Metrics for sqrt times

analyze2.0ms (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
0%	0%	50%	0%	0%	50%	0%	2
50%	25%	25%	0%	0%	50%	0%	3
66.7%	25%	12.5%	0%	0%	62.5%	0%	4
80%	25%	6.2%	0%	0%	68.7%	0%	5
88.9%	25%	3.1%	0%	0%	71.8%	0%	6
94.1%	25%	1.6%	0%	0%	73.4%	0%	7
97%	25%	0.8%	0%	0%	74.2%	0%	8
98.5%	25%	0.4%	0%	0%	74.6%	0%	9
99.2%	25%	0.2%	0%	0%	74.8%	0%	10
99.6%	25%	0.1%	0%	0%	74.9%	0%	11
99.8%	25%	0%	0%	0%	74.9%	0%	12

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample777.0ms (43.2%)

Results

766.0ms	8256×	body	256	valid
1.0ms	11×	body	256	invalid

Bogosity

preprocess134.0ms (7.5%)

Algorithm

1×	egg-herbie

Rules

88×	`fma-def`
36×	`sub-neg`
22×	`+-commutative`
12×	`*-commutative`
12×	`associate-+l-`

Problems

256×

No Errors

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	17	128
1	33	124
2	52	120
3	72	120
4	98	120
5	130	120
6	151	120
7	167	120
8	192	120

Stop Event

1×

saturated

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))
(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))
(*.f64 (sqrt.f64 (-.f64 (neg.f64 x) 1)) (sqrt.f64 (neg.f64 x)))
(neg.f64 (*.f64 (sqrt.f64 (-.f64 (neg.f64 x) 1)) (sqrt.f64 (neg.f64 x))))

Outputs
(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))
(*.f64 (sqrt.f64 (+.f64 x -1)) (sqrt.f64 x))
(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))
(*.f64 (sqrt.f64 (+.f64 x -1)) (sqrt.f64 x))
(*.f64 (sqrt.f64 (-.f64 (neg.f64 x) 1)) (sqrt.f64 (neg.f64 x)))
(*.f64 (sqrt.f64 (+.f64 (neg.f64 x) -1)) (sqrt.f64 (neg.f64 x)))
(*.f64 (sqrt.f64 (fma.f64 -1 x -1)) (sqrt.f64 (neg.f64 x)))
(*.f64 (sqrt.f64 (-.f64 -1 x)) (sqrt.f64 (neg.f64 x)))
(neg.f64 (*.f64 (sqrt.f64 (-.f64 (neg.f64 x) 1)) (sqrt.f64 (neg.f64 x))))
(*.f64 (sqrt.f64 (+.f64 (neg.f64 x) -1)) (neg.f64 (sqrt.f64 (neg.f64 x))))
(*.f64 (sqrt.f64 (neg.f64 x)) (neg.f64 (sqrt.f64 (fma.f64 -1 x -1))))
(*.f64 (sqrt.f64 (neg.f64 x)) (neg.f64 (sqrt.f64 (-.f64 -1 x))))

Compiler

Compiled 28 to 19 computations (32.1% saved)

eval0.0ms (0%)

Compiler: Compiled 8 to 6 computations (25% saved)

prune1.0ms (0.1%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.3%	(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))
▶	99.3%	(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))

Compiler

Compiled 16 to 12 computations (25% saved)

localize34.0ms (1.9%)

Localize:

Found 1 expressions with local error:

New	Accuracy	Program
✓	99.3%	(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))

Compiler

Compiled 20 to 13 computations (35% saved)

series2.0ms (0.1%)

Counts

1 → 8

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))
1.0ms	x	@	-inf	(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))
0.0ms	x	@	inf	(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))

rewrite155.0ms (8.6%)

Algorithm

1×	batch-egg-rewrite

Rules

822×	`unpow-prod-down`
586×	`prod-exp`
496×	`log-prod`
472×	`log1p-expm1-u`
472×	`expm1-log1p-u`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	23
1	122	23
2	1409	23

Stop Event

1×	node limit

Counts

1 → 22

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))

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

simplify75.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

1442×	`log-prod`
1298×	`fma-def`
892×	`associate-r`
788×	`associate-l`
436×	`times-frac`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	95	854
1	229	814
2	620	814
3	1726	806
4	7402	806

Stop Event

1×	node limit

Counts

30 → 47

Calls

Call 1

Inputs
x
(-.f64 x 1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 2))) (.f64 1/8 (/.f64 1 x)))))
(.f64 -1 (.f64 x (pow.f64 (sqrt.f64 -1) 2)))
(+.f64 (.f64 -1 (.f64 x (pow.f64 (sqrt.f64 -1) 2))) (*.f64 1/2 (pow.f64 (sqrt.f64 -1) 2)))
(+.f64 (.f64 -1 (.f64 x (pow.f64 (sqrt.f64 -1) 2))) (+.f64 (.f64 1/8 (/.f64 (pow.f64 (sqrt.f64 -1) 2) x)) (.f64 1/2 (pow.f64 (sqrt.f64 -1) 2))))
(+.f64 (.f64 -1 (.f64 x (pow.f64 (sqrt.f64 -1) 2))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 (sqrt.f64 -1) 2) (pow.f64 x 2))) (+.f64 (.f64 1/8 (/.f64 (pow.f64 (sqrt.f64 -1) 2) x)) (*.f64 1/2 (pow.f64 (sqrt.f64 -1) 2)))))
(+.f64 0 (sqrt.f64 (*.f64 x (+.f64 x -1))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 x (+.f64 x -1))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 x (+.f64 x -1)))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 x (+.f64 x -1)))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 x (+.f64 x -1)))))))
(-.f64 (+.f64 1 (sqrt.f64 (*.f64 x (+.f64 x -1)))) 1)
(pow.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 1)
(pow.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 1/6) 3)
(pow.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 3/2) 1/3)
(pow.f64 (*.f64 x (+.f64 x -1)) 1/2)
(pow.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 1/4) 2)
(pow.f64 (E.f64) (log.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (.f64 x (+.f64 x -1))))) 2)) (cbrt.f64 (log.f64 (sqrt.f64 (.f64 x (+.f64 x -1))))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sqrt.f64 (.f64 x (+.f64 x -1)))))) (sqrt.f64 (log.f64 (sqrt.f64 (.f64 x (+.f64 x -1))))))
(sqrt.f64 (*.f64 x (+.f64 x -1)))
(log.f64 (exp.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))))
(cbrt.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))))
(exp.f64 (log.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 x (+.f64 x -1)) 1/6)) 3))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 x (+.f64 x -1)) 3/2)) 1/3))
(exp.f64 (.f64 (log.f64 (.f64 x (+.f64 x -1))) 1/2))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 x (+.f64 x -1)) 1/4)) 2))
(log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))))

