (pow x 2))))))
(* (pow x 6) (+ 1/20160 (+ (/ 1/12 (pow x 4)) (* 1/360 (/ 1 (pow x 2))))))
(* 1/20160 (pow x 6))
(* (pow x 6) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 1/20160 (+ (/ 1/12 (pow x 4)) (* 1/360 (/ 1 (pow x 2))))))
(* (pow x 6) (+ 1/20160 (+ (/ 1/12 (pow x 4)) (* 1/360 (/ 1 (pow x 2))))))
(pow x 2)
(* (pow x 2) (+ 1 (* 1/12 (pow x 2))))
(* (pow x 2) (+ 1 (* 1/12 (pow x 2))))
(* (pow x 2) (+ 1 (* 1/12 (pow x 2))))
(* 1/12 (pow x 4))
(* (pow x 4) (+ 1/12 (/ 1 (pow x 2))))
(* (pow x 4) (+ 1/12 (/ 1 (pow x 2))))
(* (pow x 4) (+ 1/12 (/ 1 (pow x 2))))
(* 1/12 (pow x 4))
(* (pow x 4) (+ 1/12 (/ 1 (pow x 2))))
(* (pow x 4) (+ 1/12 (/ 1 (pow x 2))))
(* (pow x 4) (+ 1/12 (/ 1 (pow x 2))))
1
(+ 1 (* 1/12 (pow x 2)))
(+ 1 (* 1/12 (pow x 2)))
(+ 1 (* 1/12 (pow x 2)))
(* 1/12 (pow x 2))
(* (pow x 2) (+ 1/12 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1/12 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1/12 (/ 1 (pow x 2))))
(* 1/12 (pow x 2))
(* (pow x 2) (+ 1/12 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1/12 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1/12 (/ 1 (pow x 2))))
(* 1/12 (pow x 2))
(* 1/12 (pow x 2))
(* 1/12 (pow x 2))
(* 1/12 (pow x 2))
(* 1/12 (pow x 2))
(* 1/12 (pow x 2))
(* 1/12 (pow x 2))
(* 1/12 (pow x 2))
(* 1/12 (pow x 2))
(* 1/12 (pow x 2))
(* 1/12 (pow x 2))
(* 1/12 (pow x 2))
(pow x 2)
(* (pow x 2) (+ 1 (* 1/12 (pow x 2))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 1/12 (* 1/360 (pow x 2))))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 1/12 (* 1/360 (pow x 2))))))
(* 1/360 (pow x 6))
(* (pow x 6) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 1/360 (+ (* 1/12 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))
(* (pow x 6) (+ 1/360 (+ (* 1/12 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))
(* 1/360 (pow x 6))
(* (pow x 6) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 1/360 (+ (* 1/12 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))
(* (pow x 6) (+ 1/360 (+ (* 1/12 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))
1
(+ 1 (* 1/12 (pow x 2)))
(+ 1 (* (pow x 2) (+ 1/12 (* 1/360 (pow x 2)))))
(+ 1 (* (pow x 2) (+ 1/12 (* 1/360 (pow x 2)))))
(* 1/360 (pow x 4))
(* (pow x 4) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 1/360 (+ (* 1/12 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))
(* (pow x 4) (+ 1/360 (+ (* 1/12 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))
(* 1/360 (pow x 4))
(* (pow x 4) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 1/360 (+ (* 1/12 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))
(* (pow x 4) (+ 1/360 (+ (* 1/12 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))
(* 1/12 (pow x 2))
(* (pow x 2) (+ 1/12 (* 1/360 (pow x 2))))
(* (pow x 2) (+ 1/12 (* 1/360 (pow x 2))))
(* (pow x 2) (+ 1/12 (* 1/360 (pow x 2))))
(* 1/360 (pow x 4))
(* (pow x 4) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))
(* 1/360 (pow x 4))
(* (pow x 4) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 1/360 (* 1/12 (/ 1 (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)))))))
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
(* 1/360 x)
(* x (+ 1/360 (* 1/20160 (pow x 2))))
(* x (+ 1/360 (* 1/20160 (pow x 2))))
(* x (+ 1/360 (* 1/20160 (pow x 2))))
(* 1/20160 (pow x 3))
(* (pow x 3) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))
(* 1/20160 (pow x 3))
(* (pow x 3) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))
(* 1/360 (pow x 2))
(* (pow x 2) (+ 1/360 (* 1/20160 (pow x 2))))
(* (pow x 2) (+ 1/360 (* 1/20160 (pow x 2))))
(* (pow x 2) (+ 1/360 (* 1/20160 (pow x 2))))
(* 1/20160 (pow x 4))
(* (pow x 4) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))
(* 1/20160 (pow x 4))
(* (pow x 4) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))
(* 1/20160 (pow x 2))
(* 1/20160 (pow x 2))
(* 1/20160 (pow x 2))
(* 1/20160 (pow x 2))
(* 1/20160 (pow x 2))
(* 1/20160 (pow x 2))
(* 1/20160 (pow x 2))
(* 1/20160 (pow x 2))
(* 1/20160 (pow x 2))
(* 1/20160 (pow x 2))
(* 1/20160 (pow x 2))
(* 1/20160 (pow x 2))
(* 1/360 (pow x 2))
(* 1/360 (pow x 2))
(* 1/360 (pow x 2))
(* 1/360 (pow x 2))
(* 1/360 (pow x 2))
(* 1/360 (pow x 2))
(* 1/360 (pow x 2))
(* 1/360 (pow x 2))
(* 1/360 (pow x 2))
(* 1/360 (pow x 2))
(* 1/360 (pow x 2))
(* 1/360 (pow x 2))

Outputs
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 1/12 (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/12 binary64)))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 1/12 (* 1/360 (pow x 2))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64))))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 1/12 (* (pow x 2) (+ 1/360 (* 1/20160 (pow x 2))))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64)))))))))
(* 1/20160 (pow x 8))
(*.f64 #s(literal 1/20160 binary64) (pow.f64 x #s(literal 8 binary64)))
(* (pow x 8) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 #s(literal 1/20160 binary64) (/.f64 #s(literal 1/360 binary64) (.f64 x x))))
(* (pow x 8) (+ 1/20160 (+ (/ 1/12 (pow x 4)) (* 1/360 (/ 1 (pow x 2))))))
(.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 (+.f64 #s(literal 1/20160 binary64) (/.f64 #s(literal 1/360 binary64) (.f64 x x))) (/.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (*.f64 x x))))))
(* (pow x 8) (+ 1/20160 (+ (/ 1/12 (pow x 4)) (+ (* 1/360 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))
(.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 (/.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 (/.f64 #s(literal 1/360 binary64) (*.f64 x x)) (+.f64 #s(literal 1/20160 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64)))))))
(* 1/20160 (pow x 8))
(*.f64 #s(literal 1/20160 binary64) (pow.f64 x #s(literal 8 binary64)))
(* (pow x 8) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 #s(literal 1/20160 binary64) (/.f64 #s(literal 1/360 binary64) (.f64 x x))))
(* (pow x 8) (+ 1/20160 (+ (/ 1/12 (pow x 4)) (* 1/360 (/ 1 (pow x 2))))))
(.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 (+.f64 #s(literal 1/20160 binary64) (/.f64 #s(literal 1/360 binary64) (.f64 x x))) (/.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (*.f64 x x))))))
(* (pow x 8) (+ 1/20160 (+ (/ 1/12 (pow x 4)) (+ (* 1/360 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))
(.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 (/.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 (/.f64 #s(literal 1/360 binary64) (*.f64 x x)) (+.f64 #s(literal 1/20160 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64)))))))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
1
#s(literal 1 binary64)
(+ 1 (* 1/12 (pow x 2)))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/12 binary64))))
(+ 1 (* (pow x 2) (+ 1/12 (* 1/360 (pow x 2)))))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64)))))
(+ 1 (* (pow x 2) (+ 1/12 (* (pow x 2) (+ 1/360 (* 1/20160 (pow x 2)))))))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64))))))))
(* 1/20160 (pow x 6))
(*.f64 #s(literal 1/20160 binary64) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))
(.f64 (+.f64 #s(literal 1/20160 binary64) (/.f64 #s(literal 1/360 binary64) (.f64 x x))) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (+ 1/20160 (+ (/ 1/12 (pow x 4)) (* 1/360 (/ 1 (pow x 2))))))
(.f64 (+.f64 (+.f64 #s(literal 1/20160 binary64) (/.f64 #s(literal 1/360 binary64) (.f64 x x))) (/.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (*.f64 x x))))) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (+ 1/20160 (+ (/ 1/12 (pow x 4)) (+ (* 1/360 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))
(+.f64 #s(literal 1 binary64) (.f64 (+.f64 (+.f64 #s(literal 1/20160 binary64) (/.f64 #s(literal 1/360 binary64) (.f64 x x))) (/.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (*.f64 x x))))) (pow.f64 x #s(literal 6 binary64))))
(* 1/20160 (pow x 6))
(*.f64 #s(literal 1/20160 binary64) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))
(.f64 (+.f64 #s(literal 1/20160 binary64) (/.f64 #s(literal 1/360 binary64) (.f64 x x))) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (+ 1/20160 (+ (/ 1/12 (pow x 4)) (* 1/360 (/ 1 (pow x 2))))))
(.f64 (+.f64 (+.f64 #s(literal 1/20160 binary64) (/.f64 #s(literal 1/360 binary64) (.f64 x x))) (/.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (*.f64 x x))))) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (+ 1/20160 (+ (/ 1/12 (pow x 4)) (+ (* 1/360 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))
(+.f64 #s(literal 1 binary64) (.f64 (+.f64 (+.f64 #s(literal 1/20160 binary64) (/.f64 #s(literal 1/360 binary64) (.f64 x x))) (/.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (*.f64 x x))))) (pow.f64 x #s(literal 6 binary64))))
(* 1/12 (pow x 2))
(.f64 x (.f64 x #s(literal 1/12 binary64)))
(* (pow x 2) (+ 1/12 (* 1/360 (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64))))
(* (pow x 2) (+ 1/12 (* (pow x 2) (+ 1/360 (* 1/20160 (pow x 2))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64)))))))
(* (pow x 2) (+ 1/12 (* (pow x 2) (+ 1/360 (* 1/20160 (pow x 2))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64)))))))
(* 1/20160 (pow x 6))
(*.f64 #s(literal 1/20160 binary64) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))
(.f64 (+.f64 #s(literal 1/20160 binary64) (/.f64 #s(literal 1/360 binary64) (.f64 x x))) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (+ 1/20160 (+ (/ 1/12 (pow x 4)) (* 1/360 (/ 1 (pow x 2))))))
(.f64 (+.f64 (+.f64 #s(literal 1/20160 binary64) (/.f64 #s(literal 1/360 binary64) (.f64 x x))) (/.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (*.f64 x x))))) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (+ 1/20160 (+ (/ 1/12 (pow x 4)) (* 1/360 (/ 1 (pow x 2))))))
(.f64 (+.f64 (+.f64 #s(literal 1/20160 binary64) (/.f64 #s(literal 1/360 binary64) (.f64 x x))) (/.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (*.f64 x x))))) (pow.f64 x #s(literal 6 binary64)))
(* 1/20160 (pow x 6))
(*.f64 #s(literal 1/20160 binary64) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))
(.f64 (+.f64 #s(literal 1/20160 binary64) (/.f64 #s(literal 1/360 binary64) (.f64 x x))) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (+ 1/20160 (+ (/ 1/12 (pow x 4)) (* 1/360 (/ 1 (pow x 2))))))
(.f64 (+.f64 (+.f64 #s(literal 1/20160 binary64) (/.f64 #s(literal 1/360 binary64) (.f64 x x))) (/.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (*.f64 x x))))) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (+ 1/20160 (+ (/ 1/12 (pow x 4)) (* 1/360 (/ 1 (pow x 2))))))
(.f64 (+.f64 (+.f64 #s(literal 1/20160 binary64) (/.f64 #s(literal 1/360 binary64) (.f64 x x))) (/.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (*.f64 x x))))) (pow.f64 x #s(literal 6 binary64)))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 1/12 (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/12 binary64)))))
(* (pow x 2) (+ 1 (* 1/12 (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/12 binary64)))))
(* (pow x 2) (+ 1 (* 1/12 (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/12 binary64)))))
(* 1/12 (pow x 4))
(.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (.f64 x x))))
(* (pow x 4) (+ 1/12 (/ 1 (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/12 binary64)))))
(* (pow x 4) (+ 1/12 (/ 1 (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/12 binary64)))))
(* (pow x 4) (+ 1/12 (/ 1 (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/12 binary64)))))
(* 1/12 (pow x 4))
(.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (.f64 x x))))
(* (pow x 4) (+ 1/12 (/ 1 (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/12 binary64)))))
(* (pow x 4) (+ 1/12 (/ 1 (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/12 binary64)))))
(* (pow x 4) (+ 1/12 (/ 1 (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/12 binary64)))))
1
#s(literal 1 binary64)
(+ 1 (* 1/12 (pow x 2)))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/12 binary64))))
(+ 1 (* 1/12 (pow x 2)))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/12 binary64))))
(+ 1 (* 1/12 (pow x 2)))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/12 binary64))))
(* 1/12 (pow x 2))
(.f64 x (.f64 x #s(literal 1/12 binary64)))
(* (pow x 2) (+ 1/12 (/ 1 (pow x 2))))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/12 binary64))))
(* (pow x 2) (+ 1/12 (/ 1 (pow x 2))))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/12 binary64))))
(* (pow x 2) (+ 1/12 (/ 1 (pow x 2))))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/12 binary64))))
(* 1/12 (pow x 2))
(.f64 x (.f64 x #s(literal 1/12 binary64)))
(* (pow x 2) (+ 1/12 (/ 1 (pow x 2))))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/12 binary64))))
(* (pow x 2) (+ 1/12 (/ 1 (pow x 2))))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/12 binary64))))
(* (pow x 2) (+ 1/12 (/ 1 (pow x 2))))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/12 binary64))))
(* 1/12 (pow x 2))
(.f64 x (.f64 x #s(literal 1/12 binary64)))
(* 1/12 (pow x 2))
(.f64 x (.f64 x #s(literal 1/12 binary64)))
(* 1/12 (pow x 2))
(.f64 x (.f64 x #s(literal 1/12 binary64)))
(* 1/12 (pow x 2))
(.f64 x (.f64 x #s(literal 1/12 binary64)))
(* 1/12 (pow x 2))
(.f64 x (.f64 x #s(literal 1/12 binary64)))
(* 1/12 (pow x 2))
(.f64 x (.f64 x #s(literal 1/12 binary64)))
(* 1/12 (pow x 2))
(.f64 x (.f64 x #s(literal 1/12 binary64)))
(* 1/12 (pow x 2))
(.f64 x (.f64 x #s(literal 1/12 binary64)))
(* 1/12 (pow x 2))
(.f64 x (.f64 x #s(literal 1/12 binary64)))
(* 1/12 (pow x 2))
(.f64 x (.f64 x #s(literal 1/12 binary64)))
(* 1/12 (pow x 2))
(.f64 x (.f64 x #s(literal 1/12 binary64)))
(* 1/12 (pow x 2))
(.f64 x (.f64 x #s(literal 1/12 binary64)))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 1/12 (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/12 binary64)))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 1/12 (* 1/360 (pow x 2))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64))))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 1/12 (* 1/360 (pow x 2))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64))))))
(* 1/360 (pow x 6))
(*.f64 #s(literal 1/360 binary64) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal 1/360 binary64) (/.f64 #s(literal 1/12 binary64) (.f64 x x))))
(* (pow x 6) (+ 1/360 (+ (* 1/12 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))
(.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (/.f64 #s(literal 1/12 binary64) (.f64 x x)) (+.f64 #s(literal 1/360 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x)))))))
(* (pow x 6) (+ 1/360 (+ (* 1/12 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))
(.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (/.f64 #s(literal 1/12 binary64) (.f64 x x)) (+.f64 #s(literal 1/360 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x)))))))
(* 1/360 (pow x 6))
(*.f64 #s(literal 1/360 binary64) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal 1/360 binary64) (/.f64 #s(literal 1/12 binary64) (.f64 x x))))
(* (pow x 6) (+ 1/360 (+ (* 1/12 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))
(.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (/.f64 #s(literal 1/12 binary64) (.f64 x x)) (+.f64 #s(literal 1/360 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x)))))))
(* (pow x 6) (+ 1/360 (+ (* 1/12 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))
(.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (/.f64 #s(literal 1/12 binary64) (.f64 x x)) (+.f64 #s(literal 1/360 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x)))))))
1
#s(literal 1 binary64)
(+ 1 (* 1/12 (pow x 2)))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/12 binary64))))
(+ 1 (* (pow x 2) (+ 1/12 (* 1/360 (pow x 2)))))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64)))))
(+ 1 (* (pow x 2) (+ 1/12 (* 1/360 (pow x 2)))))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64)))))
(* 1/360 (pow x 4))
(.f64 x (.f64 #s(literal 1/360 binary64) (.f64 x (.f64 x x))))
(* (pow x 4) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64))))
(* (pow x 4) (+ 1/360 (+ (* 1/12 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64)))))
(* (pow x 4) (+ 1/360 (+ (* 1/12 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64)))))
(* 1/360 (pow x 4))
(.f64 x (.f64 #s(literal 1/360 binary64) (.f64 x (.f64 x x))))
(* (pow x 4) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64))))
(* (pow x 4) (+ 1/360 (+ (* 1/12 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64)))))
(* (pow x 4) (+ 1/360 (+ (* 1/12 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64)))))
(* 1/12 (pow x 2))
(.f64 x (.f64 x #s(literal 1/12 binary64)))
(* (pow x 2) (+ 1/12 (* 1/360 (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64))))
(* (pow x 2) (+ 1/12 (* 1/360 (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64))))
(* (pow x 2) (+ 1/12 (* 1/360 (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64))))
(* 1/360 (pow x 4))
(.f64 x (.f64 #s(literal 1/360 binary64) (.f64 x (.f64 x x))))
(* (pow x 4) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64))))
(* (pow x 4) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64))))
(* (pow x 4) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64))))
(* 1/360 (pow x 4))
(.f64 x (.f64 #s(literal 1/360 binary64) (.f64 x (.f64 x x))))
(* (pow x 4) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64))))
(* (pow x 4) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64))))
(* (pow x 4) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 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))))))))
(- (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)
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
(+ 1 (* x (+ 1 (* 1/2 x))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(+.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)))))))
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(* 1/360 x)
(*.f64 x #s(literal 1/360 binary64))
(* x (+ 1/360 (* 1/20160 (pow x 2))))
(.f64 x (+.f64 #s(literal 1/360 binary64) (.f64 (*.f64 x x) #s(literal 1/20160 binary64))))
(* x (+ 1/360 (* 1/20160 (pow x 2))))
(.f64 x (+.f64 #s(literal 1/360 binary64) (.f64 (*.f64 x x) #s(literal 1/20160 binary64))))
(* x (+ 1/360 (* 1/20160 (pow x 2))))
(.f64 x (+.f64 #s(literal 1/360 binary64) (.f64 (*.f64 x x) #s(literal 1/20160 binary64))))
(* 1/20160 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal 1/20160 binary64)))
(* (pow x 3) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/360 binary64) (.f64 (*.f64 x x) #s(literal 1/20160 binary64))))
(* (pow x 3) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/360 binary64) (.f64 (*.f64 x x) #s(literal 1/20160 binary64))))
(* (pow x 3) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/360 binary64) (.f64 (*.f64 x x) #s(literal 1/20160 binary64))))
(* 1/20160 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal 1/20160 binary64)))
(* (pow x 3) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/360 binary64) (.f64 (*.f64 x x) #s(literal 1/20160 binary64))))
(* (pow x 3) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/360 binary64) (.f64 (*.f64 x x) #s(literal 1/20160 binary64))))
(* (pow x 3) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/360 binary64) (.f64 (*.f64 x x) #s(literal 1/20160 binary64))))
(* 1/360 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/360 binary64))
(* (pow x 2) (+ 1/360 (* 1/20160 (pow x 2))))
(.f64 x (.f64 x (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64)))))
(* (pow x 2) (+ 1/360 (* 1/20160 (pow x 2))))
(.f64 x (.f64 x (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64)))))
(* (pow x 2) (+ 1/360 (* 1/20160 (pow x 2))))
(.f64 x (.f64 x (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64)))))
(* 1/20160 (pow x 4))
(.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x x))))
(* (pow x 4) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64)))))
(* (pow x 4) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64)))))
(* (pow x 4) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64)))))
(* 1/20160 (pow x 4))
(.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x x))))
(* (pow x 4) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64)))))
(* (pow x 4) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64)))))
(* (pow x 4) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64)))))
(* 1/20160 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/20160 binary64))
(* 1/20160 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/20160 binary64))
(* 1/20160 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/20160 binary64))
(* 1/20160 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/20160 binary64))
(* 1/20160 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/20160 binary64))
(* 1/20160 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/20160 binary64))
(* 1/20160 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/20160 binary64))
(* 1/20160 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/20160 binary64))
(* 1/20160 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/20160 binary64))
(* 1/20160 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/20160 binary64))
(* 1/20160 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/20160 binary64))
(* 1/20160 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/20160 binary64))
(* 1/360 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/360 binary64))
(* 1/360 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/360 binary64))
(* 1/360 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/360 binary64))
(* 1/360 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/360 binary64))
(* 1/360 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/360 binary64))
(* 1/360 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/360 binary64))
(* 1/360 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/360 binary64))
(* 1/360 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/360 binary64))
(* 1/360 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/360 binary64))
(* 1/360 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/360 binary64))
(* 1/360 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/360 binary64))
(* 1/360 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/360 binary64))

eval102.0ms (0.9%)

