Metrics for Kahan's exp quotient

analyze1.0ms (0%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
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 (43.6%)

Results

519.0ms	2023×	body	1024	valid
230.0ms	2843×	body	256	valid
176.0ms	1049×	body	512	valid
172.0ms	2121×	body	256	infinite
54.0ms	220×	body	2048	valid

Bogosity

preprocess108.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

1292×	`div-sub`
1216×	`fma-neg`
1162×	`fma-def`
904×	`cancel-sign-sub-inv`
864×	`associate-/r*`

Problems

136×	No Errors
120×	`(-.f64 (exp.f64 x) 1)`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	59
1	31	59
2	49	59
3	81	59
4	187	59
5	545	59
6	1645	59
7	5861	59

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)

localize64.0ms (2.4%)

Localize:

Found 2 expressions with local error:

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

Compiler

Compiled 9 to 4 computations (55.6% saved)

series4.0ms (0.2%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	(expm1.f64 x)
1.0ms	x	@	-inf	(/.f64 (expm1.f64 x) x)
0.0ms	x	@	inf	(/.f64 (expm1.f64 x) x)
0.0ms	x	@	0	(expm1.f64 x)
0.0ms	x	@	0	(/.f64 (expm1.f64 x) x)

rewrite99.0ms (3.7%)

Algorithm

1×	batch-egg-rewrite

Rules

510×	`unpow-prod-down`
354×	`cbrt-prod`
352×	`log-prod`
332×	`log1p-expm1-u`
331×	`expm1-log1p-u`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	25
1	68	25
2	882	25

Stop Event

1×	node limit

Counts

2 → 105

Calls

Call 1

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

Outputs
(+.f64 (exp.f64 x) -1)
(+.f64 0 (expm1.f64 x))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (expm1.f64 x))) 2)) (log.f64 (cbrt.f64 (exp.f64 (expm1.f64 x)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (expm1.f64 x)))) (log.f64 (sqrt.f64 (exp.f64 (expm1.f64 x)))))
(-.f64 (exp.f64 x) 1)
(-.f64 (exp.f64 x) (log.f64 (E.f64)))
(*.f64 (expm1.f64 x) 1)
(*.f64 (expm1.f64 x) (log.f64 (E.f64)))
(*.f64 1 (expm1.f64 x))
(*.f64 (cbrt.f64 (expm1.f64 x)) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2))
(*.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (cbrt.f64 (expm1.f64 x)))
(*.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 (expm1.f64 x)))
(*.f64 (pow.f64 (expm1.f64 x) 1/4) (sqrt.f64 (pow.f64 (expm1.f64 x) 3/2)))
(*.f64 (pow.f64 1 1/3) (expm1.f64 x))
(.f64 (pow.f64 (pow.f64 (.f64 (expm1.f64 x) (cbrt.f64 (expm1.f64 x))) 2) 1/3) (cbrt.f64 (cbrt.f64 (expm1.f64 x))))
(*.f64 (pow.f64 (pow.f64 (expm1.f64 x) 5/2) 1/3) (pow.f64 (expm1.f64 x) 1/6))
(.f64 (cbrt.f64 (pow.f64 (.f64 (expm1.f64 x) (cbrt.f64 (expm1.f64 x))) 2)) (cbrt.f64 (cbrt.f64 (expm1.f64 x))))
(*.f64 (cbrt.f64 (pow.f64 (expm1.f64 x) 5/2)) (pow.f64 (expm1.f64 x) 1/6))
(*.f64 (sqrt.f64 (pow.f64 (expm1.f64 x) 3/2)) (pow.f64 (expm1.f64 x) 1/4))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 5)) (pow.f64 (expm1.f64 x) 1/6))
(/.f64 (-.f64 (pow.f64 (exp.f64 x) 2) 1) (+.f64 (exp.f64 x) 1))
(/.f64 (-.f64 (exp.f64 (.f64 x 3)) 1) (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 1 (.f64 (exp.f64 x) 1))))
(pow.f64 (expm1.f64 x) 1)
(pow.f64 (cbrt.f64 (expm1.f64 x)) 3)
(pow.f64 (pow.f64 (expm1.f64 x) 2) 1/2)
(pow.f64 (pow.f64 (expm1.f64 x) 3) 1/3)
(pow.f64 (sqrt.f64 (expm1.f64 x)) 2)
(pow.f64 (E.f64) (log.f64 (expm1.f64 x)))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (expm1.f64 x))) 2)) (cbrt.f64 (log.f64 (expm1.f64 x))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (expm1.f64 x)))) (sqrt.f64 (log.f64 (expm1.f64 x))))
(sqrt.f64 (pow.f64 (expm1.f64 x) 2))
(log.f64 (exp.f64 (expm1.f64 x)))
(cbrt.f64 (pow.f64 (expm1.f64 x) 3))
(exp.f64 (log.f64 (expm1.f64 x)))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (expm1.f64 x))) 3))
(exp.f64 (.f64 (.f64 3 (log.f64 (expm1.f64 x))) 1/3))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (expm1.f64 x))) 2))
(log1p.f64 (expm1.f64 (expm1.f64 x)))
(fma.f64 1 (exp.f64 x) -1)
(fma.f64 (cbrt.f64 (pow.f64 (exp.f64 x) 2)) (cbrt.f64 (exp.f64 x)) -1)
(fma.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 (exp.f64 x)) -1)
(+.f64 0 (/.f64 (expm1.f64 x) x))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (expm1.f64 x) x))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (expm1.f64 x) x)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (expm1.f64 x) x)))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (expm1.f64 x) 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 (/.f64 (expm1.f64 x) x) (log.f64 (E.f64)))
(*.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 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 (.f64 (/.f64 1 x) (/.f64 (expm1.f64 x) x))))
(*.f64 (neg.f64 (expm1.f64 x)) (/.f64 1 (neg.f64 x)))
(*.f64 (/.f64 1 x) (expm1.f64 x))
(*.f64 (/.f64 1 x) (pow.f64 (/.f64 1 (expm1.f64 x)) -1))
(*.f64 (pow.f64 x -1/2) (/.f64 (expm1.f64 x) (sqrt.f64 x)))
(*.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 1/4) (sqrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 3/2)))
(*.f64 (pow.f64 (cbrt.f64 x) -2) (/.f64 (expm1.f64 x) (cbrt.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) (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)))
(*.f64 (pow.f64 1 1/3) (/.f64 (expm1.f64 x) x))
(.f64 (pow.f64 (.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 2) (expm1.f64 x)) 1/3) (cbrt.f64 (/.f64 1 x)))
(.f64 (pow.f64 (pow.f64 (.f64 (/.f64 (expm1.f64 x) x) (cbrt.f64 (/.f64 (expm1.f64 x) x))) 2) 1/3) (cbrt.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x))))
(*.f64 (pow.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 5/2) 1/3) (pow.f64 (/.f64 (expm1.f64 x) x) 1/6))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 x (expm1.f64 x))) 2) -1) (cbrt.f64 (/.f64 (expm1.f64 x) x)))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) -2) -1) (pow.f64 (/.f64 x (cbrt.f64 (expm1.f64 x))) -1))
(*.f64 (pow.f64 (pow.f64 (expm1.f64 x) -1/2) -1) (pow.f64 (/.f64 x (sqrt.f64 (expm1.f64 x))) -1))
(*.f64 (pow.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) 1) -1) (pow.f64 (/.f64 (cbrt.f64 x) (expm1.f64 x)) -1))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 (pow.f64 x 2) (pow.f64 (expm1.f64 x) 2))) -1) (cbrt.f64 (/.f64 (expm1.f64 x) x)))
(*.f64 (pow.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (sqrt.f64 (expm1.f64 x))) -1) (pow.f64 (/.f64 (cbrt.f64 x) (sqrt.f64 (expm1.f64 x))) -1))
(*.f64 (pow.f64 (/.f64 (sqrt.f64 x) 1) -1) (pow.f64 (/.f64 (sqrt.f64 x) (expm1.f64 x)) -1))
(*.f64 (pow.f64 (/.f64 (sqrt.f64 x) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) -1) (pow.f64 (/.f64 (sqrt.f64 x) (cbrt.f64 (expm1.f64 x))) -1))
(.f64 (cbrt.f64 (.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 2) (expm1.f64 x))) (cbrt.f64 (/.f64 1 x)))
(.f64 (cbrt.f64 (pow.f64 (.f64 (/.f64 (expm1.f64 x) x) (cbrt.f64 (/.f64 (expm1.f64 x) x))) 2)) (cbrt.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x))))
(*.f64 (cbrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 5/2)) (pow.f64 (/.f64 (expm1.f64 x) x) 1/6))
(*.f64 (sqrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 3/2)) (pow.f64 (/.f64 (expm1.f64 x) x) 1/4))
(.f64 (sqrt.f64 (.f64 (/.f64 (expm1.f64 x) x) (expm1.f64 x))) (pow.f64 x -1/2))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 5)) (pow.f64 (/.f64 (expm1.f64 x) x) 1/6))
(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) 2) 1/2)
(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)
(pow.f64 (E.f64) (log.f64 (/.f64 (expm1.f64 x) x)))
(pow.f64 (/.f64 (/.f64 x (expm1.f64 x)) 1) -1)
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (/.f64 (expm1.f64 x) x))) 2)) (cbrt.f64 (log.f64 (/.f64 (expm1.f64 x) x))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (/.f64 (expm1.f64 x) x)))) (sqrt.f64 (log.f64 (/.f64 (expm1.f64 x) x))))
(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)))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x))) 3))
(exp.f64 (.f64 (.f64 3 (log.f64 (/.f64 (expm1.f64 x) x))) 1/3))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x))) 2))
(exp.f64 (*.f64 (log.f64 (/.f64 x (expm1.f64 x))) -1))
(log1p.f64 (expm1.f64 (/.f64 (expm1.f64 x) x)))

simplify88.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

1654×	`fma-neg`
860×	`associate-/r*`
490×	`sqr-pow`
404×	`associate-r`
402×	`associate-/r/`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	313	3248
1	693	3129
2	2787	3031
3	7503	3031