Outputs
x
(-.f64 x 1/2)
(+.f64 x -1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (/.f64 1/8 x)))
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
(-.f64 (/.f64 -1/8 x) (-.f64 1/2 x))
(-.f64 x (+.f64 1/2 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 2))) (.f64 1/8 (/.f64 1 x)))))
(-.f64 (+.f64 x -1/2) (+.f64 (/.f64 1/8 x) (/.f64 1/16 (pow.f64 x 2))))
(-.f64 x (+.f64 1/2 (+.f64 (/.f64 1/8 x) (/.f64 1/16 (pow.f64 x 2)))))
(+.f64 x (+.f64 (/.f64 -1/8 x) (+.f64 -1/2 (/.f64 -1/16 (pow.f64 x 2)))))
(fma.f64 (/.f64 -1 x) (+.f64 1/8 (/.f64 1/16 x)) (+.f64 x -1/2))
(.f64 -1 (.f64 x (pow.f64 (sqrt.f64 -1) 2)))
x
(+.f64 (.f64 -1 (.f64 x (pow.f64 (sqrt.f64 -1) 2))) (*.f64 1/2 (pow.f64 (sqrt.f64 -1) 2)))
(+.f64 x -1/2)
(+.f64 (.f64 -1 (.f64 x (pow.f64 (sqrt.f64 -1) 2))) (+.f64 (.f64 1/8 (/.f64 (pow.f64 (sqrt.f64 -1) 2) x)) (.f64 1/2 (pow.f64 (sqrt.f64 -1) 2))))
(-.f64 x (+.f64 1/2 (/.f64 1/8 x)))
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
(-.f64 (/.f64 -1/8 x) (-.f64 1/2 x))
(+.f64 (.f64 -1 (.f64 x (pow.f64 (sqrt.f64 -1) 2))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 (sqrt.f64 -1) 2) (pow.f64 x 2))) (+.f64 (.f64 1/8 (/.f64 (pow.f64 (sqrt.f64 -1) 2) x)) (*.f64 1/2 (pow.f64 (sqrt.f64 -1) 2)))))
(-.f64 (+.f64 x -1/2) (+.f64 (/.f64 1/8 x) (/.f64 1/16 (pow.f64 x 2))))
(-.f64 x (+.f64 1/2 (+.f64 (/.f64 1/8 x) (/.f64 1/16 (pow.f64 x 2)))))
(+.f64 x (+.f64 (/.f64 -1/8 x) (+.f64 -1/2 (/.f64 -1/16 (pow.f64 x 2)))))
(fma.f64 (/.f64 -1 x) (+.f64 1/8 (/.f64 1/16 x)) (+.f64 x -1/2))
(+.f64 0 (sqrt.f64 (*.f64 x (+.f64 x -1))))
(sqrt.f64 (*.f64 x (+.f64 x -1)))
(sqrt.f64 (-.f64 (pow.f64 x 2) x))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 x (+.f64 x -1))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 x (+.f64 x -1)))))))
(+.f64 (.f64 2 (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 x (+.f64 x -1))))))) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))))))
(.f64 3 (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 x (+.f64 x -1)))))))
(*.f64 (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (-.f64 (pow.f64 x 2) x))))) 3)
(.f64 (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 x (+.f64 x -1)))))) 3)
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 x (+.f64 x -1)))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 x (+.f64 x -1)))))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 x (+.f64 x -1)))))))
(*.f64 2 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (-.f64 (pow.f64 x 2) x))))))
(-.f64 (+.f64 1 (sqrt.f64 (*.f64 x (+.f64 x -1)))) 1)
(sqrt.f64 (*.f64 x (+.f64 x -1)))
(sqrt.f64 (-.f64 (pow.f64 x 2) x))
(pow.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 1)
(sqrt.f64 (*.f64 x (+.f64 x -1)))
(sqrt.f64 (-.f64 (pow.f64 x 2) x))
(pow.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 1/6) 3)
(sqrt.f64 (*.f64 x (+.f64 x -1)))
(sqrt.f64 (-.f64 (pow.f64 x 2) x))
(pow.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 3/2) 1/3)
(sqrt.f64 (*.f64 x (+.f64 x -1)))
(sqrt.f64 (-.f64 (pow.f64 x 2) x))
(pow.f64 (*.f64 x (+.f64 x -1)) 1/2)
(sqrt.f64 (*.f64 x (+.f64 x -1)))
(sqrt.f64 (-.f64 (pow.f64 x 2) x))
(pow.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 1/4) 2)
(sqrt.f64 (*.f64 x (+.f64 x -1)))
(sqrt.f64 (-.f64 (pow.f64 x 2) x))
(pow.f64 (E.f64) (log.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))))
(sqrt.f64 (*.f64 x (+.f64 x -1)))
(sqrt.f64 (-.f64 (pow.f64 x 2) x))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (.f64 x (+.f64 x -1))))) 2)) (cbrt.f64 (log.f64 (sqrt.f64 (.f64 x (+.f64 x -1))))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (-.f64 (pow.f64 x 2) x)))) 2)) (cbrt.f64 (log.f64 (sqrt.f64 (-.f64 (pow.f64 x 2) x)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sqrt.f64 (.f64 x (+.f64 x -1)))))) (sqrt.f64 (log.f64 (sqrt.f64 (.f64 x (+.f64 x -1))))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sqrt.f64 (-.f64 (pow.f64 x 2) x))))) (sqrt.f64 (log.f64 (sqrt.f64 (-.f64 (pow.f64 x 2) x)))))
(sqrt.f64 (*.f64 x (+.f64 x -1)))
(sqrt.f64 (-.f64 (pow.f64 x 2) x))
(log.f64 (exp.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))))
(sqrt.f64 (*.f64 x (+.f64 x -1)))
(sqrt.f64 (-.f64 (pow.f64 x 2) x))
(cbrt.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 3/2))
(sqrt.f64 (*.f64 x (+.f64 x -1)))
(sqrt.f64 (-.f64 (pow.f64 x 2) x))
(expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))))
(sqrt.f64 (*.f64 x (+.f64 x -1)))
(sqrt.f64 (-.f64 (pow.f64 x 2) x))
(exp.f64 (log.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))))
(sqrt.f64 (*.f64 x (+.f64 x -1)))
(sqrt.f64 (-.f64 (pow.f64 x 2) x))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 x (+.f64 x -1)) 1/6)) 3))
(sqrt.f64 (*.f64 x (+.f64 x -1)))
(sqrt.f64 (-.f64 (pow.f64 x 2) x))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 x (+.f64 x -1)) 3/2)) 1/3))
(sqrt.f64 (*.f64 x (+.f64 x -1)))
(sqrt.f64 (-.f64 (pow.f64 x 2) x))
(exp.f64 (.f64 (log.f64 (.f64 x (+.f64 x -1))) 1/2))
(sqrt.f64 (*.f64 x (+.f64 x -1)))
(sqrt.f64 (-.f64 (pow.f64 x 2) x))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 x (+.f64 x -1)) 1/4)) 2))
(sqrt.f64 (*.f64 x (+.f64 x -1)))
(sqrt.f64 (-.f64 (pow.f64 x 2) x))
(log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))))
(sqrt.f64 (*.f64 x (+.f64 x -1)))
(sqrt.f64 (-.f64 (pow.f64 x 2) x))

eval13.0ms (0.7%)

Compiler: Compiled 543 to 434 computations (20.1% saved)

prune8.0ms (0.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	43	4	47
Fresh	0	0	0
Picked	1	0	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
▶	99.1%	(-.f64 (/.f64 -1/8 x) (-.f64 1/2 x))
▶	98.4%	(-.f64 x 1/2)
▶	54.6%	(sqrt.f64 (*.f64 x (+.f64 x -1)))
	97.0%	x
▶	99.1%	(-.f64 (/.f64 -1/8 x) (-.f64 1/2 x))
▶	98.4%	(-.f64 x 1/2)
▶	54.6%	(sqrt.f64 (*.f64 x (+.f64 x -1)))
	97.0%	x

Compiler

Compiled 42 to 30 computations (28.6% saved)

localize72.0ms (4%)

Localize:

Found 2 expressions with local error:

New	Accuracy	Program
✓	100.0%	(*.f64 x (+.f64 x -1))
✓	54.6%	(sqrt.f64 (*.f64 x (+.f64 x -1)))

Compiler

Compiled 39 to 26 computations (33.3% saved)

series2.0ms (0.1%)

Counts

2 → 20

Calls

6 calls:

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

rewrite63.0ms (3.5%)

Algorithm

1×	batch-egg-rewrite

Rules

786×	`unpow-prod-down`
462×	`log-prod`
461×	`log1p-expm1-u`
461×	`expm1-log1p-u`
458×	`prod-exp`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	42
1	102	42
2	1287	40

Stop Event

1×	node limit

Counts

2 → 108

Calls

Call 1

Inputs
(sqrt.f64 (*.f64 x (+.f64 x -1)))
(*.f64 x (+.f64 x -1))

