Details

analyze279.0ms (4.3%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	99.9%	0.1%	0%	0%	0%	2
0%	0%	99.9%	0.1%	0%	0%	0%	3
0%	0%	99.9%	0.1%	0%	0%	0%	4
0%	0%	99.9%	0.1%	0%	0%	0%	5
0%	0%	99.9%	0.1%	0%	0%	0%	6
8.3%	6.2%	68.6%	0.1%	0%	25%	0%	7
12.5%	9.4%	65.5%	0.1%	0%	25%	0%	8
18.8%	14%	60.8%	0.1%	0%	25%	0%	9
33.8%	21.1%	41.3%	0.1%	0%	37.4%	0%	10
39.4%	24.6%	37.8%	0.1%	0%	37.4%	0%	11
45.9%	28.7%	33.7%	0.1%	0%	37.4%	0%	12

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample1.6s (24.8%)

Results

1.2s	8256×	body	256	valid
300.0ms	2278×	body	256	invalid
72.0ms	533×	body	256	infinite

Bogosity

preprocess24.0ms (0.4%)

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 16 to 13 computations (18.8% saved)

simplify7.0ms (0.1%)

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%)

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

0.1b

Counts

3 → 2

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.1b	(.f64 (/.f64 1 2) (+.f64 x (.f64 y (sqrt.f64 z))))
▶	0.1b	(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))

Compiler

Compiled 23 to 17 computations (26.1% saved)

localize10.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 y (sqrt.f64 z) x)

Compiler

Compiled 21 to 8 computations (61.9% saved)

series6.0ms (0.1%)

Counts

1 → 25

Calls

9 calls:

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

rewrite58.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

544×	`pow1_binary64`
519×	`add-sqr-sqrt_binary64`
499×	`add-log-exp_binary64`
499×	`log1p-expm1-u_binary64`
499×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	118	7
2	1372	7

Stop Event

1×	node limit

Counts

1 → 21

Calls

Call 1

Inputs
(fma.f64 y (sqrt.f64 z) x)

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

Outputs

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

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`fma-def_binary64`
1×	`+-commutative_binary64`
1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	148
1	10	148
2	11	148

Stop Event

1×

saturated

Counts

46 → 24

Calls

Call 1

Inputs
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
(*.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)

Outputs
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
(*.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)

localize54.0ms (0.8%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 33 to 15 computations (54.5% saved)

series6.0ms (0.1%)

Counts

2 → 25

Calls

15 calls:

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

rewrite81.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

786×	`pow1_binary64`
729×	`add-log-exp_binary64`
729×	`log1p-expm1-u_binary64`
729×	`expm1-log1p-u_binary64`
711×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	15
1	148	13
2	1996	13

Stop Event

1×	node limit

Counts

2 → 46

Calls

Call 1

Inputs
(*.f64 y (sqrt.f64 z))
(+.f64 x (*.f64 y (sqrt.f64 z)))

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

Outputs

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

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

simplify44.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

2×	`fma-def_binary64`
1×	`+-commutative_binary64`
1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	148
1	10	148
2	11	148

Stop Event

1×

saturated

Counts

71 → 49

Calls

Call 1

Inputs
(*.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 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

eval16.0ms (0.2%)

Compiler: Compiled 1029 to 452 computations (56.1% saved)

prune28.0ms (0.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	64	9	73
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	65	10	75

