Metrics for Kahan's exp quotient

analyze1.0ms (0.1%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
50%	50%	50%	0%	0%	0%	0%	2
75%	75%	25%	0%	0%	0%	0%	3
87.5%	87.5%	12.5%	0%	0%	0%	0%	4
93.8%	93.7%	6.2%	0%	0%	0%	0%	5
96.9%	96.8%	3.1%	0%	0%	0%	0%	6
98.4%	98.4%	1.6%	0%	0%	0%	0%	7
99.2%	99.2%	0.8%	0%	0%	0%	0%	8
99.6%	99.6%	0.4%	0%	0%	0%	0%	9
99.8%	99.8%	0.2%	0%	0%	0%	0%	10
99.9%	99.9%	0.1%	0%	0%	0%	0%	11
100%	99.9%	0%	0%	0%	0%	0%	12

Compiler

Compiled 8 to 6 computations (25% saved)

sample1.2s (60.3%)

Results

452.0ms	1968×	body	1024	valid
273.0ms	2870×	body	256	valid
202.0ms	1138×	body	512	valid
178.0ms	2068×	body	256	infinite
49.0ms	212×	body	2048	valid

Bogosity

preprocess104.0ms (5.4%)

Algorithm

1×	egg-herbie

Rules

1290×	`div-sub`
1216×	`fma-neg`
1162×	`fma-def`
906×	`cancel-sign-sub-inv`
870×	`associate-/r*`

Problems

129×	`(-.f64 (exp.f64 x) 1)`
127×	No Errors

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	41
1	29	41
2	47	41
3	79	41
4	185	41
5	543	41
6	1635	41
7	5797	41

Stop Event

1×	node limit

Calls

Call 1

Inputs
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 (neg.f64 x)) 1) (neg.f64 x))

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

Compiler

Compiled 23 to 14 computations (39.1% saved)

eval0.0ms (0%)

Compiler: Compiled 5 to 3 computations (40% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(/.f64 (expm1.f64 x) x)
▶	100.0%	(/.f64 (expm1.f64 x) x)

Compiler

Compiled 10 to 6 computations (40% saved)

localize19.0ms (1%)

Localize:

Found 1 expressions with local error:

New	Accuracy	Program
✓	100.0%	(/.f64 (expm1.f64 x) x)

Compiler

Compiled 9 to 4 computations (55.6% saved)

series2.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(/.f64 (expm1.f64 x) x)
0.0ms	x	@	inf	(/.f64 (expm1.f64 x) x)
0.0ms	x	@	0	(/.f64 (expm1.f64 x) x)

rewrite59.0ms (3.1%)

Algorithm

1×	batch-egg-rewrite

Rules

1246×	`pow1`
1146×	`add-exp-log`
1146×	`log1p-expm1-u`
1144×	`expm1-log1p-u`
1120×	`add-log-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	11
1	120	11
2	1537	11

Stop Event

1×	node limit

Counts

1 → 31

Calls

Call 1

Inputs
(/.f64 (expm1.f64 x) x)

Outputs
(-.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 1)
(-.f64 (/.f64 (exp.f64 x) x) (/.f64 1 x))
(*.f64 (expm1.f64 x) (/.f64 1 x))
(*.f64 (/.f64 (expm1.f64 x) x) 1)
(*.f64 1 (/.f64 (expm1.f64 x) x))
(*.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 2))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 2) (cbrt.f64 (/.f64 (expm1.f64 x) x)))
(.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (.f64 (cbrt.f64 (expm1.f64 x)) (/.f64 1 x)))
(*.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) (sqrt.f64 (/.f64 (expm1.f64 x) x)))
(.f64 (sqrt.f64 (expm1.f64 x)) (.f64 (sqrt.f64 (expm1.f64 x)) (/.f64 1 x)))
(*.f64 (neg.f64 (expm1.f64 x)) (/.f64 1 (neg.f64 x)))
(*.f64 (/.f64 1 x) (expm1.f64 x))
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 x) 2)) (/.f64 (expm1.f64 x) (cbrt.f64 x)))
(*.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (expm1.f64 x) (sqrt.f64 x)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) 1) (/.f64 (cbrt.f64 (expm1.f64 x)) x))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 (/.f64 (expm1.f64 x) x)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (sqrt.f64 x)) (/.f64 (cbrt.f64 (expm1.f64 x)) (sqrt.f64 x)))
(*.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) 1) (/.f64 (sqrt.f64 (expm1.f64 x)) x))
(*.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (sqrt.f64 (expm1.f64 x)) (cbrt.f64 x)))
(pow.f64 (/.f64 (expm1.f64 x) x) 1)
(pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 3)
(pow.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 3) 1/3)
(pow.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) 2)
(pow.f64 (/.f64 x (expm1.f64 x)) -1)
(neg.f64 (/.f64 (expm1.f64 x) (neg.f64 x)))
(sqrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 2))
(log.f64 (exp.f64 (/.f64 (expm1.f64 x) x)))
(cbrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 3))
(expm1.f64 (log1p.f64 (/.f64 (expm1.f64 x) x)))
(exp.f64 (log.f64 (/.f64 (expm1.f64 x) x)))
(log1p.f64 (expm1.f64 (/.f64 (expm1.f64 x) x)))

simplify59.0ms (3%)

Algorithm

1×	egg-herbie

Rules

1756×	`fma-def`
772×	`log-prod`
580×	`div-sub`
574×	`log-div`
402×	`associate-*r/`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	96	551
1	227	547
2	789	539
3	4125	527

Stop Event

1×	node limit

Counts

43 → 47

Calls

Call 1

Inputs
1
(+.f64 1 (*.f64 1/2 x))
(+.f64 1 (+.f64 (.f64 1/6 (pow.f64 x 2)) (.f64 1/2 x)))
(+.f64 1 (+.f64 (.f64 1/24 (pow.f64 x 3)) (+.f64 (.f64 1/6 (pow.f64 x 2)) (*.f64 1/2 x))))
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(-.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 1)
(-.f64 (/.f64 (exp.f64 x) x) (/.f64 1 x))
(*.f64 (expm1.f64 x) (/.f64 1 x))
(*.f64 (/.f64 (expm1.f64 x) x) 1)
(*.f64 1 (/.f64 (expm1.f64 x) x))
(*.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 2))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 2) (cbrt.f64 (/.f64 (expm1.f64 x) x)))
(.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (.f64 (cbrt.f64 (expm1.f64 x)) (/.f64 1 x)))
(*.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) (sqrt.f64 (/.f64 (expm1.f64 x) x)))
(.f64 (sqrt.f64 (expm1.f64 x)) (.f64 (sqrt.f64 (expm1.f64 x)) (/.f64 1 x)))
(*.f64 (neg.f64 (expm1.f64 x)) (/.f64 1 (neg.f64 x)))
(*.f64 (/.f64 1 x) (expm1.f64 x))
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 x) 2)) (/.f64 (expm1.f64 x) (cbrt.f64 x)))
(*.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (expm1.f64 x) (sqrt.f64 x)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) 1) (/.f64 (cbrt.f64 (expm1.f64 x)) x))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 (/.f64 (expm1.f64 x) x)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (sqrt.f64 x)) (/.f64 (cbrt.f64 (expm1.f64 x)) (sqrt.f64 x)))
(*.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) 1) (/.f64 (sqrt.f64 (expm1.f64 x)) x))
(*.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (sqrt.f64 (expm1.f64 x)) (cbrt.f64 x)))
(pow.f64 (/.f64 (expm1.f64 x) x) 1)
(pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 3)
(pow.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 3) 1/3)
(pow.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) 2)
(pow.f64 (/.f64 x (expm1.f64 x)) -1)
(neg.f64 (/.f64 (expm1.f64 x) (neg.f64 x)))
(sqrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 2))
(log.f64 (exp.f64 (/.f64 (expm1.f64 x) x)))
(cbrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 3))
(expm1.f64 (log1p.f64 (/.f64 (expm1.f64 x) x)))
(exp.f64 (log.f64 (/.f64 (expm1.f64 x) x)))
(log1p.f64 (expm1.f64 (/.f64 (expm1.f64 x) x)))