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

simplify62.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

1970×	`fma-def`
980×	`unswap-sqr`
720×	`distribute-lft-in`
662×	`distribute-rgt-in`
574×	`*-commutative`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	301	3804
1	729	3668
2	2002	3619

Stop Event

1×	node limit

Counts

128 → 185

Calls

Call 1

Inputs
x
(-.f64 x 1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 2))) (.f64 1/8 (/.f64 1 x)))))
(*.f64 -1 x)
(+.f64 1/2 (*.f64 -1 x))
(+.f64 1/2 (+.f64 (.f64 -1 x) (.f64 1/8 (/.f64 1 x))))
(+.f64 1/2 (+.f64 (.f64 -1 x) (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x)))))
(*.f64 -1 x)
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(+.f64 0 (hypot.f64 x (sqrt.f64 (neg.f64 x))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (hypot.f64 x (sqrt.f64 (neg.f64 x))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (hypot.f64 x (sqrt.f64 (neg.f64 x)))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 x (sqrt.f64 (neg.f64 x)))))) (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 x (sqrt.f64 (neg.f64 x)))))))
(-.f64 (+.f64 1 (hypot.f64 x (sqrt.f64 (neg.f64 x)))) 1)
(*.f64 (hypot.f64 x (sqrt.f64 (neg.f64 x))) 1)
(*.f64 (hypot.f64 x (sqrt.f64 (neg.f64 x))) (log.f64 (E.f64)))
(*.f64 1 (hypot.f64 x (sqrt.f64 (neg.f64 x))))
(.f64 (cbrt.f64 x) (pow.f64 (.f64 (+.f64 x -1) (hypot.f64 x (sqrt.f64 (neg.f64 x)))) 1/3))
(.f64 (cbrt.f64 (.f64 x (+.f64 x -1))) (pow.f64 (*.f64 x (+.f64 x -1)) 1/6))
(.f64 (cbrt.f64 (+.f64 x -1)) (pow.f64 (.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 x)))) 1/3))
(.f64 (pow.f64 (.f64 x (+.f64 x -1)) 1/6) (cbrt.f64 (*.f64 x (+.f64 x -1))))
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x -1)))
(*.f64 (sqrt.f64 (+.f64 x -1)) (sqrt.f64 x))
(.f64 (pow.f64 (.f64 x (+.f64 x -1)) 1/4) (pow.f64 (*.f64 x (+.f64 x -1)) 1/4))
(.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (.f64 x (+.f64 x -1))) 2)) (pow.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 5/6) 1/3))
(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x -1)) 2)) (pow.f64 (.f64 (cbrt.f64 (+.f64 x -1)) x) 1/2))
(.f64 (sqrt.f64 (sqrt.f64 (+.f64 x -1))) (pow.f64 (.f64 (sqrt.f64 (+.f64 x -1)) x) 1/2))
(.f64 (sqrt.f64 (sqrt.f64 x)) (pow.f64 (.f64 (sqrt.f64 x) (+.f64 x -1)) 1/2))
(.f64 (sqrt.f64 (sqrt.f64 x)) (pow.f64 (pow.f64 (.f64 (+.f64 x -1) (*.f64 x (+.f64 x -1))) 1/2) 1/2))
(.f64 (sqrt.f64 (pow.f64 (.f64 x (+.f64 x -1)) 1/4)) (pow.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 3/4) 1/2))
(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)) (pow.f64 (.f64 (cbrt.f64 x) (+.f64 x -1)) 1/2))
(*.f64 (pow.f64 1 1/3) (hypot.f64 x (sqrt.f64 (neg.f64 x))))
(.f64 (pow.f64 (pow.f64 (.f64 x (+.f64 x -1)) 3/4) 1/2) (sqrt.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 1/4)))
(.f64 (pow.f64 (.f64 x (pow.f64 (cbrt.f64 (+.f64 x -1)) 2)) 1/2) (sqrt.f64 (cbrt.f64 (+.f64 x -1))))
(.f64 (pow.f64 (.f64 x (sqrt.f64 (+.f64 x -1))) 1/2) (sqrt.f64 (sqrt.f64 (+.f64 x -1))))
(.f64 (pow.f64 (.f64 (+.f64 x -1) (pow.f64 (cbrt.f64 x) 2)) 1/2) (sqrt.f64 (cbrt.f64 x)))
(.f64 (pow.f64 (.f64 (+.f64 x -1) (sqrt.f64 x)) 1/2) (sqrt.f64 (sqrt.f64 x)))
(.f64 (pow.f64 (pow.f64 (.f64 x (+.f64 x -1)) 5/6) 1/2) (sqrt.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 1/6)))
(.f64 (pow.f64 (pow.f64 (.f64 (*.f64 x (+.f64 x -1)) x) 1/2) 1/2) (sqrt.f64 (sqrt.f64 (+.f64 x -1))))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 x (+.f64 x -1)) 1/6)) 2) 3) (pow.f64 (*.f64 x (+.f64 x -1)) 1/6))
(.f64 (pow.f64 (sqrt.f64 (pow.f64 (.f64 x (+.f64 x -1)) 1/6)) 3) (pow.f64 (sqrt.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 1/6)) 3))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 x (+.f64 x -1))) 4) 1/3) (cbrt.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 1/6)))
(.f64 (pow.f64 (.f64 (*.f64 x (+.f64 x -1)) (sqrt.f64 x)) 1/3) (cbrt.f64 (sqrt.f64 (+.f64 x -1))))
(.f64 (pow.f64 (pow.f64 (.f64 x (+.f64 x -1)) 5/4) 1/3) (cbrt.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 1/4)))
(pow.f64 (*.f64 x (+.f64 x -1)) 1/2)
(pow.f64 (hypot.f64 x (sqrt.f64 (neg.f64 x))) 1)
(pow.f64 (cbrt.f64 (*.f64 x (+.f64 x -1))) 3/2)
(pow.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 1/6) 3)
(pow.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 2) 1/4)
(pow.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 3) 1/6)
(pow.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 3/2) 1/3)
(pow.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 1/4) 2)
(pow.f64 (E.f64) (log.f64 (hypot.f64 x (sqrt.f64 (neg.f64 x)))))
(pow.f64 (exp.f64 1/2) (log.f64 (*.f64 x (+.f64 x -1))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (hypot.f64 x (sqrt.f64 (neg.f64 x))))) 2)) (cbrt.f64 (log.f64 (hypot.f64 x (sqrt.f64 (neg.f64 x))))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (hypot.f64 x (sqrt.f64 (neg.f64 x)))))) (sqrt.f64 (log.f64 (hypot.f64 x (sqrt.f64 (neg.f64 x))))))
(fabs.f64 (hypot.f64 x (sqrt.f64 (neg.f64 x))))
(log.f64 (exp.f64 (hypot.f64 x (sqrt.f64 (neg.f64 x)))))
(cbrt.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 3/2))
(expm1.f64 (log1p.f64 (hypot.f64 x (sqrt.f64 (neg.f64 x)))))
(hypot.f64 x (sqrt.f64 (neg.f64 x)))
(hypot.f64 (sqrt.f64 (neg.f64 x)) x)
(exp.f64 (log.f64 (hypot.f64 x (sqrt.f64 (neg.f64 x)))))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 x (+.f64 x -1)) 1/6)) 3))
(exp.f64 (.f64 (.f64 3/2 (log.f64 (*.f64 x (+.f64 x -1)))) 1/3))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 x (+.f64 x -1)) 1/4)) 2))
(log1p.f64 (expm1.f64 (hypot.f64 x (sqrt.f64 (neg.f64 x)))))
(+.f64 (pow.f64 x 2) (neg.f64 x))
(+.f64 (pow.f64 x 2) (*.f64 (neg.f64 x) 1))
(+.f64 (neg.f64 x) (pow.f64 x 2))
(+.f64 0 (*.f64 x (+.f64 x -1)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) (+.f64 x -1))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 x) (+.f64 x -1)))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 x) (+.f64 x -1)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 x) (+.f64 x -1)))))
(-.f64 (+.f64 1 (*.f64 x (+.f64 x -1))) 1)
(/.f64 (+.f64 (pow.f64 x 6) (pow.f64 (neg.f64 x) 3)) (+.f64 (pow.f64 x 4) (-.f64 (pow.f64 (neg.f64 x) 2) (*.f64 (pow.f64 x 2) (neg.f64 x)))))
(/.f64 (-.f64 (pow.f64 x 4) (pow.f64 (neg.f64 x) 2)) (-.f64 (pow.f64 x 2) (neg.f64 x)))
(/.f64 (*.f64 x (+.f64 -1 (pow.f64 x 3))) (-.f64 (fma.f64 x x 1) (neg.f64 x)))
(/.f64 (*.f64 x (fma.f64 x x -1)) (+.f64 x 1))
(/.f64 (*.f64 (+.f64 -1 (pow.f64 x 3)) x) (-.f64 (fma.f64 x x 1) (neg.f64 x)))
(/.f64 (*.f64 (fma.f64 x x -1) x) (+.f64 x 1))
(pow.f64 (*.f64 x (+.f64 x -1)) 1)
(pow.f64 (hypot.f64 x (sqrt.f64 (neg.f64 x))) 2)
(pow.f64 (cbrt.f64 (*.f64 x (+.f64 x -1))) 3)
(pow.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 1/6) 6)
(pow.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 2) 1/2)
(pow.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 3) 1/3)
(pow.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 3/2) 2/3)
(pow.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 1/4) 4)
(pow.f64 (E.f64) (log.f64 (*.f64 x (+.f64 x -1))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (.f64 x (+.f64 x -1)))) 2)) (cbrt.f64 (log.f64 (.f64 x (+.f64 x -1)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (.f64 x (+.f64 x -1))))) (sqrt.f64 (log.f64 (.f64 x (+.f64 x -1)))))
(sqrt.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 2))
(log.f64 (pow.f64 (exp.f64 x) (+.f64 x -1)))
(cbrt.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 3))
(expm1.f64 (log1p.f64 (*.f64 x (+.f64 x -1))))
(exp.f64 (log.f64 (*.f64 x (+.f64 x -1))))
(exp.f64 (*.f64 (log.f64 (hypot.f64 x (sqrt.f64 (neg.f64 x)))) 2))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 x (+.f64 x -1)))) 3))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 x (+.f64 x -1)) 2)) 1/2))
(exp.f64 (.f64 (.f64 3 (log.f64 (*.f64 x (+.f64 x -1)))) 1/3))
(log1p.f64 (expm1.f64 (*.f64 x (+.f64 x -1))))
(fma.f64 x x (neg.f64 x))
(fma.f64 x -1 (pow.f64 x 2))
(fma.f64 -1 x (pow.f64 x 2))
(fma.f64 1 (pow.f64 x 2) (neg.f64 x))
(fma.f64 1 (neg.f64 x) (pow.f64 x 2))
(fma.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 x) 4) (neg.f64 x))
(fma.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) -1) (pow.f64 x 2))
(fma.f64 (pow.f64 x 2) 1 (*.f64 (neg.f64 x) 1))
(fma.f64 (sqrt.f64 x) (pow.f64 x 3/2) (neg.f64 x))
(fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) -1) (pow.f64 x 2))
(fma.f64 (pow.f64 (cbrt.f64 x) 4) (pow.f64 (cbrt.f64 x) 2) (neg.f64 x))
(fma.f64 (pow.f64 (cbrt.f64 (neg.f64 x)) 2) (cbrt.f64 (neg.f64 x)) (pow.f64 x 2))
(fma.f64 (sqrt.f64 (neg.f64 x)) (sqrt.f64 (neg.f64 x)) (pow.f64 x 2))
(fma.f64 (pow.f64 (cbrt.f64 x) 5) (cbrt.f64 x) (neg.f64 x))
(fma.f64 (*.f64 -1 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (pow.f64 x 2))
(fma.f64 (*.f64 -1 (sqrt.f64 x)) (sqrt.f64 x) (pow.f64 x 2))
(fma.f64 (pow.f64 x 3/2) (sqrt.f64 x) (neg.f64 x))