Error

0.0b

Counts

75 → 10

Alt Table

Click to see full alt table

Status	Error	Program
	37.2b	(.f64 (/.f64 1 2) (/.f64 (-.f64 (.f64 z (.f64 y y)) (.f64 x x)) (-.f64 (*.f64 y (sqrt.f64 z)) x)))
▶	37.2b	(.f64 (/.f64 1 2) (/.f64 1 (/.f64 (-.f64 x (.f64 y (sqrt.f64 z))) (-.f64 (.f64 x x) (.f64 z (*.f64 y y))))))
▶	0.6b	(.f64 (/.f64 1 2) (+.f64 x (pow.f64 (cbrt.f64 (.f64 y (sqrt.f64 z))) 3)))
▶	29.9b	(.f64 (/.f64 1 2) (+.f64 x (sqrt.f64 (.f64 z (*.f64 y y)))))
	25.5b	(.f64 (/.f64 1 2) (+.f64 x (cbrt.f64 (pow.f64 (.f64 y (sqrt.f64 z)) 3))))
✓	0.1b	(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
	36.0b	(*.f64 1/2 (pow.f64 (sqrt.f64 (fma.f64 y (sqrt.f64 z) x)) 2))
▶	0.1b	(.f64 1/2 (+.f64 (.f64 y (sqrt.f64 z)) x))
	33.5b	(.f64 1/2 (.f64 y (sqrt.f64 z)))
▶	29.7b	(*.f64 1/2 x)

Compiler

Compiled 278 to 205 computations (26.3% saved)

localize12.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 27 to 9 computations (66.7% saved)

series3.0ms (0%)

Counts

1 → 7

Calls

9 calls:

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

rewrite56.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

780×	`pow1_binary64`
723×	`add-log-exp_binary64`
723×	`log1p-expm1-u_binary64`
723×	`expm1-log1p-u_binary64`
705×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	7
1	149	7
2	1992	7

Stop Event

1×	node limit

Counts

1 → 35

Calls

Call 1

Inputs
(+.f64 (*.f64 y (sqrt.f64 z)) x)

Outputs

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

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	22
1	7	22

Stop Event

1×

saturated

Counts

42 → 37

Calls

Call 1

Inputs
x
(*.f64 y (sqrt.f64 z))
(*.f64 y (sqrt.f64 z))
x
(*.f64 y (sqrt.f64 z))
x
x

Outputs
x
(*.f64 y (sqrt.f64 z))
(*.f64 y (sqrt.f64 z))
x
(*.f64 y (sqrt.f64 z))
x
x

localize4.0ms (0.1%)

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

localize14.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (sqrt.f64 (.f64 z (.f64 y y))))
✓	9.3b	(.f64 z (.f64 y y))
✓	27.4b	(sqrt.f64 (.f64 z (.f64 y y)))

Compiler

Compiled 45 to 16 computations (64.4% saved)

series8.0ms (0.1%)

Counts

3 → 61

Calls

21 calls:

Time	Variable		Point	Expression
1.0ms	z	@	0	(.f64 z (.f64 y y))
1.0ms	y	@	0	(.f64 z (.f64 y y))
1.0ms	z	@	-inf	(.f64 z (.f64 y y))
1.0ms	y	@	inf	(.f64 z (.f64 y y))
0.0ms	z	@	inf	(.f64 z (.f64 y y))

rewrite82.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

895×	`pow1_binary64`
832×	`add-log-exp_binary64`
832×	`log1p-expm1-u_binary64`
832×	`expm1-log1p-u_binary64`
810×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	28
1	171	20
2	2372	20

Stop Event

1×	node limit

Counts

3 → 72

Calls

Call 1

Inputs
(sqrt.f64 (.f64 z (.f64 y y)))
(.f64 z (.f64 y y))
(+.f64 x (sqrt.f64 (.f64 z (.f64 y y))))

Outputs

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

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

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

simplify112.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

855×	`fma-neg_binary64`
783×	`fma-def_binary64`
381×	`cube-prod_binary64`
379×	`distribute-rgt-neg-in_binary64`
322×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	388
1	28	388
2	55	388
3	106	388
4	245	388
5	698	388
6	1125	388
7	1825	388
8	2344	388
9	3509	388
10	4747	388
11	6201	388
12	7564	388

Stop Event

1×	node limit

Counts

133 → 79

Calls

Call 1

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

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

localize28.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(*.f64 y (sqrt.f64 z))
✓	2.3b	(-.f64 (.f64 x x) (.f64 z (*.f64 y y)))
	9.3b	(.f64 z (.f64 y y))
✓	30.2b	(/.f64 (-.f64 x (.f64 y (sqrt.f64 z))) (-.f64 (.f64 x x) (.f64 z (.f64 y y))))