Compiler: Compiled 15496 to 1222 computations (92.1% saved)

prune64.0ms (0.6%)

Pruning

17 alts after pruning (14 fresh and 3 done)

	Pruned	Kept	Total
New	744	12	756
Fresh	0	2	2
Picked	2	3	5
Done	0	0	0
Total	746	17	763

Accuracy

100.0%

Counts

763 → 17

Alt Table

Click to see full alt table

Status	Accuracy	Program
	50.9%	(-.f64 (*.f64 #s(literal 2 binary64) (cosh.f64 x)) #s(literal 2 binary64))
	49.8%	(+.f64 (pow.f64 (E.f64) x) #s(literal -1 binary64))
	50.8%	(+.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (E.f64)) (-.f64 #s(literal 0 binary64) x)) #s(literal 2 binary64)) (exp.f64 (neg.f64 x)))
▶	99.4%	(+.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x x)))))))) (.f64 x (.f64 (.f64 x x) (.f64 #s(literal 1/360 binary64) (.f64 x (.f64 x x))))))
▶	99.3%	(+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/12 binary64))) (*.f64 x x))
▶	99.4%	(+.f64 (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64)))))) (*.f64 x x))
	99.4%	(.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64)))))) x)
	99.4%	(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64))) (.f64 x x))))))
✓	99.4%	(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64))))))
	99.3%	(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64))))))))
✓	99.3%	(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal 1/12 binary64))))
	50.0%	(.f64 (.f64 x x) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64)))))
	50.0%	(.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 1/12 binary64))))
	49.6%	(.f64 (.f64 x x) (.f64 x (.f64 #s(literal 1/360 binary64) (.f64 x (.f64 x x)))))
✓	98.8%	(*.f64 x x)
▶	7.2%	(expm1.f64 x)
▶	7.0%	x

Compiler

Compiled 446 to 249 computations (44.2% saved)

simplify134.0ms (1.2%)

Algorithm

1×	egg-herbie

Localize:

Found 13 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(expm1.f64 x)
✓	cost-diff	0	(.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64))))
✓	cost-diff	0	(.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (*.f64 x x) #s(literal 1/360 binary64)))))
✓	cost-diff	0	(.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64))))))
✓	cost-diff	128	(+.f64 (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64)))))) (*.f64 x x))
✓	cost-diff	0	(.f64 (.f64 x x) #s(literal 1/12 binary64))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/12 binary64)))
✓	cost-diff	128	(+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/12 binary64))) (*.f64 x x))
✓	cost-diff	0	(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x x)))))))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x x))))))))
✓	cost-diff	768	(+.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x x)))))))) (.f64 x (.f64 (.f64 x x) (.f64 #s(literal 1/360 binary64) (.f64 x (.f64 x x))))))

Rules

3158×	`fma-define`
2750×	`fma-lowering-fma.f32`
2750×	`fma-lowering-fma.f64`
888×	`-lowering-.f32`
888×	`-lowering-.f64`

Iterations

Useful iterations: 7 (0.0ms)

Iter	Nodes	Cost
0	28	210
1	104	180
2	354	168
3	938	165
4	1757	164
5	2131	164
6	2357	164
7	2357	162
8	3254	162
9	3301	162
10	3301	162
0	3301	162

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(+ (* (* x x) (+ 1 (* (* x x) (+ 1/12 (* x (* 1/20160 (* x (* x x)))))))) (* x (* (* x x) (* 1/360 (* x (* x x))))))
(* (* x x) (+ 1 (* (* x x) (+ 1/12 (* x (* 1/20160 (* x (* x x))))))))
(* x x)
x
(+ 1 (* (* x x) (+ 1/12 (* x (* 1/20160 (* x (* x x)))))))
1
(* (* x x) (+ 1/12 (* x (* 1/20160 (* x (* x x))))))
(+ 1/12 (* x (* 1/20160 (* x (* x x)))))
1/12
(* x (* 1/20160 (* x (* x x))))
(* 1/20160 (* x (* x x)))
1/20160
(* x (* x x))
(* x (* (* x x) (* 1/360 (* x (* x x)))))
(* (* x x) (* 1/360 (* x (* x x))))
(* 1/360 (* x (* x x)))
1/360
x
(+ (* (* x x) (* (* x x) 1/12)) (* x x))
(* (* x x) (* (* x x) 1/12))
(* x x)
x
(* (* x x) 1/12)
1/12
(+ (* x (* x (* (* x x) (+ 1/12 (* (* x x) 1/360))))) (* x x))
(* x (* x (* (* x x) (+ 1/12 (* (* x x) 1/360)))))
x
(* x (* (* x x) (+ 1/12 (* (* x x) 1/360))))
(* (* x x) (+ 1/12 (* (* x x) 1/360)))
(* x x)
(+ 1/12 (* (* x x) 1/360))
1/12
(* (* x x) 1/360)
1/360
(- (exp x) 1)
x

Outputs
(+ (* (* x x) (+ 1 (* (* x x) (+ 1/12 (* x (* 1/20160 (* x (* x x)))))))) (* x (* (* x x) (* 1/360 (* x (* x x))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/360 binary64) (.f64 x (.f64 x #s(literal 1/20160 binary64))))))))))
(* (* x x) (+ 1 (* (* x x) (+ 1/12 (* x (* 1/20160 (* x (* x x))))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x x))))))))
(* x x)
(*.f64 x x)
x
(+ 1 (* (* x x) (+ 1/12 (* x (* 1/20160 (* x (* x x)))))))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x x)))))))
1
#s(literal 1 binary64)
(* (* x x) (+ 1/12 (* x (* 1/20160 (* x (* x x))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x x))))))
(+ 1/12 (* x (* 1/20160 (* x (* x x)))))
(+.f64 #s(literal 1/12 binary64) (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x x)))))
1/12
#s(literal 1/12 binary64)
(* x (* 1/20160 (* x (* x x))))
(.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x x))))
(* 1/20160 (* x (* x x)))
(.f64 #s(literal 1/20160 binary64) (.f64 x (*.f64 x x)))
1/20160
#s(literal 1/20160 binary64)
(* x (* x x))
(.f64 x (.f64 x x))
(* x (* (* x x) (* 1/360 (* x (* x x)))))
(.f64 (.f64 x x) (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/360 binary64))))
(* (* x x) (* 1/360 (* x (* x x))))
(.f64 (.f64 x x) (.f64 (.f64 x (*.f64 x x)) #s(literal 1/360 binary64)))
(* 1/360 (* x (* x x)))
(.f64 (.f64 x (*.f64 x x)) #s(literal 1/360 binary64))
1/360
#s(literal 1/360 binary64)
x
(+ (* (* x x) (* (* x x) 1/12)) (* x x))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/12 binary64)))))
(* (* x x) (* (* x x) 1/12))
(.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (.f64 x x))))
(* x x)
(*.f64 x x)
x
(* (* x x) 1/12)
(.f64 x (.f64 x #s(literal 1/12 binary64)))
1/12
#s(literal 1/12 binary64)
(+ (* x (* x (* (* x x) (+ 1/12 (* (* x x) 1/360))))) (* x x))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64))))))
(* x (* x (* (* x x) (+ 1/12 (* (* x x) 1/360)))))
(.f64 (.f64 x x) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64)))))
x
(* x (* (* x x) (+ 1/12 (* (* x x) 1/360))))
(.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/12 binary64) (.f64 (*.f64 x x) #s(literal 1/360 binary64))))
(* (* x x) (+ 1/12 (* (* x x) 1/360)))
(.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64))))
(* x x)
(*.f64 x x)
(+ 1/12 (* (* x x) 1/360))
(+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64)))
1/12
#s(literal 1/12 binary64)
(* (* x x) 1/360)
(.f64 (.f64 x x) #s(literal 1/360 binary64))
1/360
#s(literal 1/360 binary64)
(- (exp x) 1)
(expm1.f64 x)
x

localize563.0ms (5.2%)

Localize:

Found 13 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(expm1.f64 x)
✓	accuracy	100.0%	(+.f64 (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64)))))) (*.f64 x x))
✓	accuracy	100.0%	(.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64))))
✓	accuracy	100.0%	(.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (*.f64 x x) #s(literal 1/360 binary64)))))
✓	accuracy	100.0%	(.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64))))))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(.f64 (.f64 x x) #s(literal 1/12 binary64))
✓	accuracy	100.0%	(+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/12 binary64))) (*.f64 x x))
✓	accuracy	100.0%	(.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/12 binary64)))
✓	accuracy	100.0%	(.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x x))))))
✓	accuracy	100.0%	(.f64 x (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x x))))
✓	accuracy	100.0%	(.f64 #s(literal 1/20160 binary64) (.f64 x (*.f64 x x)))
✓	accuracy	100.0%	(.f64 #s(literal 1/360 binary64) (.f64 x (*.f64 x x)))

Results

505.0ms	250×	5	exit
2.0ms	6×	0	valid

Compiler

Compiled 273 to 28 computations (89.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 196.0ms

backward-pass: 88.0ms (45% of total)

ival-mult: 50.0ms (25.6% of total)

...c/correct-round.rkt:119:19: 33.0ms (16.9% of total)

ival-add: 15.0ms (7.7% of total)

compiled-spec: 5.0ms (2.6% of total)

ival-exp: 2.0ms (1% of total)

ival-sub: 1.0ms (0.5% of total)

const: 1.0ms (0.5% of total)

series8.0ms (0.1%)

Counts

16 → 192

Calls

Call 1

Inputs
#<alt (+ (* (* x x) (+ 1 (* (* x x) (+ 1/12 (* x (* 1/20160 (* x (* x x)))))))) (* x (* (* x x) (* 1/360 (* x (* x x))))))>
#<alt (* (* x x) (+ 1 (* (* x x) (+ 1/12 (* x (* 1/20160 (* x (* x x))))))))>
#<alt (* x x)>
#<alt (+ 1 (* (* x x) (+ 1/12 (* x (* 1/20160 (* x (* x x)))))))>
#<alt (+ (* (* x x) (* (* x x) 1/12)) (* x x))>
#<alt (* (* x x) (* (* x x) 1/12))>
#<alt (* (* x x) 1/12)>
#<alt (+ (* x (* x (* (* x x) (+ 1/12 (* (* x x) 1/360))))) (* x x))>
#<alt (* x (* x (* (* x x) (+ 1/12 (* (* x x) 1/360)))))>
#<alt (* x (* (* x x) (+ 1/12 (* (* x x) 1/360))))>
#<alt (* (* x x) (+ 1/12 (* (* x x) 1/360)))>
#<alt (- (exp x) 1)>
#<alt (* 1/360 (* x (* x x)))>
#<alt (* 1/20160 (* x (* x x)))>
#<alt (* x (* 1/20160 (* x (* x x))))>
#<alt (* (* x x) (+ 1/12 (* x (* 1/20160 (* x (* x x))))))>

Outputs
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* 1/12 (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (* (pow x 2) (+ 1/12 (* 1/360 (pow x 2))))))>
#<alt (* (pow x 2) (+ 1 (* (pow x 2) (+ 1/12 (* (pow x 2) (+ 1/360 (* 1/20160 (pow x 2))))))))>
#<alt (* 1/20160 (pow x 8))>
#<alt (* (pow x 8) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))>
#<alt (* (pow x 8) (+ 1/20160 (+ (/ 1/12 (pow x 4)) (* 1/360 (/ 1 (pow x 2))))))>
#<alt (* (pow x 8) (+ 1/20160 (+ (/ 1/12 (pow x 4)) (+ (* 1/360 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))>
#<alt (* 1/20160 (pow x 8))>
#<alt (* (pow x 8) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))>
#<alt (* (pow x 8) (+ 1/20160 (+ (/ 1/12 (pow x 4)) (* 1/360 (/ 1 (pow x 2))))))>
#<alt (* (pow x 8) (+ 1/20160 (+ (/ 1/12 (pow x 4)) (+ (* 1/360 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* 1/12 (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (* (pow x 2) (+ 1/12 (* 1/20160 (pow x 4))))))>
#<alt (* (pow x 2) (+ 1 (* (pow x 2) (+ 1/12 (* 1/20160 (pow x 4))))))>
#<alt (* 1/20160 (pow x 8))>
#<alt (* (pow x 8) (+ 1/20160 (* 1/12 (/ 1 (pow x 4)))))>
#<alt (* (pow x 8) (+ 1/20160 (+ (* 1/12 (/ 1 (pow x 4))) (/ 1 (pow x 6)))))>
#<alt (* (pow x 8) (+ 1/20160 (+ (* 1/12 (/ 1 (pow x 4))) (/ 1 (pow x 6)))))>
#<alt (* 1/20160 (pow x 8))>
#<alt (* (pow x 8) (+ 1/20160 (* 1/12 (/ 1 (pow x 4)))))>
#<alt (* (pow x 8) (+ 1/20160 (+ (* 1/12 (/ 1 (pow x 4))) (/ 1 (pow x 6)))))>
#<alt (* (pow x 8) (+ 1/20160 (+ (* 1/12 (/ 1 (pow x 4))) (/ 1 (pow x 6)))))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt 1>
#<alt (+ 1 (* 1/12 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (+ 1/12 (* 1/20160 (pow x 4)))))>
#<alt (+ 1 (* (pow x 2) (+ 1/12 (* 1/20160 (pow x 4)))))>
#<alt (* 1/20160 (pow x 6))>
#<alt (* (pow x 6) (+ 1/20160 (* 1/12 (/ 1 (pow x 4)))))>
#<alt (* (pow x 6) (+ 1/20160 (+ (* 1/12 (/ 1 (pow x 4))) (/ 1 (pow x 6)))))>
#<alt (* (pow x 6) (+ 1/20160 (+ (* 1/12 (/ 1 (pow x 4))) (/ 1 (pow x 6)))))>
#<alt (* 1/20160 (pow x 6))>
#<alt (* (pow x 6) (+ 1/20160 (* 1/12 (/ 1 (pow x 4)))))>
#<alt (* (pow x 6) (+ 1/20160 (+ (* 1/12 (/ 1 (pow x 4))) (/ 1 (pow x 6)))))>
#<alt (* (pow x 6) (+ 1/20160 (+ (* 1/12 (/ 1 (pow x 4))) (/ 1 (pow x 6)))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* 1/12 (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (* 1/12 (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (* 1/12 (pow x 2))))>
#<alt (* 1/12 (pow x 4))>
#<alt (* (pow x 4) (+ 1/12 (/ 1 (pow x 2))))>
#<alt (* (pow x 4) (+ 1/12 (/ 1 (pow x 2))))>
#<alt (* (pow x 4) (+ 1/12 (/ 1 (pow x 2))))>
#<alt (* 1/12 (pow x 4))>
#<alt (* (pow x 4) (+ 1/12 (/ 1 (pow x 2))))>
#<alt (* (pow x 4) (+ 1/12 (/ 1 (pow x 2))))>
#<alt (* (pow x 4) (+ 1/12 (/ 1 (pow x 2))))>
#<alt (* 1/12 (pow x 4))>
#<alt (* 1/12 (pow x 4))>
#<alt (* 1/12 (pow x 4))>
#<alt (* 1/12 (pow x 4))>
#<alt (* 1/12 (pow x 4))>
#<alt (* 1/12 (pow x 4))>
#<alt (* 1/12 (pow x 4))>
#<alt (* 1/12 (pow x 4))>
#<alt (* 1/12 (pow x 4))>
#<alt (* 1/12 (pow x 4))>
#<alt (* 1/12 (pow x 4))>
#<alt (* 1/12 (pow x 4))>
#<alt (* 1/12 (pow x 2))>
#<alt (* 1/12 (pow x 2))>
#<alt (* 1/12 (pow x 2))>
#<alt (* 1/12 (pow x 2))>
#<alt (* 1/12 (pow x 2))>
#<alt (* 1/12 (pow x 2))>
#<alt (* 1/12 (pow x 2))>
#<alt (* 1/12 (pow x 2))>
#<alt (* 1/12 (pow x 2))>
#<alt (* 1/12 (pow x 2))>
#<alt (* 1/12 (pow x 2))>
#<alt (* 1/12 (pow x 2))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* 1/12 (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (* (pow x 2) (+ 1/12 (* 1/360 (pow x 2))))))>
#<alt (* (pow x 2) (+ 1 (* (pow x 2) (+ 1/12 (* 1/360 (pow x 2))))))>
#<alt (* 1/360 (pow x 6))>
#<alt (* (pow x 6) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (+ 1/360 (+ (* 1/12 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))>
#<alt (* (pow x 6) (+ 1/360 (+ (* 1/12 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))>
#<alt (* 1/360 (pow x 6))>
#<alt (* (pow x 6) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (+ 1/360 (+ (* 1/12 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))>
#<alt (* (pow x 6) (+ 1/360 (+ (* 1/12 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))>
#<alt (* 1/12 (pow x 4))>
#<alt (* (pow x 4) (+ 1/12 (* 1/360 (pow x 2))))>
#<alt (* (pow x 4) (+ 1/12 (* 1/360 (pow x 2))))>
#<alt (* (pow x 4) (+ 1/12 (* 1/360 (pow x 2))))>
#<alt (* 1/360 (pow x 6))>
#<alt (* (pow x 6) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))>
#<alt (* 1/360 (pow x 6))>
#<alt (* (pow x 6) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))>
#<alt (* 1/12 (pow x 3))>
#<alt (* (pow x 3) (+ 1/12 (* 1/360 (pow x 2))))>
#<alt (* (pow x 3) (+ 1/12 (* 1/360 (pow x 2))))>
#<alt (* (pow x 3) (+ 1/12 (* 1/360 (pow x 2))))>
#<alt (* 1/360 (pow x 5))>
#<alt (* (pow x 5) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))>
#<alt (* (pow x 5) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))>
#<alt (* (pow x 5) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))>
#<alt (* 1/360 (pow x 5))>
#<alt (* (pow x 5) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))>
#<alt (* (pow x 5) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))>
#<alt (* (pow x 5) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))>
#<alt (* 1/12 (pow x 2))>
#<alt (* (pow x 2) (+ 1/12 (* 1/360 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/12 (* 1/360 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/12 (* 1/360 (pow x 2))))>
#<alt (* 1/360 (pow x 4))>
#<alt (* (pow x 4) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))>
#<alt (* 1/360 (pow x 4))>
#<alt (* (pow x 4) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 1/360 (* 1/12 (/ 1 (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 (- (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)>
#<alt (* 1/360 (pow x 3))>
#<alt (* 1/360 (pow x 3))>
#<alt (* 1/360 (pow x 3))>
#<alt (* 1/360 (pow x 3))>
#<alt (* 1/360 (pow x 3))>
#<alt (* 1/360 (pow x 3))>
#<alt (* 1/360 (pow x 3))>
#<alt (* 1/360 (pow x 3))>
#<alt (* 1/360 (pow x 3))>
#<alt (* 1/360 (pow x 3))>
#<alt (* 1/360 (pow x 3))>
#<alt (* 1/360 (pow x 3))>
#<alt (* 1/20160 (pow x 3))>
#<alt (* 1/20160 (pow x 3))>
#<alt (* 1/20160 (pow x 3))>
#<alt (* 1/20160 (pow x 3))>
#<alt (* 1/20160 (pow x 3))>
#<alt (* 1/20160 (pow x 3))>
#<alt (* 1/20160 (pow x 3))>
#<alt (* 1/20160 (pow x 3))>
#<alt (* 1/20160 (pow x 3))>
#<alt (* 1/20160 (pow x 3))>
#<alt (* 1/20160 (pow x 3))>
#<alt (* 1/20160 (pow x 3))>
#<alt (* 1/20160 (pow x 4))>
#<alt (* 1/20160 (pow x 4))>
#<alt (* 1/20160 (pow x 4))>
#<alt (* 1/20160 (pow x 4))>
#<alt (* 1/20160 (pow x 4))>
#<alt (* 1/20160 (pow x 4))>
#<alt (* 1/20160 (pow x 4))>
#<alt (* 1/20160 (pow x 4))>
#<alt (* 1/20160 (pow x 4))>
#<alt (* 1/20160 (pow x 4))>
#<alt (* 1/20160 (pow x 4))>
#<alt (* 1/20160 (pow x 4))>
#<alt (* 1/12 (pow x 2))>
#<alt (* (pow x 2) (+ 1/12 (* 1/20160 (pow x 4))))>
#<alt (* (pow x 2) (+ 1/12 (* 1/20160 (pow x 4))))>
#<alt (* (pow x 2) (+ 1/12 (* 1/20160 (pow x 4))))>
#<alt (* 1/20160 (pow x 6))>
#<alt (* (pow x 6) (+ 1/20160 (* 1/12 (/ 1 (pow x 4)))))>
#<alt (* (pow x 6) (+ 1/20160 (* 1/12 (/ 1 (pow x 4)))))>
#<alt (* (pow x 6) (+ 1/20160 (* 1/12 (/ 1 (pow x 4)))))>
#<alt (* 1/20160 (pow x 6))>
#<alt (* (pow x 6) (+ 1/20160 (* 1/12 (/ 1 (pow x 4)))))>
#<alt (* (pow x 6) (+ 1/20160 (* 1/12 (/ 1 (pow x 4)))))>
#<alt (* (pow x 6) (+ 1/20160 (* 1/12 (/ 1 (pow x 4)))))>