Outputs
x
(-.f64 x 1/2)
(+.f64 x -1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (/.f64 1/8 x)))
(+.f64 x (-.f64 -1/2 (/.f64 1/8 x)))
(+.f64 -1/2 (+.f64 x (/.f64 -1/8 x)))
(-.f64 x (+.f64 1/2 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 2))) (.f64 1/8 (/.f64 1 x)))))
(-.f64 x (+.f64 1/2 (+.f64 (/.f64 1/8 x) (/.f64 1/16 (pow.f64 x 2)))))
(-.f64 x (+.f64 (+.f64 1/2 (/.f64 1/8 x)) (/.f64 1/16 (pow.f64 x 2))))
(+.f64 x (-.f64 (+.f64 -1/2 (/.f64 -1/8 x)) (/.f64 1/16 (pow.f64 x 2))))
(*.f64 -1 x)
(neg.f64 x)
(+.f64 1/2 (*.f64 -1 x))
(+.f64 1/2 (neg.f64 x))
(-.f64 1/2 x)
(+.f64 1/2 (+.f64 (.f64 -1 x) (.f64 1/8 (/.f64 1 x))))
(+.f64 1/2 (fma.f64 -1 x (/.f64 1/8 x)))
(+.f64 1/2 (-.f64 (/.f64 1/8 x) x))
(+.f64 1/2 (+.f64 (.f64 -1 x) (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x)))))
(+.f64 1/2 (fma.f64 -1 x (+.f64 (/.f64 1/8 x) (/.f64 1/16 (pow.f64 x 2)))))
(+.f64 (+.f64 1/2 (-.f64 (/.f64 1/8 x) x)) (/.f64 1/16 (pow.f64 x 2)))
(+.f64 (/.f64 1/8 x) (+.f64 (/.f64 1/16 (pow.f64 x 2)) (-.f64 1/2 x)))
(*.f64 -1 x)
(neg.f64 x)
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(-.f64 (pow.f64 x 2) x)
(*.f64 x (+.f64 x -1))
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(-.f64 (pow.f64 x 2) x)
(*.f64 x (+.f64 x -1))
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(-.f64 (pow.f64 x 2) x)
(*.f64 x (+.f64 x -1))
(pow.f64 x 2)
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(-.f64 (pow.f64 x 2) x)
(*.f64 x (+.f64 x -1))
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(-.f64 (pow.f64 x 2) x)
(*.f64 x (+.f64 x -1))
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(-.f64 (pow.f64 x 2) x)
(*.f64 x (+.f64 x -1))
(pow.f64 x 2)
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(-.f64 (pow.f64 x 2) x)
(*.f64 x (+.f64 x -1))
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(-.f64 (pow.f64 x 2) x)
(*.f64 x (+.f64 x -1))
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(-.f64 (pow.f64 x 2) x)
(*.f64 x (+.f64 x -1))
(+.f64 0 (hypot.f64 x (sqrt.f64 (neg.f64 x))))
(hypot.f64 x (sqrt.f64 (neg.f64 x)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (hypot.f64 x (sqrt.f64 (neg.f64 x))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (hypot.f64 x (sqrt.f64 (neg.f64 x)))))))
(*.f64 3 (log.f64 (cbrt.f64 (exp.f64 (hypot.f64 x (sqrt.f64 (neg.f64 x)))))))
(*.f64 (log.f64 (cbrt.f64 (exp.f64 (hypot.f64 x (sqrt.f64 (neg.f64 x)))))) 3)
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 x (sqrt.f64 (neg.f64 x)))))) (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 x (sqrt.f64 (neg.f64 x)))))))
(*.f64 2 (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 x (sqrt.f64 (neg.f64 x)))))))
(-.f64 (+.f64 1 (hypot.f64 x (sqrt.f64 (neg.f64 x)))) 1)
(hypot.f64 x (sqrt.f64 (neg.f64 x)))
(*.f64 (hypot.f64 x (sqrt.f64 (neg.f64 x))) 1)
(hypot.f64 x (sqrt.f64 (neg.f64 x)))
(*.f64 (hypot.f64 x (sqrt.f64 (neg.f64 x))) (log.f64 (E.f64)))
(hypot.f64 x (sqrt.f64 (neg.f64 x)))
(*.f64 1 (hypot.f64 x (sqrt.f64 (neg.f64 x))))
(hypot.f64 x (sqrt.f64 (neg.f64 x)))
(.f64 (cbrt.f64 x) (pow.f64 (.f64 (+.f64 x -1) (hypot.f64 x (sqrt.f64 (neg.f64 x)))) 1/3))
(.f64 (cbrt.f64 x) (cbrt.f64 (.f64 (hypot.f64 x (sqrt.f64 (neg.f64 x))) (+.f64 x -1))))
(.f64 (cbrt.f64 x) (cbrt.f64 (.f64 (+.f64 x -1) (hypot.f64 x (sqrt.f64 (neg.f64 x))))))
(.f64 (cbrt.f64 (.f64 x (+.f64 x -1))) (pow.f64 (*.f64 x (+.f64 x -1)) 1/6))
(hypot.f64 x (sqrt.f64 (neg.f64 x)))
(.f64 (cbrt.f64 (+.f64 x -1)) (pow.f64 (.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 x)))) 1/3))
(.f64 (cbrt.f64 (+.f64 x -1)) (cbrt.f64 (.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 x))))))
(.f64 (pow.f64 (.f64 x (+.f64 x -1)) 1/6) (cbrt.f64 (*.f64 x (+.f64 x -1))))
(hypot.f64 x (sqrt.f64 (neg.f64 x)))
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x -1)))
(*.f64 (sqrt.f64 (+.f64 x -1)) (sqrt.f64 x))
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x -1)))
(.f64 (pow.f64 (.f64 x (+.f64 x -1)) 1/4) (pow.f64 (*.f64 x (+.f64 x -1)) 1/4))
(hypot.f64 x (sqrt.f64 (neg.f64 x)))
(.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (.f64 x (+.f64 x -1))) 2)) (pow.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 5/6) 1/3))
(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (-.f64 (pow.f64 x 2) x)) 2)) (cbrt.f64 (pow.f64 (-.f64 (pow.f64 x 2) x) 5/6)))
(.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (.f64 x (+.f64 x -1))) 2)) (cbrt.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 5/6)))
(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x -1)) 2)) (pow.f64 (.f64 (cbrt.f64 (+.f64 x -1)) x) 1/2))
(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x -1)) 2)) (sqrt.f64 (.f64 x (cbrt.f64 (+.f64 x -1)))))
