Details

analyze471.0ms (15.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
6.2%	68.6%	25.1%	7
9.4%	65.5%	25.1%	8
14%	60.8%	25.1%	9
21.1%	41.3%	37.6%	10
24.6%	37.8%	37.6%	11
28.7%	33.7%	37.6%	12
32.8%	22.7%	44.6%	13
35.1%	20.3%	44.6%	14

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample1.2s (37.4%)

Results

962.0ms	8256×	body	128	valid
181.0ms	1547×	body	128	invalid

preprocess18.0ms (0.6%)

Algorithm

2×	egg-herbie

Rules

40×	`fma-def_binary64`
18×	`*-commutative_binary64`
12×	`associate-r_binary64`
12×	`associate-l_binary64`
8×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	48
1	59	40
2	113	40
3	149	40
0	3	3

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0
1
2

Outputs
0
1
2

Call 2

Inputs
(.f64 (/.f64 1 2) (+.f64 x (.f64 y (sqrt.f64 z))))
(.f64 (/.f64 1 2) (+.f64 y (.f64 x (sqrt.f64 z))))
(.f64 (/.f64 1 2) (+.f64 z (.f64 y (sqrt.f64 x))))
(.f64 (/.f64 1 2) (+.f64 x (.f64 z (sqrt.f64 y))))

Outputs
(.f64 (/.f64 1 2) (+.f64 x (.f64 y (sqrt.f64 z))))
(.f64 1/2 (+.f64 x (.f64 y (sqrt.f64 z))))
(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
(.f64 (/.f64 1 2) (+.f64 y (.f64 x (sqrt.f64 z))))
(.f64 1/2 (+.f64 y (.f64 x (sqrt.f64 z))))
(*.f64 1/2 (fma.f64 x (sqrt.f64 z) y))
(.f64 (/.f64 1 2) (+.f64 z (.f64 y (sqrt.f64 x))))
(.f64 1/2 (+.f64 z (.f64 y (sqrt.f64 x))))
(*.f64 1/2 (fma.f64 y (sqrt.f64 x) z))
(.f64 (/.f64 1 2) (+.f64 x (.f64 z (sqrt.f64 y))))
(.f64 1/2 (+.f64 x (.f64 z (sqrt.f64 y))))
(*.f64 1/2 (fma.f64 z (sqrt.f64 y) x))

Compiler

Compiled 13 to 10 computations (23.1% saved)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

10×	`fma-def_binary64`
8×	`*-commutative_binary64`
2×	`associate-r_binary64`
2×	`associate-l_binary64`
2×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	12
1	23	10
2	38	10
3	48	10

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

Inputs
(.f64 (/.f64 1 2) (+.f64 x (.f64 y (sqrt.f64 z))))

Outputs
(.f64 (/.f64 1 2) (+.f64 x (.f64 y (sqrt.f64 z))))
(.f64 1/2 (+.f64 x (.f64 y (sqrt.f64 z))))
(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))

eval1.0ms (0%)

Compiler: Compiled 20 to 13 computations (35% saved)

prune2.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.4b

Counts

3 → 2

Alt Table

Click to see full alt table

Status	Error	Program
	0.4b	(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
▶	0.4b	(.f64 (/.f64 1 2) (+.f64 x (.f64 y (sqrt.f64 z))))

Compiler

Compiled 46 to 34 computations (26.1% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (*.f64 y (sqrt.f64 z)))
✓	0.2b	(.f64 (/.f64 1 2) (+.f64 x (.f64 y (sqrt.f64 z))))
✓	0.3b	(*.f64 y (sqrt.f64 z))

series13.0ms (0.4%)

Counts

3 → 50

Calls

24 calls:

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

rewrite51.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

910×	`prod-diff_binary64`
189×	`expm1-udef_binary64`
189×	`log1p-udef_binary64`
113×	`add-sqr-sqrt_binary64`
107×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	27
1	229	23
2	2814	23

Stop Event

1×	node limit

Counts

3 → 74

Calls

Call 1

Inputs
(*.f64 y (sqrt.f64 z))
(.f64 (/.f64 1 2) (+.f64 x (.f64 y (sqrt.f64 z))))
(+.f64 x (*.f64 y (sqrt.f64 z)))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 y (sqrt.f64 z)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 y (sqrt.f64 z)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 y (sqrt.f64 z))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 y (sqrt.f64 z))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 y (sqrt.f64 z)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (.f64 z (.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 y) (sqrt.f64 z)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 y (sqrt.f64 z)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 y (sqrt.f64 z)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 y (sqrt.f64 z))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 y (sqrt.f64 z))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 y (sqrt.f64 z))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 y (sqrt.f64 z))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 1/2 x) (.f64 y (.f64 (sqrt.f64 z) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 y (.f64 (sqrt.f64 z) 1/2)) (.f64 1/2 x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (.f64 1/2 x) 1) (.f64 (.f64 y (.f64 (sqrt.f64 z) 1/2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 1/2 (fma.f64 y (sqrt.f64 z) x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (.f64 1/2 x) 3) (pow.f64 (.f64 y (.f64 (sqrt.f64 z) 1/2)) 3)) (+.f64 (.f64 (.f64 1/2 x) (.f64 1/2 x)) (-.f64 (.f64 (.f64 y (.f64 (sqrt.f64 z) 1/2)) (.f64 y (.f64 (sqrt.f64 z) 1/2))) (.f64 (.f64 1/2 x) (.f64 y (.f64 (sqrt.f64 z) 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 (.f64 1/2 x) (.f64 1/2 x)) (.f64 (.f64 y (.f64 (sqrt.f64 z) 1/2)) (.f64 y (.f64 (sqrt.f64 z) 1/2)))) (-.f64 (.f64 1/2 x) (.f64 y (.f64 (sqrt.f64 z) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (+.f64 (pow.f64 x 3) (pow.f64 (.f64 y (sqrt.f64 z)) 3)) 1/2) (fma.f64 x x (.f64 (.f64 y (sqrt.f64 z)) (-.f64 (.f64 y (sqrt.f64 z)) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (-.f64 (.f64 x x) (.f64 z (.f64 y y))) 1/2) (-.f64 x (.f64 y (sqrt.f64 z))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 1/2 (+.f64 (pow.f64 x 3) (pow.f64 (.f64 y (sqrt.f64 z)) 3))) (fma.f64 x x (.f64 (.f64 y (sqrt.f64 z)) (-.f64 (.f64 y (sqrt.f64 z)) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 1/2 (-.f64 (.f64 x x) (.f64 z (.f64 y y)))) (-.f64 x (.f64 y (sqrt.f64 z))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 1/2 (fma.f64 y (sqrt.f64 z) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 1/2 (fma.f64 y (sqrt.f64 z) x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 1/2 (fma.f64 y (sqrt.f64 z) x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 1/2 (fma.f64 y (sqrt.f64 z) x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (.f64 (pow.f64 (fma.f64 y (sqrt.f64 z) x) 2) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (fma.f64 y (sqrt.f64 z) x)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 1/2 (fma.f64 y (sqrt.f64 z) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 1/2 (fma.f64 y (sqrt.f64 z) x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/2 x (.f64 y (.f64 (sqrt.f64 z) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x 1/2 (.f64 y (.f64 (sqrt.f64 z) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 1/2 (fma.f64 y (sqrt.f64 z) x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 1/2 (fma.f64 y (sqrt.f64 z) x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 1/2 (fma.f64 y (sqrt.f64 z) x))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 1/2 (fma.f64 y (sqrt.f64 z) x))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 y (sqrt.f64 z) x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (.f64 x x) (-.f64 x (.f64 y (sqrt.f64 z)))) (/.f64 (.f64 z (.f64 y y)) (-.f64 x (.f64 y (sqrt.f64 z)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (fma.f64 y (sqrt.f64 z) x))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fma.f64 y (sqrt.f64 z) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) 2) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (fma.f64 y (sqrt.f64 z) x)) (sqrt.f64 (fma.f64 y (sqrt.f64 z) x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 (pow.f64 x 3) (pow.f64 (.f64 y (sqrt.f64 z)) 3)) (/.f64 1 (fma.f64 x x (.f64 (.f64 y (sqrt.f64 z)) (-.f64 (.f64 y (sqrt.f64 z)) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 (.f64 x x) (.f64 z (.f64 y y))) (/.f64 1 (-.f64 x (.f64 y (sqrt.f64 z)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 x x (.f64 (.f64 y (sqrt.f64 z)) (-.f64 (.f64 y (sqrt.f64 z)) x))) (+.f64 (pow.f64 x 3) (pow.f64 (.f64 y (sqrt.f64 z)) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 x (.f64 y (sqrt.f64 z))) (-.f64 (.f64 x x) (.f64 z (.f64 y y)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 3) (pow.f64 (.f64 y (sqrt.f64 z)) 3)) (fma.f64 x x (.f64 (.f64 y (sqrt.f64 z)) (-.f64 (.f64 y (sqrt.f64 z)) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 3) (pow.f64 (.f64 y (sqrt.f64 z)) 3)) (+.f64 (.f64 z (.f64 y y)) (-.f64 (.f64 x x) (.f64 (.f64 x y) (sqrt.f64 z)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 x x) (.f64 z (.f64 y y))) (-.f64 x (.f64 y (sqrt.f64 z))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 x 3) (pow.f64 (.f64 y (sqrt.f64 z)) 3))) (neg.f64 (fma.f64 x x (.f64 (.f64 y (sqrt.f64 z)) (-.f64 (.f64 y (sqrt.f64 z)) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (.f64 x x) (.f64 z (.f64 y y)))) (neg.f64 (-.f64 x (.f64 y (sqrt.f64 z)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 z (.f64 y y)) (.f64 x x)) (-.f64 (.f64 y (sqrt.f64 z)) x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 y (sqrt.f64 z) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 y (sqrt.f64 z) x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 y (sqrt.f64 z) x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 y (sqrt.f64 z) x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 y (sqrt.f64 z) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 y (sqrt.f64 z) x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 y (sqrt.f64 z) x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 y (sqrt.f64 z) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 z) y x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (.f64 y (sqrt.f64 z)) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 x (.f64 y (sqrt.f64 z)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (.f64 z (.f64 y y))) (cbrt.f64 (.f64 y (sqrt.f64 z))) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 x) (.f64 y (sqrt.f64 z)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (.f64 y (sqrt.f64 z))) (sqrt.f64 (.f64 y (sqrt.f64 z))) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (sqrt.f64 x) (.f64 y (sqrt.f64 z)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 y (sqrt.f64 z) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (fma.f64 y (sqrt.f64 z) x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 y (sqrt.f64 z) x)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 y (sqrt.f64 z) x)))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 y (sqrt.f64 z)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 y (sqrt.f64 z)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 y (sqrt.f64 z))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 y (sqrt.f64 z))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 y (sqrt.f64 z)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 z (*.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 y) (sqrt.f64 z)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 y (sqrt.f64 z)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 y (sqrt.f64 z)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 y (sqrt.f64 z))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 y (sqrt.f64 z))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 y (sqrt.f64 z))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 y (sqrt.f64 z))))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 1/2 x) (*.f64 y (*.f64 (sqrt.f64 z) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 y (*.f64 (sqrt.f64 z) 1/2)) (*.f64 1/2 x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 1/2 x) 1) (*.f64 (*.f64 y (*.f64 (sqrt.f64 z) 1/2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 1/2 (fma.f64 y (sqrt.f64 z) x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 1/2 x) 3) (pow.f64 (*.f64 y (*.f64 (sqrt.f64 z) 1/2)) 3)) (+.f64 (*.f64 (*.f64 1/2 x) (*.f64 1/2 x)) (-.f64 (*.f64 (*.f64 y (*.f64 (sqrt.f64 z) 1/2)) (*.f64 y (*.f64 (sqrt.f64 z) 1/2))) (*.f64 (*.f64 1/2 x) (*.f64 y (*.f64 (sqrt.f64 z) 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 1/2 x) (*.f64 1/2 x)) (*.f64 (*.f64 y (*.f64 (sqrt.f64 z) 1/2)) (*.f64 y (*.f64 (sqrt.f64 z) 1/2)))) (-.f64 (*.f64 1/2 x) (*.f64 y (*.f64 (sqrt.f64 z) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (pow.f64 x 3) (pow.f64 (*.f64 y (sqrt.f64 z)) 3)) 1/2) (fma.f64 x x (*.f64 (*.f64 y (sqrt.f64 z)) (-.f64 (*.f64 y (sqrt.f64 z)) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 (*.f64 x x) (*.f64 z (*.f64 y y))) 1/2) (-.f64 x (*.f64 y (sqrt.f64 z))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 1/2 (+.f64 (pow.f64 x 3) (pow.f64 (*.f64 y (sqrt.f64 z)) 3))) (fma.f64 x x (*.f64 (*.f64 y (sqrt.f64 z)) (-.f64 (*.f64 y (sqrt.f64 z)) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 1/2 (-.f64 (*.f64 x x) (*.f64 z (*.f64 y y)))) (-.f64 x (*.f64 y (sqrt.f64 z))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 1/2 (fma.f64 y (sqrt.f64 z) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 1/2 (fma.f64 y (sqrt.f64 z) x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 (fma.f64 y (sqrt.f64 z) x) 2) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (fma.f64 y (sqrt.f64 z) x)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 1/2 (fma.f64 y (sqrt.f64 z) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 1/2 (fma.f64 y (sqrt.f64 z) x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/2 x (*.f64 y (*.f64 (sqrt.f64 z) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x 1/2 (*.f64 y (*.f64 (sqrt.f64 z) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 y (sqrt.f64 z) x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (*.f64 x x) (-.f64 x (*.f64 y (sqrt.f64 z)))) (/.f64 (*.f64 z (*.f64 y y)) (-.f64 x (*.f64 y (sqrt.f64 z)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 y (sqrt.f64 z) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 y (sqrt.f64 z) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) 2) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 y (sqrt.f64 z) x)) (sqrt.f64 (fma.f64 y (sqrt.f64 z) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 x 3) (pow.f64 (*.f64 y (sqrt.f64 z)) 3)) (/.f64 1 (fma.f64 x x (*.f64 (*.f64 y (sqrt.f64 z)) (-.f64 (*.f64 y (sqrt.f64 z)) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 x x) (*.f64 z (*.f64 y y))) (/.f64 1 (-.f64 x (*.f64 y (sqrt.f64 z)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 x x (*.f64 (*.f64 y (sqrt.f64 z)) (-.f64 (*.f64 y (sqrt.f64 z)) x))) (+.f64 (pow.f64 x 3) (pow.f64 (*.f64 y (sqrt.f64 z)) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 x (*.f64 y (sqrt.f64 z))) (-.f64 (*.f64 x x) (*.f64 z (*.f64 y y)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 3) (pow.f64 (*.f64 y (sqrt.f64 z)) 3)) (fma.f64 x x (*.f64 (*.f64 y (sqrt.f64 z)) (-.f64 (*.f64 y (sqrt.f64 z)) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 3) (pow.f64 (*.f64 y (sqrt.f64 z)) 3)) (+.f64 (*.f64 z (*.f64 y y)) (-.f64 (*.f64 x x) (*.f64 (*.f64 x y) (sqrt.f64 z)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 x x) (*.f64 z (*.f64 y y))) (-.f64 x (*.f64 y (sqrt.f64 z))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 x 3) (pow.f64 (*.f64 y (sqrt.f64 z)) 3))) (neg.f64 (fma.f64 x x (*.f64 (*.f64 y (sqrt.f64 z)) (-.f64 (*.f64 y (sqrt.f64 z)) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (*.f64 x x) (*.f64 z (*.f64 y y)))) (neg.f64 (-.f64 x (*.f64 y (sqrt.f64 z)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 z (*.f64 y y)) (*.f64 x x)) (-.f64 (*.f64 y (sqrt.f64 z)) x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 y (sqrt.f64 z) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 y (sqrt.f64 z) x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 y (sqrt.f64 z) x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 y (sqrt.f64 z) x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 y (sqrt.f64 z) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 y (sqrt.f64 z) x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 y (sqrt.f64 z) x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 y (sqrt.f64 z) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 z) y x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 y (sqrt.f64 z)) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 x (*.f64 y (sqrt.f64 z)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 z (*.f64 y y))) (cbrt.f64 (*.f64 y (sqrt.f64 z))) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 x) (*.f64 y (sqrt.f64 z)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 y (sqrt.f64 z))) (sqrt.f64 (*.f64 y (sqrt.f64 z))) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (sqrt.f64 x) (*.f64 y (sqrt.f64 z)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 y (sqrt.f64 z) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (fma.f64 y (sqrt.f64 z) x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 y (sqrt.f64 z) x)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 y (sqrt.f64 z) x)))))))