Stop Event

1×	node limit

Counts

129 → 166

Calls

Call 1

Inputs
x
(+.f64 x (*.f64 1/2 (pow.f64 x 2)))
(+.f64 x (+.f64 (.f64 1/6 (pow.f64 x 3)) (.f64 1/2 (pow.f64 x 2))))
(+.f64 x (+.f64 (.f64 1/24 (pow.f64 x 4)) (+.f64 (.f64 1/6 (pow.f64 x 3)) (*.f64 1/2 (pow.f64 x 2)))))
(-.f64 (exp.f64 x) 1)
(-.f64 (exp.f64 x) 1)
(-.f64 (exp.f64 x) 1)
(-.f64 (exp.f64 x) 1)
(-.f64 (exp.f64 x) 1)
(-.f64 (exp.f64 x) 1)
(-.f64 (exp.f64 x) 1)
(-.f64 (exp.f64 x) 1)
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 (exp.f64 x) -1)
(+.f64 0 (expm1.f64 x))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (expm1.f64 x))) 2)) (log.f64 (cbrt.f64 (exp.f64 (expm1.f64 x)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (expm1.f64 x)))) (log.f64 (sqrt.f64 (exp.f64 (expm1.f64 x)))))
(-.f64 (exp.f64 x) 1)
(-.f64 (exp.f64 x) (log.f64 (E.f64)))
(*.f64 (expm1.f64 x) 1)
(*.f64 (expm1.f64 x) (log.f64 (E.f64)))
(*.f64 1 (expm1.f64 x))
(*.f64 (cbrt.f64 (expm1.f64 x)) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2))
(*.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (cbrt.f64 (expm1.f64 x)))
(*.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 (expm1.f64 x)))
(*.f64 (pow.f64 (expm1.f64 x) 1/4) (sqrt.f64 (pow.f64 (expm1.f64 x) 3/2)))
(*.f64 (pow.f64 1 1/3) (expm1.f64 x))
(.f64 (pow.f64 (pow.f64 (.f64 (expm1.f64 x) (cbrt.f64 (expm1.f64 x))) 2) 1/3) (cbrt.f64 (cbrt.f64 (expm1.f64 x))))
(*.f64 (pow.f64 (pow.f64 (expm1.f64 x) 5/2) 1/3) (pow.f64 (expm1.f64 x) 1/6))
(.f64 (cbrt.f64 (pow.f64 (.f64 (expm1.f64 x) (cbrt.f64 (expm1.f64 x))) 2)) (cbrt.f64 (cbrt.f64 (expm1.f64 x))))
(*.f64 (cbrt.f64 (pow.f64 (expm1.f64 x) 5/2)) (pow.f64 (expm1.f64 x) 1/6))
(*.f64 (sqrt.f64 (pow.f64 (expm1.f64 x) 3/2)) (pow.f64 (expm1.f64 x) 1/4))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 5)) (pow.f64 (expm1.f64 x) 1/6))
(/.f64 (-.f64 (pow.f64 (exp.f64 x) 2) 1) (+.f64 (exp.f64 x) 1))
(/.f64 (-.f64 (exp.f64 (.f64 x 3)) 1) (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 1 (.f64 (exp.f64 x) 1))))
(pow.f64 (expm1.f64 x) 1)
(pow.f64 (cbrt.f64 (expm1.f64 x)) 3)
(pow.f64 (pow.f64 (expm1.f64 x) 2) 1/2)
(pow.f64 (pow.f64 (expm1.f64 x) 3) 1/3)
(pow.f64 (sqrt.f64 (expm1.f64 x)) 2)
(pow.f64 (E.f64) (log.f64 (expm1.f64 x)))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (expm1.f64 x))) 2)) (cbrt.f64 (log.f64 (expm1.f64 x))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (expm1.f64 x)))) (sqrt.f64 (log.f64 (expm1.f64 x))))
(sqrt.f64 (pow.f64 (expm1.f64 x) 2))
(log.f64 (exp.f64 (expm1.f64 x)))
(cbrt.f64 (pow.f64 (expm1.f64 x) 3))
(exp.f64 (log.f64 (expm1.f64 x)))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (expm1.f64 x))) 3))
(exp.f64 (.f64 (.f64 3 (log.f64 (expm1.f64 x))) 1/3))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (expm1.f64 x))) 2))
(log1p.f64 (expm1.f64 (expm1.f64 x)))
(fma.f64 1 (exp.f64 x) -1)
(fma.f64 (cbrt.f64 (pow.f64 (exp.f64 x) 2)) (cbrt.f64 (exp.f64 x)) -1)
(fma.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 (exp.f64 x)) -1)
(+.f64 0 (/.f64 (expm1.f64 x) x))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (expm1.f64 x) x))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (expm1.f64 x) x)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (expm1.f64 x) x)))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (expm1.f64 x) 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 (/.f64 (expm1.f64 x) x) (log.f64 (E.f64)))
(*.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 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 (.f64 (/.f64 1 x) (/.f64 (expm1.f64 x) x))))
(*.f64 (neg.f64 (expm1.f64 x)) (/.f64 1 (neg.f64 x)))
(*.f64 (/.f64 1 x) (expm1.f64 x))
(*.f64 (/.f64 1 x) (pow.f64 (/.f64 1 (expm1.f64 x)) -1))
(*.f64 (pow.f64 x -1/2) (/.f64 (expm1.f64 x) (sqrt.f64 x)))
(*.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 1/4) (sqrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 3/2)))
(*.f64 (pow.f64 (cbrt.f64 x) -2) (/.f64 (expm1.f64 x) (cbrt.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) (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)))
(*.f64 (pow.f64 1 1/3) (/.f64 (expm1.f64 x) x))
(.f64 (pow.f64 (.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 2) (expm1.f64 x)) 1/3) (cbrt.f64 (/.f64 1 x)))
(.f64 (pow.f64 (pow.f64 (.f64 (/.f64 (expm1.f64 x) x) (cbrt.f64 (/.f64 (expm1.f64 x) x))) 2) 1/3) (cbrt.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x))))
(*.f64 (pow.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 5/2) 1/3) (pow.f64 (/.f64 (expm1.f64 x) x) 1/6))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 x (expm1.f64 x))) 2) -1) (cbrt.f64 (/.f64 (expm1.f64 x) x)))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) -2) -1) (pow.f64 (/.f64 x (cbrt.f64 (expm1.f64 x))) -1))
(*.f64 (pow.f64 (pow.f64 (expm1.f64 x) -1/2) -1) (pow.f64 (/.f64 x (sqrt.f64 (expm1.f64 x))) -1))
(*.f64 (pow.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) 1) -1) (pow.f64 (/.f64 (cbrt.f64 x) (expm1.f64 x)) -1))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 (pow.f64 x 2) (pow.f64 (expm1.f64 x) 2))) -1) (cbrt.f64 (/.f64 (expm1.f64 x) x)))
(*.f64 (pow.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (sqrt.f64 (expm1.f64 x))) -1) (pow.f64 (/.f64 (cbrt.f64 x) (sqrt.f64 (expm1.f64 x))) -1))
(*.f64 (pow.f64 (/.f64 (sqrt.f64 x) 1) -1) (pow.f64 (/.f64 (sqrt.f64 x) (expm1.f64 x)) -1))
(*.f64 (pow.f64 (/.f64 (sqrt.f64 x) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) -1) (pow.f64 (/.f64 (sqrt.f64 x) (cbrt.f64 (expm1.f64 x))) -1))
(.f64 (cbrt.f64 (.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 2) (expm1.f64 x))) (cbrt.f64 (/.f64 1 x)))
(.f64 (cbrt.f64 (pow.f64 (.f64 (/.f64 (expm1.f64 x) x) (cbrt.f64 (/.f64 (expm1.f64 x) x))) 2)) (cbrt.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x))))
(*.f64 (cbrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 5/2)) (pow.f64 (/.f64 (expm1.f64 x) x) 1/6))
(*.f64 (sqrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 3/2)) (pow.f64 (/.f64 (expm1.f64 x) x) 1/4))
(.f64 (sqrt.f64 (.f64 (/.f64 (expm1.f64 x) x) (expm1.f64 x))) (pow.f64 x -1/2))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 5)) (pow.f64 (/.f64 (expm1.f64 x) x) 1/6))
(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) 2) 1/2)
(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)
(pow.f64 (E.f64) (log.f64 (/.f64 (expm1.f64 x) x)))
(pow.f64 (/.f64 (/.f64 x (expm1.f64 x)) 1) -1)
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (/.f64 (expm1.f64 x) x))) 2)) (cbrt.f64 (log.f64 (/.f64 (expm1.f64 x) x))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (/.f64 (expm1.f64 x) x)))) (sqrt.f64 (log.f64 (/.f64 (expm1.f64 x) x))))
(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)))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x))) 3))
(exp.f64 (.f64 (.f64 3 (log.f64 (/.f64 (expm1.f64 x) x))) 1/3))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x))) 2))
(exp.f64 (*.f64 (log.f64 (/.f64 x (expm1.f64 x))) -1))
(log1p.f64 (expm1.f64 (/.f64 (expm1.f64 x) x)))