Outputs
1
(+.f64 1 (*.f64 1/2 x))
(fma.f64 1/2 x 1)
(+.f64 1 (+.f64 (.f64 1/6 (pow.f64 x 2)) (.f64 1/2 x)))
(+.f64 1 (fma.f64 1/6 (.f64 x x) (.f64 1/2 x)))
(+.f64 1 (fma.f64 1/2 x (.f64 x (.f64 x 1/6))))
(fma.f64 1/2 x (fma.f64 x (*.f64 x 1/6) 1))
(fma.f64 x (fma.f64 x 1/6 1/2) 1)
(+.f64 1 (+.f64 (.f64 1/24 (pow.f64 x 3)) (+.f64 (.f64 1/6 (pow.f64 x 2)) (*.f64 1/2 x))))
(+.f64 1 (fma.f64 1/24 (pow.f64 x 3) (fma.f64 1/6 (.f64 x x) (.f64 1/2 x))))
(+.f64 1 (fma.f64 1/24 (pow.f64 x 3) (fma.f64 1/2 x (.f64 x (.f64 x 1/6)))))
(fma.f64 1/24 (pow.f64 x 3) (fma.f64 1/2 x (fma.f64 x (*.f64 x 1/6) 1)))
(fma.f64 1/2 x (fma.f64 (*.f64 x x) (fma.f64 x 1/24 1/6) 1))
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(-.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 1)
(/.f64 (expm1.f64 x) x)
(-.f64 (/.f64 (exp.f64 x) x) (/.f64 1 x))
(/.f64 (expm1.f64 x) x)
(*.f64 (expm1.f64 x) (/.f64 1 x))
(/.f64 (expm1.f64 x) x)
(*.f64 (/.f64 (expm1.f64 x) x) 1)
(/.f64 (expm1.f64 x) x)
(*.f64 1 (/.f64 (expm1.f64 x) x))
(/.f64 (expm1.f64 x) x)
(*.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 2))
(/.f64 (expm1.f64 x) x)
(*.f64 (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 2) (cbrt.f64 (/.f64 (expm1.f64 x) x)))
(/.f64 (expm1.f64 x) x)
(.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (.f64 (cbrt.f64 (expm1.f64 x)) (/.f64 1 x)))
(/.f64 (expm1.f64 x) x)
(*.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) (sqrt.f64 (/.f64 (expm1.f64 x) x)))
(/.f64 (expm1.f64 x) x)
(.f64 (sqrt.f64 (expm1.f64 x)) (.f64 (sqrt.f64 (expm1.f64 x)) (/.f64 1 x)))
(/.f64 (expm1.f64 x) x)
(*.f64 (neg.f64 (expm1.f64 x)) (/.f64 1 (neg.f64 x)))
(/.f64 (expm1.f64 x) x)
(*.f64 (/.f64 1 x) (expm1.f64 x))
(/.f64 (expm1.f64 x) x)
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 x) 2)) (/.f64 (expm1.f64 x) (cbrt.f64 x)))
(/.f64 (expm1.f64 x) x)
(*.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (expm1.f64 x) (sqrt.f64 x)))
(/.f64 (expm1.f64 x) x)
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) 1) (/.f64 (cbrt.f64 (expm1.f64 x)) x))
(/.f64 (expm1.f64 x) x)
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 (/.f64 (expm1.f64 x) x)))
(*.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (pow.f64 (cbrt.f64 x) 2)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (sqrt.f64 x)) (/.f64 (cbrt.f64 (expm1.f64 x)) (sqrt.f64 x)))
(/.f64 (expm1.f64 x) x)
(*.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) 1) (/.f64 (sqrt.f64 (expm1.f64 x)) x))
(/.f64 (expm1.f64 x) x)
(*.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (sqrt.f64 (expm1.f64 x)) (cbrt.f64 x)))
(/.f64 (expm1.f64 x) x)
(pow.f64 (/.f64 (expm1.f64 x) x) 1)
(/.f64 (expm1.f64 x) x)
(pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 3)
(/.f64 (expm1.f64 x) x)
(pow.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 3) 1/3)
(/.f64 (expm1.f64 x) x)
(pow.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) 2)
(/.f64 (expm1.f64 x) x)
(pow.f64 (/.f64 x (expm1.f64 x)) -1)
(/.f64 (expm1.f64 x) x)
(neg.f64 (/.f64 (expm1.f64 x) (neg.f64 x)))
(/.f64 (expm1.f64 x) x)
(sqrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 2))
(/.f64 (expm1.f64 x) x)
(log.f64 (exp.f64 (/.f64 (expm1.f64 x) x)))
(/.f64 (expm1.f64 x) x)
(cbrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 3))
(/.f64 (expm1.f64 x) x)
(expm1.f64 (log1p.f64 (/.f64 (expm1.f64 x) x)))
(/.f64 (expm1.f64 x) x)
(exp.f64 (log.f64 (/.f64 (expm1.f64 x) x)))
(/.f64 (expm1.f64 x) x)
(log1p.f64 (expm1.f64 (/.f64 (expm1.f64 x) x)))
(/.f64 (expm1.f64 x) x)

eval23.0ms (1.2%)

Compiler: Compiled 436 to 218 computations (50% saved)

prune8.0ms (0.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	44	3	47
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	44	4	48

Accuracy

100.0%

Counts

48 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(/.f64 (expm1.f64 x) x)
▶	52.2%	(+.f64 1 (*.f64 1/2 x))
▶	49.8%	(*.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (expm1.f64 x) (sqrt.f64 x)))
	52.3%	1
✓	100.0%	(/.f64 (expm1.f64 x) x)
▶	52.2%	(+.f64 1 (*.f64 1/2 x))
▶	49.8%	(*.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (expm1.f64 x) (sqrt.f64 x)))
	52.3%	1

Compiler

Compiled 48 to 34 computations (29.2% saved)

localize55.0ms (2.8%)

Localize:

Found 3 expressions with local error:

New	Accuracy	Program
✓	99.9%	(*.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (expm1.f64 x) (sqrt.f64 x)))
✓	99.8%	(/.f64 1 (sqrt.f64 x))
✓	99.8%	(/.f64 (expm1.f64 x) (sqrt.f64 x))

Compiler

Compiled 38 to 19 computations (50% saved)

series5.0ms (0.3%)

Counts

3 → 12

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(/.f64 (expm1.f64 x) (sqrt.f64 x))
1.0ms	x	@	-inf	(*.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (expm1.f64 x) (sqrt.f64 x)))
1.0ms	x	@	-inf	(/.f64 (expm1.f64 x) (sqrt.f64 x))
1.0ms	x	@	inf	(/.f64 (expm1.f64 x) (sqrt.f64 x))
1.0ms	x	@	-inf	(/.f64 1 (sqrt.f64 x))

rewrite72.0ms (3.7%)

Algorithm

1×	batch-egg-rewrite

Rules

1938×	`pow1`
1792×	`add-exp-log`
1792×	`log1p-expm1-u`
1790×	`expm1-log1p-u`
194×	`add-sqr-sqrt`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	37
1	201	33
2	2577	33

Stop Event

1×	node limit

Counts

3 → 114

Calls

Call 1

Inputs
(/.f64 (expm1.f64 x) (sqrt.f64 x))
(/.f64 1 (sqrt.f64 x))
(*.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (expm1.f64 x) (sqrt.f64 x)))