Calls

48 calls:

Time	Variable		Point	Expression
0.0ms	x	@	inf	(* (* x x) (+ 1 (* (* x x) (+ 1/12 (* x (* 1/20160 (* x (* x x))))))))
0.0ms	x	@	inf	(* (* x x) (+ 1/12 (* x (* 1/20160 (* x (* x x))))))
0.0ms	x	@	inf	(+ (* (* x x) (* (* x x) 1/12)) (* x x))
0.0ms	x	@	-inf	(* 1/360 (* x (* x x)))
0.0ms	x	@	-inf	(* 1/20160 (* x (* x x)))

rewrite263.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

2604×	`-lowering-.f32`
2604×	`-lowering-.f64`
1368×	`fma-define`
1336×	`sum5-define`
1330×	`sum4-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	28	155
1	106	130
2	363	120
3	969	120
4	1839	120
5	2546	120
6	4052	120
7	4463	120
8	4857	120
0	8129	120

Stop Event

1×	iter limit
1×	node limit

Counts

16 → 445

Calls

Call 1

Inputs
(+ (* (* x x) (+ 1 (* (* x x) (+ 1/12 (* x (* 1/20160 (* x (* x x)))))))) (* x (* (* x x) (* 1/360 (* x (* x x))))))
(* (* x x) (+ 1 (* (* x x) (+ 1/12 (* x (* 1/20160 (* x (* x x))))))))
(* x x)
(+ 1 (* (* x x) (+ 1/12 (* x (* 1/20160 (* x (* x x)))))))
(+ (* (* x x) (* (* x x) 1/12)) (* x x))
(* (* x x) (* (* x x) 1/12))
(* (* x x) 1/12)
(+ (* x (* x (* (* x x) (+ 1/12 (* (* x x) 1/360))))) (* x x))
(* x (* x (* (* x x) (+ 1/12 (* (* x x) 1/360)))))
(* x (* (* x x) (+ 1/12 (* (* x x) 1/360))))
(* (* x x) (+ 1/12 (* (* x x) 1/360)))
(- (exp x) 1)
(* 1/360 (* x (* x x)))
(* 1/20160 (* x (* x x)))
(* x (* 1/20160 (* x (* x x))))
(* (* x x) (+ 1/12 (* x (* 1/20160 (* x (* x x))))))

Outputs
(+.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/360 binary64) (.f64 (*.f64 x x) #s(literal 1/20160 binary64))))))))
(+.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x x)))))))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 1/360 binary64))))))
(+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 1/360 binary64))))) (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x x)))))))))
(+.f64 (.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64)))))))))
(+.f64 (.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (+.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64))))))))
(+.f64 (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x #s(literal 1/360 binary64))))))) (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x x)))))))))
(+.f64 (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x #s(literal 1/360 binary64))))))) (.f64 x (+.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x x))))))))
(+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (+.f64 #s(literal 1/12 binary64) (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x x))))))) (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 1/360 binary64)))))))
(+.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x x))))))) (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x #s(literal 1/360 binary64))))))))
(+.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 1/360 binary64)))))) (.f64 (.f64 x (.f64 x x)) (.f64 x (+.f64 #s(literal 1/12 binary64) (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x x))))))))
(+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64))))))) (*.f64 x x))
(+.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/12 binary64))))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 x x) (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64)))))))
(+.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/12 binary64))))) (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64)))))))
(+.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x #s(literal 1/360 binary64))))))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x x))))))))
(+.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x #s(literal 1/360 binary64))))))) (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x x)))))))
(+.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x x)))))))) (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x #s(literal 1/360 binary64))))))))
(+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 x x) (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64)))))) (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/12 binary64))))))
(+.f64 (.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64)))))))) (.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (.f64 x x)))))
(+.f64 (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x x)))))) (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x #s(literal 1/360 binary64))))))))
(+.f64 (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64)))))) (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/12 binary64))))))
(+.f64 (.f64 x (+.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64))))))) (.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (.f64 x x)))))
(+.f64 (.f64 x (+.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x x))))))) (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x #s(literal 1/360 binary64))))))))
(+.f64 (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64))))))))) #s(literal 0 binary64)) (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64))))))))))
(+.f64 (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64))))))))) (.f64 x #s(literal 2/3 binary64))) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64))))))))) (.f64 x #s(literal 1/3 binary64))))
(+.f64 (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64))))))))) (/.f64 x #s(literal 2 binary64))) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64))))))))) (/.f64 x #s(literal 2 binary64))))
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(+.f64 (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 1/360 binary64)))) (.f64 x (.f64 x #s(literal 1/12 binary64))))
(+.f64 (.f64 (.f64 x (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x #s(literal 1/360 binary64))))) #s(literal 0 binary64)) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x #s(literal 1/360 binary64))))))
(+.f64 (.f64 (.f64 x (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x #s(literal 1/360 binary64))))) (.f64 x #s(literal 2/3 binary64))) (.f64 (.f64 x (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x #s(literal 1/360 binary64))))) (.f64 x #s(literal 1/3 binary64))))
(+.f64 (.f64 (.f64 x (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x #s(literal 1/360 binary64))))) (/.f64 x #s(literal 2 binary64))) (.f64 (.f64 x (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x #s(literal 1/360 binary64))))) (/.f64 x #s(literal 2 binary64))))
(fma.f64 x (.f64 x (.f64 x (.f64 x #s(literal 1/360 binary64)))) (.f64 x (*.f64 x #s(literal 1/12 binary64))))
(fma.f64 x (.f64 x #s(literal 1/12 binary64)) (.f64 (.f64 x x) (.f64 x (*.f64 x #s(literal 1/360 binary64)))))
(fma.f64 (.f64 x x) #s(literal 1/12 binary64) (.f64 (.f64 x x) (.f64 x (*.f64 x #s(literal 1/360 binary64)))))
(fma.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 1/360 binary64))) (.f64 x (*.f64 x #s(literal 1/12 binary64))))
(fma.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/12 binary64))) (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 1/360 binary64)))))
(fma.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 1/360 binary64)))) (.f64 x (.f64 x #s(literal 1/12 binary64))))
(fma.f64 #s(literal 1/12 binary64) (.f64 x x) (.f64 (.f64 x x) (.f64 x (*.f64 x #s(literal 1/360 binary64)))))
(fma.f64 (.f64 x (.f64 x x)) (.f64 x #s(literal 1/360 binary64)) (.f64 x (*.f64 x #s(literal 1/12 binary64))))
(fma.f64 #s(literal 1/360 binary64) (.f64 x (.f64 x (.f64 x x))) (.f64 x (*.f64 x #s(literal 1/12 binary64))))
(fma.f64 (.f64 x (.f64 x (.f64 x #s(literal 1/360 binary64)))) x (.f64 x (*.f64 x #s(literal 1/12 binary64))))
(fma.f64 (.f64 x (.f64 x #s(literal 1/12 binary64))) #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 1/360 binary64)))))
(fma.f64 (.f64 x (.f64 x #s(literal 1/360 binary64))) (.f64 x x) (.f64 x (*.f64 x #s(literal 1/12 binary64))))
(fma.f64 (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 1/360 binary64)))) #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/12 binary64))))
(fma.f64 (.f64 x #s(literal 1/360 binary64)) (.f64 x (.f64 x x)) (.f64 x (*.f64 x #s(literal 1/12 binary64))))
(fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/360 binary64) (.f64 x (*.f64 x #s(literal 1/12 binary64))))
(fma.f64 (.f64 x #s(literal 1/12 binary64)) x (.f64 (.f64 x x) (.f64 x (*.f64 x #s(literal 1/360 binary64)))))
(.f64 x (.f64 x (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x #s(literal 1/360 binary64))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x #s(literal 1/360 binary64)))))
(.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (*.f64 x #s(literal 1/360 binary64))))))
(.f64 (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x #s(literal 1/360 binary64)))) (.f64 x x))
(.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (*.f64 x #s(literal 1/360 binary64))))) #s(literal 1 binary64))
(.f64 (.f64 x (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x #s(literal 1/360 binary64))))) x)
(+.f64 (exp.f64 x) #s(literal -1 binary64))
(+.f64 #s(literal -1 binary64) (exp.f64 x))
(-.f64 (exp.f64 x) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (exp.f64 x) #s(literal -1 binary64))
(fma.f64 (exp.f64 x) #s(literal 1 binary64) #s(literal -1 binary64))
(fma.f64 (exp.f64 (.f64 x #s(literal 2/3 binary64))) (exp.f64 (.f64 x #s(literal 1/3 binary64))) #s(literal -1 binary64))
(fma.f64 (exp.f64 (.f64 x #s(literal 1/3 binary64))) (exp.f64 (.f64 x #s(literal 2/3 binary64))) #s(literal -1 binary64))
(fma.f64 (exp.f64 (/.f64 x #s(literal 2 binary64))) (exp.f64 (/.f64 x #s(literal 2 binary64))) #s(literal -1 binary64))
(expm1.f64 x)
(+.f64 (.f64 (.f64 x (.f64 x #s(literal 1/360 binary64))) #s(literal 0 binary64)) (.f64 x (.f64 x (.f64 x #s(literal 1/360 binary64)))))
(+.f64 (.f64 (.f64 x (.f64 x #s(literal 1/360 binary64))) (.f64 x #s(literal 2/3 binary64))) (.f64 (.f64 x (.f64 x #s(literal 1/360 binary64))) (.f64 x #s(literal 1/3 binary64))))
(+.f64 (.f64 (.f64 x (.f64 x #s(literal 1/360 binary64))) (/.f64 x #s(literal 2 binary64))) (.f64 (.f64 x (.f64 x #s(literal 1/360 binary64))) (/.f64 x #s(literal 2 binary64))))
(.f64 x (.f64 x (*.f64 x #s(literal 1/360 binary64))))
(.f64 (.f64 x x) (*.f64 x #s(literal 1/360 binary64)))
(.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x #s(literal 1/360 binary64)))))
(.f64 (.f64 x (*.f64 x x)) #s(literal 1/360 binary64))
(.f64 #s(literal 1/360 binary64) (.f64 x (*.f64 x x)))
(.f64 (.f64 x (.f64 x (.f64 x #s(literal 1/360 binary64)))) #s(literal 1 binary64))
(.f64 (.f64 x (*.f64 x #s(literal 1/360 binary64))) x)
(.f64 (.f64 x #s(literal 1/360 binary64)) (*.f64 x x))
(+.f64 (.f64 (.f64 (.f64 x x) #s(literal 1/20160 binary64)) #s(literal 0 binary64)) (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64))))
(+.f64 (.f64 (.f64 (.f64 x x) #s(literal 1/20160 binary64)) (.f64 x #s(literal 2/3 binary64))) (.f64 (.f64 (.f64 x x) #s(literal 1/20160 binary64)) (.f64 x #s(literal 1/3 binary64))))
(+.f64 (.f64 (.f64 (.f64 x x) #s(literal 1/20160 binary64)) (/.f64 x #s(literal 2 binary64))) (.f64 (.f64 (.f64 x x) #s(literal 1/20160 binary64)) (/.f64 x #s(literal 2 binary64))))
(.f64 x (.f64 (*.f64 x x) #s(literal 1/20160 binary64)))
(.f64 (.f64 x x) (*.f64 x #s(literal 1/20160 binary64)))
(.f64 #s(literal 1 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64))))
(.f64 #s(literal 1/20160 binary64) (.f64 x (*.f64 x x)))
(.f64 (.f64 x (*.f64 x x)) #s(literal 1/20160 binary64))
(.f64 (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64))) #s(literal 1 binary64))
(.f64 (.f64 x #s(literal 1/20160 binary64)) (*.f64 x x))
(.f64 (.f64 (*.f64 x x) #s(literal 1/20160 binary64)) x)
(+.f64 (.f64 (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64))) #s(literal 0 binary64)) (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x x)))))
(+.f64 (.f64 (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64))) (.f64 x #s(literal 2/3 binary64))) (.f64 (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64))) (.f64 x #s(literal 1/3 binary64))))
(+.f64 (.f64 (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64))) (/.f64 x #s(literal 2 binary64))) (.f64 (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64))) (/.f64 x #s(literal 2 binary64))))
(.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64))))
(.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/20160 binary64)))
(.f64 #s(literal 1 binary64) (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (*.f64 x x)))))
(.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x x))))
(.f64 (.f64 x (.f64 x x)) (.f64 x #s(literal 1/20160 binary64)))
(.f64 (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64))) x)
(.f64 (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (*.f64 x x)))) #s(literal 1 binary64))
(.f64 (.f64 x #s(literal 1/20160 binary64)) (.f64 x (.f64 x x)))
(.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/20160 binary64))
(.f64 (.f64 (.f64 x x) #s(literal 1/20160 binary64)) (.f64 x x))
(+.f64 (.f64 x (.f64 x #s(literal 1/12 binary64))) (.f64 x (.f64 x (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x x)))))))
(+.f64 (.f64 x (.f64 x (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x x)))))) (.f64 x (.f64 x #s(literal 1/12 binary64))))
(+.f64 (.f64 (.f64 x (+.f64 #s(literal 1/12 binary64) (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x x)))))) #s(literal 0 binary64)) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x x)))))))
(+.f64 (.f64 (.f64 x (+.f64 #s(literal 1/12 binary64) (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x x)))))) (.f64 x #s(literal 2/3 binary64))) (.f64 (.f64 x (+.f64 #s(literal 1/12 binary64) (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x x)))))) (.f64 x #s(literal 1/3 binary64))))
(+.f64 (.f64 (.f64 x (+.f64 #s(literal 1/12 binary64) (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x x)))))) (/.f64 x #s(literal 2 binary64))) (.f64 (.f64 x (+.f64 #s(literal 1/12 binary64) (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x x)))))) (/.f64 x #s(literal 2 binary64))))
(fma.f64 x (.f64 x #s(literal 1/12 binary64)) (.f64 x (.f64 x (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (*.f64 x x)))))))
(fma.f64 x (.f64 x (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x x))))) (.f64 x (*.f64 x #s(literal 1/12 binary64))))
(fma.f64 (.f64 x x) #s(literal 1/12 binary64) (.f64 x (.f64 x (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (*.f64 x x)))))))
(fma.f64 (.f64 x x) (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (*.f64 x #s(literal 1/12 binary64))))
(fma.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/12 binary64))) (.f64 x (.f64 x (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x x)))))))
(fma.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x x)))))) (.f64 x (.f64 x #s(literal 1/12 binary64))))
(fma.f64 #s(literal 1/12 binary64) (.f64 x x) (.f64 x (.f64 x (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (*.f64 x x)))))))
(fma.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 x (*.f64 x #s(literal 1/12 binary64))))
(fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64))) (.f64 x (*.f64 x #s(literal 1/12 binary64))))
(fma.f64 (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64))) (.f64 x (.f64 x x)) (.f64 x (*.f64 x #s(literal 1/12 binary64))))
(fma.f64 (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 x x) (.f64 x (*.f64 x #s(literal 1/12 binary64))))
(fma.f64 (.f64 x (.f64 x #s(literal 1/12 binary64))) #s(literal 1 binary64) (.f64 x (.f64 x (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x x)))))))
(fma.f64 (.f64 x (.f64 x (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x x)))))) #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/12 binary64))))
(fma.f64 (.f64 x #s(literal 1/20160 binary64)) (.f64 x (.f64 x (.f64 x (.f64 x x)))) (.f64 x (*.f64 x #s(literal 1/12 binary64))))
(fma.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x x) #s(literal 1/20160 binary64)) (.f64 x (*.f64 x #s(literal 1/12 binary64))))
(fma.f64 (.f64 x #s(literal 1/12 binary64)) x (.f64 x (.f64 x (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (*.f64 x x)))))))
(fma.f64 (.f64 x (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x x))))) x (.f64 x (*.f64 x #s(literal 1/12 binary64))))
(fma.f64 (.f64 (.f64 x x) #s(literal 1/20160 binary64)) (.f64 x (.f64 x (.f64 x x))) (.f64 x (*.f64 x #s(literal 1/12 binary64))))
(fma.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))) (.f64 x #s(literal 1/20160 binary64)) (.f64 x (*.f64 x #s(literal 1/12 binary64))))
(fma.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) #s(literal 1/20160 binary64) (.f64 x (*.f64 x #s(literal 1/12 binary64))))
(.f64 x (.f64 x (+.f64 #s(literal 1/12 binary64) (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x x)))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x x))))))
(.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (*.f64 x x)))))))
(.f64 (+.f64 #s(literal 1/12 binary64) (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x x))))) (.f64 x x))
(.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (*.f64 x x)))))) #s(literal 1 binary64))
(.f64 (.f64 x (+.f64 #s(literal 1/12 binary64) (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x x)))))) x)

simplify198.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

2428×	`sum3-define`
2236×	`-lowering-.f32`
2236×	`-lowering-.f64`
1492×	`times-frac`
1456×	`+-lowering-+.f64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	100	1528
1	340	1314
2	980	1289
3	2717	1289
4	3960	1289
5	5082	1256
6	6978	1256
7	7741	1256
0	8012	1256