simplify15.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

10×	`fma-def_binary64`
7×	`*-commutative_binary64`
3×	`associate-r_binary64`
3×	`associate-l_binary64`
2×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	371
1	21	371
2	34	371
3	40	371

Stop Event

1×

saturated

Counts

124 → 82

Calls

Call 1

Inputs
(.f64 1/2 (.f64 y (sqrt.f64 z)))
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(*.f64 1/2 x)
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(*.f64 1/2 x)
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(*.f64 1/2 x)
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(.f64 1/2 (.f64 y (sqrt.f64 z)))
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(.f64 1/2 (.f64 y (sqrt.f64 z)))
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(*.f64 1/2 x)
(*.f64 y (sqrt.f64 z))
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(+.f64 (*.f64 y (sqrt.f64 z)) x)
x
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(+.f64 (*.f64 y (sqrt.f64 z)) x)
x
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(+.f64 (*.f64 y (sqrt.f64 z)) x)
x
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(*.f64 y (sqrt.f64 z))
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(*.f64 y (sqrt.f64 z))
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(+.f64 (*.f64 y (sqrt.f64 z)) x)
x

Outputs
(.f64 1/2 (.f64 y (sqrt.f64 z)))
(.f64 (sqrt.f64 z) (.f64 1/2 y))
(.f64 y (.f64 1/2 (sqrt.f64 z)))
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
(*.f64 1/2 x)
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
(*.f64 1/2 x)
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
(*.f64 1/2 x)
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
(.f64 1/2 (.f64 y (sqrt.f64 z)))
(.f64 (sqrt.f64 z) (.f64 1/2 y))
(.f64 y (.f64 1/2 (sqrt.f64 z)))
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
(.f64 1/2 (.f64 y (sqrt.f64 z)))
(.f64 (sqrt.f64 z) (.f64 1/2 y))
(.f64 y (.f64 1/2 (sqrt.f64 z)))
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
(*.f64 1/2 x)
(*.f64 y (sqrt.f64 z))
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(fma.f64 y (sqrt.f64 z) x)
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(fma.f64 y (sqrt.f64 z) x)
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(fma.f64 y (sqrt.f64 z) x)
x
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(fma.f64 y (sqrt.f64 z) x)
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(fma.f64 y (sqrt.f64 z) x)
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(fma.f64 y (sqrt.f64 z) x)
x
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(fma.f64 y (sqrt.f64 z) x)
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(fma.f64 y (sqrt.f64 z) x)
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(fma.f64 y (sqrt.f64 z) x)
x
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(fma.f64 y (sqrt.f64 z) x)
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(fma.f64 y (sqrt.f64 z) x)
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(fma.f64 y (sqrt.f64 z) x)
(*.f64 y (sqrt.f64 z))
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(fma.f64 y (sqrt.f64 z) x)
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(fma.f64 y (sqrt.f64 z) x)
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(fma.f64 y (sqrt.f64 z) x)
(*.f64 y (sqrt.f64 z))
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(fma.f64 y (sqrt.f64 z) x)
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(fma.f64 y (sqrt.f64 z) x)
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(fma.f64 y (sqrt.f64 z) x)
x

eval20.0ms (0.6%)

Compiler: Compiled 1194 to 571 computations (52.2% saved)

prune79.0ms (2.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	74	8	82
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	76	8	84

Error

0.0b

Counts

84 → 8

Alt Table

Click to see full alt table

Status	Error	Program
	32.4b	(.f64 (/.f64 1 2) (+.f64 x (pow.f64 (sqrt.f64 (.f64 y (sqrt.f64 z))) 2)))
	0.8b	(.f64 (/.f64 1 2) (+.f64 x (pow.f64 (cbrt.f64 (.f64 y (sqrt.f64 z))) 3)))
▶	0.1b	(fma.f64 x 1/2 (.f64 y (.f64 (sqrt.f64 z) 1/2)))
	23.4b	(.f64 (/.f64 1 2) (fma.f64 (cbrt.f64 (.f64 z (.f64 y y))) (cbrt.f64 (.f64 y (sqrt.f64 z))) x))
	37.5b	(.f64 (/.f64 1 2) (.f64 (-.f64 (.f64 x x) (.f64 z (.f64 y y))) (/.f64 1 (-.f64 x (.f64 y (sqrt.f64 z))))))
	34.3b	(pow.f64 (sqrt.f64 (*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))) 2)
	1.6b	(pow.f64 (cbrt.f64 (*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))) 3)
	23.6b	(.f64 (/.f64 1 2) (+.f64 x (cbrt.f64 (pow.f64 (.f64 y (sqrt.f64 z)) 3))))

Compiler

Compiled 262 to 198 computations (24.4% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x 1/2 (.f64 y (.f64 (sqrt.f64 z) 1/2)))
✓	0.3b	(.f64 y (.f64 (sqrt.f64 z) 1/2))

series8.0ms (0.3%)

Counts

2 → 37

Calls

15 calls:

Time	Variable		Point	Expression
1.0ms	y	@	-inf	(.f64 y (.f64 (sqrt.f64 z) 1/2))
1.0ms	z	@	0	(.f64 y (.f64 (sqrt.f64 z) 1/2))
1.0ms	z	@	inf	(.f64 y (.f64 (sqrt.f64 z) 1/2))
1.0ms	x	@	0	(fma.f64 x 1/2 (.f64 y (.f64 (sqrt.f64 z) 1/2)))
1.0ms	y	@	0	(.f64 y (.f64 (sqrt.f64 z) 1/2))

rewrite41.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

826×	`pow1_binary64`
757×	`log1p-expm1-u_binary64`
757×	`expm1-log1p-u_binary64`
89×	`add-sqr-sqrt_binary64`
87×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	22
1	180	21
2	2074	21