Outputs
(-.f64 (+.f64 1 (/.f64 (expm1.f64 x) (sqrt.f64 x))) 1)
(-.f64 (/.f64 (exp.f64 x) (sqrt.f64 x)) (pow.f64 x -1/2))
(*.f64 (expm1.f64 x) (pow.f64 x -1/2))
(*.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) 1)
(*.f64 1 (/.f64 (expm1.f64 x) (sqrt.f64 x)))
(*.f64 (pow.f64 x -1/2) (expm1.f64 x))
(.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (.f64 (cbrt.f64 (expm1.f64 x)) (pow.f64 x -1/2)))
(.f64 (cbrt.f64 (/.f64 1 x)) (.f64 (cbrt.f64 (pow.f64 x -1/2)) (expm1.f64 x)))
(*.f64 (cbrt.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x))) (cbrt.f64 (/.f64 (pow.f64 (expm1.f64 x) 2) x)))
(*.f64 (cbrt.f64 (/.f64 (pow.f64 (expm1.f64 x) 2) x)) (cbrt.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x))))
(.f64 (sqrt.f64 (expm1.f64 x)) (.f64 (sqrt.f64 (expm1.f64 x)) (pow.f64 x -1/2)))
(*.f64 (pow.f64 (sqrt.f64 x) -1/2) (/.f64 (expm1.f64 x) (pow.f64 x 1/4)))
(.f64 (pow.f64 (sqrt.f64 x) -1/2) (.f64 (pow.f64 (sqrt.f64 x) -1/2) (expm1.f64 x)))
(*.f64 (sqrt.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x))) (sqrt.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x))))
(*.f64 (neg.f64 (expm1.f64 x)) (/.f64 1 (neg.f64 (sqrt.f64 x))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) 1) (/.f64 (cbrt.f64 (expm1.f64 x)) (sqrt.f64 x)))
(*.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) 1) (sqrt.f64 (/.f64 (expm1.f64 x) x)))
(*.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) (cbrt.f64 x)) (/.f64 (sqrt.f64 (expm1.f64 x)) (cbrt.f64 (sqrt.f64 x))))
(*.f64 (/.f64 1 (cbrt.f64 x)) (/.f64 (expm1.f64 x) (cbrt.f64 (sqrt.f64 x))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (cbrt.f64 x)) (cbrt.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (pow.f64 x 1/4)) (/.f64 (cbrt.f64 (expm1.f64 x)) (pow.f64 x 1/4)))
(.f64 (.f64 (pow.f64 (sqrt.f64 x) -1/2) (sqrt.f64 (expm1.f64 x))) (*.f64 (pow.f64 (sqrt.f64 x) -1/2) (sqrt.f64 (expm1.f64 x))))
(.f64 (.f64 (pow.f64 x -1/2) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (cbrt.f64 (expm1.f64 x)))
(.f64 (.f64 (pow.f64 x -1/2) (sqrt.f64 (expm1.f64 x))) (sqrt.f64 (expm1.f64 x)))
(.f64 (.f64 (expm1.f64 x) (cbrt.f64 (/.f64 1 x))) (cbrt.f64 (pow.f64 x -1/2)))
(.f64 (.f64 (expm1.f64 x) (pow.f64 (sqrt.f64 x) -1/2)) (pow.f64 (sqrt.f64 x) -1/2))
(pow.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) 1)
(pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x))) 3)
(pow.f64 (pow.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) 3) 1/3)
(pow.f64 (sqrt.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x))) 2)
(pow.f64 (/.f64 (sqrt.f64 x) (expm1.f64 x)) -1)
(neg.f64 (/.f64 (expm1.f64 x) (neg.f64 (sqrt.f64 x))))
(sqrt.f64 (/.f64 (pow.f64 (expm1.f64 x) 2) x))
(log.f64 (exp.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x))))
(cbrt.f64 (pow.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) 3))
(cbrt.f64 (*.f64 (pow.f64 (pow.f64 x -1/2) 3) (pow.f64 (expm1.f64 x) 3)))
(cbrt.f64 (*.f64 (pow.f64 (expm1.f64 x) 3) (pow.f64 (pow.f64 x -1/2) 3)))
(cbrt.f64 (/.f64 (pow.f64 (expm1.f64 x) 3) (pow.f64 x 3/2)))
(expm1.f64 (log1p.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x))))
(exp.f64 (log.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x))))
(exp.f64 (*.f64 (log.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x))) 1))
(exp.f64 (+.f64 (log.f64 (pow.f64 x -1/2)) (log.f64 (expm1.f64 x))))
(log1p.f64 (expm1.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x))))
(-.f64 (+.f64 1 (pow.f64 x -1/2)) 1)
(*.f64 1 (pow.f64 x -1/2))
(*.f64 (pow.f64 x -1/2) 1)
(*.f64 (cbrt.f64 (pow.f64 x -1/2)) (cbrt.f64 (/.f64 1 x)))
(*.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (pow.f64 x -1/2)))
(*.f64 (pow.f64 (sqrt.f64 x) -1/2) (pow.f64 (sqrt.f64 x) -1/2))
(*.f64 -1 (/.f64 1 (neg.f64 (sqrt.f64 x))))
(*.f64 (pow.f64 (cbrt.f64 x) -1) (pow.f64 (cbrt.f64 (sqrt.f64 x)) -1))
(*.f64 (pow.f64 (pow.f64 x 1/4) -1) (pow.f64 (pow.f64 x 1/4) -1))
(pow.f64 x -1/2)
(pow.f64 (sqrt.f64 x) -1)
(pow.f64 (pow.f64 x -1/2) 1)
(pow.f64 (cbrt.f64 (pow.f64 x -1/2)) 3)
(pow.f64 (pow.f64 (pow.f64 x -1/2) 3) 1/3)
(pow.f64 (pow.f64 (sqrt.f64 x) -1/2) 2)
(sqrt.f64 (/.f64 1 x))
(log.f64 (exp.f64 (pow.f64 x -1/2)))
(cbrt.f64 (pow.f64 (pow.f64 x -1/2) 3))
(expm1.f64 (log1p.f64 (pow.f64 x -1/2)))
(exp.f64 (log.f64 (pow.f64 x -1/2)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 x)) -1))
(exp.f64 (*.f64 (log.f64 (pow.f64 x -1/2)) 1))
(log1p.f64 (expm1.f64 (pow.f64 x -1/2)))
(-.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 1)
(-.f64 (/.f64 (exp.f64 x) x) (/.f64 1 x))
(/.f64 (expm1.f64 x) x)
(/.f64 (expm1.f64 x) (/.f64 (sqrt.f64 x) (pow.f64 x -1/2)))
(/.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) (sqrt.f64 x))
(/.f64 1 (*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (expm1.f64 x))))
(/.f64 1 (*.f64 (/.f64 (sqrt.f64 x) (expm1.f64 x)) (sqrt.f64 x)))
(/.f64 1 (/.f64 x (expm1.f64 x)))
(/.f64 1 (/.f64 (sqrt.f64 x) (/.f64 (expm1.f64 x) (sqrt.f64 x))))
(/.f64 (pow.f64 x -1/2) (/.f64 (sqrt.f64 x) (expm1.f64 x)))
(/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (/.f64 x (cbrt.f64 (expm1.f64 x))))
(/.f64 (cbrt.f64 (/.f64 (pow.f64 (expm1.f64 x) 2) x)) (/.f64 (sqrt.f64 x) (cbrt.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)))))
(/.f64 (sqrt.f64 (expm1.f64 x)) (/.f64 x (sqrt.f64 (expm1.f64 x))))
(/.f64 (sqrt.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x))) (/.f64 (sqrt.f64 x) (sqrt.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)))))
(/.f64 -1 (*.f64 (/.f64 (sqrt.f64 x) (expm1.f64 x)) (neg.f64 (sqrt.f64 x))))
(/.f64 -1 (*.f64 (neg.f64 (sqrt.f64 x)) (/.f64 (sqrt.f64 x) (expm1.f64 x))))
(/.f64 (neg.f64 (expm1.f64 x)) (*.f64 (sqrt.f64 x) (neg.f64 (sqrt.f64 x))))
(/.f64 (neg.f64 (expm1.f64 x)) (*.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 x)))
(/.f64 (neg.f64 (expm1.f64 x)) (neg.f64 x))
(/.f64 (.f64 (neg.f64 (expm1.f64 x)) 1) (.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 x)))
(/.f64 (.f64 (expm1.f64 x) -1) (.f64 (sqrt.f64 x) (neg.f64 (sqrt.f64 x))))
(/.f64 (.f64 (neg.f64 (expm1.f64 x)) -1) (.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 x))))
(/.f64 (.f64 -1 (neg.f64 (expm1.f64 x))) (.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 x))))
(/.f64 (neg.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x))) (neg.f64 (sqrt.f64 x)))
(/.f64 (/.f64 (expm1.f64 x) 1) x)
(/.f64 (/.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) (pow.f64 x 1/4)) (pow.f64 x 1/4))
(/.f64 (*.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) -1) (neg.f64 (sqrt.f64 x)))
(/.f64 (*.f64 (pow.f64 x -1/2) (neg.f64 (expm1.f64 x))) (neg.f64 (sqrt.f64 x)))
(/.f64 (*.f64 (neg.f64 (expm1.f64 x)) (pow.f64 x -1/2)) (neg.f64 (sqrt.f64 x)))
(/.f64 (*.f64 -1 (/.f64 (expm1.f64 x) (sqrt.f64 x))) (neg.f64 (sqrt.f64 x)))
(/.f64 (/.f64 (expm1.f64 x) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))
(/.f64 (/.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) 1) (sqrt.f64 x))
(/.f64 (/.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) (cbrt.f64 x)) (cbrt.f64 (sqrt.f64 x)))
(pow.f64 (/.f64 (expm1.f64 x) x) 1)
(pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 3)
(pow.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 3) 1/3)
(pow.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) 2)
(sqrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 2))
(log.f64 (exp.f64 (/.f64 (expm1.f64 x) x)))
(cbrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 3))
(cbrt.f64 (*.f64 (pow.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) 3) (pow.f64 (pow.f64 x -1/2) 3)))
(cbrt.f64 (*.f64 (pow.f64 (pow.f64 x -1/2) 3) (pow.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) 3)))
(cbrt.f64 (/.f64 (pow.f64 (expm1.f64 x) 3) (pow.f64 x 3)))
(cbrt.f64 (/.f64 (pow.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) 3) (pow.f64 x 3/2)))
(expm1.f64 (log1p.f64 (/.f64 (expm1.f64 x) x)))
(exp.f64 (log.f64 (/.f64 (expm1.f64 x) x)))
(exp.f64 (*.f64 (log.f64 (/.f64 (expm1.f64 x) x)) 1))
(log1p.f64 (expm1.f64 (/.f64 (expm1.f64 x) x)))