Stop Event

1×	iter limit
1×	node limit

Counts

192 → 192

Calls

Call 1

Inputs
(pow x 2)
(* (pow x 2) (+ 1 (* 1/12 (pow x 2))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 1/12 (* 1/360 (pow x 2))))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 1/12 (* (pow x 2) (+ 1/360 (* 1/20160 (pow x 2))))))))
(* 1/20160 (pow x 8))
(* (pow x 8) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))
(* (pow x 8) (+ 1/20160 (+ (/ 1/12 (pow x 4)) (* 1/360 (/ 1 (pow x 2))))))
(* (pow x 8) (+ 1/20160 (+ (/ 1/12 (pow x 4)) (+ (* 1/360 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))
(* 1/20160 (pow x 8))
(* (pow x 8) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))
(* (pow x 8) (+ 1/20160 (+ (/ 1/12 (pow x 4)) (* 1/360 (/ 1 (pow x 2))))))
(* (pow x 8) (+ 1/20160 (+ (/ 1/12 (pow x 4)) (+ (* 1/360 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))
(pow x 2)
(* (pow x 2) (+ 1 (* 1/12 (pow x 2))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 1/12 (* 1/20160 (pow x 4))))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 1/12 (* 1/20160 (pow x 4))))))
(* 1/20160 (pow x 8))
(* (pow x 8) (+ 1/20160 (* 1/12 (/ 1 (pow x 4)))))
(* (pow x 8) (+ 1/20160 (+ (* 1/12 (/ 1 (pow x 4))) (/ 1 (pow x 6)))))
(* (pow x 8) (+ 1/20160 (+ (* 1/12 (/ 1 (pow x 4))) (/ 1 (pow x 6)))))
(* 1/20160 (pow x 8))
(* (pow x 8) (+ 1/20160 (* 1/12 (/ 1 (pow x 4)))))
(* (pow x 8) (+ 1/20160 (+ (* 1/12 (/ 1 (pow x 4))) (/ 1 (pow x 6)))))
(* (pow x 8) (+ 1/20160 (+ (* 1/12 (/ 1 (pow x 4))) (/ 1 (pow x 6)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
1
(+ 1 (* 1/12 (pow x 2)))
(+ 1 (* (pow x 2) (+ 1/12 (* 1/20160 (pow x 4)))))
(+ 1 (* (pow x 2) (+ 1/12 (* 1/20160 (pow x 4)))))
(* 1/20160 (pow x 6))
(* (pow x 6) (+ 1/20160 (* 1/12 (/ 1 (pow x 4)))))
(* (pow x 6) (+ 1/20160 (+ (* 1/12 (/ 1 (pow x 4))) (/ 1 (pow x 6)))))
(* (pow x 6) (+ 1/20160 (+ (* 1/12 (/ 1 (pow x 4))) (/ 1 (pow x 6)))))
(* 1/20160 (pow x 6))
(* (pow x 6) (+ 1/20160 (* 1/12 (/ 1 (pow x 4)))))
(* (pow x 6) (+ 1/20160 (+ (* 1/12 (/ 1 (pow x 4))) (/ 1 (pow x 6)))))
(* (pow x 6) (+ 1/20160 (+ (* 1/12 (/ 1 (pow x 4))) (/ 1 (pow x 6)))))
(pow x 2)
(* (pow x 2) (+ 1 (* 1/12 (pow x 2))))
(* (pow x 2) (+ 1 (* 1/12 (pow x 2))))
(* (pow x 2) (+ 1 (* 1/12 (pow x 2))))
(* 1/12 (pow x 4))
(* (pow x 4) (+ 1/12 (/ 1 (pow x 2))))
(* (pow x 4) (+ 1/12 (/ 1 (pow x 2))))
(* (pow x 4) (+ 1/12 (/ 1 (pow x 2))))
(* 1/12 (pow x 4))
(* (pow x 4) (+ 1/12 (/ 1 (pow x 2))))
(* (pow x 4) (+ 1/12 (/ 1 (pow x 2))))
(* (pow x 4) (+ 1/12 (/ 1 (pow x 2))))
(* 1/12 (pow x 4))
(* 1/12 (pow x 4))
(* 1/12 (pow x 4))
(* 1/12 (pow x 4))
(* 1/12 (pow x 4))
(* 1/12 (pow x 4))
(* 1/12 (pow x 4))
(* 1/12 (pow x 4))
(* 1/12 (pow x 4))
(* 1/12 (pow x 4))
(* 1/12 (pow x 4))
(* 1/12 (pow x 4))
(* 1/12 (pow x 2))
(* 1/12 (pow x 2))
(* 1/12 (pow x 2))
(* 1/12 (pow x 2))
(* 1/12 (pow x 2))
(* 1/12 (pow x 2))
(* 1/12 (pow x 2))
(* 1/12 (pow x 2))
(* 1/12 (pow x 2))
(* 1/12 (pow x 2))
(* 1/12 (pow x 2))
(* 1/12 (pow x 2))
(pow x 2)
(* (pow x 2) (+ 1 (* 1/12 (pow x 2))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 1/12 (* 1/360 (pow x 2))))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 1/12 (* 1/360 (pow x 2))))))
(* 1/360 (pow x 6))
(* (pow x 6) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 1/360 (+ (* 1/12 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))
(* (pow x 6) (+ 1/360 (+ (* 1/12 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))
(* 1/360 (pow x 6))
(* (pow x 6) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 1/360 (+ (* 1/12 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))
(* (pow x 6) (+ 1/360 (+ (* 1/12 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))
(* 1/12 (pow x 4))
(* (pow x 4) (+ 1/12 (* 1/360 (pow x 2))))
(* (pow x 4) (+ 1/12 (* 1/360 (pow x 2))))
(* (pow x 4) (+ 1/12 (* 1/360 (pow x 2))))
(* 1/360 (pow x 6))
(* (pow x 6) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))
(* 1/360 (pow x 6))
(* (pow x 6) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))
(* 1/12 (pow x 3))
(* (pow x 3) (+ 1/12 (* 1/360 (pow x 2))))
(* (pow x 3) (+ 1/12 (* 1/360 (pow x 2))))
(* (pow x 3) (+ 1/12 (* 1/360 (pow x 2))))
(* 1/360 (pow x 5))
(* (pow x 5) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))
(* (pow x 5) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))
(* (pow x 5) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))
(* 1/360 (pow x 5))
(* (pow x 5) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))
(* (pow x 5) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))
(* (pow x 5) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))
(* 1/12 (pow x 2))
(* (pow x 2) (+ 1/12 (* 1/360 (pow x 2))))
(* (pow x 2) (+ 1/12 (* 1/360 (pow x 2))))
(* (pow x 2) (+ 1/12 (* 1/360 (pow x 2))))
(* 1/360 (pow x 4))
(* (pow x 4) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))
(* 1/360 (pow x 4))
(* (pow x 4) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 1/360 (* 1/12 (/ 1 (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)))))))
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(* 1/360 (pow x 3))
(* 1/360 (pow x 3))
(* 1/360 (pow x 3))
(* 1/360 (pow x 3))
(* 1/360 (pow x 3))
(* 1/360 (pow x 3))
(* 1/360 (pow x 3))
(* 1/360 (pow x 3))
(* 1/360 (pow x 3))
(* 1/360 (pow x 3))
(* 1/360 (pow x 3))
(* 1/360 (pow x 3))
(* 1/20160 (pow x 3))
(* 1/20160 (pow x 3))
(* 1/20160 (pow x 3))
(* 1/20160 (pow x 3))
(* 1/20160 (pow x 3))
(* 1/20160 (pow x 3))
(* 1/20160 (pow x 3))
(* 1/20160 (pow x 3))
(* 1/20160 (pow x 3))
(* 1/20160 (pow x 3))
(* 1/20160 (pow x 3))
(* 1/20160 (pow x 3))
(* 1/20160 (pow x 4))
(* 1/20160 (pow x 4))
(* 1/20160 (pow x 4))
(* 1/20160 (pow x 4))
(* 1/20160 (pow x 4))
(* 1/20160 (pow x 4))
(* 1/20160 (pow x 4))
(* 1/20160 (pow x 4))
(* 1/20160 (pow x 4))
(* 1/20160 (pow x 4))
(* 1/20160 (pow x 4))
(* 1/20160 (pow x 4))
(* 1/12 (pow x 2))
(* (pow x 2) (+ 1/12 (* 1/20160 (pow x 4))))
(* (pow x 2) (+ 1/12 (* 1/20160 (pow x 4))))
(* (pow x 2) (+ 1/12 (* 1/20160 (pow x 4))))
(* 1/20160 (pow x 6))
(* (pow x 6) (+ 1/20160 (* 1/12 (/ 1 (pow x 4)))))
(* (pow x 6) (+ 1/20160 (* 1/12 (/ 1 (pow x 4)))))
(* (pow x 6) (+ 1/20160 (* 1/12 (/ 1 (pow x 4)))))
(* 1/20160 (pow x 6))
(* (pow x 6) (+ 1/20160 (* 1/12 (/ 1 (pow x 4)))))
(* (pow x 6) (+ 1/20160 (* 1/12 (/ 1 (pow x 4)))))
(* (pow x 6) (+ 1/20160 (* 1/12 (/ 1 (pow x 4)))))

Outputs
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 1/12 (pow x 2))))
(.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal 1/12 binary64)))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 1/12 (* 1/360 (pow x 2))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64))))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 1/12 (* (pow x 2) (+ 1/360 (* 1/20160 (pow x 2))))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/360 binary64) (.f64 x (.f64 x #s(literal 1/20160 binary64)))))))))))
(* 1/20160 (pow x 8))
(*.f64 #s(literal 1/20160 binary64) (pow.f64 x #s(literal 8 binary64)))
(* (pow x 8) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 #s(literal 1/20160 binary64) (/.f64 #s(literal 1/360 binary64) (.f64 x x))))
(* (pow x 8) (+ 1/20160 (+ (/ 1/12 (pow x 4)) (* 1/360 (/ 1 (pow x 2))))))
(.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 (/.f64 #s(literal 1/360 binary64) (.f64 x x)) (+.f64 #s(literal 1/20160 binary64) (/.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (*.f64 x x)))))))
(* (pow x 8) (+ 1/20160 (+ (/ 1/12 (pow x 4)) (+ (* 1/360 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))
(.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 (+.f64 (/.f64 #s(literal 1/360 binary64) (.f64 x x)) (+.f64 #s(literal 1/20160 binary64) (/.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (.f64 x x)))))) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))))))
(* 1/20160 (pow x 8))
(*.f64 #s(literal 1/20160 binary64) (pow.f64 x #s(literal 8 binary64)))
(* (pow x 8) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 #s(literal 1/20160 binary64) (/.f64 #s(literal 1/360 binary64) (.f64 x x))))
(* (pow x 8) (+ 1/20160 (+ (/ 1/12 (pow x 4)) (* 1/360 (/ 1 (pow x 2))))))
(.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 (/.f64 #s(literal 1/360 binary64) (.f64 x x)) (+.f64 #s(literal 1/20160 binary64) (/.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (*.f64 x x)))))))
(* (pow x 8) (+ 1/20160 (+ (/ 1/12 (pow x 4)) (+ (* 1/360 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))
(.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 (+.f64 (/.f64 #s(literal 1/360 binary64) (.f64 x x)) (+.f64 #s(literal 1/20160 binary64) (/.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (.f64 x x)))))) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))))))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 1/12 (pow x 2))))
(.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal 1/12 binary64)))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 1/12 (* 1/20160 (pow x 4))))))
(.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x x)))))))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 1/12 (* 1/20160 (pow x 4))))))
(.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x x)))))))))
(* 1/20160 (pow x 8))
(*.f64 #s(literal 1/20160 binary64) (pow.f64 x #s(literal 8 binary64)))
(* (pow x 8) (+ 1/20160 (* 1/12 (/ 1 (pow x 4)))))
(.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 #s(literal 1/20160 binary64) (/.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (.f64 x x))))))
(* (pow x 8) (+ 1/20160 (+ (* 1/12 (/ 1 (pow x 4))) (/ 1 (pow x 6)))))
(.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))) (+.f64 #s(literal 1/20160 binary64) (/.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (*.f64 x x)))))))
(* (pow x 8) (+ 1/20160 (+ (* 1/12 (/ 1 (pow x 4))) (/ 1 (pow x 6)))))
(.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))) (+.f64 #s(literal 1/20160 binary64) (/.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (*.f64 x x)))))))
(* 1/20160 (pow x 8))
(*.f64 #s(literal 1/20160 binary64) (pow.f64 x #s(literal 8 binary64)))
(* (pow x 8) (+ 1/20160 (* 1/12 (/ 1 (pow x 4)))))
(.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 #s(literal 1/20160 binary64) (/.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (.f64 x x))))))
(* (pow x 8) (+ 1/20160 (+ (* 1/12 (/ 1 (pow x 4))) (/ 1 (pow x 6)))))
(.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))) (+.f64 #s(literal 1/20160 binary64) (/.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (*.f64 x x)))))))
(* (pow x 8) (+ 1/20160 (+ (* 1/12 (/ 1 (pow x 4))) (/ 1 (pow x 6)))))
(.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))) (+.f64 #s(literal 1/20160 binary64) (/.f64 #s(literal 1/12 binary64) (.f64 x (.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)
1
#s(literal 1 binary64)
(+ 1 (* 1/12 (pow x 2)))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal 1/12 binary64)))
(+ 1 (* (pow x 2) (+ 1/12 (* 1/20160 (pow x 4)))))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x x)))))))
(+ 1 (* (pow x 2) (+ 1/12 (* 1/20160 (pow x 4)))))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x x)))))))
(* 1/20160 (pow x 6))
(.f64 x (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x (.f64 x x))))))
(* (pow x 6) (+ 1/20160 (* 1/12 (/ 1 (pow x 4)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x x))))))
(* (pow x 6) (+ 1/20160 (+ (* 1/12 (/ 1 (pow x 4))) (/ 1 (pow x 6)))))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x x)))))))
(* (pow x 6) (+ 1/20160 (+ (* 1/12 (/ 1 (pow x 4))) (/ 1 (pow x 6)))))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x x)))))))
(* 1/20160 (pow x 6))
(.f64 x (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x (.f64 x x))))))
(* (pow x 6) (+ 1/20160 (* 1/12 (/ 1 (pow x 4)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x x))))))
(* (pow x 6) (+ 1/20160 (+ (* 1/12 (/ 1 (pow x 4))) (/ 1 (pow x 6)))))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x x)))))))
(* (pow x 6) (+ 1/20160 (+ (* 1/12 (/ 1 (pow x 4))) (/ 1 (pow x 6)))))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x x)))))))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 1/12 (pow x 2))))
(.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal 1/12 binary64)))))
(* (pow x 2) (+ 1 (* 1/12 (pow x 2))))
(.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal 1/12 binary64)))))
(* (pow x 2) (+ 1 (* 1/12 (pow x 2))))
(.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal 1/12 binary64)))))
(* 1/12 (pow x 4))
(.f64 x (.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x x))))
(* (pow x 4) (+ 1/12 (/ 1 (pow x 2))))
(.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal 1/12 binary64)))))
(* (pow x 4) (+ 1/12 (/ 1 (pow x 2))))
(.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal 1/12 binary64)))))
(* (pow x 4) (+ 1/12 (/ 1 (pow x 2))))
(.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal 1/12 binary64)))))
(* 1/12 (pow x 4))
(.f64 x (.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x x))))
(* (pow x 4) (+ 1/12 (/ 1 (pow x 2))))
(.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal 1/12 binary64)))))
(* (pow x 4) (+ 1/12 (/ 1 (pow x 2))))
(.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal 1/12 binary64)))))
(* (pow x 4) (+ 1/12 (/ 1 (pow x 2))))
(.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal 1/12 binary64)))))
(* 1/12 (pow x 4))
(.f64 x (.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x x))))
(* 1/12 (pow x 4))
(.f64 x (.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x x))))
(* 1/12 (pow x 4))
(.f64 x (.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x x))))
(* 1/12 (pow x 4))
(.f64 x (.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x x))))
(* 1/12 (pow x 4))
(.f64 x (.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x x))))
(* 1/12 (pow x 4))
(.f64 x (.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x x))))
(* 1/12 (pow x 4))
(.f64 x (.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x x))))
(* 1/12 (pow x 4))
(.f64 x (.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x x))))
(* 1/12 (pow x 4))
(.f64 x (.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x x))))
(* 1/12 (pow x 4))
(.f64 x (.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x x))))
(* 1/12 (pow x 4))
(.f64 x (.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x x))))
(* 1/12 (pow x 4))
(.f64 x (.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x x))))
(* 1/12 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/12 binary64))
(* 1/12 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/12 binary64))
(* 1/12 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/12 binary64))
(* 1/12 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/12 binary64))
(* 1/12 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/12 binary64))
(* 1/12 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/12 binary64))
(* 1/12 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/12 binary64))
(* 1/12 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/12 binary64))
(* 1/12 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/12 binary64))
(* 1/12 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/12 binary64))
(* 1/12 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/12 binary64))
(* 1/12 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/12 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 1/12 (pow x 2))))
(.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal 1/12 binary64)))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 1/12 (* 1/360 (pow x 2))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64))))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 1/12 (* 1/360 (pow x 2))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64))))))
(* 1/360 (pow x 6))
(.f64 x (.f64 #s(literal 1/360 binary64) (.f64 x (.f64 x (.f64 x (.f64 x x))))))
(* (pow x 6) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))
(.f64 (.f64 x x) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64)))))
(* (pow x 6) (+ 1/360 (+ (* 1/12 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64))))))
(* (pow x 6) (+ 1/360 (+ (* 1/12 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64))))))
(* 1/360 (pow x 6))
(.f64 x (.f64 #s(literal 1/360 binary64) (.f64 x (.f64 x (.f64 x (.f64 x x))))))
(* (pow x 6) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))
(.f64 (.f64 x x) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64)))))
(* (pow x 6) (+ 1/360 (+ (* 1/12 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64))))))
(* (pow x 6) (+ 1/360 (+ (* 1/12 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64))))))
(* 1/12 (pow x 4))
(.f64 x (.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x x))))
(* (pow x 4) (+ 1/12 (* 1/360 (pow x 2))))
(.f64 (.f64 x x) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64)))))
(* (pow x 4) (+ 1/12 (* 1/360 (pow x 2))))
(.f64 (.f64 x x) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64)))))
(* (pow x 4) (+ 1/12 (* 1/360 (pow x 2))))
(.f64 (.f64 x x) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64)))))
(* 1/360 (pow x 6))
(.f64 x (.f64 #s(literal 1/360 binary64) (.f64 x (.f64 x (.f64 x (.f64 x x))))))
(* (pow x 6) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))
(.f64 (.f64 x x) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64)))))
(* (pow x 6) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))
(.f64 (.f64 x x) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64)))))
(* (pow x 6) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))
(.f64 (.f64 x x) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64)))))
(* 1/360 (pow x 6))
(.f64 x (.f64 #s(literal 1/360 binary64) (.f64 x (.f64 x (.f64 x (.f64 x x))))))
(* (pow x 6) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))
(.f64 (.f64 x x) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64)))))
(* (pow x 6) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))
(.f64 (.f64 x x) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64)))))
(* (pow x 6) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))
(.f64 (.f64 x x) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64)))))
(* 1/12 (pow x 3))
(.f64 #s(literal 1/12 binary64) (.f64 x (*.f64 x x)))
(* (pow x 3) (+ 1/12 (* 1/360 (pow x 2))))
(.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (*.f64 x x) #s(literal 1/360 binary64)))))
(* (pow x 3) (+ 1/12 (* 1/360 (pow x 2))))
(.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (*.f64 x x) #s(literal 1/360 binary64)))))
(* (pow x 3) (+ 1/12 (* 1/360 (pow x 2))))
(.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (*.f64 x x) #s(literal 1/360 binary64)))))
(* 1/360 (pow x 5))
(.f64 #s(literal 1/360 binary64) (.f64 x (.f64 x (.f64 x (*.f64 x x)))))
(* (pow x 5) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))
(.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (*.f64 x x) #s(literal 1/360 binary64)))))
(* (pow x 5) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))
(.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (*.f64 x x) #s(literal 1/360 binary64)))))
(* (pow x 5) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))
(.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (*.f64 x x) #s(literal 1/360 binary64)))))
(* 1/360 (pow x 5))
(.f64 #s(literal 1/360 binary64) (.f64 x (.f64 x (.f64 x (*.f64 x x)))))
(* (pow x 5) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))
(.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (*.f64 x x) #s(literal 1/360 binary64)))))
(* (pow x 5) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))
(.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (*.f64 x x) #s(literal 1/360 binary64)))))
(* (pow x 5) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))
(.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (*.f64 x x) #s(literal 1/360 binary64)))))
(* 1/12 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/12 binary64))
(* (pow x 2) (+ 1/12 (* 1/360 (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64))))
(* (pow x 2) (+ 1/12 (* 1/360 (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64))))
(* (pow x 2) (+ 1/12 (* 1/360 (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64))))
(* 1/360 (pow x 4))
(.f64 #s(literal 1/360 binary64) (.f64 x (.f64 x (.f64 x x))))
(* (pow x 4) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64))))
(* (pow x 4) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64))))
(* (pow x 4) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64))))
(* 1/360 (pow x 4))
(.f64 #s(literal 1/360 binary64) (.f64 x (.f64 x (.f64 x x))))
(* (pow x 4) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64))))
(* (pow x 4) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64))))
(* (pow x 4) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 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))))))))
(- (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)
(* 1/360 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal 1/360 binary64)))
(* 1/360 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal 1/360 binary64)))
(* 1/360 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal 1/360 binary64)))
(* 1/360 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal 1/360 binary64)))
(* 1/360 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal 1/360 binary64)))
(* 1/360 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal 1/360 binary64)))
(* 1/360 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal 1/360 binary64)))
(* 1/360 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal 1/360 binary64)))
(* 1/360 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal 1/360 binary64)))
(* 1/360 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal 1/360 binary64)))
(* 1/360 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal 1/360 binary64)))
(* 1/360 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal 1/360 binary64)))
(* 1/20160 (pow x 3))
(.f64 #s(literal 1/20160 binary64) (.f64 x (*.f64 x x)))
(* 1/20160 (pow x 3))
(.f64 #s(literal 1/20160 binary64) (.f64 x (*.f64 x x)))
(* 1/20160 (pow x 3))
(.f64 #s(literal 1/20160 binary64) (.f64 x (*.f64 x x)))
(* 1/20160 (pow x 3))
(.f64 #s(literal 1/20160 binary64) (.f64 x (*.f64 x x)))
(* 1/20160 (pow x 3))
(.f64 #s(literal 1/20160 binary64) (.f64 x (*.f64 x x)))
(* 1/20160 (pow x 3))
(.f64 #s(literal 1/20160 binary64) (.f64 x (*.f64 x x)))
(* 1/20160 (pow x 3))
(.f64 #s(literal 1/20160 binary64) (.f64 x (*.f64 x x)))
(* 1/20160 (pow x 3))
(.f64 #s(literal 1/20160 binary64) (.f64 x (*.f64 x x)))
(* 1/20160 (pow x 3))
(.f64 #s(literal 1/20160 binary64) (.f64 x (*.f64 x x)))
(* 1/20160 (pow x 3))
(.f64 #s(literal 1/20160 binary64) (.f64 x (*.f64 x x)))
(* 1/20160 (pow x 3))
(.f64 #s(literal 1/20160 binary64) (.f64 x (*.f64 x x)))
(* 1/20160 (pow x 3))
(.f64 #s(literal 1/20160 binary64) (.f64 x (*.f64 x x)))
(* 1/20160 (pow x 4))
(.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x x))))
(* 1/20160 (pow x 4))
(.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x x))))
(* 1/20160 (pow x 4))
(.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x x))))
(* 1/20160 (pow x 4))
(.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x x))))
(* 1/20160 (pow x 4))
(.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x x))))
(* 1/20160 (pow x 4))
(.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x x))))
(* 1/20160 (pow x 4))
(.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x x))))
(* 1/20160 (pow x 4))
(.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x x))))
(* 1/20160 (pow x 4))
(.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x x))))
(* 1/20160 (pow x 4))
(.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x x))))
(* 1/20160 (pow x 4))
(.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x x))))
(* 1/20160 (pow x 4))
(.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x x))))
(* 1/12 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/12 binary64))
(* (pow x 2) (+ 1/12 (* 1/20160 (pow x 4))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x x))))))
(* (pow x 2) (+ 1/12 (* 1/20160 (pow x 4))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x x))))))
(* (pow x 2) (+ 1/12 (* 1/20160 (pow x 4))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x x))))))
(* 1/20160 (pow x 6))
(.f64 x (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x (.f64 x x))))))
(* (pow x 6) (+ 1/20160 (* 1/12 (/ 1 (pow x 4)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x x))))))
(* (pow x 6) (+ 1/20160 (* 1/12 (/ 1 (pow x 4)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x x))))))
(* (pow x 6) (+ 1/20160 (* 1/12 (/ 1 (pow x 4)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x x))))))
(* 1/20160 (pow x 6))
(.f64 x (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x (.f64 x x))))))
(* (pow x 6) (+ 1/20160 (* 1/12 (/ 1 (pow x 4)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x x))))))
(* (pow x 6) (+ 1/20160 (* 1/12 (/ 1 (pow x 4)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x x))))))
(* (pow x 6) (+ 1/20160 (* 1/12 (/ 1 (pow x 4)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x x))))))

