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)

Precisions

Click to see histograms. Total time spent on operations: 1.0ms

Operation ival-sqrt, time spent: 1.0ms, 90.0% of total-time

Operation ival-mult, time spent: 0.0ms, 0.0% of total-time

Operation ival-sub, time spent: 0.0ms, 0.0% of total-time

Operation const, time spent: 0.0ms, 0.0% of total-time

sample1.1s (45.1%)

Results

884.0ms	8255×	256	valid
1.0ms	10×	256	invalid
0.0ms	1×	256	valid

Precisions

Click to see histograms. Total time spent on operations: 376.0ms

Operation ival-sqrt, time spent: 241.0ms, 64.0% of total-time

Operation ival-mult, time spent: 62.0ms, 16.0% of total-time

Operation ival-sub, time spent: 60.0ms, 16.0% of total-time

Operation const, time spent: 14.0ms, 4.0% of total-time

Bogosity

preprocess200.0ms (8.6%)

Algorithm

1×	egg-herbie

Rules

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

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`x`
-	-	`(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))`
-	-	`(sqrt.f64 (-.f64 x 1))`
-	-	`(-.f64 x 1)`
-	-	`1`
-	-	`(sqrt.f64 x)`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	17	128
1	36	124
2	55	120
3	77	120
4	103	120
5	135	120
6	156	120
7	172	120
8	197	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 48 to 32 computations (33.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 35.0ms

Operation ival-sqrt, time spent: 19.0ms, 55.0% of total-time

Operation ival-sub, time spent: 9.0ms, 26.0% of total-time

Operation ival-mult, time spent: 6.0ms, 17.0% of total-time

Operation const, time spent: 2.0ms, 6.0% of total-time

eval0.0ms (0%)

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

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.2%	(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))

Compiler

Compiled 8 to 6 computations (25% saved)

localize45.0ms (1.9%)

Localize:

Found 1 expressions with local error:

New	Accuracy	Program
✓	99.2%	(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))

Compiler

Compiled 20 to 13 computations (35% saved)

Precisions

Click to see histograms. Total time spent on operations: 17.0ms

Operation ival-sqrt, time spent: 10.0ms, 57.0% of total-time

Operation ival-sub, time spent: 4.0ms, 23.0% of total-time

Operation ival-mult, time spent: 2.0ms, 11.0% of total-time

Operation const, time spent: 1.0ms, 6.0% of total-time

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))

rewrite280.0ms (12%)

Algorithm

1×	batch-egg-rewrite

Rules

824×	`unpow-prod-down`
586×	`prod-exp`
496×	`log-prod`
471×	`log1p-expm1-u`
471×	`expm1-log1p-u`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	23
1	125	23
2	1422	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)))))

simplify77.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

1442×	`log-prod`
1298×	`fma-def`
890×	`associate-r`
798×	`associate-l`
436×	`times-frac`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	95	854
1	232	814
2	623	814
3	1726	806
4	7401	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 -1/2 (+.f64 x (/.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 -1/2 (+.f64 (/.f64 -1/8 x) (/.f64 -1/16 (pow.f64 x 2)))))
(+.f64 x (fma.f64 (/.f64 -1 x) (+.f64 1/8 (/.f64 1/16 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 -1/2 (+.f64 x (/.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 -1/2 (+.f64 (/.f64 -1/8 x) (/.f64 -1/16 (pow.f64 x 2)))))
(+.f64 x (fma.f64 (/.f64 -1 x) (+.f64 1/8 (/.f64 1/16 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 (0.6%)

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

prune6.0ms (0.3%)

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
▶	99.2%	(-.f64 (/.f64 -1/8 x) (-.f64 1/2 x))
▶	98.8%	(-.f64 x 1/2)
▶	56.4%	(sqrt.f64 (*.f64 x (+.f64 x -1)))
▶	97.9%	x

Compiler

Compiled 21 to 15 computations (28.6% saved)

localize205.0ms (8.8%)

Localize:

Found 2 expressions with local error:

New	Accuracy	Program
✓	100.0%	(*.f64 x (+.f64 x -1))
✓	56.4%	(sqrt.f64 (*.f64 x (+.f64 x -1)))

Compiler

Compiled 40 to 26 computations (35% saved)

Precisions

Click to see histograms. Total time spent on operations: 24.0ms

Operation ival-sub, time spent: 6.0ms, 25.0% of total-time

Operation ival-add, time spent: 5.0ms, 21.0% of total-time

Operation ival-div, time spent: 4.0ms, 17.0% of total-time

Operation ival-mult, time spent: 4.0ms, 17.0% of total-time

Operation ival-sqrt, time spent: 3.0ms, 13.0% of total-time

Operation const, time spent: 2.0ms, 8.0% of total-time

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	(sqrt.f64 (*.f64 x (+.f64 x -1)))
0.0ms	x	@	0	(*.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)))

rewrite85.0ms (3.6%)