simplify67.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

1058×	`fma-def`
616×	`div-sub`
514×	`distribute-rgt-in`
508×	`distribute-lft-in`
500×	`log-prod`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	262	2584
1	593	2316
2	2781	2098

Stop Event

1×	node limit

Counts

126 → 148

Calls

Call 1

Inputs
1
(+.f64 1 (*.f64 1/2 x))
(+.f64 1 (+.f64 (.f64 1/6 (pow.f64 x 2)) (.f64 1/2 x)))
(+.f64 1 (+.f64 (.f64 1/24 (pow.f64 x 3)) (+.f64 (.f64 1/6 (pow.f64 x 2)) (*.f64 1/2 x))))
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(.f64 -1 (/.f64 (-.f64 (exp.f64 x) 1) (.f64 x (pow.f64 (sqrt.f64 -1) 2))))
(.f64 -1 (/.f64 (-.f64 (exp.f64 x) 1) (.f64 x (pow.f64 (sqrt.f64 -1) 2))))
(.f64 -1 (/.f64 (-.f64 (exp.f64 x) 1) (.f64 x (pow.f64 (sqrt.f64 -1) 2))))
(.f64 -1 (/.f64 (-.f64 (exp.f64 x) 1) (.f64 x (pow.f64 (sqrt.f64 -1) 2))))
(-.f64 (+.f64 1 (/.f64 (expm1.f64 x) (sqrt.f64 x))) 1)
(-.f64 (/.f64 (exp.f64 x) (sqrt.f64 x)) (pow.f64 x -1/2))
(*.f64 (expm1.f64 x) (pow.f64 x -1/2))
(*.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) 1)
(*.f64 1 (/.f64 (expm1.f64 x) (sqrt.f64 x)))
(*.f64 (pow.f64 x -1/2) (expm1.f64 x))
(.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (.f64 (cbrt.f64 (expm1.f64 x)) (pow.f64 x -1/2)))
(.f64 (cbrt.f64 (/.f64 1 x)) (.f64 (cbrt.f64 (pow.f64 x -1/2)) (expm1.f64 x)))
(*.f64 (cbrt.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x))) (cbrt.f64 (/.f64 (pow.f64 (expm1.f64 x) 2) x)))
(*.f64 (cbrt.f64 (/.f64 (pow.f64 (expm1.f64 x) 2) x)) (cbrt.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x))))
(.f64 (sqrt.f64 (expm1.f64 x)) (.f64 (sqrt.f64 (expm1.f64 x)) (pow.f64 x -1/2)))
(*.f64 (pow.f64 (sqrt.f64 x) -1/2) (/.f64 (expm1.f64 x) (pow.f64 x 1/4)))
(.f64 (pow.f64 (sqrt.f64 x) -1/2) (.f64 (pow.f64 (sqrt.f64 x) -1/2) (expm1.f64 x)))
(*.f64 (sqrt.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x))) (sqrt.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x))))
(*.f64 (neg.f64 (expm1.f64 x)) (/.f64 1 (neg.f64 (sqrt.f64 x))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) 1) (/.f64 (cbrt.f64 (expm1.f64 x)) (sqrt.f64 x)))
(*.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) 1) (sqrt.f64 (/.f64 (expm1.f64 x) x)))
(*.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) (cbrt.f64 x)) (/.f64 (sqrt.f64 (expm1.f64 x)) (cbrt.f64 (sqrt.f64 x))))
(*.f64 (/.f64 1 (cbrt.f64 x)) (/.f64 (expm1.f64 x) (cbrt.f64 (sqrt.f64 x))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (cbrt.f64 x)) (cbrt.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (pow.f64 x 1/4)) (/.f64 (cbrt.f64 (expm1.f64 x)) (pow.f64 x 1/4)))
(.f64 (.f64 (pow.f64 (sqrt.f64 x) -1/2) (sqrt.f64 (expm1.f64 x))) (*.f64 (pow.f64 (sqrt.f64 x) -1/2) (sqrt.f64 (expm1.f64 x))))
(.f64 (.f64 (pow.f64 x -1/2) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (cbrt.f64 (expm1.f64 x)))
(.f64 (.f64 (pow.f64 x -1/2) (sqrt.f64 (expm1.f64 x))) (sqrt.f64 (expm1.f64 x)))
(.f64 (.f64 (expm1.f64 x) (cbrt.f64 (/.f64 1 x))) (cbrt.f64 (pow.f64 x -1/2)))
(.f64 (.f64 (expm1.f64 x) (pow.f64 (sqrt.f64 x) -1/2)) (pow.f64 (sqrt.f64 x) -1/2))
(pow.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) 1)
(pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x))) 3)
(pow.f64 (pow.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) 3) 1/3)
(pow.f64 (sqrt.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x))) 2)
(pow.f64 (/.f64 (sqrt.f64 x) (expm1.f64 x)) -1)
(neg.f64 (/.f64 (expm1.f64 x) (neg.f64 (sqrt.f64 x))))
(sqrt.f64 (/.f64 (pow.f64 (expm1.f64 x) 2) x))
(log.f64 (exp.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x))))
(cbrt.f64 (pow.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) 3))
(cbrt.f64 (*.f64 (pow.f64 (pow.f64 x -1/2) 3) (pow.f64 (expm1.f64 x) 3)))
(cbrt.f64 (*.f64 (pow.f64 (expm1.f64 x) 3) (pow.f64 (pow.f64 x -1/2) 3)))
(cbrt.f64 (/.f64 (pow.f64 (expm1.f64 x) 3) (pow.f64 x 3/2)))
(expm1.f64 (log1p.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x))))
(exp.f64 (log.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x))))
(exp.f64 (*.f64 (log.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x))) 1))
(exp.f64 (+.f64 (log.f64 (pow.f64 x -1/2)) (log.f64 (expm1.f64 x))))
(log1p.f64 (expm1.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x))))
(-.f64 (+.f64 1 (pow.f64 x -1/2)) 1)
(*.f64 1 (pow.f64 x -1/2))
(*.f64 (pow.f64 x -1/2) 1)
(*.f64 (cbrt.f64 (pow.f64 x -1/2)) (cbrt.f64 (/.f64 1 x)))
(*.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (pow.f64 x -1/2)))
(*.f64 (pow.f64 (sqrt.f64 x) -1/2) (pow.f64 (sqrt.f64 x) -1/2))
(*.f64 -1 (/.f64 1 (neg.f64 (sqrt.f64 x))))
(*.f64 (pow.f64 (cbrt.f64 x) -1) (pow.f64 (cbrt.f64 (sqrt.f64 x)) -1))
(*.f64 (pow.f64 (pow.f64 x 1/4) -1) (pow.f64 (pow.f64 x 1/4) -1))
(pow.f64 x -1/2)
(pow.f64 (sqrt.f64 x) -1)
(pow.f64 (pow.f64 x -1/2) 1)
(pow.f64 (cbrt.f64 (pow.f64 x -1/2)) 3)
(pow.f64 (pow.f64 (pow.f64 x -1/2) 3) 1/3)
(pow.f64 (pow.f64 (sqrt.f64 x) -1/2) 2)
(sqrt.f64 (/.f64 1 x))
(log.f64 (exp.f64 (pow.f64 x -1/2)))
(cbrt.f64 (pow.f64 (pow.f64 x -1/2) 3))
(expm1.f64 (log1p.f64 (pow.f64 x -1/2)))
(exp.f64 (log.f64 (pow.f64 x -1/2)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 x)) -1))
(exp.f64 (*.f64 (log.f64 (pow.f64 x -1/2)) 1))
(log1p.f64 (expm1.f64 (pow.f64 x -1/2)))
(-.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 1)
(-.f64 (/.f64 (exp.f64 x) x) (/.f64 1 x))
(/.f64 (expm1.f64 x) x)
(/.f64 (expm1.f64 x) (/.f64 (sqrt.f64 x) (pow.f64 x -1/2)))
(/.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) (sqrt.f64 x))
(/.f64 1 (*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (expm1.f64 x))))
(/.f64 1 (*.f64 (/.f64 (sqrt.f64 x) (expm1.f64 x)) (sqrt.f64 x)))
(/.f64 1 (/.f64 x (expm1.f64 x)))
(/.f64 1 (/.f64 (sqrt.f64 x) (/.f64 (expm1.f64 x) (sqrt.f64 x))))
(/.f64 (pow.f64 x -1/2) (/.f64 (sqrt.f64 x) (expm1.f64 x)))
(/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (/.f64 x (cbrt.f64 (expm1.f64 x))))
(/.f64 (cbrt.f64 (/.f64 (pow.f64 (expm1.f64 x) 2) x)) (/.f64 (sqrt.f64 x) (cbrt.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)))))
(/.f64 (sqrt.f64 (expm1.f64 x)) (/.f64 x (sqrt.f64 (expm1.f64 x))))
(/.f64 (sqrt.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x))) (/.f64 (sqrt.f64 x) (sqrt.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)))))
(/.f64 -1 (*.f64 (/.f64 (sqrt.f64 x) (expm1.f64 x)) (neg.f64 (sqrt.f64 x))))
(/.f64 -1 (*.f64 (neg.f64 (sqrt.f64 x)) (/.f64 (sqrt.f64 x) (expm1.f64 x))))
(/.f64 (neg.f64 (expm1.f64 x)) (*.f64 (sqrt.f64 x) (neg.f64 (sqrt.f64 x))))
(/.f64 (neg.f64 (expm1.f64 x)) (*.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 x)))
(/.f64 (neg.f64 (expm1.f64 x)) (neg.f64 x))
(/.f64 (.f64 (neg.f64 (expm1.f64 x)) 1) (.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 x)))
(/.f64 (.f64 (expm1.f64 x) -1) (.f64 (sqrt.f64 x) (neg.f64 (sqrt.f64 x))))
(/.f64 (.f64 (neg.f64 (expm1.f64 x)) -1) (.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 x))))
(/.f64 (.f64 -1 (neg.f64 (expm1.f64 x))) (.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 x))))
(/.f64 (neg.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x))) (neg.f64 (sqrt.f64 x)))
(/.f64 (/.f64 (expm1.f64 x) 1) x)
(/.f64 (/.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) (pow.f64 x 1/4)) (pow.f64 x 1/4))
(/.f64 (*.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) -1) (neg.f64 (sqrt.f64 x)))
(/.f64 (*.f64 (pow.f64 x -1/2) (neg.f64 (expm1.f64 x))) (neg.f64 (sqrt.f64 x)))
(/.f64 (*.f64 (neg.f64 (expm1.f64 x)) (pow.f64 x -1/2)) (neg.f64 (sqrt.f64 x)))
(/.f64 (*.f64 -1 (/.f64 (expm1.f64 x) (sqrt.f64 x))) (neg.f64 (sqrt.f64 x)))
(/.f64 (/.f64 (expm1.f64 x) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))
(/.f64 (/.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) 1) (sqrt.f64 x))
(/.f64 (/.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) (cbrt.f64 x)) (cbrt.f64 (sqrt.f64 x)))
(pow.f64 (/.f64 (expm1.f64 x) x) 1)
(pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 3)
(pow.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 3) 1/3)
(pow.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) 2)
(sqrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 2))
(log.f64 (exp.f64 (/.f64 (expm1.f64 x) x)))
(cbrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 3))
(cbrt.f64 (*.f64 (pow.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) 3) (pow.f64 (pow.f64 x -1/2) 3)))
(cbrt.f64 (*.f64 (pow.f64 (pow.f64 x -1/2) 3) (pow.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) 3)))
(cbrt.f64 (/.f64 (pow.f64 (expm1.f64 x) 3) (pow.f64 x 3)))
(cbrt.f64 (/.f64 (pow.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) 3) (pow.f64 x 3/2)))
(expm1.f64 (log1p.f64 (/.f64 (expm1.f64 x) x)))
(exp.f64 (log.f64 (/.f64 (expm1.f64 x) x)))
(exp.f64 (*.f64 (log.f64 (/.f64 (expm1.f64 x) x)) 1))
(log1p.f64 (expm1.f64 (/.f64 (expm1.f64 x) x)))