Compiler

Compiled 99 to 24 computations (75.8% saved)

series26.0ms (0.4%)

Counts

2 → 61

Calls

18 calls:

Time	Variable		Point	Expression
4.0ms	z	@	0	(/.f64 (-.f64 x (.f64 y (sqrt.f64 z))) (-.f64 (.f64 x x) (.f64 z (.f64 y y))))
4.0ms	z	@	inf	(/.f64 (-.f64 x (.f64 y (sqrt.f64 z))) (-.f64 (.f64 x x) (.f64 z (.f64 y y))))
3.0ms	z	@	-inf	(/.f64 (-.f64 x (.f64 y (sqrt.f64 z))) (-.f64 (.f64 x x) (.f64 z (.f64 y y))))
2.0ms	x	@	inf	(/.f64 (-.f64 x (.f64 y (sqrt.f64 z))) (-.f64 (.f64 x x) (.f64 z (.f64 y y))))
2.0ms	x	@	0	(/.f64 (-.f64 x (.f64 y (sqrt.f64 z))) (-.f64 (.f64 x x) (.f64 z (.f64 y y))))

rewrite110.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

771×	`log-prod_binary64`
653×	`fma-def_binary64`
288×	`fma-neg_binary64`
242×	`expm1-udef_binary64`
242×	`log1p-udef_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	37
1	284	25
2	4382	23

Stop Event

1×	node limit

Counts

2 → 215

Calls

Call 1

Inputs
(/.f64 (-.f64 x (.f64 y (sqrt.f64 z))) (-.f64 (.f64 x x) (.f64 z (.f64 y y))))
(-.f64 (.f64 x x) (.f64 z (*.f64 y y)))

Outputs

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(#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (*.f64 (*.f64 z (*.f64 y (neg.f64 y))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (fma.f64 z (*.f64 y (neg.f64 y)) (fma.f64 z (*.f64 y (neg.f64 y)) (*.f64 y (*.f64 y z)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (neg.f64 (-.f64 (*.f64 y (*.f64 y z)) (fma.f64 z (*.f64 y (neg.f64 y)) (*.f64 y (*.f64 y z))))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (neg.f64 z) y) y (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (neg.f64 z) 1) (*.f64 y y) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (neg.f64 z) (cbrt.f64 (pow.f64 y 4))) (pow.f64 (cbrt.f64 y) 2) (*.f64 x x))))))

simplify82.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

837×	`fma-neg_binary64`
628×	`cancel-sign-sub-inv_binary64`
519×	`associate-/l/_binary64`
414×	`associate-/r/_binary64`
312×	`times-frac_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	53	1223
1	155	1133
2	526	1112
3	2684	1088
4	7683	1088