eval166.0ms (1.5%)

Compiler: Compiled 28543 to 2243 computations (92.1% saved)

prune94.0ms (0.9%)

Pruning

17 alts after pruning (9 fresh and 8 done)

	Pruned	Kept	Total
New	1026	1	1027
Fresh	1	8	9
Picked	0	5	5
Done	0	3	3
Total	1027	17	1044

Accuracy

100.0%

Counts

1044 → 17

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	50.9%	(-.f64 (*.f64 #s(literal 2 binary64) (cosh.f64 x)) #s(literal 2 binary64))
	49.8%	(+.f64 (pow.f64 (E.f64) x) #s(literal -1 binary64))
	50.8%	(+.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (E.f64)) (-.f64 #s(literal 0 binary64) x)) #s(literal 2 binary64)) (exp.f64 (neg.f64 x)))
✓	99.4%	(+.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x x)))))))) (.f64 x (.f64 (.f64 x x) (.f64 #s(literal 1/360 binary64) (.f64 x (.f64 x x))))))
✓	99.3%	(+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/12 binary64))) (*.f64 x x))
✓	99.4%	(+.f64 (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64)))))) (*.f64 x x))
▶	99.4%	(.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64)))))))) (.f64 x x))
	99.4%	(.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64)))))) x)
✓	99.4%	(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64))))))
▶	99.3%	(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64))))))))
✓	99.3%	(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal 1/12 binary64))))
▶	50.0%	(.f64 (.f64 x x) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64)))))
▶	50.0%	(.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 1/12 binary64))))
	49.6%	(.f64 (.f64 x x) (.f64 x (.f64 #s(literal 1/360 binary64) (.f64 x (.f64 x x)))))
✓	98.8%	(*.f64 x x)
✓	7.2%	(expm1.f64 x)
✓	7.0%	x

Compiler

Compiled 371 to 215 computations (42% saved)

simplify195.0ms (1.8%)

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Program
✓	cost-diff	(cosh.f64 x)
✓	cost-diff	(*.f64 #s(literal 2 binary64) (cosh.f64 x))
✓	cost-diff	(-.f64 (*.f64 #s(literal 2 binary64) (cosh.f64 x)) #s(literal 2 binary64))
✓	cost-diff	(.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64))))))
✓	cost-diff	(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64)))))))
✓	cost-diff	(*.f64 x x)
✓	cost-diff	(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64))))))))
✓	cost-diff	(+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64)))
✓	cost-diff	(.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64))))
✓	cost-diff	(*.f64 x x)
✓	cost-diff	(.f64 (.f64 x x) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64)))))
✓	cost-diff	(*.f64 x #s(literal 1/12 binary64))
✓	cost-diff	(.f64 x (.f64 x #s(literal 1/12 binary64)))
✓	cost-diff	(*.f64 x x)
✓	cost-diff	(.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 1/12 binary64))))
✓	cost-diff	(.f64 x (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/360 binary64) (.f64 (*.f64 x x) #s(literal 1/20160 binary64))))))
✓	cost-diff	(.f64 x (.f64 x (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64)))))))
✓	cost-diff	(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64))))))))
✓	cost-diff	(.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64)))))))) (.f64 x x))

Rules

2366×	`-lowering-.f32`
2366×	`-lowering-.f64`
2238×	`fma-lowering-fma.f32`
2238×	`fma-lowering-fma.f64`
1572×	`fmsub-define`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	31	241
1	119	207
2	388	202
3	1012	201
4	1771	201
5	2263	201
6	2841	201
7	3791	201
8	4608	201
9	6336	201
0	8026	201

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(* (+ 1 (* x (* x (+ 1/12 (* (* x x) (+ 1/360 (* (* x x) 1/20160))))))) (* x x))
(+ 1 (* x (* x (+ 1/12 (* (* x x) (+ 1/360 (* (* x x) 1/20160)))))))
1
(* x (* x (+ 1/12 (* (* x x) (+ 1/360 (* (* x x) 1/20160))))))
x
(* x (+ 1/12 (* (* x x) (+ 1/360 (* (* x x) 1/20160)))))
(+ 1/12 (* (* x x) (+ 1/360 (* (* x x) 1/20160))))
1/12
(* (* x x) (+ 1/360 (* (* x x) 1/20160)))
(* x x)
(+ 1/360 (* (* x x) 1/20160))
1/360
(* (* x x) 1/20160)
1/20160
(* (* x x) (* x (* x 1/12)))
(* x x)
x
(* x (* x 1/12))
(* x 1/12)
1/12
(* (* x x) (* (* x x) (+ 1/12 (* (* x x) 1/360))))
(* x x)
x
(* (* x x) (+ 1/12 (* (* x x) 1/360)))
(+ 1/12 (* (* x x) 1/360))
1/12
(* (* x x) 1/360)
1/360
(* (* x x) (+ 1 (* (* x x) (+ 1/12 (* x (* x (* (* x x) 1/20160)))))))
(* x x)
x
(+ 1 (* (* x x) (+ 1/12 (* x (* x (* (* x x) 1/20160))))))
1
(* (* x x) (+ 1/12 (* x (* x (* (* x x) 1/20160)))))
(+ 1/12 (* x (* x (* (* x x) 1/20160))))
1/12
(* x (* x (* (* x x) 1/20160)))
(* x (* (* x x) 1/20160))
(* (* x x) 1/20160)
1/20160
(- (* 2 (cosh x)) 2)
(* 2 (cosh x))
2
(cosh x)
x

Outputs
(* (+ 1 (* x (* x (+ 1/12 (* (* x x) (+ 1/360 (* (* x x) 1/20160))))))) (* x x))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64))))))))
(+ 1 (* x (* x (+ 1/12 (* (* x x) (+ 1/360 (* (* x x) 1/20160)))))))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64)))))))
1
#s(literal 1 binary64)
(* x (* x (+ 1/12 (* (* x x) (+ 1/360 (* (* x x) 1/20160))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64))))))
x
(* x (+ 1/12 (* (* x x) (+ 1/360 (* (* x x) 1/20160)))))
(.f64 x (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/360 binary64) (.f64 (*.f64 x x) #s(literal 1/20160 binary64))))))
(+ 1/12 (* (* x x) (+ 1/360 (* (* x x) 1/20160))))
(+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64)))))
1/12
#s(literal 1/12 binary64)
(* (* x x) (+ 1/360 (* (* x x) 1/20160)))
(.f64 (.f64 x x) (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64))))
(* x x)
(*.f64 x x)
(+ 1/360 (* (* x x) 1/20160))
(+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64)))
1/360
#s(literal 1/360 binary64)
(* (* x x) 1/20160)
(.f64 (.f64 x x) #s(literal 1/20160 binary64))
1/20160
#s(literal 1/20160 binary64)
(* (* x x) (* x (* x 1/12)))
(.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (.f64 x x))))
(* x x)
(*.f64 x x)
x
(* x (* x 1/12))
(.f64 #s(literal 1/12 binary64) (.f64 x x))
(* x 1/12)
(*.f64 x #s(literal 1/12 binary64))
1/12
#s(literal 1/12 binary64)
(* (* x x) (* (* x x) (+ 1/12 (* (* x x) 1/360))))
(.f64 (.f64 x x) (.f64 x (.f64 x (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64))))))
(* x x)
(*.f64 x x)
x
(* (* x x) (+ 1/12 (* (* x x) 1/360)))
(.f64 x (.f64 x (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64)))))
(+ 1/12 (* (* x x) 1/360))
(+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64)))
1/12
#s(literal 1/12 binary64)
(* (* x x) 1/360)
(.f64 (.f64 x x) #s(literal 1/360 binary64))
1/360
#s(literal 1/360 binary64)
(* (* x x) (+ 1 (* (* x x) (+ 1/12 (* x (* x (* (* x x) 1/20160)))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64))))))))
(* x x)
(*.f64 x x)
x
(+ 1 (* (* x x) (+ 1/12 (* x (* x (* (* x x) 1/20160))))))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64)))))))
1
#s(literal 1 binary64)
(* (* x x) (+ 1/12 (* x (* x (* (* x x) 1/20160)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64))))))
(+ 1/12 (* x (* x (* (* x x) 1/20160))))
(+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64)))))
1/12
#s(literal 1/12 binary64)
(* x (* x (* (* x x) 1/20160)))
(.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64))))
(* x (* (* x x) 1/20160))
(.f64 x (.f64 (*.f64 x x) #s(literal 1/20160 binary64)))
(* (* x x) 1/20160)
(.f64 (.f64 x x) #s(literal 1/20160 binary64))
1/20160
#s(literal 1/20160 binary64)
(- (* 2 (cosh x)) 2)
(+.f64 #s(literal -2 binary64) (*.f64 #s(literal 2 binary64) (cosh.f64 x)))
(* 2 (cosh x))
(*.f64 #s(literal 2 binary64) (cosh.f64 x))
2
#s(literal 2 binary64)
(cosh x)
(cosh.f64 x)
x

localize394.0ms (3.6%)

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 #s(literal 2 binary64) (cosh.f64 x))
✓	accuracy	100.0%	(cosh.f64 x)
✓	accuracy	50.9%	(-.f64 (*.f64 #s(literal 2 binary64) (cosh.f64 x)) #s(literal 2 binary64))
✓	accuracy	99.9%	(.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64))))
✓	accuracy	99.8%	(.f64 (.f64 x x) #s(literal 1/20160 binary64))
✓	accuracy	99.8%	(.f64 x (.f64 (*.f64 x x) #s(literal 1/20160 binary64)))
✓	accuracy	99.7%	(.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64))))))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	99.8%	(.f64 (.f64 x x) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64)))))
✓	accuracy	99.7%	(.f64 (.f64 x x) #s(literal 1/360 binary64))
✓	accuracy	99.7%	(.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64))))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	99.8%	(.f64 x (.f64 x #s(literal 1/12 binary64)))
✓	accuracy	99.8%	(.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 1/12 binary64))))
✓	accuracy	99.4%	(*.f64 x #s(literal 1/12 binary64))
✓	accuracy	99.8%	(.f64 (.f64 x x) #s(literal 1/20160 binary64))
✓	accuracy	99.8%	(.f64 x (.f64 x (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64)))))))
✓	accuracy	99.7%	(.f64 (.f64 x x) (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64))))
✓	accuracy	99.4%	(.f64 x (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/360 binary64) (.f64 (*.f64 x x) #s(literal 1/20160 binary64))))))

Results

320.0ms	253×	1	valid
1.0ms	3×	0	valid

Compiler

Compiled 292 to 32 computations (89% saved)

Precisions

Click to see histograms. Total time spent on operations: 154.0ms

ival-mult: 72.0ms (46.8% of total)

backward-pass: 27.0ms (17.6% of total)

...c/correct-round.rkt:119:19: 22.0ms (14.3% of total)

ival-add: 14.0ms (9.1% of total)

ival-cosh: 14.0ms (9.1% of total)

ival-sub: 4.0ms (2.6% of total)

const: 1.0ms (0.7% of total)

series7.0ms (0.1%)

Counts

22 → 264

Calls

Call 1

Inputs
#<alt (* (+ 1 (* x (* x (+ 1/12 (* (* x x) (+ 1/360 (* (* x x) 1/20160))))))) (* x x))>
#<alt (+ 1 (* x (* x (+ 1/12 (* (* x x) (+ 1/360 (* (* x x) 1/20160)))))))>
#<alt (* x (* x (+ 1/12 (* (* x x) (+ 1/360 (* (* x x) 1/20160))))))>
#<alt (* x (+ 1/12 (* (* x x) (+ 1/360 (* (* x x) 1/20160)))))>
#<alt (* (* x x) (* x (* x 1/12)))>
#<alt (* x x)>
#<alt (* x (* x 1/12))>
#<alt (* x 1/12)>
#<alt (* (* x x) (* (* x x) (+ 1/12 (* (* x x) 1/360))))>
#<alt (* (* x x) (+ 1/12 (* (* x x) 1/360)))>
#<alt (+ 1/12 (* (* x x) 1/360))>
#<alt (* (* x x) (+ 1 (* (* x x) (+ 1/12 (* x (* x (* (* x x) 1/20160)))))))>
#<alt (+ 1 (* (* x x) (+ 1/12 (* x (* x (* (* x x) 1/20160))))))>
#<alt (* (* x x) (+ 1/12 (* x (* x (* (* x x) 1/20160)))))>
#<alt (- (* 2 (cosh x)) 2)>
#<alt (* 2 (cosh x))>
#<alt (cosh x)>
#<alt (* (* x x) (+ 1/360 (* (* x x) 1/20160)))>
#<alt (* (* x x) 1/20160)>
#<alt (* (* x x) 1/360)>
#<alt (* x (* (* x x) 1/20160))>
#<alt (* x (* x (* (* x x) 1/20160)))>