Outputs
1
(+.f64 1 (*.f64 1/2 x))
(fma.f64 1/2 x 1)
(+.f64 1 (+.f64 (.f64 1/6 (pow.f64 x 2)) (.f64 1/2 x)))
(+.f64 1 (fma.f64 1/6 (.f64 x x) (.f64 1/2 x)))
(+.f64 1 (fma.f64 1/2 x (.f64 x (.f64 x 1/6))))
(fma.f64 1/2 x (fma.f64 x (*.f64 x 1/6) 1))
(+.f64 1 (+.f64 (.f64 1/24 (pow.f64 x 3)) (+.f64 (.f64 1/6 (pow.f64 x 2)) (*.f64 1/2 x))))
(+.f64 1 (fma.f64 1/24 (pow.f64 x 3) (fma.f64 1/6 (.f64 x x) (.f64 1/2 x))))
(+.f64 1 (fma.f64 1/24 (pow.f64 x 3) (fma.f64 1/2 x (.f64 x (.f64 x 1/6)))))
(fma.f64 1/24 (pow.f64 x 3) (fma.f64 1/2 x (fma.f64 x (*.f64 x 1/6) 1)))
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(.f64 -1 (/.f64 (-.f64 (exp.f64 x) 1) (.f64 x (pow.f64 (sqrt.f64 -1) 2))))
(/.f64 (expm1.f64 x) x)
(.f64 -1 (/.f64 (-.f64 (exp.f64 x) 1) (.f64 x (pow.f64 (sqrt.f64 -1) 2))))
(/.f64 (expm1.f64 x) x)
(.f64 -1 (/.f64 (-.f64 (exp.f64 x) 1) (.f64 x (pow.f64 (sqrt.f64 -1) 2))))
(/.f64 (expm1.f64 x) x)
(.f64 -1 (/.f64 (-.f64 (exp.f64 x) 1) (.f64 x (pow.f64 (sqrt.f64 -1) 2))))
(/.f64 (expm1.f64 x) x)
(-.f64 (+.f64 1 (/.f64 (expm1.f64 x) (sqrt.f64 x))) 1)
(+.f64 1 (-.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) 1))
(+.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) 0)
(/.f64 (expm1.f64 x) (sqrt.f64 x))
(-.f64 (/.f64 (exp.f64 x) (sqrt.f64 x)) (pow.f64 x -1/2))
(*.f64 (expm1.f64 x) (pow.f64 x -1/2))
(*.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) 1)
(+.f64 1 (-.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) 1))
(+.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) 0)
(/.f64 (expm1.f64 x) (sqrt.f64 x))
(*.f64 1 (/.f64 (expm1.f64 x) (sqrt.f64 x)))
(+.f64 1 (-.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) 1))
(+.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) 0)
(/.f64 (expm1.f64 x) (sqrt.f64 x))
(*.f64 (pow.f64 x -1/2) (expm1.f64 x))
(*.f64 (expm1.f64 x) (pow.f64 x -1/2))
(.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (.f64 (cbrt.f64 (expm1.f64 x)) (pow.f64 x -1/2)))
(*.f64 (expm1.f64 x) (pow.f64 x -1/2))
(.f64 (cbrt.f64 (/.f64 1 x)) (.f64 (cbrt.f64 (pow.f64 x -1/2)) (expm1.f64 x)))
(.f64 (cbrt.f64 (/.f64 1 x)) (.f64 (expm1.f64 x) (cbrt.f64 (pow.f64 x -1/2))))
(.f64 (cbrt.f64 (pow.f64 x -1/2)) (.f64 (expm1.f64 x) (cbrt.f64 (/.f64 1 x))))
(*.f64 (cbrt.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x))) (cbrt.f64 (/.f64 (pow.f64 (expm1.f64 x) 2) x)))
(*.f64 (cbrt.f64 (/.f64 (pow.f64 (expm1.f64 x) 2) x)) (cbrt.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x))))
(*.f64 (cbrt.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x))) (cbrt.f64 (/.f64 (pow.f64 (expm1.f64 x) 2) x)))
(.f64 (sqrt.f64 (expm1.f64 x)) (.f64 (sqrt.f64 (expm1.f64 x)) (pow.f64 x -1/2)))
(*.f64 (expm1.f64 x) (pow.f64 x -1/2))
(*.f64 (pow.f64 (sqrt.f64 x) -1/2) (/.f64 (expm1.f64 x) (pow.f64 x 1/4)))
(.f64 (pow.f64 (sqrt.f64 x) -1/2) (.f64 (pow.f64 (sqrt.f64 x) -1/2) (expm1.f64 x)))
(+.f64 1 (-.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) 1))
(+.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) 0)
(/.f64 (expm1.f64 x) (sqrt.f64 x))
(*.f64 (sqrt.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x))) (sqrt.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x))))
(+.f64 1 (-.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) 1))
(+.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) 0)
(/.f64 (expm1.f64 x) (sqrt.f64 x))
(*.f64 (neg.f64 (expm1.f64 x)) (/.f64 1 (neg.f64 (sqrt.f64 x))))
(+.f64 1 (-.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) 1))
(+.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) 0)
(/.f64 (expm1.f64 x) (sqrt.f64 x))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) 1) (/.f64 (cbrt.f64 (expm1.f64 x)) (sqrt.f64 x)))
(+.f64 1 (-.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) 1))
(+.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) 0)
(/.f64 (expm1.f64 x) (sqrt.f64 x))
(*.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) 1) (sqrt.f64 (/.f64 (expm1.f64 x) x)))
(*.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 (/.f64 (expm1.f64 x) x)))
(*.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) (cbrt.f64 x)) (/.f64 (sqrt.f64 (expm1.f64 x)) (cbrt.f64 (sqrt.f64 x))))
(/.f64 (/.f64 (expm1.f64 x) (cbrt.f64 (sqrt.f64 x))) (cbrt.f64 x))
(*.f64 (/.f64 1 (cbrt.f64 x)) (/.f64 (expm1.f64 x) (cbrt.f64 (sqrt.f64 x))))
(*.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) (cbrt.f64 x)) (/.f64 (sqrt.f64 (expm1.f64 x)) (cbrt.f64 (sqrt.f64 x))))
(/.f64 (/.f64 (expm1.f64 x) (cbrt.f64 (sqrt.f64 x))) (cbrt.f64 x))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (cbrt.f64 x)) (cbrt.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x))))
(*.f64 (cbrt.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x))) (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (cbrt.f64 x)))
(/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (/.f64 (cbrt.f64 x) (cbrt.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (pow.f64 x 1/4)) (/.f64 (cbrt.f64 (expm1.f64 x)) (pow.f64 x 1/4)))
(/.f64 (/.f64 (expm1.f64 x) (pow.f64 x 1/4)) (pow.f64 x 1/4))
(.f64 (.f64 (pow.f64 (sqrt.f64 x) -1/2) (sqrt.f64 (expm1.f64 x))) (*.f64 (pow.f64 (sqrt.f64 x) -1/2) (sqrt.f64 (expm1.f64 x))))
(+.f64 1 (-.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) 1))
(+.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) 0)
(/.f64 (expm1.f64 x) (sqrt.f64 x))
(.f64 (.f64 (pow.f64 x -1/2) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (cbrt.f64 (expm1.f64 x)))
(*.f64 (expm1.f64 x) (pow.f64 x -1/2))
(.f64 (.f64 (pow.f64 x -1/2) (sqrt.f64 (expm1.f64 x))) (sqrt.f64 (expm1.f64 x)))
(*.f64 (expm1.f64 x) (pow.f64 x -1/2))
(.f64 (.f64 (expm1.f64 x) (cbrt.f64 (/.f64 1 x))) (cbrt.f64 (pow.f64 x -1/2)))
(.f64 (cbrt.f64 (/.f64 1 x)) (.f64 (expm1.f64 x) (cbrt.f64 (pow.f64 x -1/2))))