Stop Event

1×	node limit

Counts

276 → 235

Calls

Call 1

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

Outputs
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z)))
(/.f64 (sqrt.f64 (/.f64 1 z)) y)
(+.f64 (.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z))) (.f64 -1 (/.f64 x (*.f64 (pow.f64 y 2) z))))
(fma.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z)) (neg.f64 (/.f64 x (.f64 z (.f64 y y)))))
(-.f64 (/.f64 (sqrt.f64 (/.f64 1 z)) y) (/.f64 x (.f64 y (.f64 y z))))
(-.f64 (/.f64 (sqrt.f64 (/.f64 1 z)) y) (/.f64 (/.f64 x (*.f64 y y)) z))
(+.f64 (.f64 (/.f64 (pow.f64 x 2) (pow.f64 y 3)) (sqrt.f64 (/.f64 1 (pow.f64 z 3)))) (+.f64 (.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z))) (.f64 -1 (/.f64 x (.f64 (pow.f64 y 2) z)))))
(fma.f64 (/.f64 (.f64 x x) (pow.f64 y 3)) (sqrt.f64 (/.f64 1 (pow.f64 z 3))) (fma.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z)) (neg.f64 (/.f64 x (.f64 z (*.f64 y y))))))
(fma.f64 (/.f64 x (/.f64 (pow.f64 y 3) x)) (sqrt.f64 (/.f64 1 (pow.f64 z 3))) (-.f64 (/.f64 (sqrt.f64 (/.f64 1 z)) y) (/.f64 x (.f64 y (.f64 y z)))))
(-.f64 (fma.f64 (.f64 (/.f64 x (pow.f64 y 3)) x) (sqrt.f64 (/.f64 1 (pow.f64 z 3))) (/.f64 (sqrt.f64 (/.f64 1 z)) y)) (/.f64 x (.f64 y (*.f64 y z))))
(+.f64 (/.f64 (sqrt.f64 (/.f64 1 z)) y) (.f64 (/.f64 x (.f64 y y)) (+.f64 (/.f64 -1 z) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 z 3))) (/.f64 x y)))))
(+.f64 (.f64 (/.f64 (pow.f64 x 2) (pow.f64 y 3)) (sqrt.f64 (/.f64 1 (pow.f64 z 3)))) (+.f64 (.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z))) (+.f64 (.f64 -1 (/.f64 x (.f64 (pow.f64 y 2) z))) (.f64 -1 (/.f64 (pow.f64 x 3) (.f64 (pow.f64 y 4) (pow.f64 z 2)))))))
(fma.f64 (/.f64 (.f64 x x) (pow.f64 y 3)) (sqrt.f64 (/.f64 1 (pow.f64 z 3))) (fma.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z)) (fma.f64 -1 (/.f64 x (.f64 z (.f64 y y))) (neg.f64 (/.f64 (pow.f64 x 3) (.f64 (pow.f64 y 4) (*.f64 z z)))))))
(fma.f64 (/.f64 x (/.f64 (pow.f64 y 3) x)) (sqrt.f64 (/.f64 1 (pow.f64 z 3))) (-.f64 (-.f64 (/.f64 (sqrt.f64 (/.f64 1 z)) y) (/.f64 x (.f64 y (.f64 y z)))) (/.f64 (pow.f64 x 3) (.f64 z (.f64 z (pow.f64 y 4))))))
(-.f64 (-.f64 (fma.f64 (.f64 (/.f64 x (pow.f64 y 3)) x) (sqrt.f64 (/.f64 1 (pow.f64 z 3))) (/.f64 (sqrt.f64 (/.f64 1 z)) y)) (/.f64 (pow.f64 x 3) (.f64 (pow.f64 y 4) (.f64 z z)))) (/.f64 x (.f64 y (*.f64 y z))))