Stop Event

1×	node limit

Counts

2 → 39

Calls

Call 1

Inputs
(.f64 y (.f64 (sqrt.f64 z) 1/2))
(fma.f64 x 1/2 (.f64 y (.f64 (sqrt.f64 z) 1/2)))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 y (.f64 (sqrt.f64 z) 1/2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 y (.f64 (sqrt.f64 z) 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 y (.f64 (sqrt.f64 z) 1/2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 y (.f64 (sqrt.f64 z) 1/2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 y (.f64 (sqrt.f64 z) 1/2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (.f64 (.f64 y y) (.f64 z 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 y) (.f64 (sqrt.f64 z) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 y (.f64 (sqrt.f64 z) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 y (.f64 (sqrt.f64 z) 1/2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 y 3) (pow.f64 (.f64 (sqrt.f64 z) 1/2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (.f64 (sqrt.f64 z) 1/2) 3) (pow.f64 y 3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 y (.f64 (sqrt.f64 z) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 y (.f64 (sqrt.f64 z) 1/2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 y (.f64 (sqrt.f64 z) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 y (*.f64 (sqrt.f64 z) 1/2))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 y (.f64 (sqrt.f64 z) 1/2)) (.f64 1/2 x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 1/2 x) (.f64 y (.f64 (sqrt.f64 z) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (.f64 1/2 x) 1) (.f64 y (.f64 (sqrt.f64 z) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 1/2 (+.f64 x (.f64 y (sqrt.f64 z)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/2 (+.f64 x (.f64 y (sqrt.f64 z))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 1/2 (+.f64 x (.f64 y (sqrt.f64 z)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (.f64 1/2 (+.f64 x (.f64 y (sqrt.f64 z)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (.f64 1/2 (+.f64 x (.f64 y (sqrt.f64 z))))) (pow.f64 (cbrt.f64 (.f64 1/2 (+.f64 x (.f64 y (sqrt.f64 z))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (.f64 1/2 (+.f64 x (.f64 y (sqrt.f64 z))))) 2) (cbrt.f64 (.f64 1/2 (+.f64 x (.f64 y (sqrt.f64 z))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (.f64 1/2 (+.f64 x (.f64 y (sqrt.f64 z))))) (sqrt.f64 (.f64 1/2 (+.f64 x (.f64 y (sqrt.f64 z))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (.f64 1/2 x) 3) (pow.f64 (.f64 y (.f64 (sqrt.f64 z) 1/2)) 3)) (+.f64 (.f64 (.f64 1/2 x) (.f64 1/2 x)) (-.f64 (.f64 (.f64 y y) (.f64 z 1/4)) (.f64 (.f64 1/2 x) (.f64 y (.f64 (sqrt.f64 z) 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 (.f64 1/2 x) (.f64 1/2 x)) (.f64 (.f64 y y) (.f64 z 1/4))) (-.f64 (.f64 1/2 x) (.f64 y (.f64 (sqrt.f64 z) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 1/2 (+.f64 x (.f64 y (sqrt.f64 z)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 1/2 (+.f64 x (.f64 y (sqrt.f64 z)))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 1/2 (+.f64 x (.f64 y (sqrt.f64 z))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 1/2 (+.f64 x (.f64 y (sqrt.f64 z))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (.f64 1/2 (+.f64 x (.f64 y (sqrt.f64 z)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (.f64 1/2 (+.f64 x (.f64 y (sqrt.f64 z))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 1/2 (+.f64 x (.f64 y (sqrt.f64 z)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 1/2 (+.f64 x (.f64 y (sqrt.f64 z)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 1/2 (+.f64 x (.f64 y (sqrt.f64 z))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 1/2 (+.f64 x (.f64 y (sqrt.f64 z))))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 1/2 (+.f64 x (.f64 y (sqrt.f64 z))))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 1/2 (+.f64 x (.f64 y (sqrt.f64 z))))))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 y (*.f64 (sqrt.f64 z) 1/2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 y (*.f64 (sqrt.f64 z) 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 y (*.f64 (sqrt.f64 z) 1/2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 y (*.f64 (sqrt.f64 z) 1/2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 y (*.f64 (sqrt.f64 z) 1/2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (*.f64 y y) (*.f64 z 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 y) (*.f64 (sqrt.f64 z) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 y (*.f64 (sqrt.f64 z) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 y (*.f64 (sqrt.f64 z) 1/2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 y 3) (pow.f64 (*.f64 (sqrt.f64 z) 1/2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (*.f64 (sqrt.f64 z) 1/2) 3) (pow.f64 y 3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 y (*.f64 (sqrt.f64 z) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 y (*.f64 (sqrt.f64 z) 1/2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 y (*.f64 (sqrt.f64 z) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 y (*.f64 (sqrt.f64 z) 1/2))))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 y (*.f64 (sqrt.f64 z) 1/2)) (*.f64 1/2 x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 1/2 x) (*.f64 y (*.f64 (sqrt.f64 z) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 1/2 x) 1) (*.f64 y (*.f64 (sqrt.f64 z) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 1/2 (+.f64 x (*.f64 y (sqrt.f64 z)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (+.f64 x (*.f64 y (sqrt.f64 z))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 1/2 (+.f64 x (*.f64 y (sqrt.f64 z)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 1/2 (+.f64 x (*.f64 y (sqrt.f64 z)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 1/2 (+.f64 x (*.f64 y (sqrt.f64 z))))) (pow.f64 (cbrt.f64 (*.f64 1/2 (+.f64 x (*.f64 y (sqrt.f64 z))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 1/2 (+.f64 x (*.f64 y (sqrt.f64 z))))) 2) (cbrt.f64 (*.f64 1/2 (+.f64 x (*.f64 y (sqrt.f64 z))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 1/2 (+.f64 x (*.f64 y (sqrt.f64 z))))) (sqrt.f64 (*.f64 1/2 (+.f64 x (*.f64 y (sqrt.f64 z))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 1/2 x) 3) (pow.f64 (*.f64 y (*.f64 (sqrt.f64 z) 1/2)) 3)) (+.f64 (*.f64 (*.f64 1/2 x) (*.f64 1/2 x)) (-.f64 (*.f64 (*.f64 y y) (*.f64 z 1/4)) (*.f64 (*.f64 1/2 x) (*.f64 y (*.f64 (sqrt.f64 z) 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 1/2 x) (*.f64 1/2 x)) (*.f64 (*.f64 y y) (*.f64 z 1/4))) (-.f64 (*.f64 1/2 x) (*.f64 y (*.f64 (sqrt.f64 z) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 1/2 (+.f64 x (*.f64 y (sqrt.f64 z)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 1/2 (+.f64 x (*.f64 y (sqrt.f64 z)))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 1/2 (+.f64 x (*.f64 y (sqrt.f64 z))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 1/2 (+.f64 x (*.f64 y (sqrt.f64 z))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 1/2 (+.f64 x (*.f64 y (sqrt.f64 z)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (*.f64 1/2 (+.f64 x (*.f64 y (sqrt.f64 z))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 1/2 (+.f64 x (*.f64 y (sqrt.f64 z)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 1/2 (+.f64 x (*.f64 y (sqrt.f64 z)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 1/2 (+.f64 x (*.f64 y (sqrt.f64 z))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 1/2 (+.f64 x (*.f64 y (sqrt.f64 z))))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 1/2 (+.f64 x (*.f64 y (sqrt.f64 z))))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 1/2 (+.f64 x (*.f64 y (sqrt.f64 z))))))))))

simplify15.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

10×	`fma-def_binary64`
7×	`*-commutative_binary64`
3×	`associate-r_binary64`
3×	`associate-l_binary64`
2×	`+-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	367
1	19	367
2	33	331
3	41	331

Stop Event

1×

saturated

Counts

76 → 44

Calls

Call 1

Inputs
(.f64 1/2 (.f64 y (sqrt.f64 z)))
(.f64 1/2 (.f64 y (sqrt.f64 z)))
(.f64 1/2 (.f64 y (sqrt.f64 z)))
(.f64 1/2 (.f64 y (sqrt.f64 z)))
(.f64 1/2 (.f64 y (sqrt.f64 z)))
(.f64 1/2 (.f64 y (sqrt.f64 z)))
(.f64 1/2 (.f64 y (sqrt.f64 z)))
(.f64 1/2 (.f64 y (sqrt.f64 z)))
(.f64 1/2 (.f64 y (sqrt.f64 z)))
(.f64 1/2 (.f64 y (sqrt.f64 z)))
(.f64 1/2 (.f64 y (sqrt.f64 z)))
(.f64 1/2 (.f64 y (sqrt.f64 z)))
(.f64 1/2 (.f64 y (sqrt.f64 z)))
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(*.f64 1/2 x)
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(*.f64 1/2 x)
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(*.f64 1/2 x)
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(.f64 1/2 (.f64 y (sqrt.f64 z)))
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(.f64 1/2 (.f64 y (sqrt.f64 z)))
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(*.f64 1/2 x)