(.f64 (cbrt.f64 (pow.f64 x -1/2)) (.f64 (expm1.f64 x) (cbrt.f64 (/.f64 1 x))))
(.f64 (.f64 (expm1.f64 x) (pow.f64 (sqrt.f64 x) -1/2)) (pow.f64 (sqrt.f64 x) -1/2))
(+.f64 1 (-.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) 1))
(+.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) 0)
(/.f64 (expm1.f64 x) (sqrt.f64 x))
(pow.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) 1)
(+.f64 1 (-.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) 1))
(+.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) 0)
(/.f64 (expm1.f64 x) (sqrt.f64 x))
(pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x))) 3)
(+.f64 1 (-.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) 1))
(+.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) 0)
(/.f64 (expm1.f64 x) (sqrt.f64 x))
(pow.f64 (pow.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) 3) 1/3)
(+.f64 1 (-.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) 1))
(+.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) 0)
(/.f64 (expm1.f64 x) (sqrt.f64 x))
(pow.f64 (sqrt.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x))) 2)
(+.f64 1 (-.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) 1))
(+.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) 0)
(/.f64 (expm1.f64 x) (sqrt.f64 x))
(pow.f64 (/.f64 (sqrt.f64 x) (expm1.f64 x)) -1)
(+.f64 1 (-.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) 1))
(+.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) 0)
(/.f64 (expm1.f64 x) (sqrt.f64 x))
(neg.f64 (/.f64 (expm1.f64 x) (neg.f64 (sqrt.f64 x))))
(+.f64 1 (-.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) 1))
(+.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) 0)
(/.f64 (expm1.f64 x) (sqrt.f64 x))
(sqrt.f64 (/.f64 (pow.f64 (expm1.f64 x) 2) x))
(log.f64 (exp.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x))))
(+.f64 1 (-.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) 1))
(+.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) 0)
(/.f64 (expm1.f64 x) (sqrt.f64 x))
(cbrt.f64 (pow.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) 3))
(+.f64 1 (-.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) 1))
(+.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) 0)
(/.f64 (expm1.f64 x) (sqrt.f64 x))
(cbrt.f64 (*.f64 (pow.f64 (pow.f64 x -1/2) 3) (pow.f64 (expm1.f64 x) 3)))
(cbrt.f64 (*.f64 (pow.f64 (expm1.f64 x) 3) (pow.f64 (pow.f64 x -1/2) 3)))
(cbrt.f64 (*.f64 (pow.f64 (pow.f64 x -1/2) 3) (pow.f64 (expm1.f64 x) 3)))
(cbrt.f64 (/.f64 (pow.f64 (expm1.f64 x) 3) (pow.f64 x 3/2)))
(expm1.f64 (log1p.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x))))
(+.f64 1 (-.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) 1))
(+.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) 0)
(/.f64 (expm1.f64 x) (sqrt.f64 x))
(exp.f64 (log.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x))))
(+.f64 1 (-.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) 1))
(+.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) 0)
(/.f64 (expm1.f64 x) (sqrt.f64 x))
(exp.f64 (*.f64 (log.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x))) 1))
(+.f64 1 (-.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) 1))
(+.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) 0)
(/.f64 (expm1.f64 x) (sqrt.f64 x))
(exp.f64 (+.f64 (log.f64 (pow.f64 x -1/2)) (log.f64 (expm1.f64 x))))
(*.f64 (expm1.f64 x) (pow.f64 x -1/2))
(log1p.f64 (expm1.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x))))
(+.f64 1 (-.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) 1))
(+.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) 0)
(/.f64 (expm1.f64 x) (sqrt.f64 x))
(-.f64 (+.f64 1 (pow.f64 x -1/2)) 1)
(+.f64 1 (-.f64 (pow.f64 x -1/2) 1))
(+.f64 (pow.f64 x -1/2) 0)
(pow.f64 x -1/2)
(*.f64 1 (pow.f64 x -1/2))
(+.f64 1 (-.f64 (pow.f64 x -1/2) 1))
(+.f64 (pow.f64 x -1/2) 0)
(pow.f64 x -1/2)
(*.f64 (pow.f64 x -1/2) 1)
(+.f64 1 (-.f64 (pow.f64 x -1/2) 1))
(+.f64 (pow.f64 x -1/2) 0)
(pow.f64 x -1/2)
(*.f64 (cbrt.f64 (pow.f64 x -1/2)) (cbrt.f64 (/.f64 1 x)))
(*.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (pow.f64 x -1/2)))
(*.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (pow.f64 x -1/2)))
(*.f64 (pow.f64 (sqrt.f64 x) -1/2) (pow.f64 (sqrt.f64 x) -1/2))
(/.f64 1 (sqrt.f64 x))
(*.f64 -1 (/.f64 1 (neg.f64 (sqrt.f64 x))))
(/.f64 1 (sqrt.f64 x))
(*.f64 (pow.f64 (cbrt.f64 x) -1) (pow.f64 (cbrt.f64 (sqrt.f64 x)) -1))
(*.f64 (/.f64 1 (cbrt.f64 x)) (/.f64 1 (cbrt.f64 (sqrt.f64 x))))
(/.f64 (/.f64 1 (cbrt.f64 x)) (cbrt.f64 (sqrt.f64 x)))
(*.f64 (pow.f64 (pow.f64 x 1/4) -1) (pow.f64 (pow.f64 x 1/4) -1))
(pow.f64 (pow.f64 x 1/4) -2)
(pow.f64 x -1/2)
(+.f64 1 (-.f64 (pow.f64 x -1/2) 1))
(+.f64 (pow.f64 x -1/2) 0)
(pow.f64 (sqrt.f64 x) -1)
(/.f64 1 (sqrt.f64 x))
(pow.f64 (pow.f64 x -1/2) 1)
(+.f64 1 (-.f64 (pow.f64 x -1/2) 1))
(+.f64 (pow.f64 x -1/2) 0)
(pow.f64 x -1/2)
(pow.f64 (cbrt.f64 (pow.f64 x -1/2)) 3)
(+.f64 1 (-.f64 (pow.f64 x -1/2) 1))
(+.f64 (pow.f64 x -1/2) 0)
(pow.f64 x -1/2)
(pow.f64 (pow.f64 (pow.f64 x -1/2) 3) 1/3)
(+.f64 1 (-.f64 (pow.f64 x -1/2) 1))
(+.f64 (pow.f64 x -1/2) 0)
(pow.f64 x -1/2)
(pow.f64 (pow.f64 (sqrt.f64 x) -1/2) 2)
(/.f64 1 (sqrt.f64 x))
(sqrt.f64 (/.f64 1 x))
(log.f64 (exp.f64 (pow.f64 x -1/2)))
(+.f64 1 (-.f64 (pow.f64 x -1/2) 1))
(+.f64 (pow.f64 x -1/2) 0)
(pow.f64 x -1/2)
(cbrt.f64 (pow.f64 (pow.f64 x -1/2) 3))
(+.f64 1 (-.f64 (pow.f64 x -1/2) 1))
(+.f64 (pow.f64 x -1/2) 0)
(pow.f64 x -1/2)
(expm1.f64 (log1p.f64 (pow.f64 x -1/2)))
(+.f64 1 (-.f64 (pow.f64 x -1/2) 1))
(+.f64 (pow.f64 x -1/2) 0)
(pow.f64 x -1/2)
(exp.f64 (log.f64 (pow.f64 x -1/2)))
(+.f64 1 (-.f64 (pow.f64 x -1/2) 1))
(+.f64 (pow.f64 x -1/2) 0)
(pow.f64 x -1/2)
(exp.f64 (*.f64 (log.f64 (sqrt.f64 x)) -1))
(/.f64 1 (sqrt.f64 x))