(+.f64 (/.f64 (sqrt.f64 (/.f64 1 z)) y) (-.f64 (.f64 (/.f64 x (.f64 y y)) (+.f64 (/.f64 -1 z) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 z 3))) (/.f64 x y)))) (/.f64 (pow.f64 x 3) (.f64 z (*.f64 z (pow.f64 y 4))))))
(/.f64 1 x)
(+.f64 (/.f64 1 x) (.f64 -1 (.f64 (/.f64 y (pow.f64 x 2)) (sqrt.f64 z))))
(+.f64 (/.f64 1 x) (neg.f64 (.f64 (/.f64 y (.f64 x x)) (sqrt.f64 z))))
(-.f64 (/.f64 1 x) (.f64 (/.f64 y (.f64 x x)) (sqrt.f64 z)))
(-.f64 (/.f64 1 x) (/.f64 (.f64 y (sqrt.f64 z)) (.f64 x x)))
(+.f64 (/.f64 (.f64 (pow.f64 y 2) z) (pow.f64 x 3)) (+.f64 (/.f64 1 x) (.f64 -1 (*.f64 (/.f64 y (pow.f64 x 2)) (sqrt.f64 z)))))
(+.f64 (+.f64 (/.f64 1 x) (neg.f64 (.f64 (/.f64 y (.f64 x x)) (sqrt.f64 z)))) (/.f64 (*.f64 y y) (/.f64 (pow.f64 x 3) z)))
(+.f64 (-.f64 (/.f64 1 x) (.f64 (/.f64 y (.f64 x x)) (sqrt.f64 z))) (/.f64 (.f64 y (.f64 y z)) (pow.f64 x 3)))
(-.f64 (fma.f64 (/.f64 (.f64 y y) (pow.f64 x 3)) z (/.f64 1 x)) (/.f64 (.f64 y (sqrt.f64 z)) (*.f64 x x)))
(+.f64 (/.f64 1 x) (.f64 (/.f64 y (.f64 x x)) (-.f64 (/.f64 (*.f64 y z) x) (sqrt.f64 z))))
(+.f64 (/.f64 (.f64 (pow.f64 y 2) z) (pow.f64 x 3)) (+.f64 (/.f64 1 x) (+.f64 (.f64 -1 (.f64 (/.f64 y (pow.f64 x 2)) (sqrt.f64 z))) (.f64 -1 (*.f64 (/.f64 (pow.f64 y 3) (pow.f64 x 4)) (sqrt.f64 (pow.f64 z 3)))))))
(+.f64 (/.f64 (.f64 y y) (/.f64 (pow.f64 x 3) z)) (+.f64 (/.f64 1 x) (fma.f64 -1 (.f64 (/.f64 y (.f64 x x)) (sqrt.f64 z)) (neg.f64 (.f64 (/.f64 (pow.f64 y 3) (pow.f64 x 4)) (sqrt.f64 (pow.f64 z 3)))))))
(+.f64 (/.f64 (.f64 y (.f64 y z)) (pow.f64 x 3)) (fma.f64 -1 (fma.f64 (/.f64 y (.f64 x x)) (sqrt.f64 z) (.f64 (/.f64 (pow.f64 y 3) (pow.f64 x 4)) (fabs.f64 (pow.f64 z 3/2)))) (/.f64 1 x)))
(-.f64 (fma.f64 (/.f64 (.f64 y y) (pow.f64 x 3)) z (/.f64 1 x)) (fma.f64 (/.f64 y (.f64 x x)) (sqrt.f64 z) (*.f64 (/.f64 (pow.f64 y 3) (pow.f64 x 4)) (pow.f64 z 3/2))))
(-.f64 (-.f64 (/.f64 1 x) (.f64 (/.f64 y (.f64 x x)) (sqrt.f64 z))) (.f64 (/.f64 (.f64 y y) (pow.f64 x 3)) (-.f64 (/.f64 (*.f64 y (pow.f64 z 3/2)) x) z)))
(/.f64 1 x)
(+.f64 (/.f64 1 x) (.f64 -1 (.f64 (/.f64 y (pow.f64 x 2)) (sqrt.f64 z))))
(+.f64 (/.f64 1 x) (neg.f64 (.f64 (/.f64 y (.f64 x x)) (sqrt.f64 z))))
(-.f64 (/.f64 1 x) (.f64 (/.f64 y (.f64 x x)) (sqrt.f64 z)))
(-.f64 (/.f64 1 x) (/.f64 (.f64 y (sqrt.f64 z)) (.f64 x x)))
(+.f64 (/.f64 (.f64 (pow.f64 y 2) z) (pow.f64 x 3)) (+.f64 (/.f64 1 x) (.f64 -1 (*.f64 (/.f64 y (pow.f64 x 2)) (sqrt.f64 z)))))
(+.f64 (+.f64 (/.f64 1 x) (neg.f64 (.f64 (/.f64 y (.f64 x x)) (sqrt.f64 z)))) (/.f64 (*.f64 y y) (/.f64 (pow.f64 x 3) z)))