Outputs
(.f64 1/2 (.f64 y (sqrt.f64 z)))
(.f64 (sqrt.f64 z) (.f64 1/2 y))
(.f64 1/2 (.f64 y (sqrt.f64 z)))
(.f64 (sqrt.f64 z) (.f64 1/2 y))
(.f64 1/2 (.f64 y (sqrt.f64 z)))
(.f64 (sqrt.f64 z) (.f64 1/2 y))
(.f64 1/2 (.f64 y (sqrt.f64 z)))
(.f64 (sqrt.f64 z) (.f64 1/2 y))
(.f64 1/2 (.f64 y (sqrt.f64 z)))
(.f64 (sqrt.f64 z) (.f64 1/2 y))
(.f64 1/2 (.f64 y (sqrt.f64 z)))
(.f64 (sqrt.f64 z) (.f64 1/2 y))
(.f64 1/2 (.f64 y (sqrt.f64 z)))
(.f64 (sqrt.f64 z) (.f64 1/2 y))
(.f64 1/2 (.f64 y (sqrt.f64 z)))
(.f64 (sqrt.f64 z) (.f64 1/2 y))
(.f64 1/2 (.f64 y (sqrt.f64 z)))
(.f64 (sqrt.f64 z) (.f64 1/2 y))
(.f64 1/2 (.f64 y (sqrt.f64 z)))
(.f64 (sqrt.f64 z) (.f64 1/2 y))
(.f64 1/2 (.f64 y (sqrt.f64 z)))
(.f64 (sqrt.f64 z) (.f64 1/2 y))
(.f64 1/2 (.f64 y (sqrt.f64 z)))
(.f64 (sqrt.f64 z) (.f64 1/2 y))
(.f64 1/2 (.f64 y (sqrt.f64 z)))
(.f64 (sqrt.f64 z) (.f64 1/2 y))
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(.f64 1/2 (+.f64 x (.f64 y (sqrt.f64 z))))
(.f64 1/2 (+.f64 (.f64 y (sqrt.f64 z)) x))
(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(.f64 1/2 (+.f64 x (.f64 y (sqrt.f64 z))))
(.f64 1/2 (+.f64 (.f64 y (sqrt.f64 z)) x))
(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(.f64 1/2 (+.f64 x (.f64 y (sqrt.f64 z))))
(.f64 1/2 (+.f64 (.f64 y (sqrt.f64 z)) x))
(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
(*.f64 1/2 x)
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(.f64 1/2 (+.f64 x (.f64 y (sqrt.f64 z))))
(.f64 1/2 (+.f64 (.f64 y (sqrt.f64 z)) x))
(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(.f64 1/2 (+.f64 x (.f64 y (sqrt.f64 z))))
(.f64 1/2 (+.f64 (.f64 y (sqrt.f64 z)) x))
(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(.f64 1/2 (+.f64 x (.f64 y (sqrt.f64 z))))
(.f64 1/2 (+.f64 (.f64 y (sqrt.f64 z)) x))
(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
(*.f64 1/2 x)
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(.f64 1/2 (+.f64 x (.f64 y (sqrt.f64 z))))
(.f64 1/2 (+.f64 (.f64 y (sqrt.f64 z)) x))
(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(.f64 1/2 (+.f64 x (.f64 y (sqrt.f64 z))))
(.f64 1/2 (+.f64 (.f64 y (sqrt.f64 z)) x))
(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(.f64 1/2 (+.f64 x (.f64 y (sqrt.f64 z))))
(.f64 1/2 (+.f64 (.f64 y (sqrt.f64 z)) x))
(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
(*.f64 1/2 x)
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(.f64 1/2 (+.f64 x (.f64 y (sqrt.f64 z))))
(.f64 1/2 (+.f64 (.f64 y (sqrt.f64 z)) x))
(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(.f64 1/2 (+.f64 x (.f64 y (sqrt.f64 z))))
(.f64 1/2 (+.f64 (.f64 y (sqrt.f64 z)) x))
(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(.f64 1/2 (+.f64 x (.f64 y (sqrt.f64 z))))
(.f64 1/2 (+.f64 (.f64 y (sqrt.f64 z)) x))
(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
(.f64 1/2 (.f64 y (sqrt.f64 z)))
(.f64 (sqrt.f64 z) (.f64 1/2 y))
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(.f64 1/2 (+.f64 x (.f64 y (sqrt.f64 z))))
(.f64 1/2 (+.f64 (.f64 y (sqrt.f64 z)) x))
(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(.f64 1/2 (+.f64 x (.f64 y (sqrt.f64 z))))
(.f64 1/2 (+.f64 (.f64 y (sqrt.f64 z)) x))
(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(.f64 1/2 (+.f64 x (.f64 y (sqrt.f64 z))))
(.f64 1/2 (+.f64 (.f64 y (sqrt.f64 z)) x))
(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
(.f64 1/2 (.f64 y (sqrt.f64 z)))
(.f64 (sqrt.f64 z) (.f64 1/2 y))
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(.f64 1/2 (+.f64 x (.f64 y (sqrt.f64 z))))
(.f64 1/2 (+.f64 (.f64 y (sqrt.f64 z)) x))
(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(.f64 1/2 (+.f64 x (.f64 y (sqrt.f64 z))))
(.f64 1/2 (+.f64 (.f64 y (sqrt.f64 z)) x))
(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(.f64 1/2 (+.f64 x (.f64 y (sqrt.f64 z))))
(.f64 1/2 (+.f64 (.f64 y (sqrt.f64 z)) x))
(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
(*.f64 1/2 x)

eval11.0ms (0.3%)

Compiler: Compiled 553 to 309 computations (44.1% saved)

prune42.0ms (1.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	41	3	44
Fresh	3	4	7
Picked	0	1	1
Done	0	0	0
Total	44	8	52

Error

0.0b

Counts

52 → 8

Alt Table

Click to see full alt table

Status	Error	Program
	32.4b	(fma.f64 x 1/2 (pow.f64 (sqrt.f64 (.f64 y (.f64 (sqrt.f64 z) 1/2))) 2))
	32.4b	(.f64 (/.f64 1 2) (+.f64 x (pow.f64 (sqrt.f64 (.f64 y (sqrt.f64 z))) 2)))
▶	0.6b	(fma.f64 x 1/2 (pow.f64 (cbrt.f64 (.f64 y (.f64 (sqrt.f64 z) 1/2))) 3))
	0.8b	(.f64 (/.f64 1 2) (+.f64 x (pow.f64 (cbrt.f64 (.f64 y (sqrt.f64 z))) 3)))
✓	0.1b	(fma.f64 x 1/2 (.f64 y (.f64 (sqrt.f64 z) 1/2)))
	23.4b	(.f64 (/.f64 1 2) (fma.f64 (cbrt.f64 (.f64 z (.f64 y y))) (cbrt.f64 (.f64 y (sqrt.f64 z))) x))
	37.5b	(.f64 (/.f64 1 2) (.f64 (-.f64 (.f64 x x) (.f64 z (.f64 y y))) (/.f64 1 (-.f64 x (.f64 y (sqrt.f64 z))))))
	23.6b	(fma.f64 x 1/2 (cbrt.f64 (pow.f64 (.f64 y (.f64 (sqrt.f64 z) 1/2)) 3)))

Compiler

Compiled 256 to 195 computations (23.8% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x 1/2 (pow.f64 (cbrt.f64 (.f64 y (.f64 (sqrt.f64 z) 1/2))) 3))
	0.3b	(.f64 y (.f64 (sqrt.f64 z) 1/2))
✓	0.7b	(pow.f64 (cbrt.f64 (.f64 y (.f64 (sqrt.f64 z) 1/2))) 3)
✓	4.1b	(cbrt.f64 (.f64 y (.f64 (sqrt.f64 z) 1/2)))

series79.0ms (2.6%)

Counts

3 → 39

Calls

21 calls:

Time	Variable		Point	Expression
26.0ms	z	@	0	(cbrt.f64 (.f64 y (.f64 (sqrt.f64 z) 1/2)))
16.0ms	z	@	-inf	(pow.f64 (cbrt.f64 (.f64 y (.f64 (sqrt.f64 z) 1/2))) 3)
11.0ms	z	@	inf	(cbrt.f64 (.f64 y (.f64 (sqrt.f64 z) 1/2)))
5.0ms	x	@	0	(fma.f64 x 1/2 (pow.f64 (cbrt.f64 (.f64 y (.f64 (sqrt.f64 z) 1/2))) 3))
3.0ms	z	@	-inf	(cbrt.f64 (.f64 y (.f64 (sqrt.f64 z) 1/2)))

rewrite57.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

509×	`log-prod_binary64`
234×	`prod-diff_binary64`
188×	`expm1-udef_binary64`
188×	`log1p-udef_binary64`
168×	`pow3_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	33
1	251	32
2	2598	32

Stop Event

1×	node limit

Counts

3 → 99

Calls

Call 1

Inputs
(cbrt.f64 (.f64 y (.f64 (sqrt.f64 z) 1/2)))
(pow.f64 (cbrt.f64 (.f64 y (.f64 (sqrt.f64 z) 1/2))) 3)
(fma.f64 x 1/2 (pow.f64 (cbrt.f64 (.f64 y (.f64 (sqrt.f64 z) 1/2))) 3))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (cbrt.f64 (*.f64 y (*.f64 (sqrt.f64 z) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (cbrt.f64 (*.f64 y (*.f64 (sqrt.f64 z) 1/2))))) (cbrt.f64 (exp.f64 (cbrt.f64 (*.f64 y (*.f64 (sqrt.f64 z) 1/2))))))) (log.f64 (cbrt.f64 (exp.f64 (cbrt.f64 (*.f64 y (*.f64 (sqrt.f64 z) 1/2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (cbrt.f64 (*.f64 y (*.f64 (sqrt.f64 z) 1/2)))))) (log.f64 (sqrt.f64 (exp.f64 (cbrt.f64 (*.f64 y (*.f64 (sqrt.f64 z) 1/2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (cbrt.f64 (*.f64 y (*.f64 (sqrt.f64 z) 1/2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 y (*.f64 (sqrt.f64 z) 1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (cbrt.f64 (*.f64 y (*.f64 (sqrt.f64 z) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (*.f64 y (*.f64 (sqrt.f64 z) 1/2)))) (cbrt.f64 (cbrt.f64 (*.f64 (*.f64 y y) (*.f64 z 1/4)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (*.f64 y (*.f64 (sqrt.f64 z) 1/2)))) (pow.f64 (cbrt.f64 (*.f64 (*.f64 y y) (*.f64 z 1/4))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (*.f64 (*.f64 y y) (*.f64 z 1/4)))) (cbrt.f64 (cbrt.f64 (*.f64 y (*.f64 (sqrt.f64 z) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 y) (cbrt.f64 (*.f64 (sqrt.f64 z) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (sqrt.f64 z) 1/2)) (cbrt.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 y (*.f64 (sqrt.f64 z) 1/2)) 1/6) (pow.f64 (*.f64 y (*.f64 (sqrt.f64 z) 1/2)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 y (sqrt.f64 z))) (cbrt.f64 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 (*.f64 y y) (*.f64 z 1/4))) 1/3) (cbrt.f64 (cbrt.f64 (*.f64 y (*.f64 (sqrt.f64 z) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (cbrt.f64 (*.f64 y (*.f64 (sqrt.f64 z) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (*.f64 y (*.f64 (sqrt.f64 z) 1/2))) 1/3) (pow.f64 (sqrt.f64 (*.f64 y (*.f64 (sqrt.f64 z) 1/2))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 y (sqrt.f64 z)) 1/3) (cbrt.f64 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 y (*.f64 (sqrt.f64 z) 1/2)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 y (*.f64 (sqrt.f64 z) 1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 y (*.f64 (sqrt.f64 z) 1/2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 y (*.f64 (sqrt.f64 z) 1/2)) 1/6) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (cbrt.f64 (*.f64 (*.f64 y y) (*.f64 z 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (cbrt.f64 (*.f64 y (*.f64 (sqrt.f64 z) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (cbrt.f64 (*.f64 y (*.f64 (sqrt.f64 z) 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (cbrt.f64 (*.f64 y (*.f64 (sqrt.f64 z) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 y (*.f64 (sqrt.f64 z) 1/2))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 y (*.f64 (sqrt.f64 z) 1/2)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (cbrt.f64 (*.f64 y (*.f64 (sqrt.f64 z) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (cbrt.f64 (*.f64 y (*.f64 (sqrt.f64 z) 1/2)))))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 y (*.f64 (sqrt.f64 z) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (pow.f64 (exp.f64 y) (*.f64 (sqrt.f64 z) 1/2))) (cbrt.f64 (pow.f64 (exp.f64 y) (*.f64 (sqrt.f64 z) 1/2))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 y) (*.f64 (sqrt.f64 z) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 y) (*.f64 (sqrt.f64 z) 1/2)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 y) (*.f64 (sqrt.f64 z) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 y (*.f64 (sqrt.f64 z) 1/2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 y (*.f64 (sqrt.f64 z) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 z) (*.f64 1/2 y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (*.f64 y (sqrt.f64 z)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 z) 1/2) y)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 y (*.f64 (sqrt.f64 z) 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 y (*.f64 (sqrt.f64 z) 1/2))) (cbrt.f64 (*.f64 (*.f64 y y) (*.f64 z 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 y (*.f64 (sqrt.f64 z) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (*.f64 y y) (*.f64 z 1/4))) (cbrt.f64 (*.f64 y (*.f64 (sqrt.f64 z) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (*.f64 (*.f64 y y) (*.f64 z 1/4)))) (*.f64 (cbrt.f64 (cbrt.f64 (*.f64 y (*.f64 (sqrt.f64 z) 1/2)))) (cbrt.f64 (*.f64 (*.f64 y y) (*.f64 z 1/4)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 y) (*.f64 (cbrt.f64 (*.f64 (sqrt.f64 z) 1/2)) (cbrt.f64 (*.f64 (*.f64 y y) (*.f64 z 1/4)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 y) 2) (*.f64 (cbrt.f64 y) (*.f64 (sqrt.f64 z) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 z 1/4)) (*.f64 (cbrt.f64 (*.f64 (sqrt.f64 z) 1/2)) y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 y (*.f64 (sqrt.f64 z) 1/2)) 1/6) (*.f64 (pow.f64 (*.f64 y (*.f64 (sqrt.f64 z) 1/2)) 1/6) (cbrt.f64 (*.f64 (*.f64 y y) (*.f64 z 1/4)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 y) (*.f64 (sqrt.f64 y) (*.f64 (sqrt.f64 z) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (sqrt.f64 z) 1/2)) (*.f64 (sqrt.f64 (*.f64 (sqrt.f64 z) 1/2)) y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 y (*.f64 (sqrt.f64 z) 1/2))) (sqrt.f64 (*.f64 y (*.f64 (sqrt.f64 z) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 y (sqrt.f64 z)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 y 1/2) (sqrt.f64 z))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 y (cbrt.f64 (*.f64 z 1/4))) (cbrt.f64 (*.f64 (sqrt.f64 z) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 y (sqrt.f64 (*.f64 (sqrt.f64 z) 1/2))) (sqrt.f64 (*.f64 (sqrt.f64 z) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (*.f64 (sqrt.f64 z) 1/2) (pow.f64 (cbrt.f64 y) 2)) (cbrt.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (*.f64 (sqrt.f64 z) 1/2) (sqrt.f64 y)) (sqrt.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (cbrt.f64 (*.f64 (*.f64 y y) (*.f64 z 1/4))) 1) (cbrt.f64 (*.f64 y (*.f64 (sqrt.f64 z) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (cbrt.f64 (*.f64 (*.f64 y y) (*.f64 z 1/4))) (cbrt.f64 (cbrt.f64 (*.f64 (*.f64 y y) (*.f64 z 1/4))))) (cbrt.f64 (cbrt.f64 (*.f64 y (*.f64 (sqrt.f64 z) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (cbrt.f64 (*.f64 (*.f64 y y) (*.f64 z 1/4))) (cbrt.f64 y)) (cbrt.f64 (*.f64 (sqrt.f64 z) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (cbrt.f64 (*.f64 (*.f64 y y) (*.f64 z 1/4))) (pow.f64 (*.f64 y (*.f64 (sqrt.f64 z) 1/2)) 1/6)) (pow.f64 (*.f64 y (*.f64 (sqrt.f64 z) 1/2)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (*.f64 y y) (*.f64 z 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 y) (*.f64 (sqrt.f64 z) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 y (*.f64 (sqrt.f64 z) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 y (*.f64 (sqrt.f64 z) 1/2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 y 3) (pow.f64 (*.f64 (sqrt.f64 z) 1/2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (*.f64 (sqrt.f64 z) 1/2) 3) (pow.f64 y 3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 y (*.f64 (sqrt.f64 z) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 y (*.f64 (sqrt.f64 z) 1/2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 y (*.f64 (sqrt.f64 z) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 y (*.f64 (sqrt.f64 z) 1/2))))))))