Outputs
x
(+.f64 x (*.f64 1/2 (pow.f64 x 2)))
(fma.f64 1/2 (pow.f64 x 2) x)
(*.f64 (fma.f64 x 1/2 1) x)
(+.f64 x (+.f64 (.f64 1/6 (pow.f64 x 3)) (.f64 1/2 (pow.f64 x 2))))
(+.f64 x (fma.f64 1/6 (pow.f64 x 3) (*.f64 1/2 (pow.f64 x 2))))
(+.f64 x (fma.f64 1/2 (pow.f64 x 2) (*.f64 1/6 (pow.f64 x 3))))
(+.f64 x (.f64 (pow.f64 x 2) (+.f64 1/2 (.f64 x 1/6))))
(+.f64 x (+.f64 (.f64 1/24 (pow.f64 x 4)) (+.f64 (.f64 1/6 (pow.f64 x 3)) (*.f64 1/2 (pow.f64 x 2)))))
(+.f64 x (fma.f64 1/24 (pow.f64 x 4) (fma.f64 1/6 (pow.f64 x 3) (*.f64 1/2 (pow.f64 x 2)))))
(+.f64 x (fma.f64 1/24 (pow.f64 x 4) (fma.f64 1/2 (pow.f64 x 2) (*.f64 1/6 (pow.f64 x 3)))))
(+.f64 x (fma.f64 1/24 (pow.f64 x 4) (.f64 (pow.f64 x 2) (+.f64 1/2 (.f64 x 1/6)))))
(-.f64 (exp.f64 x) 1)
(expm1.f64 x)
(-.f64 (exp.f64 x) 1)
(expm1.f64 x)
(-.f64 (exp.f64 x) 1)
(expm1.f64 x)
(-.f64 (exp.f64 x) 1)
(expm1.f64 x)
(-.f64 (exp.f64 x) 1)
(expm1.f64 x)
(-.f64 (exp.f64 x) 1)
(expm1.f64 x)
(-.f64 (exp.f64 x) 1)
(expm1.f64 x)
(-.f64 (exp.f64 x) 1)
(expm1.f64 x)
1
(+.f64 1 (*.f64 1/2 x))
(+.f64 1 (*.f64 x 1/2))
(fma.f64 x 1/2 1)
(+.f64 1 (+.f64 (.f64 1/6 (pow.f64 x 2)) (.f64 1/2 x)))
(+.f64 1 (fma.f64 1/6 (pow.f64 x 2) (*.f64 x 1/2)))
(+.f64 1 (fma.f64 x 1/2 (*.f64 (pow.f64 x 2) 1/6)))
(+.f64 1 (.f64 x (+.f64 1/2 (.f64 x 1/6))))
(+.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 (pow.f64 x 2) (*.f64 x 1/2))))
(+.f64 (fma.f64 (pow.f64 x 3) 1/24 (*.f64 (pow.f64 x 2) 1/6)) (fma.f64 x 1/2 1))
(+.f64 (fma.f64 x 1/2 1) (.f64 (pow.f64 x 2) (+.f64 1/6 (.f64 x 1/24))))
(/.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 (exp.f64 x) -1)
(expm1.f64 x)
(+.f64 0 (expm1.f64 x))
(expm1.f64 x)
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (expm1.f64 x))) 2)) (log.f64 (cbrt.f64 (exp.f64 (expm1.f64 x)))))
(*.f64 3 (log.f64 (cbrt.f64 (exp.f64 (expm1.f64 x)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (expm1.f64 x)))) (log.f64 (sqrt.f64 (exp.f64 (expm1.f64 x)))))
(*.f64 2 (log.f64 (sqrt.f64 (exp.f64 (expm1.f64 x)))))
(-.f64 (exp.f64 x) 1)
(expm1.f64 x)
(-.f64 (exp.f64 x) (log.f64 (E.f64)))
(expm1.f64 x)
(*.f64 (expm1.f64 x) 1)
(expm1.f64 x)
(*.f64 (expm1.f64 x) (log.f64 (E.f64)))
(expm1.f64 x)
(*.f64 1 (expm1.f64 x))
(expm1.f64 x)
(*.f64 (cbrt.f64 (expm1.f64 x)) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2))
(expm1.f64 x)
(*.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (cbrt.f64 (expm1.f64 x)))
(expm1.f64 x)
(*.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 (expm1.f64 x)))
(expm1.f64 x)
(*.f64 (pow.f64 (expm1.f64 x) 1/4) (sqrt.f64 (pow.f64 (expm1.f64 x) 3/2)))
(*.f64 (pow.f64 (expm1.f64 x) 1/4) (pow.f64 (expm1.f64 x) 3/4))
(*.f64 (pow.f64 1 1/3) (expm1.f64 x))
(expm1.f64 x)
(.f64 (pow.f64 (pow.f64 (.f64 (expm1.f64 x) (cbrt.f64 (expm1.f64 x))) 2) 1/3) (cbrt.f64 (cbrt.f64 (expm1.f64 x))))
(.f64 (cbrt.f64 (pow.f64 (.f64 (expm1.f64 x) (cbrt.f64 (expm1.f64 x))) 2)) (cbrt.f64 (cbrt.f64 (expm1.f64 x))))
(*.f64 (cbrt.f64 (pow.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 4) 2)) (cbrt.f64 (cbrt.f64 (expm1.f64 x))))
(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 8)) (cbrt.f64 (cbrt.f64 (expm1.f64 x))))
(*.f64 (pow.f64 (pow.f64 (expm1.f64 x) 5/2) 1/3) (pow.f64 (expm1.f64 x) 1/6))
(*.f64 (cbrt.f64 (pow.f64 (expm1.f64 x) 5/2)) (pow.f64 (expm1.f64 x) 1/6))
(.f64 (cbrt.f64 (pow.f64 (.f64 (expm1.f64 x) (cbrt.f64 (expm1.f64 x))) 2)) (cbrt.f64 (cbrt.f64 (expm1.f64 x))))
(*.f64 (cbrt.f64 (pow.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 4) 2)) (cbrt.f64 (cbrt.f64 (expm1.f64 x))))
(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 8)) (cbrt.f64 (cbrt.f64 (expm1.f64 x))))
(*.f64 (cbrt.f64 (pow.f64 (expm1.f64 x) 5/2)) (pow.f64 (expm1.f64 x) 1/6))
(*.f64 (sqrt.f64 (pow.f64 (expm1.f64 x) 3/2)) (pow.f64 (expm1.f64 x) 1/4))
(*.f64 (pow.f64 (expm1.f64 x) 1/4) (sqrt.f64 (pow.f64 (expm1.f64 x) 3/2)))
(*.f64 (pow.f64 (expm1.f64 x) 1/4) (pow.f64 (expm1.f64 x) 3/4))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 5)) (pow.f64 (expm1.f64 x) 1/6))
(*.f64 (pow.f64 (expm1.f64 x) 1/6) (sqrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 5)))
(*.f64 (pow.f64 (expm1.f64 x) 1/6) (pow.f64 (cbrt.f64 (expm1.f64 x)) 5/2))
(/.f64 (-.f64 (pow.f64 (exp.f64 x) 2) 1) (+.f64 (exp.f64 x) 1))
(/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (+.f64 (exp.f64 x) 1))
(/.f64 (+.f64 -1 (pow.f64 (exp.f64 x) 2)) (+.f64 (exp.f64 x) 1))
(/.f64 (expm1.f64 (*.f64 2 x)) (+.f64 (exp.f64 x) 1))
(/.f64 (-.f64 (exp.f64 (.f64 x 3)) 1) (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 1 (.f64 (exp.f64 x) 1))))
(/.f64 (expm1.f64 (*.f64 x 3)) (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 (exp.f64 x) 1)))
(/.f64 (expm1.f64 (*.f64 x 3)) (+.f64 (exp.f64 x) (+.f64 1 (pow.f64 (exp.f64 x) 2))))
(pow.f64 (expm1.f64 x) 1)
(expm1.f64 x)
(pow.f64 (cbrt.f64 (expm1.f64 x)) 3)
(expm1.f64 x)
(pow.f64 (pow.f64 (expm1.f64 x) 2) 1/2)
(expm1.f64 x)
(pow.f64 (pow.f64 (expm1.f64 x) 3) 1/3)
(expm1.f64 x)
(pow.f64 (sqrt.f64 (expm1.f64 x)) 2)
(expm1.f64 x)
(pow.f64 (E.f64) (log.f64 (expm1.f64 x)))
(expm1.f64 x)
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (expm1.f64 x))) 2)) (cbrt.f64 (log.f64 (expm1.f64 x))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (expm1.f64 x)))) (sqrt.f64 (log.f64 (expm1.f64 x))))
(sqrt.f64 (pow.f64 (expm1.f64 x) 2))
(expm1.f64 x)
(log.f64 (exp.f64 (expm1.f64 x)))
(expm1.f64 x)
(cbrt.f64 (pow.f64 (expm1.f64 x) 3))
(expm1.f64 x)
(exp.f64 (log.f64 (expm1.f64 x)))
(expm1.f64 x)
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (expm1.f64 x))) 3))
(expm1.f64 x)
(exp.f64 (.f64 (.f64 3 (log.f64 (expm1.f64 x))) 1/3))
(expm1.f64 x)
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (expm1.f64 x))) 2))
(expm1.f64 x)
(log1p.f64 (expm1.f64 (expm1.f64 x)))
(expm1.f64 x)
(fma.f64 1 (exp.f64 x) -1)
(expm1.f64 x)
(fma.f64 (cbrt.f64 (pow.f64 (exp.f64 x) 2)) (cbrt.f64 (exp.f64 x)) -1)
(fma.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 (exp.f64 x)) -1)
(expm1.f64 x)
(+.f64 0 (/.f64 (expm1.f64 x) x))
(/.f64 (expm1.f64 x) x)
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (expm1.f64 x) x))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (expm1.f64 x) x)))))
(*.f64 3 (log.f64 (cbrt.f64 (exp.f64 (/.f64 (expm1.f64 x) x)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (expm1.f64 x) x)))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (expm1.f64 x) x)))))
(*.f64 2 (log.f64 (sqrt.f64 (exp.f64 (/.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 (/.f64 (expm1.f64 x) x) (log.f64 (E.f64)))
(/.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 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 (.f64 (/.f64 1 x) (/.f64 (expm1.f64 x) 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 x) (pow.f64 (/.f64 1 (expm1.f64 x)) -1))
(/.f64 (expm1.f64 x) x)
(*.f64 (pow.f64 x -1/2) (/.f64 (expm1.f64 x) (sqrt.f64 x)))
(*.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 1/4) (sqrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 3/2)))
(*.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 1/4) (pow.f64 (/.f64 (expm1.f64 x) x) 3/4))
(*.f64 (pow.f64 (cbrt.f64 x) -2) (/.f64 (expm1.f64 x) (cbrt.f64 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) (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 (pow.f64 (cbrt.f64 x) -2) (/.f64 (expm1.f64 x) (cbrt.f64 x)))
(*.f64 (pow.f64 1 1/3) (/.f64 (expm1.f64 x) x))
(/.f64 (expm1.f64 x) x)
(.f64 (pow.f64 (.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 2) (expm1.f64 x)) 1/3) (cbrt.f64 (/.f64 1 x)))
(.f64 (cbrt.f64 (.f64 (expm1.f64 x) (pow.f64 (/.f64 (expm1.f64 x) x) 2))) (cbrt.f64 (/.f64 1 x)))
(.f64 (pow.f64 (pow.f64 (.f64 (/.f64 (expm1.f64 x) x) (cbrt.f64 (/.f64 (expm1.f64 x) x))) 2) 1/3) (cbrt.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x))))
(.f64 (cbrt.f64 (pow.f64 (.f64 (/.f64 (expm1.f64 x) x) (cbrt.f64 (/.f64 (expm1.f64 x) x))) 2)) (cbrt.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x))))
(*.f64 (cbrt.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 4) 2)) (cbrt.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x))))
(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 8)) (cbrt.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x))))
(*.f64 (pow.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 5/2) 1/3) (pow.f64 (/.f64 (expm1.f64 x) x) 1/6))
(*.f64 (cbrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 5/2)) (pow.f64 (/.f64 (expm1.f64 x) x) 1/6))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 x (expm1.f64 x))) 2) -1) (cbrt.f64 (/.f64 (expm1.f64 x) x)))
(*.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) (/.f64 1 (pow.f64 (cbrt.f64 (/.f64 x (expm1.f64 x))) 2)))
(/.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) (pow.f64 (cbrt.f64 (/.f64 x (expm1.f64 x))) 2))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) -2) -1) (pow.f64 (/.f64 x (cbrt.f64 (expm1.f64 x))) -1))
(/.f64 (expm1.f64 x) x)
(*.f64 (pow.f64 (pow.f64 (expm1.f64 x) -1/2) -1) (pow.f64 (/.f64 x (sqrt.f64 (expm1.f64 x))) -1))
(*.f64 (/.f64 1 (pow.f64 (expm1.f64 x) -1/2)) (/.f64 1 (/.f64 x (sqrt.f64 (expm1.f64 x)))))
(*.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) x) (/.f64 1 (pow.f64 (expm1.f64 x) -1/2)))
(/.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) x) (pow.f64 (expm1.f64 x) -1/2))
(*.f64 (pow.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) 1) -1) (pow.f64 (/.f64 (cbrt.f64 x) (expm1.f64 x)) -1))
(*.f64 (pow.f64 (cbrt.f64 x) -2) (/.f64 (expm1.f64 x) (cbrt.f64 x)))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 (pow.f64 x 2) (pow.f64 (expm1.f64 x) 2))) -1) (cbrt.f64 (/.f64 (expm1.f64 x) x)))
(*.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) (/.f64 1 (cbrt.f64 (/.f64 (pow.f64 x 2) (pow.f64 (expm1.f64 x) 2)))))
(/.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) (cbrt.f64 (/.f64 (pow.f64 x 2) (pow.f64 (expm1.f64 x) 2))))
(*.f64 (pow.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (sqrt.f64 (expm1.f64 x))) -1) (pow.f64 (/.f64 (cbrt.f64 x) (sqrt.f64 (expm1.f64 x))) -1))
(*.f64 (/.f64 1 (/.f64 (pow.f64 (cbrt.f64 x) 2) (sqrt.f64 (expm1.f64 x)))) (/.f64 1 (/.f64 (cbrt.f64 x) (sqrt.f64 (expm1.f64 x)))))
(.f64 (.f64 (/.f64 1 (pow.f64 (cbrt.f64 x) 2)) (sqrt.f64 (expm1.f64 x))) (*.f64 (/.f64 1 (cbrt.f64 x)) (sqrt.f64 (expm1.f64 x))))
(.f64 (/.f64 (.f64 (pow.f64 (cbrt.f64 x) -2) (sqrt.f64 (expm1.f64 x))) (cbrt.f64 x)) (sqrt.f64 (expm1.f64 x)))
(*.f64 (pow.f64 (/.f64 (sqrt.f64 x) 1) -1) (pow.f64 (/.f64 (sqrt.f64 x) (expm1.f64 x)) -1))
(/.f64 (expm1.f64 x) x)
(*.f64 (pow.f64 (/.f64 (sqrt.f64 x) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) -1) (pow.f64 (/.f64 (sqrt.f64 x) (cbrt.f64 (expm1.f64 x))) -1))
(*.f64 (/.f64 1 (/.f64 (sqrt.f64 x) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2))) (/.f64 1 (/.f64 (sqrt.f64 x) (cbrt.f64 (expm1.f64 x)))))
(.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (*.f64 (/.f64 1 (sqrt.f64 x)) (cbrt.f64 (expm1.f64 x))))
(/.f64 (*.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (/.f64 (sqrt.f64 x) (cbrt.f64 (expm1.f64 x))))
(.f64 (cbrt.f64 (.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 2) (expm1.f64 x))) (cbrt.f64 (/.f64 1 x)))
(.f64 (cbrt.f64 (.f64 (expm1.f64 x) (pow.f64 (/.f64 (expm1.f64 x) x) 2))) (cbrt.f64 (/.f64 1 x)))
(.f64 (cbrt.f64 (pow.f64 (.f64 (/.f64 (expm1.f64 x) x) (cbrt.f64 (/.f64 (expm1.f64 x) x))) 2)) (cbrt.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x))))
(*.f64 (cbrt.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 4) 2)) (cbrt.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x))))
(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 8)) (cbrt.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x))))
(*.f64 (cbrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 5/2)) (pow.f64 (/.f64 (expm1.f64 x) x) 1/6))
(*.f64 (sqrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 3/2)) (pow.f64 (/.f64 (expm1.f64 x) x) 1/4))
(*.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 1/4) (sqrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 3/2)))
(*.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 1/4) (pow.f64 (/.f64 (expm1.f64 x) x) 3/4))
(.f64 (sqrt.f64 (.f64 (/.f64 (expm1.f64 x) x) (expm1.f64 x))) (pow.f64 x -1/2))
(*.f64 (pow.f64 x -1/2) (sqrt.f64 (/.f64 (pow.f64 (expm1.f64 x) 2) x)))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 5)) (pow.f64 (/.f64 (expm1.f64 x) x) 1/6))
(*.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 1/6) (sqrt.f64 (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 5)))
(*.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 1/6) (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 5/2))
(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) 2) 1/2)
(/.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)
(pow.f64 (E.f64) (log.f64 (/.f64 (expm1.f64 x) x)))
(/.f64 (expm1.f64 x) x)
(pow.f64 (/.f64 (/.f64 x (expm1.f64 x)) 1) -1)
(/.f64 (expm1.f64 x) x)
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (/.f64 (expm1.f64 x) x))) 2)) (cbrt.f64 (log.f64 (/.f64 (expm1.f64 x) x))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (/.f64 (expm1.f64 x) x)))) (sqrt.f64 (log.f64 (/.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)
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x))) 3))
(/.f64 (expm1.f64 x) x)
(exp.f64 (.f64 (.f64 3 (log.f64 (/.f64 (expm1.f64 x) x))) 1/3))
(/.f64 (expm1.f64 x) x)
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x))) 2))
(/.f64 (expm1.f64 x) x)
(exp.f64 (*.f64 (log.f64 (/.f64 x (expm1.f64 x))) -1))
(/.f64 (expm1.f64 x) x)
(log1p.f64 (expm1.f64 (/.f64 (expm1.f64 x) x)))
(/.f64 (expm1.f64 x) x)