Outputs
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* 1/12 (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (* (pow x 2) (+ 1/12 (* 1/360 (pow x 2))))))>
#<alt (* (pow x 2) (+ 1 (* (pow x 2) (+ 1/12 (* (pow x 2) (+ 1/360 (* 1/20160 (pow x 2))))))))>
#<alt (* 1/20160 (pow x 8))>
#<alt (* (pow x 8) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))>
#<alt (* (pow x 8) (+ 1/20160 (+ (/ 1/12 (pow x 4)) (* 1/360 (/ 1 (pow x 2))))))>
#<alt (* (pow x 8) (+ 1/20160 (+ (/ 1/12 (pow x 4)) (+ (* 1/360 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))>
#<alt (* 1/20160 (pow x 8))>
#<alt (* (pow x 8) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))>
#<alt (* (pow x 8) (+ 1/20160 (+ (/ 1/12 (pow x 4)) (* 1/360 (/ 1 (pow x 2))))))>
#<alt (* (pow x 8) (+ 1/20160 (+ (/ 1/12 (pow x 4)) (+ (* 1/360 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))>
#<alt 1>
#<alt (+ 1 (* 1/12 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (+ 1/12 (* 1/360 (pow x 2)))))>
#<alt (+ 1 (* (pow x 2) (+ 1/12 (* (pow x 2) (+ 1/360 (* 1/20160 (pow x 2)))))))>
#<alt (* 1/20160 (pow x 6))>
#<alt (* (pow x 6) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (+ 1/20160 (+ (/ 1/12 (pow x 4)) (* 1/360 (/ 1 (pow x 2))))))>
#<alt (* (pow x 6) (+ 1/20160 (+ (/ 1/12 (pow x 4)) (+ (* 1/360 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))>
#<alt (* 1/20160 (pow x 6))>
#<alt (* (pow x 6) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (+ 1/20160 (+ (/ 1/12 (pow x 4)) (* 1/360 (/ 1 (pow x 2))))))>
#<alt (* (pow x 6) (+ 1/20160 (+ (/ 1/12 (pow x 4)) (+ (* 1/360 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))>
#<alt (* 1/12 (pow x 2))>
#<alt (* (pow x 2) (+ 1/12 (* 1/360 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/12 (* (pow x 2) (+ 1/360 (* 1/20160 (pow x 2))))))>
#<alt (* (pow x 2) (+ 1/12 (* (pow x 2) (+ 1/360 (* 1/20160 (pow x 2))))))>
#<alt (* 1/20160 (pow x 6))>
#<alt (* (pow x 6) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (+ 1/20160 (+ (/ 1/12 (pow x 4)) (* 1/360 (/ 1 (pow x 2))))))>
#<alt (* (pow x 6) (+ 1/20160 (+ (/ 1/12 (pow x 4)) (* 1/360 (/ 1 (pow x 2))))))>
#<alt (* 1/20160 (pow x 6))>
#<alt (* (pow x 6) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (+ 1/20160 (+ (/ 1/12 (pow x 4)) (* 1/360 (/ 1 (pow x 2))))))>
#<alt (* (pow x 6) (+ 1/20160 (+ (/ 1/12 (pow x 4)) (* 1/360 (/ 1 (pow x 2))))))>
#<alt (* 1/12 x)>
#<alt (* x (+ 1/12 (* 1/360 (pow x 2))))>
#<alt (* x (+ 1/12 (* (pow x 2) (+ 1/360 (* 1/20160 (pow x 2))))))>
#<alt (* x (+ 1/12 (* (pow x 2) (+ 1/360 (* 1/20160 (pow x 2))))))>
#<alt (* 1/20160 (pow x 5))>
#<alt (* (pow x 5) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))>
#<alt (* (pow x 5) (+ 1/20160 (+ (/ 1/12 (pow x 4)) (* 1/360 (/ 1 (pow x 2))))))>
#<alt (* (pow x 5) (+ 1/20160 (+ (/ 1/12 (pow x 4)) (* 1/360 (/ 1 (pow x 2))))))>
#<alt (* 1/20160 (pow x 5))>
#<alt (* (pow x 5) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))>
#<alt (* -1 (* (pow x 5) (- (* -1 (/ (+ 1/360 (* 1/12 (/ 1 (pow x 2)))) (pow x 2))) 1/20160)))>
#<alt (* -1 (* (pow x 5) (- (* -1 (/ (+ 1/360 (* 1/12 (/ 1 (pow x 2)))) (pow x 2))) 1/20160)))>
#<alt (* 1/12 (pow x 4))>
#<alt (* 1/12 (pow x 4))>
#<alt (* 1/12 (pow x 4))>
#<alt (* 1/12 (pow x 4))>
#<alt (* 1/12 (pow x 4))>
#<alt (* 1/12 (pow x 4))>
#<alt (* 1/12 (pow x 4))>
#<alt (* 1/12 (pow x 4))>
#<alt (* 1/12 (pow x 4))>
#<alt (* 1/12 (pow x 4))>
#<alt (* 1/12 (pow x 4))>
#<alt (* 1/12 (pow x 4))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (* 1/12 (pow x 2))>
#<alt (* 1/12 (pow x 2))>
#<alt (* 1/12 (pow x 2))>
#<alt (* 1/12 (pow x 2))>
#<alt (* 1/12 (pow x 2))>
#<alt (* 1/12 (pow x 2))>
#<alt (* 1/12 (pow x 2))>
#<alt (* 1/12 (pow x 2))>
#<alt (* 1/12 (pow x 2))>
#<alt (* 1/12 (pow x 2))>
#<alt (* 1/12 (pow x 2))>
#<alt (* 1/12 (pow x 2))>
#<alt (* 1/12 x)>
#<alt (* 1/12 x)>
#<alt (* 1/12 x)>
#<alt (* 1/12 x)>
#<alt (* 1/12 x)>
#<alt (* 1/12 x)>
#<alt (* 1/12 x)>
#<alt (* 1/12 x)>
#<alt (* 1/12 x)>
#<alt (* 1/12 x)>
#<alt (* 1/12 x)>
#<alt (* 1/12 x)>
#<alt (* 1/12 (pow x 4))>
#<alt (* (pow x 4) (+ 1/12 (* 1/360 (pow x 2))))>
#<alt (* (pow x 4) (+ 1/12 (* 1/360 (pow x 2))))>
#<alt (* (pow x 4) (+ 1/12 (* 1/360 (pow x 2))))>
#<alt (* 1/360 (pow x 6))>
#<alt (* (pow x 6) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))>
#<alt (* 1/360 (pow x 6))>
#<alt (* (pow x 6) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))>
#<alt (* 1/12 (pow x 2))>
#<alt (* (pow x 2) (+ 1/12 (* 1/360 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/12 (* 1/360 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/12 (* 1/360 (pow x 2))))>
#<alt (* 1/360 (pow x 4))>
#<alt (* (pow x 4) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))>
#<alt (* 1/360 (pow x 4))>
#<alt (* (pow x 4) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))>
#<alt 1/12>
#<alt (+ 1/12 (* 1/360 (pow x 2)))>
#<alt (+ 1/12 (* 1/360 (pow x 2)))>
#<alt (+ 1/12 (* 1/360 (pow x 2)))>
#<alt (* 1/360 (pow x 2))>
#<alt (* (pow x 2) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))>
#<alt (* 1/360 (pow x 2))>
#<alt (* (pow x 2) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* 1/12 (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (* (pow x 2) (+ 1/12 (* 1/20160 (pow x 4))))))>
#<alt (* (pow x 2) (+ 1 (* (pow x 2) (+ 1/12 (* 1/20160 (pow x 4))))))>
#<alt (* 1/20160 (pow x 8))>
#<alt (* (pow x 8) (+ 1/20160 (* 1/12 (/ 1 (pow x 4)))))>
#<alt (* (pow x 8) (+ 1/20160 (+ (* 1/12 (/ 1 (pow x 4))) (/ 1 (pow x 6)))))>
#<alt (* (pow x 8) (+ 1/20160 (+ (* 1/12 (/ 1 (pow x 4))) (/ 1 (pow x 6)))))>
#<alt (* 1/20160 (pow x 8))>
#<alt (* (pow x 8) (+ 1/20160 (* 1/12 (/ 1 (pow x 4)))))>
#<alt (* (pow x 8) (+ 1/20160 (+ (* 1/12 (/ 1 (pow x 4))) (/ 1 (pow x 6)))))>
#<alt (* (pow x 8) (+ 1/20160 (+ (* 1/12 (/ 1 (pow x 4))) (/ 1 (pow x 6)))))>
#<alt 1>
#<alt (+ 1 (* 1/12 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (+ 1/12 (* 1/20160 (pow x 4)))))>
#<alt (+ 1 (* (pow x 2) (+ 1/12 (* 1/20160 (pow x 4)))))>
#<alt (* 1/20160 (pow x 6))>
#<alt (* (pow x 6) (+ 1/20160 (* 1/12 (/ 1 (pow x 4)))))>
#<alt (* (pow x 6) (+ 1/20160 (+ (* 1/12 (/ 1 (pow x 4))) (/ 1 (pow x 6)))))>
#<alt (* (pow x 6) (+ 1/20160 (+ (* 1/12 (/ 1 (pow x 4))) (/ 1 (pow x 6)))))>
#<alt (* 1/20160 (pow x 6))>
#<alt (* (pow x 6) (+ 1/20160 (* 1/12 (/ 1 (pow x 4)))))>
#<alt (* (pow x 6) (+ 1/20160 (+ (* 1/12 (/ 1 (pow x 4))) (/ 1 (pow x 6)))))>
#<alt (* (pow x 6) (+ 1/20160 (+ (* 1/12 (/ 1 (pow x 4))) (/ 1 (pow x 6)))))>
#<alt (* 1/12 (pow x 2))>
#<alt (* (pow x 2) (+ 1/12 (* 1/20160 (pow x 4))))>
#<alt (* (pow x 2) (+ 1/12 (* 1/20160 (pow x 4))))>
#<alt (* (pow x 2) (+ 1/12 (* 1/20160 (pow x 4))))>
#<alt (* 1/20160 (pow x 6))>
#<alt (* (pow x 6) (+ 1/20160 (* 1/12 (/ 1 (pow x 4)))))>
#<alt (* (pow x 6) (+ 1/20160 (* 1/12 (/ 1 (pow x 4)))))>
#<alt (* (pow x 6) (+ 1/20160 (* 1/12 (/ 1 (pow x 4)))))>
#<alt (* 1/20160 (pow x 6))>
#<alt (* (pow x 6) (+ 1/20160 (* 1/12 (/ 1 (pow x 4)))))>
#<alt (* (pow x 6) (+ 1/20160 (* 1/12 (/ 1 (pow x 4)))))>
#<alt (* (pow x 6) (+ 1/20160 (* 1/12 (/ 1 (pow x 4)))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* 1/12 (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (* (pow x 2) (+ 1/12 (* 1/360 (pow x 2))))))>
#<alt (* (pow x 2) (+ 1 (* (pow x 2) (+ 1/12 (* (pow x 2) (+ 1/360 (* 1/20160 (pow x 2))))))))>
#<alt (- (+ (exp x) (/ 1 (exp x))) 2)>
#<alt (- (+ (exp x) (/ 1 (exp x))) 2)>
#<alt (- (+ (exp x) (/ 1 (exp x))) 2)>
#<alt (- (+ (exp x) (/ 1 (exp x))) 2)>
#<alt (- (+ (exp x) (/ 1 (exp x))) 2)>
#<alt (- (+ (exp x) (/ 1 (exp x))) 2)>
#<alt (- (+ (exp x) (/ 1 (exp x))) 2)>
#<alt (- (+ (exp x) (/ 1 (exp x))) 2)>
#<alt 2>
#<alt (+ 2 (pow x 2))>
#<alt (+ 2 (* (pow x 2) (+ 1 (* 1/12 (pow x 2)))))>
#<alt (+ 2 (* (pow x 2) (+ 1 (* (pow x 2) (+ 1/12 (* 1/360 (pow x 2)))))))>
#<alt (+ (exp x) (/ 1 (exp x)))>
#<alt (+ (exp x) (/ 1 (exp x)))>
#<alt (+ (exp x) (/ 1 (exp x)))>
#<alt (+ (exp x) (/ 1 (exp x)))>
#<alt (+ (exp x) (/ 1 (exp x)))>
#<alt (+ (exp x) (/ 1 (exp x)))>
#<alt (+ (exp x) (/ 1 (exp x)))>
#<alt (+ (exp x) (/ 1 (exp x)))>
#<alt 1>
#<alt (+ 1 (* 1/2 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (+ 1/2 (* 1/24 (pow x 2)))))>
#<alt (+ 1 (* (pow x 2) (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/720 (pow x 2)))))))>
#<alt (* 1/2 (+ (exp x) (/ 1 (exp x))))>
#<alt (* 1/2 (+ (exp x) (/ 1 (exp x))))>
#<alt (* 1/2 (+ (exp x) (/ 1 (exp x))))>
#<alt (* 1/2 (+ (exp x) (/ 1 (exp x))))>
#<alt (* 1/2 (+ (exp x) (/ 1 (exp x))))>
#<alt (* 1/2 (+ (exp x) (/ 1 (exp x))))>
#<alt (* 1/2 (+ (exp x) (/ 1 (exp x))))>
#<alt (* 1/2 (+ (exp x) (/ 1 (exp x))))>
#<alt (* 1/360 (pow x 2))>
#<alt (* (pow x 2) (+ 1/360 (* 1/20160 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/360 (* 1/20160 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/360 (* 1/20160 (pow x 2))))>
#<alt (* 1/20160 (pow x 4))>
#<alt (* (pow x 4) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))>
#<alt (* 1/20160 (pow x 4))>
#<alt (* (pow x 4) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))>
#<alt (* 1/20160 (pow x 2))>
#<alt (* 1/20160 (pow x 2))>
#<alt (* 1/20160 (pow x 2))>
#<alt (* 1/20160 (pow x 2))>
#<alt (* 1/20160 (pow x 2))>
#<alt (* 1/20160 (pow x 2))>
#<alt (* 1/20160 (pow x 2))>
#<alt (* 1/20160 (pow x 2))>
#<alt (* 1/20160 (pow x 2))>
#<alt (* 1/20160 (pow x 2))>
#<alt (* 1/20160 (pow x 2))>
#<alt (* 1/20160 (pow x 2))>
#<alt (* 1/360 (pow x 2))>
#<alt (* 1/360 (pow x 2))>
#<alt (* 1/360 (pow x 2))>
#<alt (* 1/360 (pow x 2))>
#<alt (* 1/360 (pow x 2))>
#<alt (* 1/360 (pow x 2))>
#<alt (* 1/360 (pow x 2))>
#<alt (* 1/360 (pow x 2))>
#<alt (* 1/360 (pow x 2))>
#<alt (* 1/360 (pow x 2))>
#<alt (* 1/360 (pow x 2))>
#<alt (* 1/360 (pow x 2))>
#<alt (* 1/20160 (pow x 3))>
#<alt (* 1/20160 (pow x 3))>
#<alt (* 1/20160 (pow x 3))>
#<alt (* 1/20160 (pow x 3))>
#<alt (* 1/20160 (pow x 3))>
#<alt (* 1/20160 (pow x 3))>
#<alt (* 1/20160 (pow x 3))>
#<alt (* 1/20160 (pow x 3))>
#<alt (* 1/20160 (pow x 3))>
#<alt (* 1/20160 (pow x 3))>
#<alt (* 1/20160 (pow x 3))>
#<alt (* 1/20160 (pow x 3))>
#<alt (* 1/20160 (pow x 4))>
#<alt (* 1/20160 (pow x 4))>
#<alt (* 1/20160 (pow x 4))>
#<alt (* 1/20160 (pow x 4))>
#<alt (* 1/20160 (pow x 4))>
#<alt (* 1/20160 (pow x 4))>
#<alt (* 1/20160 (pow x 4))>
#<alt (* 1/20160 (pow x 4))>
#<alt (* 1/20160 (pow x 4))>
#<alt (* 1/20160 (pow x 4))>
#<alt (* 1/20160 (pow x 4))>
#<alt (* 1/20160 (pow x 4))>

Calls

66 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(- (* 2 (cosh x)) 2)
1.0ms	x	@	-inf	(- (* 2 (cosh x)) 2)
0.0ms	x	@	-inf	(* x 1/12)
0.0ms	x	@	0	(* x 1/12)
0.0ms	x	@	0	(- (* 2 (cosh x)) 2)

rewrite245.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

2292×	`-lowering-.f32`
2292×	`-lowering-.f64`
1666×	`/-lowering-/.f32`
1666×	`/-lowering-/.f64`
1470×	`+-lowering-+.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	31	189
1	120	160
2	402	156
3	1144	155
4	2390	155
5	4937	155
0	8262	155

Stop Event

1×	iter limit
1×	node limit

Counts

22 → 686

Calls

Call 1

Inputs
(* (+ 1 (* x (* x (+ 1/12 (* (* x x) (+ 1/360 (* (* x x) 1/20160))))))) (* x x))
(+ 1 (* x (* x (+ 1/12 (* (* x x) (+ 1/360 (* (* x x) 1/20160)))))))
(* x (* x (+ 1/12 (* (* x x) (+ 1/360 (* (* x x) 1/20160))))))
(* x (+ 1/12 (* (* x x) (+ 1/360 (* (* x x) 1/20160)))))
(* (* x x) (* x (* x 1/12)))
(* x x)
(* x (* x 1/12))
(* x 1/12)
(* (* x x) (* (* x x) (+ 1/12 (* (* x x) 1/360))))
(* (* x x) (+ 1/12 (* (* x x) 1/360)))
(+ 1/12 (* (* x x) 1/360))
(* (* x x) (+ 1 (* (* x x) (+ 1/12 (* x (* x (* (* x x) 1/20160)))))))
(+ 1 (* (* x x) (+ 1/12 (* x (* x (* (* x x) 1/20160))))))
(* (* x x) (+ 1/12 (* x (* x (* (* x x) 1/20160)))))
(- (* 2 (cosh x)) 2)
(* 2 (cosh x))
(cosh x)
(* (* x x) (+ 1/360 (* (* x x) 1/20160)))
(* (* x x) 1/20160)
(* (* x x) 1/360)
(* x (* (* x x) 1/20160))
(* x (* x (* (* x x) 1/20160)))

Outputs
(+.f64 (.f64 x x) (.f64 (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64))))) (.f64 x (.f64 x (*.f64 x x)))))
(+.f64 (.f64 (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x #s(literal 1/360 binary64)))) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/20160 binary64)))))))
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(*.f64 #s(literal 4 binary64) (/.f64 (/.f64 (cosh.f64 x) #s(literal 4 binary64)) #s(literal 1 binary64)))
(*.f64 #s(literal 4 binary64) (pow.f64 (/.f64 (cosh.f64 x) #s(literal 4 binary64)) #s(literal 1 binary64)))
(*.f64 #s(literal 4 binary64) (pow.f64 (/.f64 (/.f64 (cosh.f64 x) #s(literal 4 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)))
(*.f64 (/.f64 (cosh.f64 x) #s(literal -1/2 binary64)) #s(literal -1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (/.f64 (cosh.f64 x) #s(literal 1/2 binary64)))
(*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (cosh.f64 x)))
(.f64 (.f64 (cosh.f64 x) #s(literal 4 binary64)) #s(literal 1/4 binary64))
(.f64 (.f64 (cosh.f64 x) #s(literal -4 binary64)) #s(literal -1/4 binary64))
(*.f64 #s(literal -1/2 binary64) (/.f64 (cosh.f64 x) #s(literal -1/2 binary64)))
(*.f64 (-.f64 #s(literal 0 binary64) (cosh.f64 x)) #s(literal -1 binary64))
(*.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/4 binary64) (cosh.f64 x))) #s(literal 1/8 binary64))
(*.f64 (/.f64 (cosh.f64 x) #s(literal 2 binary64)) #s(literal 2 binary64))
(*.f64 #s(literal -4 binary64) (/.f64 (cosh.f64 x) #s(literal -4 binary64)))
(*.f64 #s(literal -4 binary64) (pow.f64 (/.f64 (cosh.f64 x) #s(literal -4 binary64)) #s(literal 1 binary64)))
(.f64 #s(literal 1/4 binary64) (.f64 (cosh.f64 x) #s(literal 4 binary64)))
(.f64 #s(literal -1/4 binary64) (.f64 (cosh.f64 x) #s(literal -4 binary64)))
(*.f64 (/.f64 (cosh.f64 x) #s(literal -2 binary64)) #s(literal -2 binary64))
(*.f64 (/.f64 (cosh.f64 x) #s(literal 4 binary64)) #s(literal 4 binary64))
(*.f64 (pow.f64 (/.f64 (cosh.f64 x) #s(literal -2 binary64)) #s(literal 1 binary64)) #s(literal -2 binary64))
(*.f64 (pow.f64 (/.f64 (cosh.f64 x) #s(literal 4 binary64)) #s(literal 1 binary64)) #s(literal 4 binary64))
(*.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/4 binary64) (cosh.f64 x))) #s(literal 1 binary64)) #s(literal 1/8 binary64))
(*.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -4 binary64) (/.f64 #s(literal 1/2 binary64) (cosh.f64 x)))) #s(literal -1 binary64)) #s(literal 1/8 binary64))
(.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (cosh.f64 x) #s(literal 4 binary64))) #s(literal -1 binary64)) #s(literal 1/8 binary64))
(+.f64 (.f64 x (.f64 x #s(literal 1/360 binary64))) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/20160 binary64))))
(+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/20160 binary64))) (.f64 x (.f64 x #s(literal 1/360 binary64))))
(fma.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/360 binary64))) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/20160 binary64))))
(fma.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/20160 binary64))) (.f64 x (.f64 x #s(literal 1/360 binary64))))
(fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64))) (.f64 x (*.f64 x #s(literal 1/360 binary64))))
(fma.f64 x (.f64 x #s(literal 1/360 binary64)) (.f64 (.f64 x x) (.f64 (*.f64 x x) #s(literal 1/20160 binary64))))
(fma.f64 (.f64 x x) #s(literal 1/360 binary64) (.f64 (.f64 x x) (.f64 (*.f64 x x) #s(literal 1/20160 binary64))))
(fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/20160 binary64)) (.f64 x (*.f64 x #s(literal 1/360 binary64))))
(fma.f64 #s(literal 1/360 binary64) (.f64 x x) (.f64 (.f64 x x) (.f64 (*.f64 x x) #s(literal 1/20160 binary64))))
(fma.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x x))) (.f64 x (*.f64 x #s(literal 1/360 binary64))))
(fma.f64 (.f64 (.f64 x x) #s(literal 1/20160 binary64)) (.f64 x x) (.f64 x (*.f64 x #s(literal 1/360 binary64))))
(fma.f64 (.f64 x (.f64 x #s(literal 1/360 binary64))) #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/20160 binary64))))
(fma.f64 (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64))) x (.f64 x (*.f64 x #s(literal 1/360 binary64))))
(fma.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/20160 binary64))) #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/360 binary64))))
(fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/20160 binary64) (.f64 x (*.f64 x #s(literal 1/360 binary64))))
(fma.f64 (.f64 x (.f64 x x)) (.f64 x #s(literal 1/20160 binary64)) (.f64 x (*.f64 x #s(literal 1/360 binary64))))
(fma.f64 (.f64 x #s(literal 1/360 binary64)) x (.f64 (.f64 x x) (.f64 (*.f64 x x) #s(literal 1/20160 binary64))))
(fma.f64 (.f64 x #s(literal 1/20160 binary64)) (.f64 x (.f64 x x)) (.f64 x (*.f64 x #s(literal 1/360 binary64))))
(.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/360 binary64) (.f64 (*.f64 x x) #s(literal 1/20160 binary64)))))
(.f64 x (.f64 x (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64))))
(.f64 (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64))) (.f64 x x))
(.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/360 binary64) (.f64 (*.f64 x x) #s(literal 1/20160 binary64)))) #s(literal 1 binary64))
(.f64 (.f64 x (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64)))) x)
(.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) #s(literal 1/20160 binary64)))
(.f64 x (.f64 x #s(literal 1/20160 binary64)))
(.f64 (.f64 x x) #s(literal 1/20160 binary64))
(.f64 #s(literal 1/20160 binary64) (.f64 x x))
(.f64 (.f64 (*.f64 x x) #s(literal 1/20160 binary64)) #s(literal 1 binary64))
(.f64 (.f64 x #s(literal 1/20160 binary64)) x)
(.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal 1/360 binary64))))
(.f64 x (.f64 x #s(literal 1/360 binary64)))
(.f64 (.f64 x x) #s(literal 1/360 binary64))
(.f64 #s(literal 1/360 binary64) (.f64 x x))
(.f64 (.f64 x (*.f64 x #s(literal 1/360 binary64))) #s(literal 1 binary64))
(.f64 (.f64 x #s(literal 1/360 binary64)) x)
(.f64 #s(literal 1 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64))))
(.f64 x (.f64 (*.f64 x x) #s(literal 1/20160 binary64)))
(.f64 (.f64 x x) (*.f64 x #s(literal 1/20160 binary64)))
(.f64 #s(literal 1/20160 binary64) (.f64 x (*.f64 x x)))
(.f64 (.f64 (*.f64 x x) #s(literal 1/20160 binary64)) x)
(.f64 (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64))) #s(literal 1 binary64))
(.f64 (.f64 x (*.f64 x x)) #s(literal 1/20160 binary64))
(.f64 (.f64 x #s(literal 1/20160 binary64)) (*.f64 x x))
(.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 (*.f64 x x) #s(literal 1/20160 binary64))))
(.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64))))
(.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/20160 binary64)))
(.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x (.f64 x x))))
(.f64 (.f64 (.f64 x x) #s(literal 1/20160 binary64)) (.f64 x x))
(.f64 (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64))) x)
(.f64 (.f64 (.f64 x x) (.f64 (*.f64 x x) #s(literal 1/20160 binary64))) #s(literal 1 binary64))
(.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/20160 binary64))
(.f64 (.f64 x (.f64 x x)) (.f64 x #s(literal 1/20160 binary64)))
(.f64 (.f64 x #s(literal 1/20160 binary64)) (.f64 x (.f64 x x)))

simplify210.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

2652×	`-lowering-.f32`
2652×	`-lowering-.f64`
1982×	`+-lowering-+.f64`
1982×	`+-lowering-+.f32`
1386×	`fma-define`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	110	2138
1	386	1818
2	1174	1803
3	3367	1801
4	5325	1775
0	8119	1775