(exp.f64 (*.f64 (log.f64 (pow.f64 x -1/2)) 1))
(+.f64 1 (-.f64 (pow.f64 x -1/2) 1))
(+.f64 (pow.f64 x -1/2) 0)
(pow.f64 x -1/2)
(log1p.f64 (expm1.f64 (pow.f64 x -1/2)))
(+.f64 1 (-.f64 (pow.f64 x -1/2) 1))
(+.f64 (pow.f64 x -1/2) 0)
(pow.f64 x -1/2)
(-.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 1)
(/.f64 (expm1.f64 x) x)
(-.f64 (/.f64 (exp.f64 x) x) (/.f64 1 x))
(/.f64 (expm1.f64 x) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (expm1.f64 x) (/.f64 (sqrt.f64 x) (pow.f64 x -1/2)))
(*.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) (pow.f64 x -1/2))
(*.f64 (expm1.f64 x) (/.f64 (pow.f64 x -1/2) (sqrt.f64 x)))
(/.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) (sqrt.f64 x))
(/.f64 (expm1.f64 x) x)
(/.f64 1 (*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (expm1.f64 x))))
(/.f64 (expm1.f64 x) x)
(/.f64 1 (*.f64 (/.f64 (sqrt.f64 x) (expm1.f64 x)) (sqrt.f64 x)))
(/.f64 (expm1.f64 x) x)
(/.f64 1 (/.f64 x (expm1.f64 x)))
(/.f64 (expm1.f64 x) x)
(/.f64 1 (/.f64 (sqrt.f64 x) (/.f64 (expm1.f64 x) (sqrt.f64 x))))
(/.f64 (expm1.f64 x) x)
(/.f64 (pow.f64 x -1/2) (/.f64 (sqrt.f64 x) (expm1.f64 x)))
(*.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) (pow.f64 x -1/2))
(*.f64 (expm1.f64 x) (/.f64 (pow.f64 x -1/2) (sqrt.f64 x)))
(/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (/.f64 x (cbrt.f64 (expm1.f64 x))))
(/.f64 (expm1.f64 x) x)
(/.f64 (cbrt.f64 (/.f64 (pow.f64 (expm1.f64 x) 2) x)) (/.f64 (sqrt.f64 x) (cbrt.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)))))
(*.f64 (cbrt.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x))) (/.f64 (cbrt.f64 (/.f64 (pow.f64 (expm1.f64 x) 2) x)) (sqrt.f64 x)))
(/.f64 (sqrt.f64 (expm1.f64 x)) (/.f64 x (sqrt.f64 (expm1.f64 x))))
(/.f64 (expm1.f64 x) x)
(/.f64 (sqrt.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x))) (/.f64 (sqrt.f64 x) (sqrt.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)))))
(/.f64 (expm1.f64 x) x)
(/.f64 -1 (*.f64 (/.f64 (sqrt.f64 x) (expm1.f64 x)) (neg.f64 (sqrt.f64 x))))
(/.f64 (expm1.f64 x) x)
(/.f64 -1 (*.f64 (neg.f64 (sqrt.f64 x)) (/.f64 (sqrt.f64 x) (expm1.f64 x))))
(/.f64 (expm1.f64 x) x)
(/.f64 (neg.f64 (expm1.f64 x)) (*.f64 (sqrt.f64 x) (neg.f64 (sqrt.f64 x))))
(/.f64 (expm1.f64 x) x)
(/.f64 (neg.f64 (expm1.f64 x)) (*.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 x)))
(/.f64 (expm1.f64 x) x)
(/.f64 (neg.f64 (expm1.f64 x)) (neg.f64 x))
(/.f64 (expm1.f64 x) x)
(/.f64 (.f64 (neg.f64 (expm1.f64 x)) 1) (.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 x)))
(/.f64 (expm1.f64 x) x)
(/.f64 (.f64 (expm1.f64 x) -1) (.f64 (sqrt.f64 x) (neg.f64 (sqrt.f64 x))))
(/.f64 (expm1.f64 x) x)
(/.f64 (.f64 (neg.f64 (expm1.f64 x)) -1) (.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 x))))
(/.f64 (expm1.f64 x) x)
(/.f64 (.f64 -1 (neg.f64 (expm1.f64 x))) (.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 x))))
(/.f64 (expm1.f64 x) x)
(/.f64 (neg.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x))) (neg.f64 (sqrt.f64 x)))
(/.f64 (expm1.f64 x) x)
(/.f64 (/.f64 (expm1.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (/.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) (pow.f64 x 1/4)) (pow.f64 x 1/4))
(/.f64 (expm1.f64 x) x)
(/.f64 (*.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) -1) (neg.f64 (sqrt.f64 x)))
(/.f64 (expm1.f64 x) x)
(/.f64 (*.f64 (pow.f64 x -1/2) (neg.f64 (expm1.f64 x))) (neg.f64 (sqrt.f64 x)))
(*.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) (pow.f64 x -1/2))
(*.f64 (expm1.f64 x) (/.f64 (pow.f64 x -1/2) (sqrt.f64 x)))
(/.f64 (*.f64 (neg.f64 (expm1.f64 x)) (pow.f64 x -1/2)) (neg.f64 (sqrt.f64 x)))
(*.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) (pow.f64 x -1/2))
(*.f64 (expm1.f64 x) (/.f64 (pow.f64 x -1/2) (sqrt.f64 x)))
(/.f64 (*.f64 -1 (/.f64 (expm1.f64 x) (sqrt.f64 x))) (neg.f64 (sqrt.f64 x)))
(/.f64 (expm1.f64 x) x)
(/.f64 (/.f64 (expm1.f64 x) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))
(/.f64 (expm1.f64 x) x)
(/.f64 (/.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) 1) (sqrt.f64 x))
(/.f64 (expm1.f64 x) x)
(/.f64 (/.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) (cbrt.f64 x)) (cbrt.f64 (sqrt.f64 x)))
(/.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) (*.f64 (cbrt.f64 (sqrt.f64 x)) (cbrt.f64 x)))
(/.f64 (expm1.f64 x) (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 (sqrt.f64 x))) (sqrt.f64 x)))
(pow.f64 (/.f64 (expm1.f64 x) x) 1)
(/.f64 (expm1.f64 x) x)
(pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 3)
(/.f64 (expm1.f64 x) x)
(pow.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 3) 1/3)
(/.f64 (expm1.f64 x) x)
(pow.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) 2)
(/.f64 (expm1.f64 x) x)
(sqrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 2))
(/.f64 (expm1.f64 x) x)
(log.f64 (exp.f64 (/.f64 (expm1.f64 x) x)))
(/.f64 (expm1.f64 x) x)
(cbrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 3))
(/.f64 (expm1.f64 x) x)
(cbrt.f64 (*.f64 (pow.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) 3) (pow.f64 (pow.f64 x -1/2) 3)))
(cbrt.f64 (*.f64 (pow.f64 (pow.f64 x -1/2) 3) (pow.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) 3)))
(cbrt.f64 (*.f64 (pow.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) 3) (pow.f64 (pow.f64 x -1/2) 3)))
(cbrt.f64 (/.f64 (pow.f64 (expm1.f64 x) 3) (pow.f64 x 3)))
(/.f64 (expm1.f64 x) x)
(cbrt.f64 (/.f64 (pow.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) 3) (pow.f64 x 3/2)))
(expm1.f64 (log1p.f64 (/.f64 (expm1.f64 x) x)))
(/.f64 (expm1.f64 x) x)
(exp.f64 (log.f64 (/.f64 (expm1.f64 x) x)))
(/.f64 (expm1.f64 x) x)
(exp.f64 (*.f64 (log.f64 (/.f64 (expm1.f64 x) x)) 1))
(/.f64 (expm1.f64 x) x)
(log1p.f64 (expm1.f64 (/.f64 (expm1.f64 x) x)))
(/.f64 (expm1.f64 x) x)