eval35.0ms (1.3%)

Compiler: Compiled 1872 to 916 computations (51.1% saved)

prune27.0ms (1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	162	4	166
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	162	5	167

Accuracy

100.0%

Counts

167 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(/.f64 (expm1.f64 x) x)
▶	59.7%	(+.f64 1 (.f64 x (+.f64 1/2 (.f64 x 1/6))))
▶	48.3%	(+.f64 1 (*.f64 x 1/2))
▶	99.9%	(*.f64 (/.f64 1 x) (expm1.f64 x))
	48.4%	1
✓	100.0%	(/.f64 (expm1.f64 x) x)
▶	59.7%	(+.f64 1 (.f64 x (+.f64 1/2 (.f64 x 1/6))))
▶	48.3%	(+.f64 1 (*.f64 x 1/2))
▶	99.9%	(*.f64 (/.f64 1 x) (expm1.f64 x))
	48.4%	1

Compiler

Compiled 60 to 46 computations (23.3% saved)

localize93.0ms (3.5%)

Localize:

Found 4 expressions with local error:

New	Accuracy	Program
✓	99.9%	(.f64 x (+.f64 1/2 (.f64 x 1/6)))
✓	99.5%	(*.f64 x 1/6)
	100.0%	(expm1.f64 x)
✓	99.9%	(*.f64 (/.f64 1 x) (expm1.f64 x))

Compiler

Compiled 54 to 38 computations (29.6% saved)

series3.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(.f64 x (+.f64 1/2 (.f64 x 1/6)))
0.0ms	x	@	-inf	(.f64 x (+.f64 1/2 (.f64 x 1/6)))
0.0ms	x	@	-inf	(*.f64 x 1/6)
0.0ms	x	@	inf	(*.f64 x 1/6)
0.0ms	x	@	0	(.f64 x (+.f64 1/2 (.f64 x 1/6)))

rewrite74.0ms (2.8%)

Algorithm

1×	batch-egg-rewrite

Rules

882×	`log-prod`
828×	`log1p-expm1-u`
827×	`expm1-log1p-u`
568×	`prod-diff`
380×	`pow-exp`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	52
1	173	48
2	2316	48

Stop Event

1×	node limit

Counts

3 → 115

Calls

Call 1

Inputs
(*.f64 (/.f64 1 x) (expm1.f64 x))
(*.f64 x 1/6)
(.f64 x (+.f64 1/2 (.f64 x 1/6)))