Stop Event

1×	iter limit
1×	node limit

Counts

264 → 264

Calls

Call 1

Inputs
(pow x 2)
(* (pow x 2) (+ 1 (* 1/12 (pow x 2))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 1/12 (* 1/360 (pow x 2))))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 1/12 (* (pow x 2) (+ 1/360 (* 1/20160 (pow x 2))))))))
(* 1/20160 (pow x 8))
(* (pow x 8) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))
(* (pow x 8) (+ 1/20160 (+ (/ 1/12 (pow x 4)) (* 1/360 (/ 1 (pow x 2))))))
(* (pow x 8) (+ 1/20160 (+ (/ 1/12 (pow x 4)) (+ (* 1/360 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))
(* 1/20160 (pow x 8))
(* (pow x 8) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))
(* (pow x 8) (+ 1/20160 (+ (/ 1/12 (pow x 4)) (* 1/360 (/ 1 (pow x 2))))))
(* (pow x 8) (+ 1/20160 (+ (/ 1/12 (pow x 4)) (+ (* 1/360 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))
1
(+ 1 (* 1/12 (pow x 2)))
(+ 1 (* (pow x 2) (+ 1/12 (* 1/360 (pow x 2)))))
(+ 1 (* (pow x 2) (+ 1/12 (* (pow x 2) (+ 1/360 (* 1/20160 (pow x 2)))))))
(* 1/20160 (pow x 6))
(* (pow x 6) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 1/20160 (+ (/ 1/12 (pow x 4)) (* 1/360 (/ 1 (pow x 2))))))
(* (pow x 6) (+ 1/20160 (+ (/ 1/12 (pow x 4)) (+ (* 1/360 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))
(* 1/20160 (pow x 6))
(* (pow x 6) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 1/20160 (+ (/ 1/12 (pow x 4)) (* 1/360 (/ 1 (pow x 2))))))
(* (pow x 6) (+ 1/20160 (+ (/ 1/12 (pow x 4)) (+ (* 1/360 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))
(* 1/12 (pow x 2))
(* (pow x 2) (+ 1/12 (* 1/360 (pow x 2))))
(* (pow x 2) (+ 1/12 (* (pow x 2) (+ 1/360 (* 1/20160 (pow x 2))))))
(* (pow x 2) (+ 1/12 (* (pow x 2) (+ 1/360 (* 1/20160 (pow x 2))))))
(* 1/20160 (pow x 6))
(* (pow x 6) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 1/20160 (+ (/ 1/12 (pow x 4)) (* 1/360 (/ 1 (pow x 2))))))
(* (pow x 6) (+ 1/20160 (+ (/ 1/12 (pow x 4)) (* 1/360 (/ 1 (pow x 2))))))
(* 1/20160 (pow x 6))
(* (pow x 6) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 1/20160 (+ (/ 1/12 (pow x 4)) (* 1/360 (/ 1 (pow x 2))))))
(* (pow x 6) (+ 1/20160 (+ (/ 1/12 (pow x 4)) (* 1/360 (/ 1 (pow x 2))))))
(* 1/12 x)
(* x (+ 1/12 (* 1/360 (pow x 2))))
(* x (+ 1/12 (* (pow x 2) (+ 1/360 (* 1/20160 (pow x 2))))))
(* x (+ 1/12 (* (pow x 2) (+ 1/360 (* 1/20160 (pow x 2))))))
(* 1/20160 (pow x 5))
(* (pow x 5) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))
(* (pow x 5) (+ 1/20160 (+ (/ 1/12 (pow x 4)) (* 1/360 (/ 1 (pow x 2))))))
(* (pow x 5) (+ 1/20160 (+ (/ 1/12 (pow x 4)) (* 1/360 (/ 1 (pow x 2))))))
(* 1/20160 (pow x 5))
(* (pow x 5) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/360 (* 1/12 (/ 1 (pow x 2)))) (pow x 2))) 1/20160)))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/360 (* 1/12 (/ 1 (pow x 2)))) (pow x 2))) 1/20160)))
(* 1/12 (pow x 4))
(* 1/12 (pow x 4))
(* 1/12 (pow x 4))
(* 1/12 (pow x 4))
(* 1/12 (pow x 4))
(* 1/12 (pow x 4))
(* 1/12 (pow x 4))
(* 1/12 (pow x 4))
(* 1/12 (pow x 4))
(* 1/12 (pow x 4))
(* 1/12 (pow x 4))
(* 1/12 (pow x 4))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 1/12 (pow x 2))
(* 1/12 (pow x 2))
(* 1/12 (pow x 2))
(* 1/12 (pow x 2))
(* 1/12 (pow x 2))
(* 1/12 (pow x 2))
(* 1/12 (pow x 2))
(* 1/12 (pow x 2))
(* 1/12 (pow x 2))
(* 1/12 (pow x 2))
(* 1/12 (pow x 2))
(* 1/12 (pow x 2))
(* 1/12 x)
(* 1/12 x)
(* 1/12 x)
(* 1/12 x)
(* 1/12 x)
(* 1/12 x)
(* 1/12 x)
(* 1/12 x)
(* 1/12 x)
(* 1/12 x)
(* 1/12 x)
(* 1/12 x)
(* 1/12 (pow x 4))
(* (pow x 4) (+ 1/12 (* 1/360 (pow x 2))))
(* (pow x 4) (+ 1/12 (* 1/360 (pow x 2))))
(* (pow x 4) (+ 1/12 (* 1/360 (pow x 2))))
(* 1/360 (pow x 6))
(* (pow x 6) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))
(* 1/360 (pow x 6))
(* (pow x 6) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))
(* 1/12 (pow x 2))
(* (pow x 2) (+ 1/12 (* 1/360 (pow x 2))))
(* (pow x 2) (+ 1/12 (* 1/360 (pow x 2))))
(* (pow x 2) (+ 1/12 (* 1/360 (pow x 2))))
(* 1/360 (pow x 4))
(* (pow x 4) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))
(* 1/360 (pow x 4))
(* (pow x 4) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))
1/12
(+ 1/12 (* 1/360 (pow x 2)))
(+ 1/12 (* 1/360 (pow x 2)))
(+ 1/12 (* 1/360 (pow x 2)))
(* 1/360 (pow x 2))
(* (pow x 2) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))
(* 1/360 (pow x 2))
(* (pow x 2) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/360 (* 1/12 (/ 1 (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* 1/12 (pow x 2))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 1/12 (* 1/20160 (pow x 4))))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 1/12 (* 1/20160 (pow x 4))))))
(* 1/20160 (pow x 8))
(* (pow x 8) (+ 1/20160 (* 1/12 (/ 1 (pow x 4)))))
(* (pow x 8) (+ 1/20160 (+ (* 1/12 (/ 1 (pow x 4))) (/ 1 (pow x 6)))))
(* (pow x 8) (+ 1/20160 (+ (* 1/12 (/ 1 (pow x 4))) (/ 1 (pow x 6)))))
(* 1/20160 (pow x 8))
(* (pow x 8) (+ 1/20160 (* 1/12 (/ 1 (pow x 4)))))
(* (pow x 8) (+ 1/20160 (+ (* 1/12 (/ 1 (pow x 4))) (/ 1 (pow x 6)))))
(* (pow x 8) (+ 1/20160 (+ (* 1/12 (/ 1 (pow x 4))) (/ 1 (pow x 6)))))
1
(+ 1 (* 1/12 (pow x 2)))
(+ 1 (* (pow x 2) (+ 1/12 (* 1/20160 (pow x 4)))))
(+ 1 (* (pow x 2) (+ 1/12 (* 1/20160 (pow x 4)))))
(* 1/20160 (pow x 6))
(* (pow x 6) (+ 1/20160 (* 1/12 (/ 1 (pow x 4)))))
(* (pow x 6) (+ 1/20160 (+ (* 1/12 (/ 1 (pow x 4))) (/ 1 (pow x 6)))))
(* (pow x 6) (+ 1/20160 (+ (* 1/12 (/ 1 (pow x 4))) (/ 1 (pow x 6)))))
(* 1/20160 (pow x 6))
(* (pow x 6) (+ 1/20160 (* 1/12 (/ 1 (pow x 4)))))
(* (pow x 6) (+ 1/20160 (+ (* 1/12 (/ 1 (pow x 4))) (/ 1 (pow x 6)))))
(* (pow x 6) (+ 1/20160 (+ (* 1/12 (/ 1 (pow x 4))) (/ 1 (pow x 6)))))
(* 1/12 (pow x 2))
(* (pow x 2) (+ 1/12 (* 1/20160 (pow x 4))))
(* (pow x 2) (+ 1/12 (* 1/20160 (pow x 4))))
(* (pow x 2) (+ 1/12 (* 1/20160 (pow x 4))))
(* 1/20160 (pow x 6))
(* (pow x 6) (+ 1/20160 (* 1/12 (/ 1 (pow x 4)))))
(* (pow x 6) (+ 1/20160 (* 1/12 (/ 1 (pow x 4)))))
(* (pow x 6) (+ 1/20160 (* 1/12 (/ 1 (pow x 4)))))
(* 1/20160 (pow x 6))
(* (pow x 6) (+ 1/20160 (* 1/12 (/ 1 (pow x 4)))))
(* (pow x 6) (+ 1/20160 (* 1/12 (/ 1 (pow x 4)))))
(* (pow x 6) (+ 1/20160 (* 1/12 (/ 1 (pow x 4)))))
(pow x 2)
(* (pow x 2) (+ 1 (* 1/12 (pow x 2))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 1/12 (* 1/360 (pow x 2))))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 1/12 (* (pow x 2) (+ 1/360 (* 1/20160 (pow x 2))))))))
(- (+ (exp x) (/ 1 (exp x))) 2)
(- (+ (exp x) (/ 1 (exp x))) 2)
(- (+ (exp x) (/ 1 (exp x))) 2)
(- (+ (exp x) (/ 1 (exp x))) 2)
(- (+ (exp x) (/ 1 (exp x))) 2)
(- (+ (exp x) (/ 1 (exp x))) 2)
(- (+ (exp x) (/ 1 (exp x))) 2)
(- (+ (exp x) (/ 1 (exp x))) 2)
2
(+ 2 (pow x 2))
(+ 2 (* (pow x 2) (+ 1 (* 1/12 (pow x 2)))))
(+ 2 (* (pow x 2) (+ 1 (* (pow x 2) (+ 1/12 (* 1/360 (pow x 2)))))))
(+ (exp x) (/ 1 (exp x)))
(+ (exp x) (/ 1 (exp x)))
(+ (exp x) (/ 1 (exp x)))
(+ (exp x) (/ 1 (exp x)))
(+ (exp x) (/ 1 (exp x)))
(+ (exp x) (/ 1 (exp x)))
(+ (exp x) (/ 1 (exp x)))
(+ (exp x) (/ 1 (exp x)))
1
(+ 1 (* 1/2 (pow x 2)))
(+ 1 (* (pow x 2) (+ 1/2 (* 1/24 (pow x 2)))))
(+ 1 (* (pow x 2) (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/720 (pow x 2)))))))
(* 1/2 (+ (exp x) (/ 1 (exp x))))
(* 1/2 (+ (exp x) (/ 1 (exp x))))
(* 1/2 (+ (exp x) (/ 1 (exp x))))
(* 1/2 (+ (exp x) (/ 1 (exp x))))
(* 1/2 (+ (exp x) (/ 1 (exp x))))
(* 1/2 (+ (exp x) (/ 1 (exp x))))
(* 1/2 (+ (exp x) (/ 1 (exp x))))
(* 1/2 (+ (exp x) (/ 1 (exp x))))
(* 1/360 (pow x 2))
(* (pow x 2) (+ 1/360 (* 1/20160 (pow x 2))))
(* (pow x 2) (+ 1/360 (* 1/20160 (pow x 2))))
(* (pow x 2) (+ 1/360 (* 1/20160 (pow x 2))))
(* 1/20160 (pow x 4))
(* (pow x 4) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))
(* 1/20160 (pow x 4))
(* (pow x 4) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))
(* 1/20160 (pow x 2))
(* 1/20160 (pow x 2))
(* 1/20160 (pow x 2))
(* 1/20160 (pow x 2))
(* 1/20160 (pow x 2))
(* 1/20160 (pow x 2))
(* 1/20160 (pow x 2))
(* 1/20160 (pow x 2))
(* 1/20160 (pow x 2))
(* 1/20160 (pow x 2))
(* 1/20160 (pow x 2))
(* 1/20160 (pow x 2))
(* 1/360 (pow x 2))
(* 1/360 (pow x 2))
(* 1/360 (pow x 2))
(* 1/360 (pow x 2))
(* 1/360 (pow x 2))
(* 1/360 (pow x 2))
(* 1/360 (pow x 2))
(* 1/360 (pow x 2))
(* 1/360 (pow x 2))
(* 1/360 (pow x 2))
(* 1/360 (pow x 2))
(* 1/360 (pow x 2))
(* 1/20160 (pow x 3))
(* 1/20160 (pow x 3))
(* 1/20160 (pow x 3))
(* 1/20160 (pow x 3))
(* 1/20160 (pow x 3))
(* 1/20160 (pow x 3))
(* 1/20160 (pow x 3))
(* 1/20160 (pow x 3))
(* 1/20160 (pow x 3))
(* 1/20160 (pow x 3))
(* 1/20160 (pow x 3))
(* 1/20160 (pow x 3))
(* 1/20160 (pow x 4))
(* 1/20160 (pow x 4))
(* 1/20160 (pow x 4))
(* 1/20160 (pow x 4))
(* 1/20160 (pow x 4))
(* 1/20160 (pow x 4))
(* 1/20160 (pow x 4))
(* 1/20160 (pow x 4))
(* 1/20160 (pow x 4))
(* 1/20160 (pow x 4))
(* 1/20160 (pow x 4))
(* 1/20160 (pow x 4))