(.f64 (fabs.f64 (cbrt.f64 (+.f64 x -1))) (sqrt.f64 (.f64 x (cbrt.f64 (+.f64 x -1)))))
(.f64 (cbrt.f64 (+.f64 x -1)) (sqrt.f64 (.f64 x (cbrt.f64 (+.f64 x -1)))))
(.f64 (sqrt.f64 (sqrt.f64 (+.f64 x -1))) (pow.f64 (.f64 (sqrt.f64 (+.f64 x -1)) x) 1/2))
(.f64 (sqrt.f64 (sqrt.f64 (+.f64 x -1))) (sqrt.f64 (.f64 x (sqrt.f64 (+.f64 x -1)))))
(.f64 (sqrt.f64 (sqrt.f64 x)) (pow.f64 (.f64 (sqrt.f64 x) (+.f64 x -1)) 1/2))
(.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (.f64 (+.f64 x -1) (sqrt.f64 x))))
(.f64 (sqrt.f64 (sqrt.f64 x)) (pow.f64 (pow.f64 (.f64 (+.f64 x -1) (*.f64 x (+.f64 x -1))) 1/2) 1/2))
(.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 (.f64 (+.f64 x -1) (-.f64 (pow.f64 x 2) x)))))
(.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 (.f64 x (*.f64 (+.f64 x -1) (+.f64 x -1))))))
(.f64 (sqrt.f64 (sqrt.f64 x)) (pow.f64 (.f64 x (*.f64 (+.f64 x -1) (+.f64 x -1))) 1/4))
(.f64 (sqrt.f64 (pow.f64 (.f64 x (+.f64 x -1)) 1/4)) (pow.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 3/4) 1/2))
(*.f64 (sqrt.f64 (pow.f64 (-.f64 (pow.f64 x 2) x) 1/4)) (sqrt.f64 (pow.f64 (-.f64 (pow.f64 x 2) x) 3/4)))
(.f64 (pow.f64 (.f64 x (+.f64 x -1)) 3/8) (pow.f64 (*.f64 x (+.f64 x -1)) 1/8))
(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)) (pow.f64 (.f64 (cbrt.f64 x) (+.f64 x -1)) 1/2))
(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)) (sqrt.f64 (.f64 (cbrt.f64 x) (+.f64 x -1))))
(.f64 (fabs.f64 (cbrt.f64 x)) (sqrt.f64 (.f64 (cbrt.f64 x) (+.f64 x -1))))
(.f64 (cbrt.f64 x) (sqrt.f64 (.f64 (cbrt.f64 x) (+.f64 x -1))))
(*.f64 (pow.f64 1 1/3) (hypot.f64 x (sqrt.f64 (neg.f64 x))))
(hypot.f64 x (sqrt.f64 (neg.f64 x)))
(.f64 (pow.f64 (pow.f64 (.f64 x (+.f64 x -1)) 3/4) 1/2) (sqrt.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 1/4)))
(*.f64 (sqrt.f64 (pow.f64 (-.f64 (pow.f64 x 2) x) 1/4)) (sqrt.f64 (pow.f64 (-.f64 (pow.f64 x 2) x) 3/4)))
(.f64 (pow.f64 (.f64 x (+.f64 x -1)) 3/8) (pow.f64 (*.f64 x (+.f64 x -1)) 1/8))
(.f64 (pow.f64 (.f64 x (pow.f64 (cbrt.f64 (+.f64 x -1)) 2)) 1/2) (sqrt.f64 (cbrt.f64 (+.f64 x -1))))
(.f64 (sqrt.f64 (.f64 x (pow.f64 (cbrt.f64 (+.f64 x -1)) 2))) (sqrt.f64 (cbrt.f64 (+.f64 x -1))))
(.f64 (pow.f64 (.f64 x (sqrt.f64 (+.f64 x -1))) 1/2) (sqrt.f64 (sqrt.f64 (+.f64 x -1))))
(.f64 (sqrt.f64 (sqrt.f64 (+.f64 x -1))) (sqrt.f64 (.f64 x (sqrt.f64 (+.f64 x -1)))))
(.f64 (pow.f64 (.f64 (+.f64 x -1) (pow.f64 (cbrt.f64 x) 2)) 1/2) (sqrt.f64 (cbrt.f64 x)))
(.f64 (sqrt.f64 (.f64 (+.f64 x -1) (pow.f64 (cbrt.f64 x) 2))) (sqrt.f64 (cbrt.f64 x)))
(.f64 (pow.f64 (.f64 (+.f64 x -1) (sqrt.f64 x)) 1/2) (sqrt.f64 (sqrt.f64 x)))
(.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (.f64 (+.f64 x -1) (sqrt.f64 x))))
(.f64 (pow.f64 (pow.f64 (.f64 x (+.f64 x -1)) 5/6) 1/2) (sqrt.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 1/6)))
(*.f64 (sqrt.f64 (pow.f64 (-.f64 (pow.f64 x 2) x) 5/6)) (sqrt.f64 (pow.f64 (-.f64 (pow.f64 x 2) x) 1/6)))
(*.f64 (sqrt.f64 (pow.f64 (-.f64 (pow.f64 x 2) x) 5/6)) (fabs.f64 (pow.f64 (-.f64 (pow.f64 x 2) x) 1/12)))
(.f64 (pow.f64 (.f64 x (+.f64 x -1)) 5/12) (pow.f64 (*.f64 x (+.f64 x -1)) 1/12))
(.f64 (pow.f64 (pow.f64 (.f64 (*.f64 x (+.f64 x -1)) x) 1/2) 1/2) (sqrt.f64 (sqrt.f64 (+.f64 x -1))))
(.f64 (sqrt.f64 (sqrt.f64 (+.f64 x -1))) (sqrt.f64 (sqrt.f64 (.f64 x (-.f64 (pow.f64 x 2) x)))))
(.f64 (sqrt.f64 (sqrt.f64 (+.f64 x -1))) (sqrt.f64 (sqrt.f64 (.f64 (pow.f64 x 2) (+.f64 x -1)))))
(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 x -1))) (pow.f64 (-.f64 (pow.f64 x 3) (pow.f64 x 2)) 1/4))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 x (+.f64 x -1)) 1/6)) 2) 3) (pow.f64 (*.f64 x (+.f64 x -1)) 1/6))
(hypot.f64 x (sqrt.f64 (neg.f64 x)))
(.f64 (pow.f64 (sqrt.f64 (pow.f64 (.f64 x (+.f64 x -1)) 1/6)) 3) (pow.f64 (sqrt.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 1/6)) 3))
(hypot.f64 x (sqrt.f64 (neg.f64 x)))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 x (+.f64 x -1))) 4) 1/3) (cbrt.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 1/6)))
(*.f64 (cbrt.f64 (pow.f64 (-.f64 (pow.f64 x 2) x) 1/6)) (cbrt.f64 (pow.f64 (cbrt.f64 (-.f64 (pow.f64 x 2) x)) 4)))
(.f64 (cbrt.f64 (pow.f64 (.f64 x (+.f64 x -1)) 1/6)) (cbrt.f64 (pow.f64 (cbrt.f64 (*.f64 x (+.f64 x -1))) 4)))
(.f64 (pow.f64 (.f64 (*.f64 x (+.f64 x -1)) (sqrt.f64 x)) 1/3) (cbrt.f64 (sqrt.f64 (+.f64 x -1))))
(.f64 (cbrt.f64 (.f64 x (*.f64 (+.f64 x -1) (sqrt.f64 x)))) (cbrt.f64 (sqrt.f64 (+.f64 x -1))))
(.f64 (cbrt.f64 (.f64 (*.f64 x (+.f64 x -1)) (sqrt.f64 x))) (cbrt.f64 (sqrt.f64 (+.f64 x -1))))
(.f64 (pow.f64 (pow.f64 (.f64 x (+.f64 x -1)) 5/4) 1/3) (cbrt.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 1/4)))