Outputs
(+.f64 0 (/.f64 (expm1.f64 x) x))
(+.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (/.f64 (expm1.f64 x) x))) (cbrt.f64 (exp.f64 (/.f64 (expm1.f64 x) x))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (expm1.f64 x) x)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (expm1.f64 x) x)))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (expm1.f64 x) x)))))
(-.f64 (exp.f64 (log1p.f64 (/.f64 (expm1.f64 x) x))) 1)
(-.f64 (/.f64 (exp.f64 x) x) (/.f64 1 x))
(/.f64 1 (/.f64 x (expm1.f64 x)))
(/.f64 (expm1.f64 x) x)
(/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (/.f64 x (cbrt.f64 (expm1.f64 x))))
(/.f64 (sqrt.f64 (expm1.f64 x)) (/.f64 x (sqrt.f64 (expm1.f64 x))))
(/.f64 (neg.f64 (expm1.f64 x)) (neg.f64 x))
(/.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) (sqrt.f64 x))
(/.f64 (*.f64 (expm1.f64 x) -1) (neg.f64 x))
(/.f64 (*.f64 -1 (expm1.f64 x)) (neg.f64 x))
(/.f64 (/.f64 (expm1.f64 x) 1) x)
(/.f64 (/.f64 (expm1.f64 x) (pow.f64 (cbrt.f64 x) 2)) (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)
(sqrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 2))
(log.f64 (exp.f64 (/.f64 (expm1.f64 x) x)))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 (expm1.f64 x) x))))
(cbrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 3))
(cbrt.f64 (*.f64 (pow.f64 (/.f64 1 x) 3) (pow.f64 (expm1.f64 x) 3)))
(cbrt.f64 (*.f64 (pow.f64 (expm1.f64 x) 3) (pow.f64 (/.f64 1 x) 3)))
(cbrt.f64 (/.f64 (pow.f64 (expm1.f64 x) 3) (pow.f64 x 3)))
(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))
(exp.f64 (.f64 (.f64 (log.f64 (/.f64 (expm1.f64 x) x)) 1) 1))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x))) 3))
(exp.f64 (.f64 (.f64 3 (log.f64 (/.f64 (expm1.f64 x) x))) 1/3))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x))) 2))
(log1p.f64 (expm1.f64 (/.f64 (expm1.f64 x) x)))
(+.f64 0 (*.f64 x 1/6))
(+.f64 (log.f64 (*.f64 (cbrt.f64 (pow.f64 (exp.f64 x) 1/6)) (cbrt.f64 (pow.f64 (exp.f64 x) 1/6)))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 x) 1/6))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 x) 1/6))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 x) 1/6))))
(-.f64 (exp.f64 (log1p.f64 (*.f64 x 1/6))) 1)
(pow.f64 (*.f64 x 1/6) 1)
(pow.f64 (cbrt.f64 (*.f64 x 1/6)) 3)
(pow.f64 (*.f64 (pow.f64 x 3) 1/216) 1/3)
(pow.f64 (sqrt.f64 (*.f64 x 1/6)) 2)
(sqrt.f64 (*.f64 (pow.f64 x 2) 1/36))
(log.f64 (pow.f64 (exp.f64 x) 1/6))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 x 1/6))))
(cbrt.f64 (*.f64 (pow.f64 x 3) 1/216))
(expm1.f64 (log1p.f64 (*.f64 x 1/6)))
(exp.f64 (log.f64 (*.f64 x 1/6)))
(exp.f64 (.f64 (log.f64 (.f64 x 1/6)) 1))
(exp.f64 (.f64 (.f64 (log.f64 (*.f64 x 1/6)) 1) 1))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 x 1/6))) 3))
(exp.f64 (.f64 (.f64 (log.f64 (*.f64 x 1/6)) 3) 1/3))
(exp.f64 (.f64 (.f64 3 (log.f64 (*.f64 x 1/6))) 1/3))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 x 1/6))) 2))
(log1p.f64 (expm1.f64 (*.f64 x 1/6)))
(+.f64 0 (*.f64 x (fma.f64 x 1/6 1/2)))
(+.f64 (.f64 x 1/2) (.f64 1/6 (pow.f64 x 2)))
(+.f64 (.f64 1/6 (pow.f64 x 2)) (.f64 x 1/2))
(+.f64 (.f64 (.f64 x 1/2) 1) (.f64 (.f64 1/6 (pow.f64 x 2)) 1))
(+.f64 (log.f64 (*.f64 (cbrt.f64 (pow.f64 (exp.f64 x) (fma.f64 x 1/6 1/2))) (cbrt.f64 (pow.f64 (exp.f64 x) (fma.f64 x 1/6 1/2))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 x) (fma.f64 x 1/6 1/2)))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 x) (fma.f64 x 1/6 1/2)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 x) (fma.f64 x 1/6 1/2)))))
(-.f64 (exp.f64 (log1p.f64 (*.f64 x (fma.f64 x 1/6 1/2)))) 1)
(/.f64 (+.f64 (pow.f64 (.f64 x 1/2) 3) (pow.f64 (.f64 1/6 (pow.f64 x 2)) 3)) (fma.f64 (.f64 x 1/2) (.f64 x 1/2) (-.f64 (.f64 (.f64 1/6 (pow.f64 x 2)) (.f64 1/6 (pow.f64 x 2))) (.f64 (.f64 x 1/2) (.f64 1/6 (pow.f64 x 2))))))
(/.f64 (-.f64 (.f64 (.f64 x 1/2) (.f64 x 1/2)) (.f64 (.f64 1/6 (pow.f64 x 2)) (.f64 1/6 (pow.f64 x 2)))) (-.f64 (.f64 x 1/2) (.f64 1/6 (pow.f64 x 2))))
(/.f64 (.f64 x (fma.f64 (pow.f64 x 3) 1/216 1/8)) (fma.f64 (.f64 x 1/6) (fma.f64 x 1/6 -1/2) 1/4))
(/.f64 (.f64 x (-.f64 1/4 (.f64 (pow.f64 x 2) 1/36))) (+.f64 1/2 (*.f64 -1/6 x)))
(/.f64 (.f64 (fma.f64 (pow.f64 x 3) 1/216 1/8) x) (fma.f64 (.f64 x 1/6) (fma.f64 x 1/6 -1/2) 1/4))
(/.f64 (.f64 (-.f64 1/4 (.f64 (pow.f64 x 2) 1/36)) x) (+.f64 1/2 (*.f64 -1/6 x)))
(pow.f64 (*.f64 x (fma.f64 x 1/6 1/2)) 1)
(pow.f64 (cbrt.f64 (*.f64 x (fma.f64 x 1/6 1/2))) 3)
(pow.f64 (pow.f64 (*.f64 x (fma.f64 x 1/6 1/2)) 3) 1/3)
(pow.f64 (sqrt.f64 (*.f64 x (fma.f64 x 1/6 1/2))) 2)
(sqrt.f64 (pow.f64 (*.f64 x (fma.f64 x 1/6 1/2)) 2))
(log.f64 (pow.f64 (exp.f64 x) (fma.f64 x 1/6 1/2)))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 x (fma.f64 x 1/6 1/2)))))
(log.f64 (.f64 (exp.f64 (.f64 1/6 (pow.f64 x 2))) (exp.f64 (*.f64 x 1/2))))
(cbrt.f64 (pow.f64 (*.f64 x (fma.f64 x 1/6 1/2)) 3))
(cbrt.f64 (*.f64 (pow.f64 x 3) (pow.f64 (fma.f64 x 1/6 1/2) 3)))
(cbrt.f64 (*.f64 (pow.f64 (fma.f64 x 1/6 1/2) 3) (pow.f64 x 3)))
(expm1.f64 (log1p.f64 (*.f64 x (fma.f64 x 1/6 1/2))))
(exp.f64 (log.f64 (*.f64 x (fma.f64 x 1/6 1/2))))
(exp.f64 (.f64 (log.f64 (.f64 x (fma.f64 x 1/6 1/2))) 1))
(exp.f64 (.f64 (.f64 (log.f64 (*.f64 x (fma.f64 x 1/6 1/2))) 1) 1))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 x (fma.f64 x 1/6 1/2)))) 3))
(exp.f64 (.f64 (.f64 3 (log.f64 (*.f64 x (fma.f64 x 1/6 1/2)))) 1/3))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 x (fma.f64 x 1/6 1/2)))) 2))
(log1p.f64 (expm1.f64 (*.f64 x (fma.f64 x 1/6 1/2))))
(fma.f64 1 (.f64 x 1/2) (.f64 1/6 (pow.f64 x 2)))
(fma.f64 1 (.f64 1/6 (pow.f64 x 2)) (.f64 x 1/2))
(fma.f64 x (.f64 x 1/6) (.f64 x 1/2))
(fma.f64 x 1/2 (*.f64 1/6 (pow.f64 x 2)))
(fma.f64 1/6 (pow.f64 x 2) (*.f64 x 1/2))
(fma.f64 (.f64 x 1/6) x (.f64 x 1/2))
(fma.f64 1/2 x (*.f64 1/6 (pow.f64 x 2)))
(fma.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) 1/2) (.f64 1/6 (pow.f64 x 2)))
(fma.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (.f64 x 1/6)) (*.f64 x 1/2))
(fma.f64 (pow.f64 (cbrt.f64 (.f64 x 1/6)) 2) (.f64 (cbrt.f64 (.f64 x 1/6)) x) (.f64 x 1/2))
(fma.f64 (pow.f64 x 2) 1/6 (*.f64 x 1/2))
(fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) 1/2) (.f64 1/6 (pow.f64 x 2)))
(fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (.f64 x 1/6)) (*.f64 x 1/2))
(fma.f64 (sqrt.f64 (.f64 x 1/6)) (.f64 (sqrt.f64 (.f64 x 1/6)) x) (.f64 x 1/2))
(fma.f64 (.f64 x 1/2) 1 (.f64 (*.f64 1/6 (pow.f64 x 2)) 1))
(fma.f64 (.f64 (cbrt.f64 (.f64 x 1/2)) (cbrt.f64 (.f64 x 1/2))) (cbrt.f64 (.f64 x 1/2)) (*.f64 1/6 (pow.f64 x 2)))
(fma.f64 (.f64 (cbrt.f64 (.f64 1/6 (pow.f64 x 2))) (cbrt.f64 (.f64 1/6 (pow.f64 x 2)))) (cbrt.f64 (.f64 1/6 (pow.f64 x 2))) (*.f64 x 1/2))
(fma.f64 (sqrt.f64 (.f64 x 1/2)) (sqrt.f64 (.f64 x 1/2)) (*.f64 1/6 (pow.f64 x 2)))
(fma.f64 (sqrt.f64 (.f64 1/6 (pow.f64 x 2))) (sqrt.f64 (.f64 1/6 (pow.f64 x 2))) (*.f64 x 1/2))
(fma.f64 (.f64 (sqrt.f64 (.f64 x 1/6)) (sqrt.f64 x)) (.f64 (sqrt.f64 (.f64 x 1/6)) (sqrt.f64 x)) (*.f64 x 1/2))
(fma.f64 (.f64 (sqrt.f64 x) (sqrt.f64 (.f64 x 1/6))) (.f64 (sqrt.f64 x) (sqrt.f64 (.f64 x 1/6))) (*.f64 x 1/2))
(fma.f64 (.f64 1/2 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (.f64 1/6 (pow.f64 x 2)))
(fma.f64 (.f64 1/2 (sqrt.f64 x)) (sqrt.f64 x) (.f64 1/6 (pow.f64 x 2)))
(fma.f64 (.f64 (.f64 x 1/6) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (*.f64 x 1/2))
(fma.f64 (.f64 (.f64 x 1/6) (sqrt.f64 x)) (sqrt.f64 x) (*.f64 x 1/2))
(fma.f64 (.f64 x (pow.f64 (cbrt.f64 (.f64 x 1/6)) 2)) (cbrt.f64 (.f64 x 1/6)) (.f64 x 1/2))
(fma.f64 (.f64 x (sqrt.f64 (.f64 x 1/6))) (sqrt.f64 (.f64 x 1/6)) (.f64 x 1/2))

simplify58.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

1170×	`distribute-lft-in`
1110×	`distribute-rgt-in`
754×	`unswap-sqr`
430×	`times-frac`
392×	`associate-/r*`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	302	3556
1	675	3060
2	2074	2898

