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

analyze3.0ms (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)

sample741.0ms (43.9%)

Results

732.0ms	8256×	256	valid
0.0ms	2×	256	invalid

Bogosity

preprocess283.0ms (16.7%)

Algorithm

1×	egg-herbie

Rules

1658×	`fma-def`
1232×	`sub-neg`
1138×	`distribute-lft-out`
834×	`associate-+r+`
718×	`*-commutative`

FPErrors

Click to see full error table

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	96
1	36	96
2	56	96
3	102	96
4	149	96
5	234	96
6	367	96
7	641	96
8	1249	96
9	2118	96
10	4747	96
11	6461	96
12	7221	96
13	7519	96
14	7575	96
15	7607	96
16	7863	96

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

Symmetry

(abs x)

Compiler

Compiled 43 to 23 computations (46.5% 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)

localize31.0ms (1.9%)

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)

series2.0ms (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	@	-inf	(sqrt.f64 (-.f64 1 (*.f64 x x)))
0.0ms	x	@	0	(sqrt.f64 (-.f64 1 (*.f64 x x)))

rewrite173.0ms (10.2%)

Algorithm

1×	batch-egg-rewrite

Rules

626×	`unpow-prod-down`
409×	`log1p-expm1-u`
409×	`expm1-log1p-u`
404×	`log-prod`
390×	`cbrt-prod`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	106	20
2	1201	20

Stop Event

1×	node limit

Counts

1 → 47

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 (cbrt.f64 (pow.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 (pow.f64 (-.f64 1 (pow.f64 x 2)) 1/6) (cbrt.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))
(*.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 (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) (sqrt.f64 (pow.f64 (-.f64 1 (pow.f64 x 2)) 1/6)))
(*.f64 (cbrt.f64 (pow.f64 (-.f64 1 (pow.f64 x 2)) 5/4)) (sqrt.f64 (pow.f64 (-.f64 1 (pow.f64 x 2)) 1/6)))
(/.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 (pow.f64 (-.f64 1 (pow.f64 x 2)) 1/6) 3)
(pow.f64 (cbrt.f64 (-.f64 1 (pow.f64 x 2))) 3/2)
(pow.f64 (pow.f64 (-.f64 1 (pow.f64 x 2)) 3/2) 1/3)
(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)) 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)))))

simplify70.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

1130×	`distribute-lft-in`
1040×	`distribute-rgt-in`
722×	`fma-def`
602×	`fma-neg`
564×	`associate-r`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	186	2299
1	426	2287
2	1081	2219
3	3781	2219

Stop Event

1×	node limit

Counts

59 → 104

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 (cbrt.f64 (pow.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 (pow.f64 (-.f64 1 (pow.f64 x 2)) 1/6) (cbrt.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))
(*.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 (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) (sqrt.f64 (pow.f64 (-.f64 1 (pow.f64 x 2)) 1/6)))
(*.f64 (cbrt.f64 (pow.f64 (-.f64 1 (pow.f64 x 2)) 5/4)) (sqrt.f64 (pow.f64 (-.f64 1 (pow.f64 x 2)) 1/6)))
(/.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 (pow.f64 (-.f64 1 (pow.f64 x 2)) 1/6) 3)
(pow.f64 (cbrt.f64 (-.f64 1 (pow.f64 x 2))) 3/2)
(pow.f64 (pow.f64 (-.f64 1 (pow.f64 x 2)) 3/2) 1/3)
(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)) 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 1/16 (/.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 (/.f64 1/2 x) (sqrt.f64 -1)) (-.f64 (fma.f64 x (sqrt.f64 -1) (/.f64 (/.f64 1/16 (pow.f64 x 5)) (pow.f64 (sqrt.f64 -1) 5))) (/.f64 (/.f64 -1/8 (sqrt.f64 -1)) (pow.f64 x 3))))
(+.f64 (fma.f64 x (sqrt.f64 -1) (/.f64 (/.f64 1/2 x) (sqrt.f64 -1))) (+.f64 (/.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 -1 (.f64 x (sqrt.f64 -1)))
(neg.f64 (*.f64 x (sqrt.f64 -1)))
(*.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))))
(-.f64 (/.f64 (/.f64 -1/2 x) (sqrt.f64 -1)) (*.f64 x (sqrt.f64 -1)))
(fma.f64 x (neg.f64 (sqrt.f64 -1)) (/.f64 (/.f64 -1/2 (sqrt.f64 -1)) x))
(-.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 (.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 (/.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 -1/16 (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 (cbrt.f64 (pow.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)))))))
(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 (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 (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)) 1/4) (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 (fabs.f64 (pow.f64 (-.f64 1 (pow.f64 x 2)) 1/8)) (sqrt.f64 (pow.f64 (-.f64 1 (pow.f64 x 2)) 3/4)))
(*.f64 (pow.f64 (-.f64 1 (pow.f64 x 2)) 1/8) (pow.f64 (-.f64 1 (pow.f64 x 2)) 3/8))
(*.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 (fma.f64 x x 1) (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 (fabs.f64 (pow.f64 (-.f64 1 (pow.f64 x 2)) 1/8)) (sqrt.f64 (pow.f64 (-.f64 1 (pow.f64 x 2)) 3/4)))
(*.f64 (pow.f64 (-.f64 1 (pow.f64 x 2)) 1/8) (pow.f64 (-.f64 1 (pow.f64 x 2)) 3/8))
(*.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 (pow.f64 (-.f64 1 (pow.f64 x 2)) 1/12) (pow.f64 (-.f64 1 (pow.f64 x 2)) 5/12))
(*.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) (sqrt.f64 (pow.f64 (-.f64 1 (pow.f64 x 2)) 1/6)))
(*.f64 (sqrt.f64 (pow.f64 (-.f64 1 (pow.f64 x 2)) 1/6)) (cbrt.f64 (pow.f64 (-.f64 1 (pow.f64 x 2)) 5/4)))
(*.f64 (cbrt.f64 (pow.f64 (-.f64 1 (pow.f64 x 2)) 5/4)) (pow.f64 (-.f64 1 (pow.f64 x 2)) 1/12))
(*.f64 (cbrt.f64 (pow.f64 (-.f64 1 (pow.f64 x 2)) 5/4)) (sqrt.f64 (pow.f64 (-.f64 1 (pow.f64 x 2)) 1/6)))
(*.f64 (sqrt.f64 (pow.f64 (-.f64 1 (pow.f64 x 2)) 1/6)) (cbrt.f64 (pow.f64 (-.f64 1 (pow.f64 x 2)) 5/4)))
(*.f64 (cbrt.f64 (pow.f64 (-.f64 1 (pow.f64 x 2)) 5/4)) (pow.f64 (-.f64 1 (pow.f64 x 2)) 1/12))
(/.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 (fma.f64 x x 1) (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 (pow.f64 (-.f64 1 (pow.f64 x 2)) 1/6) 3)
(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)) 3/2) 1/3)
(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)) 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 (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 (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))))
(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)))