(+.f64 (-.f64 (/.f64 1 x) (.f64 (/.f64 y (.f64 x x)) (sqrt.f64 z))) (/.f64 (.f64 y (.f64 y z)) (pow.f64 x 3)))
(-.f64 (fma.f64 (/.f64 (.f64 y y) (pow.f64 x 3)) z (/.f64 1 x)) (/.f64 (.f64 y (sqrt.f64 z)) (*.f64 x x)))
(+.f64 (/.f64 1 x) (.f64 (/.f64 y (.f64 x x)) (-.f64 (/.f64 (*.f64 y z) x) (sqrt.f64 z))))
(+.f64 (/.f64 (.f64 (pow.f64 y 2) z) (pow.f64 x 3)) (+.f64 (/.f64 1 x) (+.f64 (.f64 -1 (.f64 (/.f64 y (pow.f64 x 2)) (sqrt.f64 z))) (.f64 -1 (*.f64 (/.f64 (pow.f64 y 3) (pow.f64 x 4)) (sqrt.f64 (pow.f64 z 3)))))))
(+.f64 (/.f64 (.f64 y y) (/.f64 (pow.f64 x 3) z)) (+.f64 (/.f64 1 x) (fma.f64 -1 (.f64 (/.f64 y (.f64 x x)) (sqrt.f64 z)) (neg.f64 (.f64 (/.f64 (pow.f64 y 3) (pow.f64 x 4)) (sqrt.f64 (pow.f64 z 3)))))))
(+.f64 (/.f64 (.f64 y (.f64 y z)) (pow.f64 x 3)) (fma.f64 -1 (fma.f64 (/.f64 y (.f64 x x)) (sqrt.f64 z) (.f64 (/.f64 (pow.f64 y 3) (pow.f64 x 4)) (fabs.f64 (pow.f64 z 3/2)))) (/.f64 1 x)))
(-.f64 (fma.f64 (/.f64 (.f64 y y) (pow.f64 x 3)) z (/.f64 1 x)) (fma.f64 (/.f64 y (.f64 x x)) (sqrt.f64 z) (*.f64 (/.f64 (pow.f64 y 3) (pow.f64 x 4)) (pow.f64 z 3/2))))
(-.f64 (-.f64 (/.f64 1 x) (.f64 (/.f64 y (.f64 x x)) (sqrt.f64 z))) (.f64 (/.f64 (.f64 y y) (pow.f64 x 3)) (-.f64 (/.f64 (*.f64 y (pow.f64 z 3/2)) x) z)))
(/.f64 1 x)
(+.f64 (/.f64 1 x) (.f64 -1 (.f64 (/.f64 y (pow.f64 x 2)) (sqrt.f64 z))))
(+.f64 (/.f64 1 x) (neg.f64 (.f64 (/.f64 y (.f64 x x)) (sqrt.f64 z))))
(-.f64 (/.f64 1 x) (.f64 (/.f64 y (.f64 x x)) (sqrt.f64 z)))
(-.f64 (/.f64 1 x) (/.f64 (.f64 y (sqrt.f64 z)) (.f64 x x)))
(+.f64 (/.f64 (.f64 (pow.f64 y 2) z) (pow.f64 x 3)) (+.f64 (/.f64 1 x) (.f64 -1 (*.f64 (/.f64 y (pow.f64 x 2)) (sqrt.f64 z)))))
(+.f64 (+.f64 (/.f64 1 x) (neg.f64 (.f64 (/.f64 y (.f64 x x)) (sqrt.f64 z)))) (/.f64 (*.f64 y y) (/.f64 (pow.f64 x 3) z)))
(+.f64 (-.f64 (/.f64 1 x) (.f64 (/.f64 y (.f64 x x)) (sqrt.f64 z))) (/.f64 (.f64 y (.f64 y z)) (pow.f64 x 3)))
(-.f64 (fma.f64 (/.f64 (.f64 y y) (pow.f64 x 3)) z (/.f64 1 x)) (/.f64 (.f64 y (sqrt.f64 z)) (*.f64 x x)))
(+.f64 (/.f64 1 x) (.f64 (/.f64 y (.f64 x x)) (-.f64 (/.f64 (*.f64 y z) x) (sqrt.f64 z))))
(+.f64 (/.f64 (.f64 (pow.f64 y 2) z) (pow.f64 x 3)) (+.f64 (/.f64 1 x) (+.f64 (.f64 -1 (.f64 (/.f64 y (pow.f64 x 2)) (sqrt.f64 z))) (.f64 -1 (*.f64 (/.f64 (pow.f64 y 3) (pow.f64 x 4)) (sqrt.f64 (pow.f64 z 3)))))))