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simplify83.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

678×	`unswap-sqr_binary64`
660×	`sqr-pow_binary64`
337×	`pow-sqr_binary64`
314×	`cube-prod_binary64`
294×	`*-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	17	417
1	39	417
2	80	383
3	178	383
4	590	383
5	871	383
6	1312	383
7	1363	383
8	1433	383
9	1526	383
10	1649	383
11	1820	383
12	2805	383
13	3218	383
14	3697	383
15	4282	383

Stop Event

1×	node limit

Counts

138 → 105

Calls

Call 1

Inputs
(.f64 (pow.f64 y 1/3) (.f64 (cbrt.f64 1/2) (pow.f64 z 1/6)))
(.f64 (pow.f64 y 1/3) (.f64 (cbrt.f64 1/2) (pow.f64 z 1/6)))
(.f64 (pow.f64 y 1/3) (.f64 (cbrt.f64 1/2) (pow.f64 z 1/6)))
(.f64 (pow.f64 y 1/3) (.f64 (cbrt.f64 1/2) (pow.f64 z 1/6)))
(.f64 (pow.f64 y 1/3) (.f64 (cbrt.f64 1/2) (pow.f64 z 1/6)))
(.f64 (pow.f64 y 1/3) (.f64 (cbrt.f64 1/2) (pow.f64 z 1/6)))
(.f64 (pow.f64 y 1/3) (.f64 (cbrt.f64 1/2) (pow.f64 z 1/6)))
(.f64 (pow.f64 y 1/3) (.f64 (cbrt.f64 1/2) (pow.f64 z 1/6)))
(.f64 1/2 (.f64 y (sqrt.f64 z)))
(.f64 1/2 (.f64 y (sqrt.f64 z)))
(.f64 1/2 (.f64 y (sqrt.f64 z)))
(.f64 1/2 (.f64 y (sqrt.f64 z)))
(.f64 1/2 (.f64 y (sqrt.f64 z)))
(.f64 1/2 (.f64 y (sqrt.f64 z)))
(.f64 1/2 (.f64 y (sqrt.f64 z)))
(.f64 1/2 (.f64 y (sqrt.f64 z)))
(.f64 1/2 (.f64 y (sqrt.f64 z)))
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(*.f64 1/2 x)
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(*.f64 1/2 x)
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))
(+.f64 (.f64 1/2 x) (.f64 1/2 (*.f64 y (sqrt.f64 z))))

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

eval43.0ms (1.4%)

Compiler: Compiled 1881 to 1176 computations (37.5% saved)

prune195.0ms (6.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	118	4	122
Fresh	3	3	6
Picked	0	1	1
Done	1	0	1
Total	122	8	130

Error

Counts

130 → 8

Alt Table

Click to see full alt table

Status	Error	Program
	32.4b	(fma.f64 x 1/2 (pow.f64 (sqrt.f64 (.f64 y (.f64 (sqrt.f64 z) 1/2))) 2))
	32.4b	(.f64 (/.f64 1 2) (+.f64 x (pow.f64 (sqrt.f64 (.f64 y (sqrt.f64 z))) 2)))
	23.4b	(fma.f64 x 1/2 (.f64 (cbrt.f64 (.f64 (.f64 y y) (.f64 z 1/4))) (cbrt.f64 (.f64 y (.f64 (sqrt.f64 z) 1/2)))))
✓	0.6b	(fma.f64 x 1/2 (pow.f64 (cbrt.f64 (.f64 y (.f64 (sqrt.f64 z) 1/2))) 3))
	0.8b	(.f64 (/.f64 1 2) (+.f64 x (pow.f64 (cbrt.f64 (.f64 y (sqrt.f64 z))) 3)))
▶	0.3b	(fma.f64 x 1/2 (.f64 (sqrt.f64 (.f64 (sqrt.f64 z) 1/2)) (.f64 (sqrt.f64 (.f64 (sqrt.f64 z) 1/2)) y)))
	0.4b	(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
	0.5b	(fma.f64 x 1/2 (.f64 (cbrt.f64 (.f64 z 1/4)) (.f64 (cbrt.f64 (.f64 (sqrt.f64 z) 1/2)) y)))

Compiler

Compiled 247 to 190 computations (23.1% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x 1/2 (.f64 (sqrt.f64 (.f64 (sqrt.f64 z) 1/2)) (.f64 (sqrt.f64 (.f64 (sqrt.f64 z) 1/2)) y)))
✓	0.1b	(sqrt.f64 (*.f64 (sqrt.f64 z) 1/2))
✓	0.3b	(.f64 (sqrt.f64 (.f64 (sqrt.f64 z) 1/2)) y)
✓	0.3b	(.f64 (sqrt.f64 (.f64 (sqrt.f64 z) 1/2)) (.f64 (sqrt.f64 (.f64 (sqrt.f64 z) 1/2)) y))

series34.0ms (1.1%)

Counts

4 → 65

Calls

24 calls:

Time	Variable		Point	Expression
19.0ms	y	@	0	(.f64 (sqrt.f64 (.f64 (sqrt.f64 z) 1/2)) y)
1.0ms	z	@	-inf	(.f64 (sqrt.f64 (.f64 (sqrt.f64 z) 1/2)) y)
1.0ms	y	@	0	(.f64 (sqrt.f64 (.f64 (sqrt.f64 z) 1/2)) (.f64 (sqrt.f64 (.f64 (sqrt.f64 z) 1/2)) y))
1.0ms	z	@	0	(.f64 (sqrt.f64 (.f64 (sqrt.f64 z) 1/2)) y)
1.0ms	z	@	-inf	(sqrt.f64 (*.f64 (sqrt.f64 z) 1/2))

rewrite57.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

902×	`log1p-expm1-u_binary64`
902×	`expm1-log1p-u_binary64`
106×	`add-sqr-sqrt_binary64`
104×	`*-un-lft-identity_binary64`
104×	`pow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	41
1	219	41
2	2513	41