Algorithm

1×	batch-egg-rewrite

Rules

790×	`unpow-prod-down`
462×	`log-prod`
460×	`log1p-expm1-u`
460×	`expm1-log1p-u`
458×	`prod-exp`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	42
1	102	42
2	1289	40

Stop Event

1×	node limit

Counts

2 → 107

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 1 (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))))
(.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 (+.f64 x -1))) (pow.f64 (*.f64 x (+.f64 x -1)) 1/6))
(.f64 (cbrt.f64 x) (pow.f64 (.f64 (+.f64 x -1) (hypot.f64 x (sqrt.f64 (neg.f64 x)))) 1/3))
(*.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 (.f64 (hypot.f64 x (sqrt.f64 (neg.f64 x))) (sqrt.f64 x)) 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 (pow.f64 (*.f64 x (+.f64 x -1)) 1/6) 3)
(pow.f64 (cbrt.f64 (*.f64 x (+.f64 x -1))) 3/2)
(pow.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 3/2) 1/3)
(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)) 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 (.f64 1/4 (log.f64 (*.f64 x (+.f64 x -1)))) 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 (+.f64 x -1)) x)) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (+.f64 x -1)) x))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (+.f64 x -1)) x))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (+.f64 x -1)) x))))
(-.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 (pow.f64 (*.f64 x (+.f64 x -1)) 1/6) 6)
(pow.f64 (cbrt.f64 (*.f64 x (+.f64 x -1))) 3)
(pow.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 3/2) 2/3)
(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)) 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 (+.f64 x -1)) x))
(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 (.f64 2 (log.f64 (*.f64 x (+.f64 x -1)))) 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 (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 (*.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 (cbrt.f64 x) 5) (cbrt.f64 x) (neg.f64 x))
(fma.f64 (pow.f64 (cbrt.f64 x) 4) (pow.f64 (cbrt.f64 x) 2) (neg.f64 x))
(fma.f64 (pow.f64 x 3/2) (sqrt.f64 x) (neg.f64 x))

simplify104.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

1814×	`fma-def`
860×	`unswap-sqr`
736×	`distribute-lft-in`
674×	`distribute-rgt-in`
584×	`*-commutative`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	298	3775
1	731	3642
2	1988	3595

Stop Event

1×	node limit

Counts

127 → 182

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

eval53.0ms (2.3%)

Compiler: Compiled 2145 to 1398 computations (34.8% saved)

prune23.0ms (1%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	182	0	182
Fresh	0	0	0
Picked	0	4	4
Done	0	0	0
Total	182	4	186

Accuracy

100.0%

Counts

186 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.2%	(-.f64 (/.f64 -1/8 x) (-.f64 1/2 x))
✓	98.8%	(-.f64 x 1/2)
✓	56.4%	(sqrt.f64 (*.f64 x (+.f64 x -1)))
✓	97.9%	x

Compiler

Compiled 46 to 32 computations (30.4% saved)

regimes10.0ms (0.4%)

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:

5.0ms	(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))
4.0ms	x

Results

Accuracy	Segments	Branch
99.2%	1	`x`
99.2%	1	`(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes4.0ms (0.2%)

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
99.2%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes3.0ms (0.1%)

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
98.8%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes5.0ms (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:

5.0ms

Results

Accuracy	Segments	Branch
97.9%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

simplify7.0ms (0.3%)

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	31	66
2	46	66
3	62	66
4	99	66
5	131	66
6	145	66
7	168	66
8	193	66
9	194	66

Stop Event

1×	done
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)

soundness116.0ms (5%)

Rules

1442×	`log-prod`
1298×	`fma-def`
890×	`associate-r`
798×	`associate-l`
436×	`times-frac`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	95	854
1	232	814
2	623	814
3	1726	806
4	7401	806

Stop Event

1×	node limit

Compiler

Compiled 175 to 143 computations (18.3% saved)

end0.0ms (0%)

preprocess40.0ms (1.7%)

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

analyze2.0ms (0.1%)

sample1.1s (45.1%)

preprocess200.0ms (8.6%)

eval0.0ms (0%)

prune1.0ms (0%)

localize45.0ms (1.9%)

series2.0ms (0.1%)

rewrite280.0ms (12%)

simplify77.0ms (3.3%)

eval13.0ms (0.6%)

prune6.0ms (0.3%)

localize205.0ms (8.8%)

series2.0ms (0.1%)

rewrite85.0ms (3.6%)

simplify104.0ms (4.4%)

eval53.0ms (2.3%)

prune23.0ms (1%)

regimes10.0ms (0.4%)

regimes4.0ms (0.2%)

regimes3.0ms (0.1%)

regimes5.0ms (0.2%)

simplify7.0ms (0.3%)

soundness116.0ms (5%)

end0.0ms (0%)

preprocess40.0ms (1.7%)

Profiling