Stop Event

1×	node limit

Counts

151 → 147

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 1/6 x)
(*.f64 1/6 x)
(*.f64 1/6 x)
(*.f64 1/6 x)
(*.f64 1/6 x)
(*.f64 1/6 x)
(*.f64 1/6 x)
(*.f64 1/6 x)
(*.f64 1/6 x)
(*.f64 1/6 x)
(*.f64 1/6 x)
(*.f64 1/6 x)
(*.f64 1/2 x)
(+.f64 (.f64 1/6 (pow.f64 x 2)) (.f64 1/2 x))
(+.f64 (.f64 1/6 (pow.f64 x 2)) (.f64 1/2 x))
(+.f64 (.f64 1/6 (pow.f64 x 2)) (.f64 1/2 x))
(*.f64 1/6 (pow.f64 x 2))
(+.f64 (.f64 1/6 (pow.f64 x 2)) (.f64 1/2 x))
(+.f64 (.f64 1/6 (pow.f64 x 2)) (.f64 1/2 x))
(+.f64 (.f64 1/6 (pow.f64 x 2)) (.f64 1/2 x))
(*.f64 1/6 (pow.f64 x 2))
(+.f64 (.f64 1/6 (pow.f64 x 2)) (.f64 1/2 x))
(+.f64 (.f64 1/6 (pow.f64 x 2)) (.f64 1/2 x))
(+.f64 (.f64 1/6 (pow.f64 x 2)) (.f64 1/2 x))
(+.f64 0 (/.f64 (expm1.f64 x) x))
(+.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (/.f64 (expm1.f64 x) x))) (cbrt.f64 (exp.f64 (/.f64 (expm1.f64 x) x))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (expm1.f64 x) x)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (expm1.f64 x) x)))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (expm1.f64 x) x)))))
(-.f64 (exp.f64 (log1p.f64 (/.f64 (expm1.f64 x) x))) 1)
(-.f64 (/.f64 (exp.f64 x) x) (/.f64 1 x))
(/.f64 1 (/.f64 x (expm1.f64 x)))
(/.f64 (expm1.f64 x) x)
(/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (/.f64 x (cbrt.f64 (expm1.f64 x))))
(/.f64 (sqrt.f64 (expm1.f64 x)) (/.f64 x (sqrt.f64 (expm1.f64 x))))
(/.f64 (neg.f64 (expm1.f64 x)) (neg.f64 x))
(/.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) (sqrt.f64 x))
(/.f64 (*.f64 (expm1.f64 x) -1) (neg.f64 x))
(/.f64 (*.f64 -1 (expm1.f64 x)) (neg.f64 x))
(/.f64 (/.f64 (expm1.f64 x) 1) x)
(/.f64 (/.f64 (expm1.f64 x) (pow.f64 (cbrt.f64 x) 2)) (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)
(sqrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 2))
(log.f64 (exp.f64 (/.f64 (expm1.f64 x) x)))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 (expm1.f64 x) x))))
(cbrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 3))
(cbrt.f64 (*.f64 (pow.f64 (/.f64 1 x) 3) (pow.f64 (expm1.f64 x) 3)))
(cbrt.f64 (*.f64 (pow.f64 (expm1.f64 x) 3) (pow.f64 (/.f64 1 x) 3)))
(cbrt.f64 (/.f64 (pow.f64 (expm1.f64 x) 3) (pow.f64 x 3)))
(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))
(exp.f64 (.f64 (.f64 (log.f64 (/.f64 (expm1.f64 x) x)) 1) 1))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x))) 3))
(exp.f64 (.f64 (.f64 3 (log.f64 (/.f64 (expm1.f64 x) x))) 1/3))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x))) 2))
(log1p.f64 (expm1.f64 (/.f64 (expm1.f64 x) x)))
(+.f64 0 (*.f64 x 1/6))
(+.f64 (log.f64 (*.f64 (cbrt.f64 (pow.f64 (exp.f64 x) 1/6)) (cbrt.f64 (pow.f64 (exp.f64 x) 1/6)))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 x) 1/6))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 x) 1/6))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 x) 1/6))))
(-.f64 (exp.f64 (log1p.f64 (*.f64 x 1/6))) 1)
(pow.f64 (*.f64 x 1/6) 1)
(pow.f64 (cbrt.f64 (*.f64 x 1/6)) 3)
(pow.f64 (*.f64 (pow.f64 x 3) 1/216) 1/3)
(pow.f64 (sqrt.f64 (*.f64 x 1/6)) 2)
(sqrt.f64 (*.f64 (pow.f64 x 2) 1/36))
(log.f64 (pow.f64 (exp.f64 x) 1/6))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 x 1/6))))
(cbrt.f64 (*.f64 (pow.f64 x 3) 1/216))
(expm1.f64 (log1p.f64 (*.f64 x 1/6)))
(exp.f64 (log.f64 (*.f64 x 1/6)))
(exp.f64 (.f64 (log.f64 (.f64 x 1/6)) 1))
(exp.f64 (.f64 (.f64 (log.f64 (*.f64 x 1/6)) 1) 1))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 x 1/6))) 3))
(exp.f64 (.f64 (.f64 (log.f64 (*.f64 x 1/6)) 3) 1/3))
(exp.f64 (.f64 (.f64 3 (log.f64 (*.f64 x 1/6))) 1/3))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 x 1/6))) 2))
(log1p.f64 (expm1.f64 (*.f64 x 1/6)))
(+.f64 0 (*.f64 x (fma.f64 x 1/6 1/2)))
(+.f64 (.f64 x 1/2) (.f64 1/6 (pow.f64 x 2)))
(+.f64 (.f64 1/6 (pow.f64 x 2)) (.f64 x 1/2))
(+.f64 (.f64 (.f64 x 1/2) 1) (.f64 (.f64 1/6 (pow.f64 x 2)) 1))
(+.f64 (log.f64 (*.f64 (cbrt.f64 (pow.f64 (exp.f64 x) (fma.f64 x 1/6 1/2))) (cbrt.f64 (pow.f64 (exp.f64 x) (fma.f64 x 1/6 1/2))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 x) (fma.f64 x 1/6 1/2)))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 x) (fma.f64 x 1/6 1/2)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 x) (fma.f64 x 1/6 1/2)))))
(-.f64 (exp.f64 (log1p.f64 (*.f64 x (fma.f64 x 1/6 1/2)))) 1)
(/.f64 (+.f64 (pow.f64 (.f64 x 1/2) 3) (pow.f64 (.f64 1/6 (pow.f64 x 2)) 3)) (fma.f64 (.f64 x 1/2) (.f64 x 1/2) (-.f64 (.f64 (.f64 1/6 (pow.f64 x 2)) (.f64 1/6 (pow.f64 x 2))) (.f64 (.f64 x 1/2) (.f64 1/6 (pow.f64 x 2))))))
(/.f64 (-.f64 (.f64 (.f64 x 1/2) (.f64 x 1/2)) (.f64 (.f64 1/6 (pow.f64 x 2)) (.f64 1/6 (pow.f64 x 2)))) (-.f64 (.f64 x 1/2) (.f64 1/6 (pow.f64 x 2))))
(/.f64 (.f64 x (fma.f64 (pow.f64 x 3) 1/216 1/8)) (fma.f64 (.f64 x 1/6) (fma.f64 x 1/6 -1/2) 1/4))
(/.f64 (.f64 x (-.f64 1/4 (.f64 (pow.f64 x 2) 1/36))) (+.f64 1/2 (*.f64 -1/6 x)))
(/.f64 (.f64 (fma.f64 (pow.f64 x 3) 1/216 1/8) x) (fma.f64 (.f64 x 1/6) (fma.f64 x 1/6 -1/2) 1/4))
(/.f64 (.f64 (-.f64 1/4 (.f64 (pow.f64 x 2) 1/36)) x) (+.f64 1/2 (*.f64 -1/6 x)))
(pow.f64 (*.f64 x (fma.f64 x 1/6 1/2)) 1)
(pow.f64 (cbrt.f64 (*.f64 x (fma.f64 x 1/6 1/2))) 3)
(pow.f64 (pow.f64 (*.f64 x (fma.f64 x 1/6 1/2)) 3) 1/3)
(pow.f64 (sqrt.f64 (*.f64 x (fma.f64 x 1/6 1/2))) 2)
(sqrt.f64 (pow.f64 (*.f64 x (fma.f64 x 1/6 1/2)) 2))
(log.f64 (pow.f64 (exp.f64 x) (fma.f64 x 1/6 1/2)))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 x (fma.f64 x 1/6 1/2)))))
(log.f64 (.f64 (exp.f64 (.f64 1/6 (pow.f64 x 2))) (exp.f64 (*.f64 x 1/2))))
(cbrt.f64 (pow.f64 (*.f64 x (fma.f64 x 1/6 1/2)) 3))
(cbrt.f64 (*.f64 (pow.f64 x 3) (pow.f64 (fma.f64 x 1/6 1/2) 3)))
(cbrt.f64 (*.f64 (pow.f64 (fma.f64 x 1/6 1/2) 3) (pow.f64 x 3)))
(expm1.f64 (log1p.f64 (*.f64 x (fma.f64 x 1/6 1/2))))
(exp.f64 (log.f64 (*.f64 x (fma.f64 x 1/6 1/2))))
(exp.f64 (.f64 (log.f64 (.f64 x (fma.f64 x 1/6 1/2))) 1))
(exp.f64 (.f64 (.f64 (log.f64 (*.f64 x (fma.f64 x 1/6 1/2))) 1) 1))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 x (fma.f64 x 1/6 1/2)))) 3))
(exp.f64 (.f64 (.f64 3 (log.f64 (*.f64 x (fma.f64 x 1/6 1/2)))) 1/3))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 x (fma.f64 x 1/6 1/2)))) 2))
(log1p.f64 (expm1.f64 (*.f64 x (fma.f64 x 1/6 1/2))))
(fma.f64 1 (.f64 x 1/2) (.f64 1/6 (pow.f64 x 2)))
(fma.f64 1 (.f64 1/6 (pow.f64 x 2)) (.f64 x 1/2))
(fma.f64 x (.f64 x 1/6) (.f64 x 1/2))
(fma.f64 x 1/2 (*.f64 1/6 (pow.f64 x 2)))
(fma.f64 1/6 (pow.f64 x 2) (*.f64 x 1/2))
(fma.f64 (.f64 x 1/6) x (.f64 x 1/2))
(fma.f64 1/2 x (*.f64 1/6 (pow.f64 x 2)))
(fma.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) 1/2) (.f64 1/6 (pow.f64 x 2)))
(fma.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (.f64 x 1/6)) (*.f64 x 1/2))
(fma.f64 (pow.f64 (cbrt.f64 (.f64 x 1/6)) 2) (.f64 (cbrt.f64 (.f64 x 1/6)) x) (.f64 x 1/2))
(fma.f64 (pow.f64 x 2) 1/6 (*.f64 x 1/2))
(fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) 1/2) (.f64 1/6 (pow.f64 x 2)))
(fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (.f64 x 1/6)) (*.f64 x 1/2))
(fma.f64 (sqrt.f64 (.f64 x 1/6)) (.f64 (sqrt.f64 (.f64 x 1/6)) x) (.f64 x 1/2))
(fma.f64 (.f64 x 1/2) 1 (.f64 (*.f64 1/6 (pow.f64 x 2)) 1))
(fma.f64 (.f64 (cbrt.f64 (.f64 x 1/2)) (cbrt.f64 (.f64 x 1/2))) (cbrt.f64 (.f64 x 1/2)) (*.f64 1/6 (pow.f64 x 2)))
(fma.f64 (.f64 (cbrt.f64 (.f64 1/6 (pow.f64 x 2))) (cbrt.f64 (.f64 1/6 (pow.f64 x 2)))) (cbrt.f64 (.f64 1/6 (pow.f64 x 2))) (*.f64 x 1/2))
(fma.f64 (sqrt.f64 (.f64 x 1/2)) (sqrt.f64 (.f64 x 1/2)) (*.f64 1/6 (pow.f64 x 2)))
(fma.f64 (sqrt.f64 (.f64 1/6 (pow.f64 x 2))) (sqrt.f64 (.f64 1/6 (pow.f64 x 2))) (*.f64 x 1/2))
(fma.f64 (.f64 (sqrt.f64 (.f64 x 1/6)) (sqrt.f64 x)) (.f64 (sqrt.f64 (.f64 x 1/6)) (sqrt.f64 x)) (*.f64 x 1/2))
(fma.f64 (.f64 (sqrt.f64 x) (sqrt.f64 (.f64 x 1/6))) (.f64 (sqrt.f64 x) (sqrt.f64 (.f64 x 1/6))) (*.f64 x 1/2))
(fma.f64 (.f64 1/2 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (.f64 1/6 (pow.f64 x 2)))
(fma.f64 (.f64 1/2 (sqrt.f64 x)) (sqrt.f64 x) (.f64 1/6 (pow.f64 x 2)))
(fma.f64 (.f64 (.f64 x 1/6) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (*.f64 x 1/2))
(fma.f64 (.f64 (.f64 x 1/6) (sqrt.f64 x)) (sqrt.f64 x) (*.f64 x 1/2))
(fma.f64 (.f64 x (pow.f64 (cbrt.f64 (.f64 x 1/6)) 2)) (cbrt.f64 (.f64 x 1/6)) (.f64 x 1/2))
(fma.f64 (.f64 x (sqrt.f64 (.f64 x 1/6))) (sqrt.f64 (.f64 x 1/6)) (.f64 x 1/2))