Stop Event

1×	node limit

Counts

4 → 79

Calls

Call 1

Inputs
(.f64 (sqrt.f64 (.f64 (sqrt.f64 z) 1/2)) (.f64 (sqrt.f64 (.f64 (sqrt.f64 z) 1/2)) y))
(.f64 (sqrt.f64 (.f64 (sqrt.f64 z) 1/2)) y)
(sqrt.f64 (*.f64 (sqrt.f64 z) 1/2))
(fma.f64 x 1/2 (.f64 (sqrt.f64 (.f64 (sqrt.f64 z) 1/2)) (.f64 (sqrt.f64 (.f64 (sqrt.f64 z) 1/2)) y)))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 (sqrt.f64 z) (.f64 1/2 y)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (sqrt.f64 z) (.f64 1/2 y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 (sqrt.f64 z) (.f64 1/2 y)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 (sqrt.f64 z) (.f64 1/2 y))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 (sqrt.f64 z) (.f64 1/2 y))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (.f64 (.f64 z 1/4) (.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (pow.f64 (exp.f64 (sqrt.f64 z)) 1/2) y))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 (sqrt.f64 z) (.f64 1/2 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 (sqrt.f64 z) (.f64 1/2 y)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (.f64 (sqrt.f64 z) 1/2) 3) (pow.f64 y 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (.f64 (sqrt.f64 z) 1/2) 3/2) (pow.f64 (.f64 (sqrt.f64 (.f64 (sqrt.f64 z) 1/2)) y) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (.f64 (sqrt.f64 (.f64 (sqrt.f64 z) 1/2)) y) 3) (pow.f64 (.f64 (sqrt.f64 z) 1/2) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 (sqrt.f64 z) (.f64 1/2 y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 (sqrt.f64 z) (.f64 1/2 y))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 (sqrt.f64 z) (.f64 1/2 y))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 (sqrt.f64 z) (.f64 1/2 y))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 (sqrt.f64 (.f64 (sqrt.f64 z) 1/2)) y))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (sqrt.f64 (.f64 (sqrt.f64 z) 1/2)) y) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 (sqrt.f64 (.f64 (sqrt.f64 z) 1/2)) y) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 (sqrt.f64 (.f64 (sqrt.f64 z) 1/2)) y)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 (sqrt.f64 (.f64 (sqrt.f64 z) 1/2)) y)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (.f64 (.f64 (sqrt.f64 z) 1/2) (.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 y) (sqrt.f64 (.f64 (sqrt.f64 z) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 (sqrt.f64 (.f64 (sqrt.f64 z) 1/2)) y))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 (sqrt.f64 (.f64 (sqrt.f64 z) 1/2)) y) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (.f64 (sqrt.f64 z) 1/2) 3/2) (pow.f64 y 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 y 3) (pow.f64 (.f64 (sqrt.f64 z) 1/2) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 (sqrt.f64 (.f64 (sqrt.f64 z) 1/2)) y)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 (sqrt.f64 (.f64 (sqrt.f64 z) 1/2)) y)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 (sqrt.f64 (.f64 (sqrt.f64 z) 1/2)) y)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 (sqrt.f64 (*.f64 (sqrt.f64 z) 1/2)) y)))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (.f64 (sqrt.f64 z) 1/2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (.f64 (sqrt.f64 z) 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (sqrt.f64 (.f64 (sqrt.f64 z) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (.f64 (sqrt.f64 z) 1/2)) (cbrt.f64 (sqrt.f64 (.f64 (sqrt.f64 z) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (sqrt.f64 (.f64 (sqrt.f64 z) 1/2))) (cbrt.f64 (.f64 (sqrt.f64 z) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 (sqrt.f64 z) 1/2) 1/4) (pow.f64 (.f64 (sqrt.f64 z) 1/2) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 z 1/4) (sqrt.f64 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 1/2) (pow.f64 z 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (cbrt.f64 (.f64 z 1/4))) (sqrt.f64 (cbrt.f64 (.f64 (sqrt.f64 z) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 1 1/2) (sqrt.f64 (.f64 (sqrt.f64 z) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (.f64 z 1/4)) 1/2) (pow.f64 (cbrt.f64 (.f64 (sqrt.f64 z) 1/2)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (sqrt.f64 z) 1/2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 (sqrt.f64 z) 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 (sqrt.f64 z) 1/2) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (.f64 (sqrt.f64 z) 1/2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 (sqrt.f64 z) 1/2) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (.f64 (sqrt.f64 z) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (.f64 (sqrt.f64 z) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (.f64 (sqrt.f64 z) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 (sqrt.f64 z) 1/2) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (.f64 (sqrt.f64 z) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 (sqrt.f64 z) 1/2)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (sqrt.f64 z) 1/2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (.f64 (sqrt.f64 z) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (.f64 (sqrt.f64 z) 1/2))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (sqrt.f64 z) (.f64 1/2 y)) (.f64 1/2 x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 1/2 x) (.f64 (sqrt.f64 z) (.f64 1/2 y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (.f64 1/2 x) 1) (.f64 (sqrt.f64 z) (.f64 1/2 y)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 x 1/2 (.f64 (sqrt.f64 z) (.f64 1/2 y))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fma.f64 x 1/2 (.f64 (sqrt.f64 z) (.f64 1/2 y))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (fma.f64 x 1/2 (.f64 (sqrt.f64 z) (.f64 1/2 y))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (fma.f64 x 1/2 (.f64 (sqrt.f64 z) (.f64 1/2 y)))) (pow.f64 (cbrt.f64 (fma.f64 x 1/2 (.f64 (sqrt.f64 z) (.f64 1/2 y)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (fma.f64 x 1/2 (.f64 (sqrt.f64 z) (.f64 1/2 y)))) 2) (cbrt.f64 (fma.f64 x 1/2 (.f64 (sqrt.f64 z) (.f64 1/2 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (fma.f64 x 1/2 (.f64 (sqrt.f64 z) (.f64 1/2 y)))) (sqrt.f64 (fma.f64 x 1/2 (.f64 (sqrt.f64 z) (.f64 1/2 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (.f64 1/2 x) 3) (pow.f64 (.f64 (sqrt.f64 z) (.f64 1/2 y)) 3)) (+.f64 (.f64 (.f64 1/2 x) (.f64 1/2 x)) (-.f64 (.f64 (.f64 z 1/4) (.f64 y y)) (.f64 (.f64 1/2 x) (.f64 (sqrt.f64 z) (.f64 1/2 y))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 (.f64 1/2 x) (.f64 1/2 x)) (.f64 (.f64 z 1/4) (.f64 y y))) (-.f64 (.f64 1/2 x) (.f64 (sqrt.f64 z) (.f64 1/2 y))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 x 1/2 (.f64 (sqrt.f64 z) (.f64 1/2 y))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x 1/2 (.f64 (sqrt.f64 z) (.f64 1/2 y))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 x 1/2 (.f64 (sqrt.f64 z) (.f64 1/2 y)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 x 1/2 (.f64 (sqrt.f64 z) (.f64 1/2 y)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 x 1/2 (.f64 (sqrt.f64 z) (.f64 1/2 y))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 x 1/2 (.f64 (sqrt.f64 z) (.f64 1/2 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 x 1/2 (.f64 (sqrt.f64 z) (.f64 1/2 y))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 x 1/2 (.f64 (sqrt.f64 z) (.f64 1/2 y))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 x 1/2 (.f64 (sqrt.f64 z) (.f64 1/2 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (fma.f64 x 1/2 (.f64 (sqrt.f64 z) (.f64 1/2 y)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 x 1/2 (.f64 (sqrt.f64 z) (.f64 1/2 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 x 1/2 (.f64 (sqrt.f64 z) (.f64 1/2 y)))))))))

simplify109.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

892×	`unswap-sqr_binary64`
466×	`sqr-pow_binary64`
352×	`cube-prod_binary64`
290×	`*-commutative_binary64`
229×	`pow-sqr_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	19	862
1	40	697
2	85	679
3	190	643
4	642	643
5	995	643
6	1602	643
7	1657	643
8	1729	643
9	1824	643
10	1953	643
11	2135	643
12	3307	643
13	3724	643
14	4283	643
15	4908	643

Stop Event

1×	node limit

Counts

144 → 87

Calls

Call 1

Inputs
(.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z))
(.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z))
(.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z))
(.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z))
(.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z))
(.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z))
(.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z))
(.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z))
(.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z))
(.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z))
(.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z))
(.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z))
(.f64 (.f64 (sqrt.f64 1/2) y) (pow.f64 z 1/4))
(.f64 (.f64 (sqrt.f64 1/2) y) (pow.f64 z 1/4))
(.f64 (.f64 (sqrt.f64 1/2) y) (pow.f64 z 1/4))
(.f64 (.f64 (sqrt.f64 1/2) y) (pow.f64 z 1/4))
(.f64 (.f64 (sqrt.f64 1/2) y) (pow.f64 z 1/4))
(.f64 (.f64 (sqrt.f64 1/2) y) (pow.f64 z 1/4))
(.f64 (.f64 (sqrt.f64 1/2) y) (pow.f64 z 1/4))
(.f64 (.f64 (sqrt.f64 1/2) y) (pow.f64 z 1/4))
(.f64 (.f64 (sqrt.f64 1/2) y) (pow.f64 z 1/4))
(.f64 (.f64 (sqrt.f64 1/2) y) (pow.f64 z 1/4))
(.f64 (.f64 (sqrt.f64 1/2) y) (pow.f64 z 1/4))
(.f64 (.f64 (sqrt.f64 1/2) y) (pow.f64 z 1/4))
(.f64 (.f64 (sqrt.f64 1/2) y) (pow.f64 z 1/4))
(.f64 (.f64 (sqrt.f64 1/2) y) (pow.f64 z 1/4))
(.f64 (.f64 (sqrt.f64 1/2) y) (pow.f64 z 1/4))
(.f64 (.f64 (sqrt.f64 1/2) y) (pow.f64 z 1/4))
(.f64 (.f64 (sqrt.f64 1/2) y) (pow.f64 z 1/4))
(.f64 (.f64 (sqrt.f64 1/2) y) (pow.f64 z 1/4))
(.f64 (.f64 (sqrt.f64 1/2) y) (pow.f64 z 1/4))
(.f64 (.f64 (sqrt.f64 1/2) y) (pow.f64 z 1/4))
(*.f64 (sqrt.f64 1/2) (pow.f64 z 1/4))
(*.f64 (sqrt.f64 1/2) (pow.f64 z 1/4))
(*.f64 (sqrt.f64 1/2) (pow.f64 z 1/4))
(*.f64 (sqrt.f64 1/2) (pow.f64 z 1/4))
(*.f64 (sqrt.f64 1/2) (pow.f64 z 1/4))
(*.f64 (sqrt.f64 1/2) (pow.f64 z 1/4))
(*.f64 (sqrt.f64 1/2) (pow.f64 z 1/4))
(*.f64 (sqrt.f64 1/2) (pow.f64 z 1/4))
(.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z))
(+.f64 (.f64 1/2 x) (.f64 (*.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z)))
(+.f64 (.f64 1/2 x) (.f64 (*.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z)))
(+.f64 (.f64 1/2 x) (.f64 (*.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z)))
(*.f64 1/2 x)
(+.f64 (.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z)) (*.f64 1/2 x))
(+.f64 (.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z)) (*.f64 1/2 x))
(+.f64 (.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z)) (*.f64 1/2 x))
(*.f64 1/2 x)
(+.f64 (.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z)) (*.f64 1/2 x))
(+.f64 (.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z)) (*.f64 1/2 x))
(+.f64 (.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z)) (*.f64 1/2 x))
(*.f64 1/2 x)
(*.f64 1/2 x)
(+.f64 (.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z)) (*.f64 1/2 x))
(+.f64 (.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z)) (*.f64 1/2 x))
(+.f64 (.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z)) (*.f64 1/2 x))
(.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z))
(+.f64 (.f64 1/2 x) (.f64 (*.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z)))
(+.f64 (.f64 1/2 x) (.f64 (*.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z)))
(+.f64 (.f64 1/2 x) (.f64 (*.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z)))
(.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z))
(+.f64 (.f64 1/2 x) (.f64 (*.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z)))
(+.f64 (.f64 1/2 x) (.f64 (*.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z)))
(+.f64 (.f64 1/2 x) (.f64 (*.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z)))