(*.f64 (cbrt.f64 (pow.f64 (-.f64 (pow.f64 x 2) x) 5/4)) (cbrt.f64 (pow.f64 (-.f64 (pow.f64 x 2) x) 1/4)))
(.f64 (cbrt.f64 (pow.f64 (.f64 x (+.f64 x -1)) 5/4)) (cbrt.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 1/4)))
(pow.f64 (*.f64 x (+.f64 x -1)) 1/2)
(hypot.f64 x (sqrt.f64 (neg.f64 x)))
(pow.f64 (hypot.f64 x (sqrt.f64 (neg.f64 x))) 1)
(hypot.f64 x (sqrt.f64 (neg.f64 x)))
(pow.f64 (cbrt.f64 (*.f64 x (+.f64 x -1))) 3/2)
(hypot.f64 x (sqrt.f64 (neg.f64 x)))
(pow.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 1/6) 3)
(hypot.f64 x (sqrt.f64 (neg.f64 x)))
(pow.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 2) 1/4)
(pow.f64 (pow.f64 (-.f64 (pow.f64 x 2) x) 2) 1/4)
(pow.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 3) 1/6)
(hypot.f64 x (sqrt.f64 (neg.f64 x)))
(pow.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 3/2) 1/3)
(hypot.f64 x (sqrt.f64 (neg.f64 x)))
(pow.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 1/4) 2)
(hypot.f64 x (sqrt.f64 (neg.f64 x)))
(pow.f64 (E.f64) (log.f64 (hypot.f64 x (sqrt.f64 (neg.f64 x)))))
(hypot.f64 x (sqrt.f64 (neg.f64 x)))
(pow.f64 (exp.f64 1/2) (log.f64 (*.f64 x (+.f64 x -1))))
(hypot.f64 x (sqrt.f64 (neg.f64 x)))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (hypot.f64 x (sqrt.f64 (neg.f64 x))))) 2)) (cbrt.f64 (log.f64 (hypot.f64 x (sqrt.f64 (neg.f64 x))))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (hypot.f64 x (sqrt.f64 (neg.f64 x)))))) (sqrt.f64 (log.f64 (hypot.f64 x (sqrt.f64 (neg.f64 x))))))
(fabs.f64 (hypot.f64 x (sqrt.f64 (neg.f64 x))))
(hypot.f64 x (sqrt.f64 (neg.f64 x)))
(log.f64 (exp.f64 (hypot.f64 x (sqrt.f64 (neg.f64 x)))))
(hypot.f64 x (sqrt.f64 (neg.f64 x)))
(cbrt.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 3/2))
(hypot.f64 x (sqrt.f64 (neg.f64 x)))
(expm1.f64 (log1p.f64 (hypot.f64 x (sqrt.f64 (neg.f64 x)))))
(hypot.f64 x (sqrt.f64 (neg.f64 x)))
(hypot.f64 x (sqrt.f64 (neg.f64 x)))
(hypot.f64 (sqrt.f64 (neg.f64 x)) x)
(hypot.f64 x (sqrt.f64 (neg.f64 x)))
(exp.f64 (log.f64 (hypot.f64 x (sqrt.f64 (neg.f64 x)))))
(hypot.f64 x (sqrt.f64 (neg.f64 x)))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 x (+.f64 x -1)) 1/6)) 3))
(hypot.f64 x (sqrt.f64 (neg.f64 x)))
(exp.f64 (.f64 (.f64 3/2 (log.f64 (*.f64 x (+.f64 x -1)))) 1/3))
(hypot.f64 x (sqrt.f64 (neg.f64 x)))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 x (+.f64 x -1)) 1/4)) 2))
(hypot.f64 x (sqrt.f64 (neg.f64 x)))
(log1p.f64 (expm1.f64 (hypot.f64 x (sqrt.f64 (neg.f64 x)))))
(hypot.f64 x (sqrt.f64 (neg.f64 x)))
(+.f64 (pow.f64 x 2) (neg.f64 x))
(-.f64 (pow.f64 x 2) x)
(*.f64 x (+.f64 x -1))
(+.f64 (pow.f64 x 2) (*.f64 (neg.f64 x) 1))
(-.f64 (pow.f64 x 2) x)
(*.f64 x (+.f64 x -1))
(+.f64 (neg.f64 x) (pow.f64 x 2))
(-.f64 (pow.f64 x 2) x)
(*.f64 x (+.f64 x -1))
(+.f64 0 (*.f64 x (+.f64 x -1)))
(-.f64 (pow.f64 x 2) x)
(*.f64 x (+.f64 x -1))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) (+.f64 x -1))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 x) (+.f64 x -1)))))
(*.f64 3 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 x) (+.f64 x -1)))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 x) (+.f64 x -1)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 x) (+.f64 x -1)))))
(-.f64 (pow.f64 x 2) x)
(*.f64 x (+.f64 x -1))
(-.f64 (+.f64 1 (*.f64 x (+.f64 x -1))) 1)
(-.f64 (pow.f64 x 2) x)
(*.f64 x (+.f64 x -1))
(/.f64 (+.f64 (pow.f64 x 6) (pow.f64 (neg.f64 x) 3)) (+.f64 (pow.f64 x 4) (-.f64 (pow.f64 (neg.f64 x) 2) (*.f64 (pow.f64 x 2) (neg.f64 x)))))
(/.f64 (+.f64 (pow.f64 x 6) (pow.f64 (neg.f64 x) 3)) (+.f64 (pow.f64 x 4) (-.f64 (pow.f64 (neg.f64 x) 2) (pow.f64 (neg.f64 x) 3))))
(/.f64 (-.f64 (pow.f64 x 6) (pow.f64 x 3)) (+.f64 (pow.f64 x 2) (+.f64 (pow.f64 x 3) (pow.f64 x 4))))
(/.f64 (-.f64 (pow.f64 x 6) (pow.f64 x 3)) (+.f64 (pow.f64 x 4) (fma.f64 x x (pow.f64 x 3))))
(/.f64 (-.f64 (pow.f64 x 4) (pow.f64 (neg.f64 x) 2)) (-.f64 (pow.f64 x 2) (neg.f64 x)))
(/.f64 (-.f64 (pow.f64 x 4) (pow.f64 x 2)) (fma.f64 x x x))
(/.f64 (*.f64 x (+.f64 -1 (pow.f64 x 3))) (-.f64 (fma.f64 x x 1) (neg.f64 x)))
(/.f64 x (/.f64 (-.f64 (fma.f64 x x 1) (neg.f64 x)) (+.f64 -1 (pow.f64 x 3))))
(/.f64 (fma.f64 x -1 (pow.f64 x 4)) (+.f64 x (fma.f64 x x 1)))
(/.f64 (-.f64 (pow.f64 x 4) x) (+.f64 x (fma.f64 x x 1)))
(/.f64 (*.f64 x (fma.f64 x x -1)) (+.f64 x 1))
(/.f64 (fma.f64 x x -1) (/.f64 (+.f64 x 1) x))
(/.f64 (+.f64 (pow.f64 x 3) (neg.f64 x)) (+.f64 x 1))
(/.f64 (-.f64 (pow.f64 x 3) x) (+.f64 x 1))
(/.f64 (*.f64 (+.f64 -1 (pow.f64 x 3)) x) (-.f64 (fma.f64 x x 1) (neg.f64 x)))
(/.f64 x (/.f64 (-.f64 (fma.f64 x x 1) (neg.f64 x)) (+.f64 -1 (pow.f64 x 3))))