Outputs
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 1/12 (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/12 binary64)))))
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(* (pow x 8) (+ 1/20160 (+ (* 1/12 (/ 1 (pow x 4))) (/ 1 (pow x 6)))))
(.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (+.f64 #s(literal 1/20160 binary64) (/.f64 (/.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x x))) x))))
(* (pow x 8) (+ 1/20160 (+ (* 1/12 (/ 1 (pow x 4))) (/ 1 (pow x 6)))))
(.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (+.f64 #s(literal 1/20160 binary64) (/.f64 (/.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x x))) x))))
(* 1/20160 (pow x 8))
(*.f64 #s(literal 1/20160 binary64) (pow.f64 x #s(literal 8 binary64)))
(* (pow x 8) (+ 1/20160 (* 1/12 (/ 1 (pow x 4)))))
(.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 #s(literal 1/20160 binary64) (/.f64 (/.f64 #s(literal 1/12 binary64) (.f64 x (*.f64 x x))) x)))
(* (pow x 8) (+ 1/20160 (+ (* 1/12 (/ 1 (pow x 4))) (/ 1 (pow x 6)))))
(.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (+.f64 #s(literal 1/20160 binary64) (/.f64 (/.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x x))) x))))
(* (pow x 8) (+ 1/20160 (+ (* 1/12 (/ 1 (pow x 4))) (/ 1 (pow x 6)))))
(.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (+.f64 #s(literal 1/20160 binary64) (/.f64 (/.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x x))) x))))
1
#s(literal 1 binary64)
(+ 1 (* 1/12 (pow x 2)))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/12 binary64))))
(+ 1 (* (pow x 2) (+ 1/12 (* 1/20160 (pow x 4)))))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64)))))))
(+ 1 (* (pow x 2) (+ 1/12 (* 1/20160 (pow x 4)))))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64)))))))
(* 1/20160 (pow x 6))
(.f64 (.f64 x x) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64)))))
(* (pow x 6) (+ 1/20160 (* 1/12 (/ 1 (pow x 4)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64))))))
(* (pow x 6) (+ 1/20160 (+ (* 1/12 (/ 1 (pow x 4))) (/ 1 (pow x 6)))))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64)))))))
(* (pow x 6) (+ 1/20160 (+ (* 1/12 (/ 1 (pow x 4))) (/ 1 (pow x 6)))))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64)))))))
(* 1/20160 (pow x 6))
(.f64 (.f64 x x) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64)))))
(* (pow x 6) (+ 1/20160 (* 1/12 (/ 1 (pow x 4)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64))))))
(* (pow x 6) (+ 1/20160 (+ (* 1/12 (/ 1 (pow x 4))) (/ 1 (pow x 6)))))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64)))))))
(* (pow x 6) (+ 1/20160 (+ (* 1/12 (/ 1 (pow x 4))) (/ 1 (pow x 6)))))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64)))))))
(* 1/12 (pow x 2))
(.f64 x (.f64 x #s(literal 1/12 binary64)))
(* (pow x 2) (+ 1/12 (* 1/20160 (pow x 4))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64))))))
(* (pow x 2) (+ 1/12 (* 1/20160 (pow x 4))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64))))))
(* (pow x 2) (+ 1/12 (* 1/20160 (pow x 4))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64))))))
(* 1/20160 (pow x 6))
(.f64 (.f64 x x) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64)))))
(* (pow x 6) (+ 1/20160 (* 1/12 (/ 1 (pow x 4)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64))))))
(* (pow x 6) (+ 1/20160 (* 1/12 (/ 1 (pow x 4)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64))))))
(* (pow x 6) (+ 1/20160 (* 1/12 (/ 1 (pow x 4)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64))))))
(* 1/20160 (pow x 6))
(.f64 (.f64 x x) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64)))))
(* (pow x 6) (+ 1/20160 (* 1/12 (/ 1 (pow x 4)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64))))))
(* (pow x 6) (+ 1/20160 (* 1/12 (/ 1 (pow x 4)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64))))))
(* (pow x 6) (+ 1/20160 (* 1/12 (/ 1 (pow x 4)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64))))))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 1/12 (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/12 binary64)))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 1/12 (* 1/360 (pow x 2))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64))))))
(* (pow x 2) (+ 1 (* (pow x 2) (+ 1/12 (* (pow x 2) (+ 1/360 (* 1/20160 (pow x 2))))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64)))))))))
(- (+ (exp x) (/ 1 (exp x))) 2)
(+.f64 (exp.f64 x) (+.f64 (/.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -2 binary64)))
(- (+ (exp x) (/ 1 (exp x))) 2)
(+.f64 (exp.f64 x) (+.f64 (/.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -2 binary64)))
(- (+ (exp x) (/ 1 (exp x))) 2)
(+.f64 (exp.f64 x) (+.f64 (/.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -2 binary64)))
(- (+ (exp x) (/ 1 (exp x))) 2)
(+.f64 (exp.f64 x) (+.f64 (/.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -2 binary64)))
(- (+ (exp x) (/ 1 (exp x))) 2)
(+.f64 (exp.f64 x) (+.f64 (/.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -2 binary64)))
(- (+ (exp x) (/ 1 (exp x))) 2)
(+.f64 (exp.f64 x) (+.f64 (/.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -2 binary64)))
(- (+ (exp x) (/ 1 (exp x))) 2)
(+.f64 (exp.f64 x) (+.f64 (/.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -2 binary64)))
(- (+ (exp x) (/ 1 (exp x))) 2)
(+.f64 (exp.f64 x) (+.f64 (/.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -2 binary64)))
2
#s(literal 2 binary64)
(+ 2 (pow x 2))
(+.f64 #s(literal 2 binary64) (*.f64 x x))
(+ 2 (* (pow x 2) (+ 1 (* 1/12 (pow x 2)))))
(+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/12 binary64))))))
(+ 2 (* (pow x 2) (+ 1 (* (pow x 2) (+ 1/12 (* 1/360 (pow x 2)))))))
(+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64)))))))
(+ (exp x) (/ 1 (exp x)))
(+.f64 (exp.f64 x) (/.f64 #s(literal 1 binary64) (exp.f64 x)))
(+ (exp x) (/ 1 (exp x)))
(+.f64 (exp.f64 x) (/.f64 #s(literal 1 binary64) (exp.f64 x)))
(+ (exp x) (/ 1 (exp x)))
(+.f64 (exp.f64 x) (/.f64 #s(literal 1 binary64) (exp.f64 x)))
(+ (exp x) (/ 1 (exp x)))
(+.f64 (exp.f64 x) (/.f64 #s(literal 1 binary64) (exp.f64 x)))
(+ (exp x) (/ 1 (exp x)))
(+.f64 (exp.f64 x) (/.f64 #s(literal 1 binary64) (exp.f64 x)))
(+ (exp x) (/ 1 (exp x)))
(+.f64 (exp.f64 x) (/.f64 #s(literal 1 binary64) (exp.f64 x)))
(+ (exp x) (/ 1 (exp x)))
(+.f64 (exp.f64 x) (/.f64 #s(literal 1 binary64) (exp.f64 x)))
(+ (exp x) (/ 1 (exp x)))
(+.f64 (exp.f64 x) (/.f64 #s(literal 1 binary64) (exp.f64 x)))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 (pow x 2)))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/2 binary64))))
(+ 1 (* (pow x 2) (+ 1/2 (* 1/24 (pow x 2)))))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64)))))
(+ 1 (* (pow x 2) (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/720 (pow x 2)))))))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal 1/720 binary64))))))))
(* 1/2 (+ (exp x) (/ 1 (exp x))))
(+.f64 (*.f64 (exp.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/2 binary64) (exp.f64 x)))
(* 1/2 (+ (exp x) (/ 1 (exp x))))
(+.f64 (*.f64 (exp.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/2 binary64) (exp.f64 x)))
(* 1/2 (+ (exp x) (/ 1 (exp x))))
(+.f64 (*.f64 (exp.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/2 binary64) (exp.f64 x)))
(* 1/2 (+ (exp x) (/ 1 (exp x))))
(+.f64 (*.f64 (exp.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/2 binary64) (exp.f64 x)))
(* 1/2 (+ (exp x) (/ 1 (exp x))))
(+.f64 (*.f64 (exp.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/2 binary64) (exp.f64 x)))
(* 1/2 (+ (exp x) (/ 1 (exp x))))
(+.f64 (*.f64 (exp.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/2 binary64) (exp.f64 x)))
(* 1/2 (+ (exp x) (/ 1 (exp x))))
(+.f64 (*.f64 (exp.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/2 binary64) (exp.f64 x)))
(* 1/2 (+ (exp x) (/ 1 (exp x))))
(+.f64 (*.f64 (exp.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/2 binary64) (exp.f64 x)))
(* 1/360 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/360 binary64))
(* (pow x 2) (+ 1/360 (* 1/20160 (pow x 2))))
(.f64 x (.f64 x (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64)))))
(* (pow x 2) (+ 1/360 (* 1/20160 (pow x 2))))
(.f64 x (.f64 x (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64)))))
(* (pow x 2) (+ 1/360 (* 1/20160 (pow x 2))))
(.f64 x (.f64 x (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64)))))
(* 1/20160 (pow x 4))
(.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64))))
(* (pow x 4) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64)))))
(* (pow x 4) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64)))))
(* (pow x 4) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64)))))
(* 1/20160 (pow x 4))
(.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64))))
(* (pow x 4) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64)))))
(* (pow x 4) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64)))))
(* (pow x 4) (+ 1/20160 (* 1/360 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64)))))
(* 1/20160 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/20160 binary64))
(* 1/20160 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/20160 binary64))
(* 1/20160 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/20160 binary64))
(* 1/20160 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/20160 binary64))
(* 1/20160 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/20160 binary64))
(* 1/20160 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/20160 binary64))
(* 1/20160 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/20160 binary64))
(* 1/20160 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/20160 binary64))
(* 1/20160 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/20160 binary64))
(* 1/20160 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/20160 binary64))
(* 1/20160 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/20160 binary64))
(* 1/20160 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/20160 binary64))
(* 1/360 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/360 binary64))
(* 1/360 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/360 binary64))
(* 1/360 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/360 binary64))
(* 1/360 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/360 binary64))
(* 1/360 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/360 binary64))
(* 1/360 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/360 binary64))
(* 1/360 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/360 binary64))
(* 1/360 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/360 binary64))
(* 1/360 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/360 binary64))
(* 1/360 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/360 binary64))
(* 1/360 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/360 binary64))
(* 1/360 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/360 binary64))
(* 1/20160 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal 1/20160 binary64)))
(* 1/20160 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal 1/20160 binary64)))
(* 1/20160 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal 1/20160 binary64)))
(* 1/20160 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal 1/20160 binary64)))
(* 1/20160 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal 1/20160 binary64)))
(* 1/20160 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal 1/20160 binary64)))
(* 1/20160 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal 1/20160 binary64)))
(* 1/20160 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal 1/20160 binary64)))
(* 1/20160 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal 1/20160 binary64)))
(* 1/20160 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal 1/20160 binary64)))
(* 1/20160 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal 1/20160 binary64)))
(* 1/20160 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal 1/20160 binary64)))
(* 1/20160 (pow x 4))
(.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64))))
(* 1/20160 (pow x 4))
(.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64))))
(* 1/20160 (pow x 4))
(.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64))))
(* 1/20160 (pow x 4))
(.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64))))
(* 1/20160 (pow x 4))
(.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64))))
(* 1/20160 (pow x 4))
(.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64))))
(* 1/20160 (pow x 4))
(.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64))))
(* 1/20160 (pow x 4))
(.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64))))
(* 1/20160 (pow x 4))
(.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64))))
(* 1/20160 (pow x 4))
(.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64))))
(* 1/20160 (pow x 4))
(.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64))))
(* 1/20160 (pow x 4))
(.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64))))

eval419.0ms (3.9%)

Compiler: Compiled 21192 to 2233 computations (89.5% saved)

prune100.0ms (0.9%)

Pruning

20 alts after pruning (9 fresh and 11 done)

	Pruned	Kept	Total
New	1132	7	1139
Fresh	2	2	4
Picked	1	4	5
Done	1	7	8
Total	1136	20	1156

Accuracy

100.0%

Counts

1156 → 20

Alt Table

Click to see full alt table

Status	Accuracy	Program
	50.8%	(-.f64 (/.f64 (-.f64 (exp.f64 (+.f64 x x)) #s(literal -1 binary64)) (exp.f64 x)) #s(literal 2 binary64))
	50.2%	(-.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/12 binary64)))))) #s(literal 2 binary64))
	50.1%	(-.f64 (+.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal 2 binary64))
✓	50.9%	(-.f64 (*.f64 #s(literal 2 binary64) (cosh.f64 x)) #s(literal 2 binary64))
	49.8%	(+.f64 (pow.f64 (E.f64) x) #s(literal -1 binary64))
✓	99.4%	(+.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x x)))))))) (.f64 x (.f64 (.f64 x x) (.f64 #s(literal 1/360 binary64) (.f64 x (.f64 x x))))))
✓	99.3%	(+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/12 binary64))) (*.f64 x x))
✓	99.4%	(+.f64 (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64)))))) (*.f64 x x))
	98.8%	(.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64))))))) (.f64 x x))
✓	99.4%	(.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64)))))))) (.f64 x x))
	49.5%	(.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64))))) (.f64 x x))
	99.4%	(.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64)))))) x)
✓	99.3%	(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal 1/12 binary64))))
✓	50.0%	(.f64 (.f64 x x) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64)))))
	50.0%	(.f64 (.f64 x x) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64)))))))
	49.6%	(.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/360 binary64))))
✓	50.0%	(.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 1/12 binary64))))
✓	98.8%	(*.f64 x x)
✓	7.2%	(expm1.f64 x)
✓	7.0%	x

Compiler

Compiled 676 to 263 computations (61.1% saved)

regimes17.0ms (0.2%)

Counts

29 → 1

Calls

Call 1

Inputs
x
(*.f64 x x)
(-.f64 (+.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal 2 binary64))
(.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 1/12 binary64))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal 1/12 binary64))))
(.f64 (.f64 x x) (.f64 x (.f64 #s(literal 1/360 binary64) (.f64 x (.f64 x x)))))
(.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/360 binary64))))
(+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/12 binary64))) (*.f64 x x))
(.f64 (.f64 x x) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64)))))
(-.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/12 binary64)))))) #s(literal 2 binary64))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64))))))
(.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64)))))) x)
(.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64))))) (.f64 x x))
(.f64 (.f64 x x) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64)))))))
(+.f64 (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64)))))) (*.f64 x x))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64))))))))
(.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64))))))) (.f64 x x))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64)))))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64))) (.f64 x x))))))
(.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64)))))))) (.f64 x x))
(+.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x x)))))))) (.f64 x (.f64 (.f64 x x) (.f64 #s(literal 1/360 binary64) (.f64 x (.f64 x x))))))
(expm1.f64 x)
(+.f64 (exp.f64 x) #s(literal -1 binary64))
(+.f64 (pow.f64 (E.f64) x) #s(literal -1 binary64))
(-.f64 (*.f64 #s(literal 2 binary64) (cosh.f64 x)) #s(literal 2 binary64))
(+.f64 (-.f64 (exp.f64 x) #s(literal 2 binary64)) (exp.f64 (neg.f64 x)))
(+.f64 (exp.f64 x) (+.f64 (/.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -2 binary64)))
(-.f64 (/.f64 (-.f64 (exp.f64 (+.f64 x x)) #s(literal -1 binary64)) (exp.f64 x)) #s(literal 2 binary64))
(+.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (E.f64)) (-.f64 #s(literal 0 binary64) x)) #s(literal 2 binary64)) (exp.f64 (neg.f64 x)))

Outputs

(+.f64 (*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/12 binary64) (*.f64 x (*.f64 #s(literal 1/20160 binary64) (*.f64 x (*.f64 x x)))))))) (*.f64 x (*.f64 (*.f64 x x) (*.f64 #s(literal 1/360 binary64) (*.f64 x (*.f64 x x))))))

Calls

2 calls:

9.0ms	x
6.0ms	(+.f64 (-.f64 (exp.f64 x) #s(literal 2 binary64)) (exp.f64 (neg.f64 x)))

Results

Accuracy	Segments	Branch
99.4%	1	`x`
99.4%	1	`(+.f64 (-.f64 (exp.f64 x) #s(literal 2 binary64)) (exp.f64 (neg.f64 x)))`

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes7.0ms (0.1%)

Counts

20 → 1

Calls

Call 1

Inputs
x
(*.f64 x x)
(-.f64 (+.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal 2 binary64))
(.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 1/12 binary64))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal 1/12 binary64))))
(.f64 (.f64 x x) (.f64 x (.f64 #s(literal 1/360 binary64) (.f64 x (.f64 x x)))))
(.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/360 binary64))))
(+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/12 binary64))) (*.f64 x x))
(.f64 (.f64 x x) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64)))))
(-.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/12 binary64)))))) #s(literal 2 binary64))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64))))))
(.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64)))))) x)
(.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64))))) (.f64 x x))
(.f64 (.f64 x x) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64)))))))
(+.f64 (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64)))))) (*.f64 x x))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64))))))))
(.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64))))))) (.f64 x x))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64)))))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64))) (.f64 x x))))))
(.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64)))))))) (.f64 x x))

Outputs

(*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/12 binary64) (*.f64 (+.f64 #s(literal 1/360 binary64) (*.f64 (*.f64 x x) #s(literal 1/20160 binary64))) (*.f64 x x))))))

Calls

1 calls:

6.0ms

Results

Accuracy	Segments	Branch
99.4%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes6.0ms (0.1%)

Counts

18 → 1

Calls

Call 1

Inputs
x
(*.f64 x x)
(-.f64 (+.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal 2 binary64))
(.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 1/12 binary64))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal 1/12 binary64))))
(.f64 (.f64 x x) (.f64 x (.f64 #s(literal 1/360 binary64) (.f64 x (.f64 x x)))))
(.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/360 binary64))))
(+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/12 binary64))) (*.f64 x x))
(.f64 (.f64 x x) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64)))))
(-.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/12 binary64)))))) #s(literal 2 binary64))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64))))))
(.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64)))))) x)
(.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64))))) (.f64 x x))
(.f64 (.f64 x x) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64)))))))
(+.f64 (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64)))))) (*.f64 x x))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64))))))))
(.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64))))))) (.f64 x x))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64)))))))))

Outputs

(*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/12 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/360 binary64) (*.f64 (*.f64 x x) #s(literal 1/20160 binary64)))))))))

Calls

1 calls:

5.0ms

Results

Accuracy	Segments	Branch
99.4%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes45.0ms (0.4%)

Counts

17 → 1

Calls

Call 1

Inputs
x
(*.f64 x x)
(-.f64 (+.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal 2 binary64))
(.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 1/12 binary64))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal 1/12 binary64))))
(.f64 (.f64 x x) (.f64 x (.f64 #s(literal 1/360 binary64) (.f64 x (.f64 x x)))))
(.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/360 binary64))))
(+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/12 binary64))) (*.f64 x x))
(.f64 (.f64 x x) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64)))))
(-.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/12 binary64)))))) #s(literal 2 binary64))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64))))))
(.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64)))))) x)
(.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64))))) (.f64 x x))
(.f64 (.f64 x x) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64)))))))
(+.f64 (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64)))))) (*.f64 x x))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/20160 binary64))))))))
(.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64))))))) (.f64 x x))

Outputs
(.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64)))))) x)

Calls

1 calls:

44.0ms

Results

Accuracy	Segments	Branch
99.4%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes4.0ms (0%)

Counts

11 → 1

Calls

Call 1

Inputs
x
(*.f64 x x)
(-.f64 (+.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal 2 binary64))
(.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 1/12 binary64))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal 1/12 binary64))))
(.f64 (.f64 x x) (.f64 x (.f64 #s(literal 1/360 binary64) (.f64 x (.f64 x x)))))
(.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/360 binary64))))
(+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/12 binary64))) (*.f64 x x))
(.f64 (.f64 x x) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64)))))
(-.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/12 binary64)))))) #s(literal 2 binary64))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64))))))

Outputs
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64))))))

Calls

1 calls:

4.0ms

Results

Accuracy	Segments	Branch
99.4%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes4.0ms (0%)

Counts

10 → 1

Calls

Call 1

Inputs
x
(*.f64 x x)
(-.f64 (+.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal 2 binary64))
(.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 1/12 binary64))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal 1/12 binary64))))
(.f64 (.f64 x x) (.f64 x (.f64 #s(literal 1/360 binary64) (.f64 x (.f64 x x)))))
(.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/360 binary64))))
(+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/12 binary64))) (*.f64 x x))
(.f64 (.f64 x x) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64)))))
(-.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/12 binary64)))))) #s(literal 2 binary64))

Outputs
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal 1/12 binary64))))

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
99.3%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0%)

Counts

4 → 1

Calls

Call 1

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

Outputs
(*.f64 x x)

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
98.8%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes1.0ms (0%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
x

Outputs
x

Calls

1 calls:

1.0ms

Results

Accuracy	Segments	Branch
7.0%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

simplify31.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	130
1	77	130

Stop Event

1×

saturated

Calls

Call 1

Inputs
(+.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x x)))))))) (.f64 x (.f64 (.f64 x x) (.f64 #s(literal 1/360 binary64) (.f64 x (.f64 x x))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64))) (.f64 x x))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64)))))))))
(.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64)))))) x)
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal 1/12 binary64))))
(*.f64 x x)
x

Outputs
(+.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x x)))))))) (.f64 x (.f64 (.f64 x x) (.f64 #s(literal 1/360 binary64) (.f64 x (.f64 x x))))))
(+.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 #s(literal 1/20160 binary64) (.f64 x (.f64 x x)))))))) (.f64 x (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) #s(literal 1/360 binary64)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64))) (.f64 x x))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64))))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/360 binary64) (.f64 (.f64 x x) #s(literal 1/20160 binary64)))))))))
(.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64)))))) x)
(.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64)))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/12 binary64) (.f64 (.f64 x x) #s(literal 1/360 binary64))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal 1/12 binary64))))
(*.f64 x x)
x

soundness1.2s (11.3%)

Rules

2910×	`sum3-define`
2812×	`-lowering-.f32`
2812×	`-lowering-.f64`
2450×	`+-lowering-+.f64`
2450×	`+-lowering-+.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	25	135
1	93	118
2	319	115
3	964	115
4	2268	115
5	3274	115
6	4965	115
7	6569	115
8	7322	115
0	8003	115
0	7	8
1	19	7
2	37	7
3	62	7
4	116	7
5	214	7
6	498	7
7	950	7
8	1161	7
9	1232	7
10	1246	7
0	1246	7
0	92	1542
1	316	1229
2	933	1207
3	2733	1207
4	5962	1207
5	7926	1207
0	8136	1207
0	67	495
1	193	430
2	534	423
3	1516	423
4	2671	423
5	6037	423
6	7680	423
0	8142	423

Stop Event

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

Compiler

Compiled 384 to 196 computations (49% saved)

preprocess51.0ms (0.5%)

Remove: (abs x)
Compiler: Compiled 592 to 244 computations (58.8% saved)

analyze0.0ms (0%)

sample4.0s (36.7%)

preprocess65.0ms (0.6%)

explain327.0ms (3%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify39.0ms (0.4%)

localize234.0ms (2.2%)

series3.0ms (0%)

rewrite226.0ms (2.1%)

simplify188.0ms (1.7%)

eval41.0ms (0.4%)

prune52.0ms (0.5%)

simplify432.0ms (4%)

localize296.0ms (2.7%)

series9.0ms (0.1%)

rewrite192.0ms (1.8%)

simplify209.0ms (1.9%)

eval102.0ms (0.9%)

prune64.0ms (0.6%)

simplify134.0ms (1.2%)

localize563.0ms (5.2%)

series8.0ms (0.1%)

rewrite263.0ms (2.4%)

simplify198.0ms (1.8%)

eval166.0ms (1.5%)

prune94.0ms (0.9%)

simplify195.0ms (1.8%)

localize394.0ms (3.6%)

series7.0ms (0.1%)

rewrite245.0ms (2.3%)

simplify210.0ms (1.9%)

eval419.0ms (3.9%)

prune100.0ms (0.9%)

regimes17.0ms (0.2%)

regimes7.0ms (0.1%)

regimes6.0ms (0.1%)

regimes45.0ms (0.4%)

regimes4.0ms (0%)

regimes4.0ms (0%)

regimes2.0ms (0%)

regimes1.0ms (0%)

simplify31.0ms (0.3%)

soundness1.2s (11.3%)

preprocess51.0ms (0.5%)

end0.0ms (0%)

Profiling