Outputs
(.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z))
(.f64 (pow.f64 (sqrt.f64 1/2) 2) (.f64 y (sqrt.f64 z)))
(.f64 1/2 (.f64 y (sqrt.f64 z)))
(.f64 y (.f64 1/2 (sqrt.f64 z)))
(.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z))
(.f64 (pow.f64 (sqrt.f64 1/2) 2) (.f64 y (sqrt.f64 z)))
(.f64 1/2 (.f64 y (sqrt.f64 z)))
(.f64 y (.f64 1/2 (sqrt.f64 z)))
(.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z))
(.f64 (pow.f64 (sqrt.f64 1/2) 2) (.f64 y (sqrt.f64 z)))
(.f64 1/2 (.f64 y (sqrt.f64 z)))
(.f64 y (.f64 1/2 (sqrt.f64 z)))
(.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z))
(.f64 (pow.f64 (sqrt.f64 1/2) 2) (.f64 y (sqrt.f64 z)))
(.f64 1/2 (.f64 y (sqrt.f64 z)))
(.f64 y (.f64 1/2 (sqrt.f64 z)))
(.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z))
(.f64 (pow.f64 (sqrt.f64 1/2) 2) (.f64 y (sqrt.f64 z)))
(.f64 1/2 (.f64 y (sqrt.f64 z)))
(.f64 y (.f64 1/2 (sqrt.f64 z)))
(.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z))
(.f64 (pow.f64 (sqrt.f64 1/2) 2) (.f64 y (sqrt.f64 z)))
(.f64 1/2 (.f64 y (sqrt.f64 z)))
(.f64 y (.f64 1/2 (sqrt.f64 z)))
(.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z))
(.f64 (pow.f64 (sqrt.f64 1/2) 2) (.f64 y (sqrt.f64 z)))
(.f64 1/2 (.f64 y (sqrt.f64 z)))
(.f64 y (.f64 1/2 (sqrt.f64 z)))
(.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z))
(.f64 (pow.f64 (sqrt.f64 1/2) 2) (.f64 y (sqrt.f64 z)))
(.f64 1/2 (.f64 y (sqrt.f64 z)))
(.f64 y (.f64 1/2 (sqrt.f64 z)))
(.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z))
(.f64 (pow.f64 (sqrt.f64 1/2) 2) (.f64 y (sqrt.f64 z)))
(.f64 1/2 (.f64 y (sqrt.f64 z)))
(.f64 y (.f64 1/2 (sqrt.f64 z)))
(.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z))
(.f64 (pow.f64 (sqrt.f64 1/2) 2) (.f64 y (sqrt.f64 z)))
(.f64 1/2 (.f64 y (sqrt.f64 z)))
(.f64 y (.f64 1/2 (sqrt.f64 z)))
(.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z))
(.f64 (pow.f64 (sqrt.f64 1/2) 2) (.f64 y (sqrt.f64 z)))
(.f64 1/2 (.f64 y (sqrt.f64 z)))
(.f64 y (.f64 1/2 (sqrt.f64 z)))
(.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z))
(.f64 (pow.f64 (sqrt.f64 1/2) 2) (.f64 y (sqrt.f64 z)))
(.f64 1/2 (.f64 y (sqrt.f64 z)))
(.f64 y (.f64 1/2 (sqrt.f64 z)))
(.f64 (.f64 (sqrt.f64 1/2) y) (pow.f64 z 1/4))
(.f64 (sqrt.f64 1/2) (.f64 y (pow.f64 z 1/4)))
(.f64 y (.f64 (sqrt.f64 1/2) (pow.f64 z 1/4)))
(.f64 (.f64 (sqrt.f64 1/2) y) (pow.f64 z 1/4))
(.f64 (sqrt.f64 1/2) (.f64 y (pow.f64 z 1/4)))
(.f64 y (.f64 (sqrt.f64 1/2) (pow.f64 z 1/4)))
(.f64 (.f64 (sqrt.f64 1/2) y) (pow.f64 z 1/4))
(.f64 (sqrt.f64 1/2) (.f64 y (pow.f64 z 1/4)))
(.f64 y (.f64 (sqrt.f64 1/2) (pow.f64 z 1/4)))
(.f64 (.f64 (sqrt.f64 1/2) y) (pow.f64 z 1/4))
(.f64 (sqrt.f64 1/2) (.f64 y (pow.f64 z 1/4)))
(.f64 y (.f64 (sqrt.f64 1/2) (pow.f64 z 1/4)))
(.f64 (.f64 (sqrt.f64 1/2) y) (pow.f64 z 1/4))
(.f64 (sqrt.f64 1/2) (.f64 y (pow.f64 z 1/4)))
(.f64 y (.f64 (sqrt.f64 1/2) (pow.f64 z 1/4)))
(.f64 (.f64 (sqrt.f64 1/2) y) (pow.f64 z 1/4))
(.f64 (sqrt.f64 1/2) (.f64 y (pow.f64 z 1/4)))
(.f64 y (.f64 (sqrt.f64 1/2) (pow.f64 z 1/4)))
(.f64 (.f64 (sqrt.f64 1/2) y) (pow.f64 z 1/4))
(.f64 (sqrt.f64 1/2) (.f64 y (pow.f64 z 1/4)))
(.f64 y (.f64 (sqrt.f64 1/2) (pow.f64 z 1/4)))
(.f64 (.f64 (sqrt.f64 1/2) y) (pow.f64 z 1/4))
(.f64 (sqrt.f64 1/2) (.f64 y (pow.f64 z 1/4)))
(.f64 y (.f64 (sqrt.f64 1/2) (pow.f64 z 1/4)))
(.f64 (.f64 (sqrt.f64 1/2) y) (pow.f64 z 1/4))
(.f64 (sqrt.f64 1/2) (.f64 y (pow.f64 z 1/4)))
(.f64 y (.f64 (sqrt.f64 1/2) (pow.f64 z 1/4)))
(.f64 (.f64 (sqrt.f64 1/2) y) (pow.f64 z 1/4))
(.f64 (sqrt.f64 1/2) (.f64 y (pow.f64 z 1/4)))
(.f64 y (.f64 (sqrt.f64 1/2) (pow.f64 z 1/4)))
(.f64 (.f64 (sqrt.f64 1/2) y) (pow.f64 z 1/4))
(.f64 (sqrt.f64 1/2) (.f64 y (pow.f64 z 1/4)))
(.f64 y (.f64 (sqrt.f64 1/2) (pow.f64 z 1/4)))
(.f64 (.f64 (sqrt.f64 1/2) y) (pow.f64 z 1/4))
(.f64 (sqrt.f64 1/2) (.f64 y (pow.f64 z 1/4)))
(.f64 y (.f64 (sqrt.f64 1/2) (pow.f64 z 1/4)))
(.f64 (.f64 (sqrt.f64 1/2) y) (pow.f64 z 1/4))
(.f64 (sqrt.f64 1/2) (.f64 y (pow.f64 z 1/4)))
(.f64 y (.f64 (sqrt.f64 1/2) (pow.f64 z 1/4)))
(.f64 (.f64 (sqrt.f64 1/2) y) (pow.f64 z 1/4))
(.f64 (sqrt.f64 1/2) (.f64 y (pow.f64 z 1/4)))
(.f64 y (.f64 (sqrt.f64 1/2) (pow.f64 z 1/4)))
(.f64 (.f64 (sqrt.f64 1/2) y) (pow.f64 z 1/4))
(.f64 (sqrt.f64 1/2) (.f64 y (pow.f64 z 1/4)))
(.f64 y (.f64 (sqrt.f64 1/2) (pow.f64 z 1/4)))
(.f64 (.f64 (sqrt.f64 1/2) y) (pow.f64 z 1/4))
(.f64 (sqrt.f64 1/2) (.f64 y (pow.f64 z 1/4)))
(.f64 y (.f64 (sqrt.f64 1/2) (pow.f64 z 1/4)))
(.f64 (.f64 (sqrt.f64 1/2) y) (pow.f64 z 1/4))
(.f64 (sqrt.f64 1/2) (.f64 y (pow.f64 z 1/4)))
(.f64 y (.f64 (sqrt.f64 1/2) (pow.f64 z 1/4)))
(.f64 (.f64 (sqrt.f64 1/2) y) (pow.f64 z 1/4))
(.f64 (sqrt.f64 1/2) (.f64 y (pow.f64 z 1/4)))
(.f64 y (.f64 (sqrt.f64 1/2) (pow.f64 z 1/4)))
(.f64 (.f64 (sqrt.f64 1/2) y) (pow.f64 z 1/4))
(.f64 (sqrt.f64 1/2) (.f64 y (pow.f64 z 1/4)))
(.f64 y (.f64 (sqrt.f64 1/2) (pow.f64 z 1/4)))
(.f64 (.f64 (sqrt.f64 1/2) y) (pow.f64 z 1/4))
(.f64 (sqrt.f64 1/2) (.f64 y (pow.f64 z 1/4)))
(.f64 y (.f64 (sqrt.f64 1/2) (pow.f64 z 1/4)))
(*.f64 (sqrt.f64 1/2) (pow.f64 z 1/4))
(*.f64 (sqrt.f64 1/2) (pow.f64 z 1/4))
(*.f64 (sqrt.f64 1/2) (pow.f64 z 1/4))
(*.f64 (sqrt.f64 1/2) (pow.f64 z 1/4))
(*.f64 (sqrt.f64 1/2) (pow.f64 z 1/4))
(*.f64 (sqrt.f64 1/2) (pow.f64 z 1/4))
(*.f64 (sqrt.f64 1/2) (pow.f64 z 1/4))
(*.f64 (sqrt.f64 1/2) (pow.f64 z 1/4))
(.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z))
(.f64 (pow.f64 (sqrt.f64 1/2) 2) (.f64 y (sqrt.f64 z)))
(.f64 1/2 (.f64 y (sqrt.f64 z)))
(.f64 y (.f64 1/2 (sqrt.f64 z)))
(+.f64 (.f64 1/2 x) (.f64 (*.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z)))
(fma.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z) (.f64 1/2 x))
(fma.f64 1/2 (.f64 y (sqrt.f64 z)) (.f64 1/2 x))
(.f64 1/2 (+.f64 x (.f64 y (sqrt.f64 z))))
(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
(+.f64 (.f64 1/2 x) (.f64 (*.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z)))
(fma.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z) (.f64 1/2 x))
(fma.f64 1/2 (.f64 y (sqrt.f64 z)) (.f64 1/2 x))
(.f64 1/2 (+.f64 x (.f64 y (sqrt.f64 z))))
(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
(+.f64 (.f64 1/2 x) (.f64 (*.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z)))
(fma.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z) (.f64 1/2 x))
(fma.f64 1/2 (.f64 y (sqrt.f64 z)) (.f64 1/2 x))
(.f64 1/2 (+.f64 x (.f64 y (sqrt.f64 z))))
(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
(*.f64 1/2 x)
(+.f64 (.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z)) (*.f64 1/2 x))
(fma.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z) (.f64 1/2 x))
(fma.f64 1/2 (.f64 y (sqrt.f64 z)) (.f64 1/2 x))
(.f64 1/2 (+.f64 x (.f64 y (sqrt.f64 z))))
(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
(+.f64 (.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z)) (*.f64 1/2 x))
(fma.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z) (.f64 1/2 x))
(fma.f64 1/2 (.f64 y (sqrt.f64 z)) (.f64 1/2 x))
(.f64 1/2 (+.f64 x (.f64 y (sqrt.f64 z))))
(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
(+.f64 (.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z)) (*.f64 1/2 x))
(fma.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z) (.f64 1/2 x))
(fma.f64 1/2 (.f64 y (sqrt.f64 z)) (.f64 1/2 x))
(.f64 1/2 (+.f64 x (.f64 y (sqrt.f64 z))))
(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
(*.f64 1/2 x)
(+.f64 (.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z)) (*.f64 1/2 x))
(fma.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z) (.f64 1/2 x))
(fma.f64 1/2 (.f64 y (sqrt.f64 z)) (.f64 1/2 x))
(.f64 1/2 (+.f64 x (.f64 y (sqrt.f64 z))))
(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
(+.f64 (.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z)) (*.f64 1/2 x))
(fma.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z) (.f64 1/2 x))
(fma.f64 1/2 (.f64 y (sqrt.f64 z)) (.f64 1/2 x))
(.f64 1/2 (+.f64 x (.f64 y (sqrt.f64 z))))
(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
(+.f64 (.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z)) (*.f64 1/2 x))
(fma.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z) (.f64 1/2 x))
(fma.f64 1/2 (.f64 y (sqrt.f64 z)) (.f64 1/2 x))
(.f64 1/2 (+.f64 x (.f64 y (sqrt.f64 z))))
(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
(*.f64 1/2 x)
(*.f64 1/2 x)
(+.f64 (.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z)) (*.f64 1/2 x))
(fma.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z) (.f64 1/2 x))
(fma.f64 1/2 (.f64 y (sqrt.f64 z)) (.f64 1/2 x))
(.f64 1/2 (+.f64 x (.f64 y (sqrt.f64 z))))
(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
(+.f64 (.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z)) (*.f64 1/2 x))
(fma.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z) (.f64 1/2 x))
(fma.f64 1/2 (.f64 y (sqrt.f64 z)) (.f64 1/2 x))
(.f64 1/2 (+.f64 x (.f64 y (sqrt.f64 z))))
(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
(+.f64 (.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z)) (*.f64 1/2 x))
(fma.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z) (.f64 1/2 x))
(fma.f64 1/2 (.f64 y (sqrt.f64 z)) (.f64 1/2 x))
(.f64 1/2 (+.f64 x (.f64 y (sqrt.f64 z))))
(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
(.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z))
(.f64 (pow.f64 (sqrt.f64 1/2) 2) (.f64 y (sqrt.f64 z)))
(.f64 1/2 (.f64 y (sqrt.f64 z)))
(.f64 y (.f64 1/2 (sqrt.f64 z)))
(+.f64 (.f64 1/2 x) (.f64 (*.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z)))
(fma.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z) (.f64 1/2 x))
(fma.f64 1/2 (.f64 y (sqrt.f64 z)) (.f64 1/2 x))
(.f64 1/2 (+.f64 x (.f64 y (sqrt.f64 z))))
(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
(+.f64 (.f64 1/2 x) (.f64 (*.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z)))
(fma.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z) (.f64 1/2 x))
(fma.f64 1/2 (.f64 y (sqrt.f64 z)) (.f64 1/2 x))
(.f64 1/2 (+.f64 x (.f64 y (sqrt.f64 z))))
(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
(+.f64 (.f64 1/2 x) (.f64 (*.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z)))
(fma.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z) (.f64 1/2 x))
(fma.f64 1/2 (.f64 y (sqrt.f64 z)) (.f64 1/2 x))
(.f64 1/2 (+.f64 x (.f64 y (sqrt.f64 z))))
(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
(.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z))
(.f64 (pow.f64 (sqrt.f64 1/2) 2) (.f64 y (sqrt.f64 z)))
(.f64 1/2 (.f64 y (sqrt.f64 z)))
(.f64 y (.f64 1/2 (sqrt.f64 z)))
(+.f64 (.f64 1/2 x) (.f64 (*.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z)))
(fma.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z) (.f64 1/2 x))
(fma.f64 1/2 (.f64 y (sqrt.f64 z)) (.f64 1/2 x))
(.f64 1/2 (+.f64 x (.f64 y (sqrt.f64 z))))
(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
(+.f64 (.f64 1/2 x) (.f64 (*.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z)))
(fma.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z) (.f64 1/2 x))
(fma.f64 1/2 (.f64 y (sqrt.f64 z)) (.f64 1/2 x))
(.f64 1/2 (+.f64 x (.f64 y (sqrt.f64 z))))
(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
(+.f64 (.f64 1/2 x) (.f64 (*.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z)))
(fma.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) y) (sqrt.f64 z) (.f64 1/2 x))
(fma.f64 1/2 (.f64 y (sqrt.f64 z)) (.f64 1/2 x))
(.f64 1/2 (+.f64 x (.f64 y (sqrt.f64 z))))
(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))