eval40.0ms (2.4%)

Compiler: Compiled 1631 to 1399 computations (14.2% saved)

prune13.0ms (0.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	102	2	104
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	102	3	105

Accuracy

100.0%

Counts

105 → 3

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)))
	98.8%	1
▶	99.5%	(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
✓	100.0%	(sqrt.f64 (-.f64 1 (*.f64 x x)))
	98.8%	1

Compiler

Compiled 34 to 28 computations (17.6% saved)

localize42.0ms (2.5%)

Localize:

Found 1 expressions with local error:

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

Compiler

Compiled 21 to 17 computations (19% saved)

series1.0ms (0.1%)

Counts

1 → 0

Calls

3 calls:

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

rewrite171.0ms (10.1%)

Algorithm

1×	batch-egg-rewrite

Rules

840×	`associate-r`
756×	`expm1-udef`
738×	`associate-l`
410×	`unpow-prod-down`
286×	`log-prod`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	69	16
2	713	16
3	7641	16

Stop Event

1×	node limit

Counts

1 → 25

Calls

Call 1

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

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

simplify51.0ms (3%)

Algorithm

1×	egg-herbie

Rules

740×	`times-frac`
692×	`distribute-lft-out`
618×	`fma-neg`
518×	`associate--l+`
490×	`fma-def`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	88	545
1	208	543
2	570	543
3	2573	165

Stop Event

1×	node limit

Counts

25 → 33

Calls

Call 1

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

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

eval17.0ms (1%)

Compiler: Compiled 421 to 376 computations (10.7% saved)

prune5.0ms (0.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	33	0	33
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	33	3	36

Accuracy

100.0%

Counts

36 → 3

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)))
	98.8%	1
✓	99.5%	(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
✓	100.0%	(sqrt.f64 (-.f64 1 (*.f64 x x)))
	98.8%	1

Compiler

Compiled 34 to 28 computations (17.6% saved)

localize0.0ms (0%)

eval0.0ms (0%)

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

prune2.0ms (0.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	2	2
Total	3	3

Accuracy

100.0%

Counts

3 → 3

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)))
	98.8%	1
✓	99.5%	(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
✓	100.0%	(sqrt.f64 (-.f64 1 (*.f64 x x)))
	98.8%	1

Compiler

Compiled 34 to 28 computations (17.6% saved)

localize0.0ms (0%)

eval0.0ms (0%)

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

prune3.0ms (0.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	2	2
Total	3	3

Accuracy

100.0%

Counts

3 → 3

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)))
	98.8%	1

Compiler

Compiled 32 to 26 computations (18.8% saved)

regimes9.0ms (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
2.0ms	(*.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 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
98.8%	1	`x`

Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	24
1	20	24
2	27	24
3	31	24
4	33	24

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

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

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

Compiler

Compiled 9 to 7 computations (22.2% saved)

soundness0.0ms (0%)

end0.0ms (0%)

preprocess25.0ms (1.5%)

Remove: (abs x)
Compiler: Compiled 72 to 52 computations (27.8% saved)

analyze3.0ms (0.1%)

sample741.0ms (43.9%)

preprocess283.0ms (16.7%)

eval0.0ms (0%)

prune1.0ms (0.1%)

localize31.0ms (1.9%)

series2.0ms (0.1%)

rewrite173.0ms (10.2%)

simplify70.0ms (4.2%)

eval40.0ms (2.4%)

prune13.0ms (0.8%)

localize42.0ms (2.5%)

series1.0ms (0.1%)

rewrite171.0ms (10.1%)

simplify51.0ms (3%)

eval17.0ms (1%)

prune5.0ms (0.3%)

localize0.0ms (0%)

eval0.0ms (0%)

prune2.0ms (0.1%)

localize0.0ms (0%)

eval0.0ms (0%)

prune3.0ms (0.2%)

regimes9.0ms (0.6%)

regimes3.0ms (0.2%)

simplify3.0ms (0.2%)

soundness0.0ms (0%)

end0.0ms (0%)

preprocess25.0ms (1.5%)

Profiling