(/.f64 (fma.f64 x -1 (pow.f64 x 4)) (+.f64 x (fma.f64 x x 1)))
(/.f64 (-.f64 (pow.f64 x 4) x) (+.f64 x (fma.f64 x x 1)))
(/.f64 (*.f64 (fma.f64 x x -1) x) (+.f64 x 1))
(/.f64 (fma.f64 x x -1) (/.f64 (+.f64 x 1) x))
(/.f64 (+.f64 (pow.f64 x 3) (neg.f64 x)) (+.f64 x 1))
(/.f64 (-.f64 (pow.f64 x 3) x) (+.f64 x 1))
(pow.f64 (*.f64 x (+.f64 x -1)) 1)
(-.f64 (pow.f64 x 2) x)
(*.f64 x (+.f64 x -1))
(pow.f64 (hypot.f64 x (sqrt.f64 (neg.f64 x))) 2)
(-.f64 (pow.f64 x 2) x)
(*.f64 x (+.f64 x -1))
(pow.f64 (cbrt.f64 (*.f64 x (+.f64 x -1))) 3)
(-.f64 (pow.f64 x 2) x)
(*.f64 x (+.f64 x -1))
(pow.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 1/6) 6)
(-.f64 (pow.f64 x 2) x)
(*.f64 x (+.f64 x -1))
(pow.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 2) 1/2)
(-.f64 (pow.f64 x 2) x)
(*.f64 x (+.f64 x -1))
(pow.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 3) 1/3)
(-.f64 (pow.f64 x 2) x)
(*.f64 x (+.f64 x -1))
(pow.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 3/2) 2/3)
(-.f64 (pow.f64 x 2) x)
(*.f64 x (+.f64 x -1))
(pow.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 1/4) 4)
(-.f64 (pow.f64 x 2) x)
(*.f64 x (+.f64 x -1))
(pow.f64 (E.f64) (log.f64 (*.f64 x (+.f64 x -1))))
(-.f64 (pow.f64 x 2) x)
(*.f64 x (+.f64 x -1))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (.f64 x (+.f64 x -1)))) 2)) (cbrt.f64 (log.f64 (.f64 x (+.f64 x -1)))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (-.f64 (pow.f64 x 2) x))) 2)) (cbrt.f64 (log.f64 (-.f64 (pow.f64 x 2) x))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (.f64 x (+.f64 x -1))))) (sqrt.f64 (log.f64 (.f64 x (+.f64 x -1)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (-.f64 (pow.f64 x 2) x)))) (sqrt.f64 (log.f64 (-.f64 (pow.f64 x 2) x))))
(sqrt.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 2))
(-.f64 (pow.f64 x 2) x)
(*.f64 x (+.f64 x -1))
(log.f64 (pow.f64 (exp.f64 x) (+.f64 x -1)))
(-.f64 (pow.f64 x 2) x)
(*.f64 x (+.f64 x -1))
(cbrt.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 3))
(-.f64 (pow.f64 x 2) x)
(*.f64 x (+.f64 x -1))
(expm1.f64 (log1p.f64 (*.f64 x (+.f64 x -1))))
(-.f64 (pow.f64 x 2) x)
(*.f64 x (+.f64 x -1))
(exp.f64 (log.f64 (*.f64 x (+.f64 x -1))))
(-.f64 (pow.f64 x 2) x)
(*.f64 x (+.f64 x -1))
(exp.f64 (*.f64 (log.f64 (hypot.f64 x (sqrt.f64 (neg.f64 x)))) 2))
(-.f64 (pow.f64 x 2) x)
(*.f64 x (+.f64 x -1))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 x (+.f64 x -1)))) 3))
(-.f64 (pow.f64 x 2) x)
(*.f64 x (+.f64 x -1))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 x (+.f64 x -1)) 2)) 1/2))
(-.f64 (pow.f64 x 2) x)
(*.f64 x (+.f64 x -1))
(exp.f64 (.f64 (.f64 3 (log.f64 (*.f64 x (+.f64 x -1)))) 1/3))
(-.f64 (pow.f64 x 2) x)
(*.f64 x (+.f64 x -1))
(log1p.f64 (expm1.f64 (*.f64 x (+.f64 x -1))))
(-.f64 (pow.f64 x 2) x)
(*.f64 x (+.f64 x -1))
(fma.f64 x x (neg.f64 x))
(-.f64 (pow.f64 x 2) x)
(*.f64 x (+.f64 x -1))
(fma.f64 x -1 (pow.f64 x 2))
(-.f64 (pow.f64 x 2) x)
(*.f64 x (+.f64 x -1))
(fma.f64 -1 x (pow.f64 x 2))
(-.f64 (pow.f64 x 2) x)
(*.f64 x (+.f64 x -1))
(fma.f64 1 (pow.f64 x 2) (neg.f64 x))
(-.f64 (pow.f64 x 2) x)
(*.f64 x (+.f64 x -1))
(fma.f64 1 (neg.f64 x) (pow.f64 x 2))
(-.f64 (pow.f64 x 2) x)
(*.f64 x (+.f64 x -1))
(fma.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 x) 4) (neg.f64 x))
(-.f64 (pow.f64 x 2) x)
(*.f64 x (+.f64 x -1))
(fma.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) -1) (pow.f64 x 2))
(-.f64 (pow.f64 x 2) x)
(*.f64 x (+.f64 x -1))
(fma.f64 (pow.f64 x 2) 1 (*.f64 (neg.f64 x) 1))
(-.f64 (pow.f64 x 2) x)
(*.f64 x (+.f64 x -1))
(fma.f64 (sqrt.f64 x) (pow.f64 x 3/2) (neg.f64 x))
(-.f64 (*.f64 (sqrt.f64 x) (pow.f64 x 3/2)) x)
(fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) -1) (pow.f64 x 2))
(-.f64 (pow.f64 x 2) x)
(*.f64 x (+.f64 x -1))
(fma.f64 (pow.f64 (cbrt.f64 x) 4) (pow.f64 (cbrt.f64 x) 2) (neg.f64 x))
(-.f64 (pow.f64 x 2) x)
(*.f64 x (+.f64 x -1))
(fma.f64 (pow.f64 (cbrt.f64 (neg.f64 x)) 2) (cbrt.f64 (neg.f64 x)) (pow.f64 x 2))
(-.f64 (pow.f64 x 2) x)
(*.f64 x (+.f64 x -1))
(fma.f64 (sqrt.f64 (neg.f64 x)) (sqrt.f64 (neg.f64 x)) (pow.f64 x 2))
(-.f64 (pow.f64 x 2) x)
(*.f64 x (+.f64 x -1))
(fma.f64 (pow.f64 (cbrt.f64 x) 5) (cbrt.f64 x) (neg.f64 x))
(-.f64 (pow.f64 x 2) x)
(*.f64 x (+.f64 x -1))
(fma.f64 (*.f64 -1 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (pow.f64 x 2))
(-.f64 (pow.f64 x 2) x)
(*.f64 x (+.f64 x -1))
(fma.f64 (*.f64 -1 (sqrt.f64 x)) (sqrt.f64 x) (pow.f64 x 2))
(-.f64 (pow.f64 x 2) x)
(*.f64 x (+.f64 x -1))
(fma.f64 (pow.f64 x 3/2) (sqrt.f64 x) (neg.f64 x))
(fma.f64 (sqrt.f64 x) (pow.f64 x 3/2) (neg.f64 x))
(-.f64 (*.f64 (sqrt.f64 x) (pow.f64 x 3/2)) x)