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 1/2 x (*.f64 1/6 (pow.f64 x 2))))
(+.f64 1 (*.f64 x (fma.f64 x 1/6 1/2)))
(+.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 1/2 x (*.f64 1/6 (pow.f64 x 2)))))
(+.f64 1 (fma.f64 1/24 (pow.f64 x 3) (*.f64 x (fma.f64 x 1/6 1/2))))
(/.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 1/6 x)
(*.f64 x 1/6)
(*.f64 1/6 x)
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(fma.f64 1/2 x (*.f64 1/6 (pow.f64 x 2)))
(*.f64 x (fma.f64 x 1/6 1/2))
(fma.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (.f64 x 1/6)) (*.f64 x 1/2))
(fma.f64 1/2 x (*.f64 1/6 (pow.f64 x 2)))
(*.f64 x (fma.f64 x 1/6 1/2))
(fma.f64 (pow.f64 (cbrt.f64 (.f64 x 1/6)) 2) (.f64 (cbrt.f64 (.f64 x 1/6)) x) (.f64 x 1/2))
(fma.f64 1/2 x (*.f64 1/6 (pow.f64 x 2)))
(*.f64 x (fma.f64 x 1/6 1/2))
(fma.f64 (pow.f64 x 2) 1/6 (*.f64 x 1/2))
(fma.f64 1/2 x (*.f64 1/6 (pow.f64 x 2)))
(*.f64 x (fma.f64 x 1/6 1/2))
(fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) 1/2) (.f64 1/6 (pow.f64 x 2)))
(fma.f64 1/2 x (*.f64 1/6 (pow.f64 x 2)))
(*.f64 x (fma.f64 x 1/6 1/2))
(fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (.f64 x 1/6)) (*.f64 x 1/2))
(fma.f64 1/2 x (*.f64 1/6 (pow.f64 x 2)))
(*.f64 x (fma.f64 x 1/6 1/2))
(fma.f64 (sqrt.f64 (.f64 x 1/6)) (.f64 (sqrt.f64 (.f64 x 1/6)) x) (.f64 x 1/2))
(fma.f64 1/2 x (*.f64 1/6 (pow.f64 x 2)))
(*.f64 x (fma.f64 x 1/6 1/2))
(fma.f64 (.f64 x 1/2) 1 (.f64 (*.f64 1/6 (pow.f64 x 2)) 1))
(fma.f64 1/2 x (*.f64 1/6 (pow.f64 x 2)))
(*.f64 x (fma.f64 x 1/6 1/2))
(fma.f64 (.f64 (cbrt.f64 (.f64 x 1/2)) (cbrt.f64 (.f64 x 1/2))) (cbrt.f64 (.f64 x 1/2)) (*.f64 1/6 (pow.f64 x 2)))
(fma.f64 1/2 x (*.f64 1/6 (pow.f64 x 2)))
(*.f64 x (fma.f64 x 1/6 1/2))
(fma.f64 (.f64 (cbrt.f64 (.f64 1/6 (pow.f64 x 2))) (cbrt.f64 (.f64 1/6 (pow.f64 x 2)))) (cbrt.f64 (.f64 1/6 (pow.f64 x 2))) (*.f64 x 1/2))
(fma.f64 1/2 x (*.f64 1/6 (pow.f64 x 2)))
(*.f64 x (fma.f64 x 1/6 1/2))
(fma.f64 (sqrt.f64 (.f64 x 1/2)) (sqrt.f64 (.f64 x 1/2)) (*.f64 1/6 (pow.f64 x 2)))
(fma.f64 1/2 x (*.f64 1/6 (pow.f64 x 2)))
(*.f64 x (fma.f64 x 1/6 1/2))
(fma.f64 (sqrt.f64 (.f64 1/6 (pow.f64 x 2))) (sqrt.f64 (.f64 1/6 (pow.f64 x 2))) (*.f64 x 1/2))
(fma.f64 1/2 x (*.f64 1/6 (pow.f64 x 2)))
(*.f64 x (fma.f64 x 1/6 1/2))
(fma.f64 (.f64 (sqrt.f64 (.f64 x 1/6)) (sqrt.f64 x)) (.f64 (sqrt.f64 (.f64 x 1/6)) (sqrt.f64 x)) (*.f64 x 1/2))
(fma.f64 1/2 x (*.f64 1/6 (pow.f64 x 2)))
(*.f64 x (fma.f64 x 1/6 1/2))
(fma.f64 (.f64 (sqrt.f64 x) (sqrt.f64 (.f64 x 1/6))) (.f64 (sqrt.f64 x) (sqrt.f64 (.f64 x 1/6))) (*.f64 x 1/2))
(fma.f64 1/2 x (*.f64 1/6 (pow.f64 x 2)))
(*.f64 x (fma.f64 x 1/6 1/2))
(fma.f64 (.f64 1/2 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (.f64 1/6 (pow.f64 x 2)))
(fma.f64 1/2 x (*.f64 1/6 (pow.f64 x 2)))
(*.f64 x (fma.f64 x 1/6 1/2))
(fma.f64 (.f64 1/2 (sqrt.f64 x)) (sqrt.f64 x) (.f64 1/6 (pow.f64 x 2)))
(fma.f64 1/2 x (*.f64 1/6 (pow.f64 x 2)))
(*.f64 x (fma.f64 x 1/6 1/2))
(fma.f64 (.f64 (.f64 x 1/6) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (*.f64 x 1/2))
(fma.f64 1/2 x (*.f64 1/6 (pow.f64 x 2)))
(*.f64 x (fma.f64 x 1/6 1/2))
(fma.f64 (.f64 (.f64 x 1/6) (sqrt.f64 x)) (sqrt.f64 x) (*.f64 x 1/2))
(fma.f64 1/2 x (*.f64 1/6 (pow.f64 x 2)))
(*.f64 x (fma.f64 x 1/6 1/2))
(fma.f64 (.f64 x (pow.f64 (cbrt.f64 (.f64 x 1/6)) 2)) (cbrt.f64 (.f64 x 1/6)) (.f64 x 1/2))
(fma.f64 1/2 x (*.f64 1/6 (pow.f64 x 2)))
(*.f64 x (fma.f64 x 1/6 1/2))
(fma.f64 (.f64 x (sqrt.f64 (.f64 x 1/6))) (sqrt.f64 (.f64 x 1/6)) (.f64 x 1/2))
(fma.f64 1/2 x (*.f64 1/6 (pow.f64 x 2)))
(*.f64 x (fma.f64 x 1/6 1/2))

eval103.0ms (3.8%)