eval42.0ms (1.3%)

Compiler: Compiled 1902 to 1280 computations (32.7% saved)

prune275.0ms (8.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	109	3	112
Fresh	5	1	6
Picked	0	1	1
Done	0	1	1
Total	114	6	120

Error

Counts

120 → 6

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.6b	(fma.f64 x 1/2 (pow.f64 (cbrt.f64 (.f64 y (.f64 (sqrt.f64 z) 1/2))) 3))
	32.4b	(fma.f64 x 1/2 (pow.f64 (sqrt.f64 (.f64 (sqrt.f64 z) (.f64 1/2 y))) 2))
✓	0.3b	(fma.f64 x 1/2 (.f64 (sqrt.f64 (.f64 (sqrt.f64 z) 1/2)) (.f64 (sqrt.f64 (.f64 (sqrt.f64 z) 1/2)) y)))
	0.4b	(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
	0.3b	(fma.f64 x 1/2 (.f64 (sqrt.f64 (.f64 (sqrt.f64 z) 1/2)) (.f64 (.f64 (sqrt.f64 1/2) y) (pow.f64 z 1/4))))
	0.3b	(fma.f64 x 1/2 (.f64 (.f64 (sqrt.f64 (cbrt.f64 (.f64 z 1/4))) (sqrt.f64 (cbrt.f64 (.f64 (sqrt.f64 z) 1/2)))) (.f64 (sqrt.f64 (.f64 (sqrt.f64 z) 1/2)) y)))

Compiler

Compiled 105 to 81 computations (22.9% saved)

regimes125.0ms (4%)

Accuracy

Total -56.7b remaining (-43990.1%)

Threshold costs -56.7b (-43990.1%)

Counts

20 → 1

Calls

Call 1

Inputs
(fma.f64 x 1/2 (pow.f64 (sqrt.f64 (.f64 (sqrt.f64 z) (.f64 1/2 y))) 2))
(fma.f64 x 1/2 (.f64 (sqrt.f64 (.f64 (sqrt.f64 z) 1/2)) (.f64 (.f64 (sqrt.f64 1/2) y) (pow.f64 z 1/4))))
(fma.f64 x 1/2 (.f64 (.f64 (sqrt.f64 (cbrt.f64 (.f64 z 1/4))) (sqrt.f64 (cbrt.f64 (.f64 (sqrt.f64 z) 1/2)))) (.f64 (sqrt.f64 (.f64 (sqrt.f64 z) 1/2)) y)))
(fma.f64 x 1/2 (.f64 (cbrt.f64 (.f64 (.f64 y y) (.f64 z 1/4))) (cbrt.f64 (.f64 y (.f64 (sqrt.f64 z) 1/2)))))
(fma.f64 x 1/2 (.f64 (sqrt.f64 (.f64 (sqrt.f64 z) 1/2)) (.f64 (sqrt.f64 (.f64 (sqrt.f64 z) 1/2)) y)))
(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
(fma.f64 x 1/2 (.f64 (cbrt.f64 (.f64 z 1/4)) (.f64 (cbrt.f64 (.f64 (sqrt.f64 z) 1/2)) y)))
(fma.f64 x 1/2 (pow.f64 (sqrt.f64 (.f64 y (.f64 (sqrt.f64 z) 1/2))) 2))
(fma.f64 x 1/2 (pow.f64 (cbrt.f64 (.f64 y (.f64 (sqrt.f64 z) 1/2))) 3))
(fma.f64 x 1/2 (cbrt.f64 (pow.f64 (.f64 y (.f64 (sqrt.f64 z) 1/2)) 3)))
(.f64 (/.f64 1 2) (+.f64 x (pow.f64 (sqrt.f64 (.f64 y (sqrt.f64 z))) 2)))
(.f64 (/.f64 1 2) (+.f64 x (pow.f64 (cbrt.f64 (.f64 y (sqrt.f64 z))) 3)))
(fma.f64 x 1/2 (.f64 y (.f64 (sqrt.f64 z) 1/2)))
(.f64 (/.f64 1 2) (fma.f64 (cbrt.f64 (.f64 z (.f64 y y))) (cbrt.f64 (.f64 y (sqrt.f64 z))) x))
(.f64 (/.f64 1 2) (.f64 (-.f64 (.f64 x x) (.f64 z (.f64 y y))) (/.f64 1 (-.f64 x (.f64 y (sqrt.f64 z))))))
(pow.f64 (sqrt.f64 (*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))) 2)
(pow.f64 (cbrt.f64 (*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))) 3)
(.f64 (/.f64 1 2) (+.f64 x (cbrt.f64 (pow.f64 (.f64 y (sqrt.f64 z)) 3))))
(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
(.f64 (/.f64 1 2) (+.f64 x (.f64 y (sqrt.f64 z))))

Outputs
(fma.f64 x 1/2 (.f64 y (.f64 (sqrt.f64 z) 1/2)))

Results

Time	Error	Segments	Branch
10.0ms	0.1b	1	`x`
21.0ms	0.1b	1	`y`
10.0ms	0.1b	1	`z`
13.0ms	0.1b	1	`(.f64 (/.f64 1 2) (+.f64 x (.f64 y (sqrt.f64 z))))`
24.0ms	0.1b	1	`(+.f64 x (*.f64 y (sqrt.f64 z)))`
10.0ms	0.1b	1	`(*.f64 y (sqrt.f64 z))`
12.0ms	0.1b	1	`(*.f64 y (sqrt.f64 z))`
10.0ms	0.1b	1	`(sqrt.f64 z)`

Compiler

Compiled 325 to 202 computations (37.8% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	11	13

Stop Event

1×

saturated

Calls

Call 1

Inputs
(fma.f64 x 1/2 (.f64 y (.f64 (sqrt.f64 z) 1/2)))

Outputs
(fma.f64 x 1/2 (.f64 y (.f64 (sqrt.f64 z) 1/2)))
(fma.f64 x 1/2 (.f64 y (.f64 1/2 (sqrt.f64 z))))

end17.0ms (0.5%)

Stop Event

1×

fuel

Compiler

Compiled 24 to 18 computations (25% saved)

Details

analyze471.0ms (15.2%)

sample1.2s (37.4%)

preprocess18.0ms (0.6%)

simplify7.0ms (0.2%)

eval1.0ms (0%)

prune2.0ms (0.1%)

localize7.0ms (0.2%)

series13.0ms (0.4%)

rewrite51.0ms (1.7%)

simplify15.0ms (0.5%)

eval20.0ms (0.6%)

prune79.0ms (2.6%)

localize6.0ms (0.2%)

series8.0ms (0.3%)

rewrite41.0ms (1.3%)

simplify15.0ms (0.5%)

eval11.0ms (0.3%)

prune42.0ms (1.4%)

localize9.0ms (0.3%)

series79.0ms (2.6%)

rewrite57.0ms (1.8%)

simplify83.0ms (2.7%)

eval43.0ms (1.4%)

prune195.0ms (6.3%)

localize8.0ms (0.3%)

series34.0ms (1.1%)

rewrite57.0ms (1.8%)

simplify109.0ms (3.5%)

eval42.0ms (1.3%)

prune275.0ms (8.9%)

regimes125.0ms (4%)

simplify2.0ms (0.1%)

end17.0ms (0.5%)

Profiling