eval31.0ms (1.6%)

Compiler: Compiled 1815 to 826 computations (54.5% saved)

prune19.0ms (1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	147	1	148
Fresh	0	1	1
Picked	1	1	2
Done	0	1	1
Total	148	4	152

Accuracy

100.0%

Counts

152 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	49.7%	(/.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) (sqrt.f64 x))
✓	100.0%	(/.f64 (expm1.f64 x) x)
✓	52.2%	(+.f64 1 (*.f64 1/2 x))
	52.3%	1
▶	49.7%	(/.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) (sqrt.f64 x))
✓	100.0%	(/.f64 (expm1.f64 x) x)
✓	52.2%	(+.f64 1 (*.f64 1/2 x))
	52.3%	1

Compiler

Compiled 44 to 30 computations (31.8% saved)

localize24.0ms (1.3%)

Localize:

Found 1 expressions with local error:

New	Accuracy	Program
	99.8%	(/.f64 (expm1.f64 x) (sqrt.f64 x))

Compiler

Compiled 20 to 6 computations (70% saved)

eval12.0ms (0.6%)

Compiler: Compiled 701 to 289 computations (58.8% saved)

prune10.0ms (0.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	53	0	53
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	53	4	57

Accuracy

100.0%

Counts

57 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	49.7%	(/.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) (sqrt.f64 x))
✓	100.0%	(/.f64 (expm1.f64 x) x)
✓	52.2%	(+.f64 1 (*.f64 1/2 x))
	52.3%	1
✓	49.7%	(/.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) (sqrt.f64 x))
✓	100.0%	(/.f64 (expm1.f64 x) x)
✓	52.2%	(+.f64 1 (*.f64 1/2 x))
	52.3%	1

Compiler

Compiled 44 to 30 computations (31.8% saved)

localize0.0ms (0%)

eval0.0ms (0%)

Compiler: Compiled 1 to 1 computations (0% saved)

prune3.0ms (0.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	3	3
Total	4	4

Accuracy

100.0%

Counts

4 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	49.7%	(/.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) (sqrt.f64 x))
✓	100.0%	(/.f64 (expm1.f64 x) x)
✓	52.2%	(+.f64 1 (*.f64 1/2 x))
	52.3%	1

Compiler

Compiled 57 to 33 computations (42.1% saved)

regimes9.0ms (0.5%)

Counts

6 → 1

Calls

Call 1

Inputs
1
(+.f64 1 (*.f64 1/2 x))
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) (sqrt.f64 x))
(*.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (expm1.f64 x) (sqrt.f64 x)))

Outputs
(/.f64 (expm1.f64 x) x)

Calls

2 calls:

5.0ms	x
3.0ms	(/.f64 (-.f64 (exp.f64 x) 1) x)

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(/.f64 (-.f64 (exp.f64 x) 1) x)`

Compiler

Compiled 44 to 24 computations (45.5% saved)

regimes4.0ms (0.2%)

Accuracy

Total -0.6b remaining (-2.1%)

Threshold costs -0.6b (-2.1%)

Counts

2 → 1

Calls

Call 1

Inputs
1
(+.f64 1 (*.f64 1/2 x))

Outputs
1

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
52.3%	1	`x`

Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify15.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

2× 1-exp

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	9	12

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(/.f64 (expm1.f64 x) x)
1

Outputs
(/.f64 (expm1.f64 x) x)
1

Compiler

Compiled 7 to 5 computations (28.6% saved)

soundness124.0ms (6.4%)

Rules

1290×	`div-sub`
1216×	`fma-neg`
1162×	`fma-def`
906×	`cancel-sign-sub-inv`
870×	`associate-/r*`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	41
1	29	41
2	47	41
3	79	41
4	185	41
5	543	41
6	1635	41
7	5797	41

Stop Event

1×	node limit

Compiler

Compiled 11 to 7 computations (36.4% saved)

end0.0ms (0%)

preprocess38.0ms (2%)

Compiler: Compiled 72 to 48 computations (33.3% saved)

analyze1.0ms (0.1%)

sample1.2s (60.3%)

preprocess104.0ms (5.4%)

eval0.0ms (0%)

prune1.0ms (0%)

localize19.0ms (1%)

series2.0ms (0.1%)

rewrite59.0ms (3.1%)

simplify59.0ms (3%)

eval23.0ms (1.2%)

prune8.0ms (0.4%)

localize55.0ms (2.8%)

series5.0ms (0.3%)

rewrite72.0ms (3.7%)

simplify67.0ms (3.5%)

eval31.0ms (1.6%)

prune19.0ms (1%)

localize24.0ms (1.3%)

eval12.0ms (0.6%)

prune10.0ms (0.5%)

localize0.0ms (0%)

eval0.0ms (0%)

prune3.0ms (0.1%)

regimes9.0ms (0.5%)

regimes4.0ms (0.2%)

simplify15.0ms (0.8%)

soundness124.0ms (6.4%)

end0.0ms (0%)

preprocess38.0ms (2%)

Profiling