Metrics for Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3

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%	100%	0%	0%	0%	0%	2
0%	0%	50%	0%	0%	50%	0%	3
50%	25%	25%	0%	0%	50%	0%	4
75%	37.5%	12.5%	0%	0%	50%	0%	5
87.5%	43.7%	6.2%	0%	0%	50%	0%	6
93.8%	46.9%	3.1%	0%	0%	50%	0%	7
96.9%	48.4%	1.6%	0%	0%	50%	0%	8
98.4%	49.2%	0.8%	0%	0%	50%	0%	9
99.2%	49.6%	0.4%	0%	0%	50%	0%	10
99.6%	49.8%	0.2%	0%	0%	50%	0%	11
99.8%	49.9%	0.1%	0%	0%	50%	0%	12

Compiler

Compiled 8 to 6 computations (25% saved)

sample661.0ms (36.9%)

Results

649.0ms	8256×	body	256	valid
0.0ms	2×	body	256	invalid

Bogosity

preprocess190.0ms (10.6%)

Algorithm

1×	egg-herbie

Rules

1654×	`fma-def`
1224×	`sub-neg`
1138×	`distribute-lft-out`
828×	`associate-+r+`
716×	`*-commutative`

Problems

256×

No Errors

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	69
1	30	69
2	48	69
3	93	69
4	136	69
5	218	69
6	344	69
7	620	69
8	1231	69
9	2097	69
10	4724	69
11	6430	69
12	7198	69
13	7496	69
14	7552	69
15	7584	69
16	7854	69

Stop Event

1×	node limit

Calls

Call 1

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

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

Symmetry

(abs x)

Compiler

Compiled 25 to 14 computations (44% saved)

eval0.0ms (0%)

Compiler: Compiled 7 to 5 computations (28.6% saved)

prune1.0ms (0.1%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(sqrt.f64 (-.f64 1 (*.f64 x x)))
▶	100.0%	(sqrt.f64 (-.f64 1 (*.f64 x x)))

Compiler

Compiled 14 to 10 computations (28.6% saved)

localize27.0ms (1.5%)

Localize:

Found 1 expressions with local error:

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

Compiler

Compiled 18 to 9 computations (50% saved)

series1.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

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

rewrite95.0ms (5.3%)

Algorithm

1×	batch-egg-rewrite

Rules

620×	`unpow-prod-down`
410×	`log1p-expm1-u`
410×	`expm1-log1p-u`
404×	`log-prod`
388×	`cbrt-prod`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	103	20
2	1199	20

Stop Event

1×	node limit

Counts

1 → 48

Calls

Call 1

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

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

simplify59.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

1070×	`distribute-lft-in`
978×	`distribute-rgt-in`
702×	`fma-def`
606×	`fma-neg`
594×	`associate-r`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	188	2319
1	433	2270
2	1114	2210
3	3795	2210

Stop Event

1×	node limit

Counts

60 → 107

Calls

Call 1

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

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

eval43.0ms (2.4%)

Compiler: Compiled 1668 to 1435 computations (14% saved)

prune14.0ms (0.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	104	3	107
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	104	4	108

Accuracy

100.0%

Counts

108 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.5%	(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
✓	100.0%	(sqrt.f64 (-.f64 1 (*.f64 x x)))
▶	100.0%	(exp.f64 (*.f64 1/2 (log1p.f64 (neg.f64 (pow.f64 x 2)))))
	99.1%	1
▶	99.5%	(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
✓	100.0%	(sqrt.f64 (-.f64 1 (*.f64 x x)))
▶	100.0%	(exp.f64 (*.f64 1/2 (log1p.f64 (neg.f64 (pow.f64 x 2)))))
	99.1%	1

Compiler

Compiled 52 to 44 computations (15.4% saved)

localize68.0ms (3.8%)

Localize:

Found 3 expressions with local error:

New	Accuracy	Program
✓	100.0%	(*.f64 -1/2 (pow.f64 x 2))
✓	100.0%	(*.f64 1/2 (log1p.f64 (neg.f64 (pow.f64 x 2))))
✓	100.0%	(log1p.f64 (neg.f64 (pow.f64 x 2)))

Compiler

Compiled 51 to 41 computations (19.6% saved)

series4.0ms (0.2%)

Counts

3 → 24

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(log1p.f64 (neg.f64 (pow.f64 x 2)))
1.0ms	x	@	inf	(log1p.f64 (neg.f64 (pow.f64 x 2)))
0.0ms	x	@	-inf	(log1p.f64 (neg.f64 (pow.f64 x 2)))
0.0ms	x	@	0	(*.f64 -1/2 (pow.f64 x 2))
0.0ms	x	@	inf	(*.f64 -1/2 (pow.f64 x 2))

rewrite213.0ms (11.9%)

Algorithm

1×	batch-egg-rewrite

Rules

780×	`unpow-prod-down`
514×	`log-prod`
504×	`cbrt-prod`
411×	`log1p-expm1-u`
411×	`expm1-log1p-u`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	14	58
1	132	50
2	1454	44

Stop Event

1×	node limit

Counts

3 → 78

Calls

Call 1

Inputs
(log1p.f64 (neg.f64 (pow.f64 x 2)))
(*.f64 1/2 (log1p.f64 (neg.f64 (pow.f64 x 2))))
(*.f64 -1/2 (pow.f64 x 2))

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

simplify84.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

1818×	`fma-def`
1168×	`fma-neg`
674×	`log-prod`
632×	`unswap-sqr`
446×	`associate-+l+`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	268	3212
1	643	3062
2	1923	3030
3	6697	2968

Stop Event

1×	node limit

Counts

102 → 181

Calls

Call 1

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

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

eval116.0ms (6.4%)