Compiler: Compiled 2760 to 1910 computations (30.8% saved)

prune30.0ms (1.1%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	212	1	213
Fresh	0	1	1
Picked	0	3	3
Done	0	1	1
Total	212	6	218

Accuracy

100.0%

Counts

218 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(/.f64 (expm1.f64 x) x)
✓	59.7%	(+.f64 1 (.f64 x (+.f64 1/2 (.f64 x 1/6))))
✓	48.3%	(+.f64 1 (*.f64 x 1/2))
✓	99.9%	(*.f64 (/.f64 1 x) (expm1.f64 x))
▶	48.3%	(*.f64 (/.f64 1 x) x)
	48.4%	1
✓	100.0%	(/.f64 (expm1.f64 x) x)
✓	59.7%	(+.f64 1 (.f64 x (+.f64 1/2 (.f64 x 1/6))))
✓	48.3%	(+.f64 1 (*.f64 x 1/2))
✓	99.9%	(*.f64 (/.f64 1 x) (expm1.f64 x))
▶	48.3%	(*.f64 (/.f64 1 x) x)
	48.4%	1

Compiler

Compiled 72 to 54 computations (25% saved)

localize21.0ms (0.8%)

Localize:

Found 1 expressions with local error:

New	Accuracy	Program
✓	99.7%	(*.f64 (/.f64 1 x) x)

Compiler

Compiled 12 to 8 computations (33.3% saved)

series0.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(*.f64 (/.f64 1 x) x)
0.0ms	x	@	inf	(*.f64 (/.f64 1 x) x)
0.0ms	x	@	-inf	(*.f64 (/.f64 1 x) x)

rewrite46.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

506×	`associate-r`
418×	`associate-l`
376×	`frac-times`
300×	`unpow-prod-down`
220×	`cbrt-prod`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	1
1	86	1
2	655	1

Stop Event

1×	node limit

Counts

1 → 30

Calls

Call 1

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

Outputs
-6
-4
-3
-5/2
-2
-3/2
-1
-2/3
-1/2
-1/3
-1/4
-1/6
0
1/9
1/6
1/4
1/3
1/2
2/3
1
4/3
3/2
2
5/2
3
4
5
6
8
9

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

2× 1-exp

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	42
1	33	42

Stop Event

1×

saturated

Counts

42 → 30

Calls

Call 1

Inputs
1
1
1
1
1
1
1
1
1
1
1
1
-6
-4
-3
-5/2
-2
-3/2
-1
-2/3
-1/2
-1/3
-1/4
-1/6
0
1/9
1/6
1/4
1/3
1/2
2/3
1
4/3
3/2
2
5/2
3
4
5
6
8
9

Outputs
1
1
1
1
1
1
1
1
1
1
1
1
-6
-4
-3
-5/2
-2
-3/2
-1
-2/3
-1/2
-1/3
-1/4
-1/6
0
1/9
1/6
1/4
1/3
1/2
2/3
1
4/3
3/2
2
5/2
3
4
5
6
8
9

eval3.0ms (0.1%)

Compiler: Compiled 31 to 31 computations (0% saved)

prune10.0ms (0.4%)

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	26	4	30
Fresh	0	1	1
Picked	1	0	1
Done	0	4	4
Total	27	9	36

Accuracy

100.0%

Counts

36 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(/.f64 (expm1.f64 x) x)
✓	59.7%	(+.f64 1 (.f64 x (+.f64 1/2 (.f64 x 1/6))))
✓	48.3%	(+.f64 1 (*.f64 x 1/2))
✓	99.9%	(*.f64 (/.f64 1 x) (expm1.f64 x))
	9.8%	9
	48.4%	1
	11.5%	2/3
	9.8%	1/9
	3.4%	0
✓	100.0%	(/.f64 (expm1.f64 x) x)
✓	59.7%	(+.f64 1 (.f64 x (+.f64 1/2 (.f64 x 1/6))))
✓	48.3%	(+.f64 1 (*.f64 x 1/2))
✓	99.9%	(*.f64 (/.f64 1 x) (expm1.f64 x))
	9.8%	9
	48.4%	1
	11.5%	2/3
	9.8%	1/9
	3.4%	0

Compiler

Compiled 76 to 62 computations (18.4% saved)

localize0.0ms (0%)

eval0.0ms (0%)

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

prune5.0ms (0.2%)

Pruning

9 alts after pruning (5 fresh and 4 done)

	Kept	Total
New	0	0
Fresh	5	5
Picked	0	0
Done	4	4
Total	9	9

Accuracy

100.0%

Counts

9 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(/.f64 (expm1.f64 x) x)
✓	59.7%	(+.f64 1 (.f64 x (+.f64 1/2 (.f64 x 1/6))))
✓	48.3%	(+.f64 1 (*.f64 x 1/2))
✓	99.9%	(*.f64 (/.f64 1 x) (expm1.f64 x))
	9.8%	9
	48.4%	1
	11.5%	2/3
	9.8%	1/9
	3.4%	0

Compiler

Compiled 79 to 60 computations (24.1% saved)

regimes16.0ms (0.6%)

Counts

11 → 1

Calls

Call 1

Inputs
0
1/9
2/3
1
9
(*.f64 (/.f64 1 x) x)
(+.f64 1 (*.f64 x 1/2))
(+.f64 1 (.f64 x (+.f64 1/2 (.f64 x 1/6))))
(/.f64 (expm1.f64 x) x)
(*.f64 (/.f64 1 x) (expm1.f64 x))
(/.f64 (-.f64 (exp.f64 x) 1) x)

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

Calls

2 calls:

10.0ms	x
4.0ms	(/.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 50 to 35 computations (30% saved)

regimes7.0ms (0.3%)

Counts

8 → 1

Calls

Call 1

Inputs
0
1/9
2/3
1
9
(*.f64 (/.f64 1 x) x)
(+.f64 1 (*.f64 x 1/2))
(+.f64 1 (.f64 x (+.f64 1/2 (.f64 x 1/6))))

Outputs
(+.f64 1 (.f64 x (+.f64 1/2 (.f64 x 1/6))))

Calls

1 calls:

6.0ms

Results

Accuracy	Segments	Branch
59.7%	1	`x`

Compiler

Compiled 27 to 21 computations (22.2% saved)

regimes7.0ms (0.3%)

Counts

7 → 1

Calls

Call 1

Inputs
0
1/9
2/3
1
9
(*.f64 (/.f64 1 x) x)
(+.f64 1 (*.f64 x 1/2))

Outputs
1

Calls

1 calls:

6.0ms

Results

Accuracy	Segments	Branch
48.4%	1	`x`

Compiler

Compiled 18 to 14 computations (22.2% saved)

regimes4.0ms (0.2%)

Counts

3 → 1

Calls

Call 1

Inputs
0
1/9
2/3

Outputs
2/3

Calls

1 calls:

4.0ms

Results

Accuracy	Segments	Branch
11.5%	1	`x`

Compiler

Compiled 6 to 5 computations (16.7% saved)

regimes4.0ms (0.1%)

Counts

2 → 1

Calls

Call 1

Inputs
0
1/9

Outputs
1/9

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
9.8%	1	`x`

Compiler

Compiled 5 to 4 computations (20% saved)

regimes3.0ms (0.1%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
0

Outputs
0

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
3.4%	1	`x`

Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative`
4×	`*-commutative`
2×	`1-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	52
1	23	52

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(/.f64 (expm1.f64 x) x)
(+.f64 1 (.f64 x (+.f64 1/2 (.f64 x 1/6))))
1
2/3
1/9
0

Outputs
(/.f64 (expm1.f64 x) x)
(+.f64 1 (.f64 x (+.f64 1/2 (.f64 x 1/6))))
1
2/3
1/9
0

Compiler

Compiled 23 to 19 computations (17.4% saved)

soundness496.0ms (18.6%)

Rules

1654×	`fma-neg`
1292×	`div-sub`
1216×	`fma-neg`
1162×	`fma-def`
904×	`cancel-sign-sub-inv`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	59
1	31	59
2	49	59
3	81	59
4	187	59
5	545	59
6	1645	59
7	5861	59
0	8	25
1	68	25
2	882	25
0	8	1
1	86	1
2	655	1
0	8	1
1	86	1
2	655	1
0	8	1
1	86	1
2	655	1
0	313	3248
1	693	3129
2	2787	3031
3	7503	3031

Stop Event

1×	node limit
1×	node limit
1×	node limit
1×	node limit
1×	node limit
1×	node limit

Compiler

Compiled 104 to 76 computations (26.9% saved)

end0.0ms (0%)

preprocess84.0ms (3.1%)

Compiler: Compiled 96 to 68 computations (29.2% saved)

analyze1.0ms (0%)

sample1.2s (43.6%)

preprocess108.0ms (4.1%)

eval0.0ms (0%)

prune1.0ms (0%)

localize64.0ms (2.4%)

series4.0ms (0.2%)

rewrite99.0ms (3.7%)

simplify88.0ms (3.3%)

eval35.0ms (1.3%)

prune27.0ms (1%)

localize93.0ms (3.5%)

series3.0ms (0.1%)

rewrite74.0ms (2.8%)

simplify58.0ms (2.2%)

eval103.0ms (3.8%)

prune30.0ms (1.1%)

localize21.0ms (0.8%)

series0.0ms (0%)

rewrite46.0ms (1.7%)

simplify4.0ms (0.2%)

eval3.0ms (0.1%)

prune10.0ms (0.4%)

localize0.0ms (0%)

eval0.0ms (0%)

prune5.0ms (0.2%)

regimes16.0ms (0.6%)

regimes7.0ms (0.3%)

regimes7.0ms (0.3%)

regimes4.0ms (0.2%)

regimes4.0ms (0.1%)

regimes3.0ms (0.1%)

simplify4.0ms (0.1%)

soundness496.0ms (18.6%)

end0.0ms (0%)

preprocess84.0ms (3.1%)

Profiling