eval151.0ms (8.4%)

Compiler: Compiled 2180 to 1432 computations (34.3% saved)

prune25.0ms (1.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	185	0	185
Fresh	0	1	1
Picked	0	3	3
Done	0	0	0
Total	185	4	189

Accuracy

100.0%

Counts

189 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.1%	(-.f64 (/.f64 -1/8 x) (-.f64 1/2 x))
✓	98.4%	(-.f64 x 1/2)
✓	54.6%	(sqrt.f64 (*.f64 x (+.f64 x -1)))
	97.0%	x
✓	99.1%	(-.f64 (/.f64 -1/8 x) (-.f64 1/2 x))
✓	98.4%	(-.f64 x 1/2)
✓	54.6%	(sqrt.f64 (*.f64 x (+.f64 x -1)))
	97.0%	x

Compiler

Compiled 42 to 30 computations (28.6% 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
✓	99.1%	(-.f64 (/.f64 -1/8 x) (-.f64 1/2 x))
✓	98.4%	(-.f64 x 1/2)
✓	54.6%	(sqrt.f64 (*.f64 x (+.f64 x -1)))
	97.0%	x
✓	99.1%	(-.f64 (/.f64 -1/8 x) (-.f64 1/2 x))
✓	98.4%	(-.f64 x 1/2)
✓	54.6%	(sqrt.f64 (*.f64 x (+.f64 x -1)))
	97.0%	x

Compiler

Compiled 42 to 30 computations (28.6% saved)

localize0.0ms (0%)

eval0.0ms (0%)

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

prune2.0ms (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
✓	99.1%	(-.f64 (/.f64 -1/8 x) (-.f64 1/2 x))
✓	98.4%	(-.f64 x 1/2)
✓	54.6%	(sqrt.f64 (*.f64 x (+.f64 x -1)))
	97.0%	x

Compiler

Compiled 46 to 32 computations (30.4% saved)

regimes29.0ms (1.6%)

Counts

5 → 1

Calls

Call 1

Inputs
x
(-.f64 x 1/2)
(-.f64 (/.f64 -1/8 x) (-.f64 1/2 x))
(sqrt.f64 (*.f64 x (+.f64 x -1)))
(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))

Outputs
(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))

Calls

2 calls:

23.0ms	x
5.0ms	(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))

Results

Accuracy	Segments	Branch
99.3%	1	`x`
99.3%	1	`(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))`

Compiler

Compiled 35 to 24 computations (31.4% saved)

regimes5.0ms (0.3%)

Counts

4 → 1

Calls

Call 1

Inputs
x
(-.f64 x 1/2)
(-.f64 (/.f64 -1/8 x) (-.f64 1/2 x))
(sqrt.f64 (*.f64 x (+.f64 x -1)))

Outputs
(-.f64 (/.f64 -1/8 x) (-.f64 1/2 x))

Calls

1 calls:

4.0ms

Results

Accuracy	Segments	Branch
99.1%	1	`x`

Compiler

Compiled 20 to 13 computations (35% saved)

regimes4.0ms (0.2%)

Counts

2 → 1

Calls

Call 1

Inputs
x
(-.f64 x 1/2)

Outputs
(-.f64 x 1/2)

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
98.4%	1	`x`

Compiler

Compiled 7 to 4 computations (42.9% saved)

regimes3.0ms (0.2%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
x

Outputs
x

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
97.0%	1	`x`

Compiler

Compiled 4 to 2 computations (50% saved)

simplify7.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

72×	`unsub-neg`
42×	`neg-mul-1`
26×	`+-commutative`
22×	`sub-neg`
20×	`distribute-lft-neg-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	66
1	28	66
2	43	66
3	59	66
4	96	66
5	128	66
6	142	66
7	165	66
8	190	66
9	191	66

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))
(-.f64 (/.f64 -1/8 x) (-.f64 1/2 x))
(-.f64 x 1/2)
x

Outputs
(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))
(*.f64 (sqrt.f64 (+.f64 x -1)) (sqrt.f64 x))
(-.f64 (/.f64 -1/8 x) (-.f64 1/2 x))
(+.f64 (/.f64 -1/8 x) (-.f64 x 1/2))
(-.f64 x 1/2)
x

Compiler

Compiled 22 to 16 computations (27.3% saved)

soundness113.0ms (6.3%)

Rules

1442×	`log-prod`
1298×	`fma-def`
892×	`associate-r`
788×	`associate-l`
436×	`times-frac`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	95	854
1	229	814
2	620	814
3	1726	806
4	7402	806

Stop Event

1×	node limit

Compiler

Compiled 175 to 143 computations (18.3% saved)

end0.0ms (0%)

preprocess59.0ms (3.3%)

Compiler: Compiled 54 to 38 computations (29.6% saved)

analyze2.0ms (0.1%)

sample777.0ms (43.2%)

preprocess134.0ms (7.5%)

eval0.0ms (0%)

prune1.0ms (0.1%)

localize34.0ms (1.9%)

series2.0ms (0.1%)

rewrite155.0ms (8.6%)

simplify75.0ms (4.1%)

eval13.0ms (0.7%)

prune8.0ms (0.4%)

localize72.0ms (4%)

series2.0ms (0.1%)

rewrite63.0ms (3.5%)

simplify62.0ms (3.5%)

eval151.0ms (8.4%)

prune25.0ms (1.4%)

localize0.0ms (0%)

eval0.0ms (0%)

prune3.0ms (0.1%)

localize0.0ms (0%)

eval0.0ms (0%)

prune2.0ms (0.1%)

regimes29.0ms (1.6%)

regimes5.0ms (0.3%)

regimes4.0ms (0.2%)

regimes3.0ms (0.2%)

simplify7.0ms (0.4%)

soundness113.0ms (6.3%)

end0.0ms (0%)

preprocess59.0ms (3.3%)

Profiling