Compiler: Compiled 2842 to 2418 computations (14.9% saved)

prune24.0ms (1.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	181	0	181
Fresh	0	1	1
Picked	0	2	2
Done	0	1	1
Total	181	4	185

Accuracy

100.0%

Counts

185 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.5%	(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
✓	100.0%	(sqrt.f64 (-.f64 1 (*.f64 x x)))
✓	100.0%	(exp.f64 (*.f64 1/2 (log1p.f64 (neg.f64 (pow.f64 x 2)))))
	99.1%	1
✓	99.5%	(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
✓	100.0%	(sqrt.f64 (-.f64 1 (*.f64 x x)))
✓	100.0%	(exp.f64 (*.f64 1/2 (log1p.f64 (neg.f64 (pow.f64 x 2)))))
	99.1%	1

Compiler

Compiled 52 to 44 computations (15.4% saved)

localize0.0ms (0%)

eval0.0ms (0%)

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

prune3.0ms (0.2%)

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
✓	99.5%	(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
✓	100.0%	(sqrt.f64 (-.f64 1 (*.f64 x x)))
✓	100.0%	(exp.f64 (*.f64 1/2 (log1p.f64 (neg.f64 (pow.f64 x 2)))))
	99.1%	1
✓	99.5%	(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
✓	100.0%	(sqrt.f64 (-.f64 1 (*.f64 x x)))
✓	100.0%	(exp.f64 (*.f64 1/2 (log1p.f64 (neg.f64 (pow.f64 x 2)))))
	99.1%	1

Compiler

Compiled 52 to 44 computations (15.4% 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
✓	99.5%	(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
✓	100.0%	(sqrt.f64 (-.f64 1 (*.f64 x x)))
✓	100.0%	(exp.f64 (*.f64 1/2 (log1p.f64 (neg.f64 (pow.f64 x 2)))))
	99.1%	1

Compiler

Compiled 49 to 41 computations (16.3% saved)

regimes12.0ms (0.7%)

Counts

4 → 1

Calls

Call 1

Inputs
1
(sqrt.f64 (-.f64 1 (*.f64 x x)))
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(exp.f64 (*.f64 1/2 (log1p.f64 (neg.f64 (pow.f64 x 2)))))

Outputs
(exp.f64 (*.f64 1/2 (log1p.f64 (neg.f64 (pow.f64 x 2)))))

Calls

4 calls:

3.0ms	x
3.0ms	(*.f64 x x)
2.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))
2.0ms	(-.f64 1 (*.f64 x x))

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(sqrt.f64 (-.f64 1 (*.f64 x x)))`
100.0%	1	`(-.f64 1 (*.f64 x x))`
100.0%	1	`(*.f64 x x)`

Compiler

Compiled 42 to 31 computations (26.2% saved)

regimes12.0ms (0.6%)

Counts

3 → 1

Calls

Call 1

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

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

Calls

4 calls:

3.0ms	x
3.0ms	(-.f64 1 (*.f64 x x))
2.0ms	(*.f64 x x)
2.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(sqrt.f64 (-.f64 1 (*.f64 x x)))`
100.0%	1	`(-.f64 1 (*.f64 x x))`
100.0%	1	`(*.f64 x x)`

Compiler

Compiled 34 to 24 computations (29.4% saved)

regimes3.0ms (0.2%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
1

Outputs
1

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
99.1%	1	`x`

Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

8×	`sub-neg`
8×	`+-commutative`
8×	`*-commutative`
6×	`neg-mul-1`
6×	`neg-sub0`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	52
1	28	52
2	36	52
3	41	52
4	43	52

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(exp.f64 (*.f64 1/2 (log1p.f64 (neg.f64 (pow.f64 x 2)))))
(sqrt.f64 (-.f64 1 (*.f64 x x)))
1

Outputs
(exp.f64 (*.f64 1/2 (log1p.f64 (neg.f64 (pow.f64 x 2)))))
(sqrt.f64 (-.f64 1 (*.f64 x x)))
1

Compiler

Compiled 18 to 15 computations (16.7% saved)

soundness91.0ms (5.1%)

Rules

620×	`unpow-prod-down`
410×	`log1p-expm1-u`
410×	`expm1-log1p-u`
404×	`log-prod`
388×	`cbrt-prod`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	103	20
2	1199	20

Stop Event

1×	node limit

Compiler

Compiled 59 to 40 computations (32.2% saved)

end0.0ms (0%)

preprocess64.0ms (3.6%)

Remove: (abs x)
Compiler: Compiled 64 to 52 computations (18.8% saved)

analyze2.0ms (0.1%)

sample661.0ms (36.9%)

preprocess190.0ms (10.6%)

eval0.0ms (0%)

prune1.0ms (0.1%)

localize27.0ms (1.5%)

series1.0ms (0.1%)

rewrite95.0ms (5.3%)

simplify59.0ms (3.3%)

eval43.0ms (2.4%)

prune14.0ms (0.8%)

localize68.0ms (3.8%)

series4.0ms (0.2%)

rewrite213.0ms (11.9%)

simplify84.0ms (4.7%)

eval116.0ms (6.4%)

prune24.0ms (1.4%)

localize0.0ms (0%)

eval0.0ms (0%)

prune3.0ms (0.2%)

localize0.0ms (0%)

eval0.0ms (0%)

prune3.0ms (0.1%)

regimes12.0ms (0.7%)

regimes12.0ms (0.6%)

regimes3.0ms (0.2%)

simplify4.0ms (0.2%)

soundness91.0ms (5.1%)

end0.0ms (0%)

preprocess64.0ms (3.6%)

Profiling