(+.f64 (/.f64 (.f64 y y) (/.f64 (pow.f64 x 3) z)) (+.f64 (/.f64 1 x) (fma.f64 -1 (.f64 (/.f64 y (.f64 x x)) (sqrt.f64 z)) (neg.f64 (.f64 (/.f64 (pow.f64 y 3) (pow.f64 x 4)) (sqrt.f64 (pow.f64 z 3)))))))
(+.f64 (/.f64 (.f64 y (.f64 y z)) (pow.f64 x 3)) (fma.f64 -1 (fma.f64 (/.f64 y (.f64 x x)) (sqrt.f64 z) (.f64 (/.f64 (pow.f64 y 3) (pow.f64 x 4)) (fabs.f64 (pow.f64 z 3/2)))) (/.f64 1 x)))
(-.f64 (fma.f64 (/.f64 (.f64 y y) (pow.f64 x 3)) z (/.f64 1 x)) (fma.f64 (/.f64 y (.f64 x x)) (sqrt.f64 z) (*.f64 (/.f64 (pow.f64 y 3) (pow.f64 x 4)) (pow.f64 z 3/2))))
(-.f64 (-.f64 (/.f64 1 x) (.f64 (/.f64 y (.f64 x x)) (sqrt.f64 z))) (.f64 (/.f64 (.f64 y y) (pow.f64 x 3)) (-.f64 (/.f64 (*.f64 y (pow.f64 z 3/2)) x) z)))
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z)))
(/.f64 (sqrt.f64 (/.f64 1 z)) y)
(+.f64 (.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z))) (.f64 -1 (/.f64 x (*.f64 (pow.f64 y 2) z))))
(fma.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z)) (neg.f64 (/.f64 x (.f64 z (.f64 y y)))))
(-.f64 (/.f64 (sqrt.f64 (/.f64 1 z)) y) (/.f64 x (.f64 y (.f64 y z))))
(-.f64 (/.f64 (sqrt.f64 (/.f64 1 z)) y) (/.f64 (/.f64 x (*.f64 y y)) z))
(+.f64 (.f64 (/.f64 (pow.f64 x 2) (pow.f64 y 3)) (sqrt.f64 (/.f64 1 (pow.f64 z 3)))) (+.f64 (.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z))) (.f64 -1 (/.f64 x (.f64 (pow.f64 y 2) z)))))
(fma.f64 (/.f64 (.f64 x x) (pow.f64 y 3)) (sqrt.f64 (/.f64 1 (pow.f64 z 3))) (fma.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z)) (neg.f64 (/.f64 x (.f64 z (*.f64 y y))))))
(fma.f64 (/.f64 x (/.f64 (pow.f64 y 3) x)) (sqrt.f64 (/.f64 1 (pow.f64 z 3))) (-.f64 (/.f64 (sqrt.f64 (/.f64 1 z)) y) (/.f64 x (.f64 y (.f64 y z)))))
(-.f64 (fma.f64 (.f64 (/.f64 x (pow.f64 y 3)) x) (sqrt.f64 (/.f64 1 (pow.f64 z 3))) (/.f64 (sqrt.f64 (/.f64 1 z)) y)) (/.f64 x (.f64 y (*.f64 y z))))
(+.f64 (/.f64 (sqrt.f64 (/.f64 1 z)) y) (.f64 (/.f64 x (.f64 y y)) (+.f64 (/.f64 -1 z) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 z 3))) (/.f64 x y)))))
(+.f64 (.f64 (/.f64 (pow.f64 x 2) (pow.f64 y 3)) (sqrt.f64 (/.f64 1 (pow.f64 z 3)))) (+.f64 (.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z))) (+.f64 (.f64 -1 (/.f64 x (.f64 (pow.f64 y 2) z))) (.f64 -1 (/.f64 (pow.f64 x 3) (.f64 (pow.f64 y 4) (pow.f64 z 2)))))))
(fma.f64 (/.f64 (.f64 x x) (pow.f64 y 3)) (sqrt.f64 (/.f64 1 (pow.f64 z 3))) (fma.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z)) (fma.f64 -1 (/.f64 x (.f64 z (.f64 y y))) (neg.f64 (/.f64 (pow.f64 x 3) (.f64 (pow.f64 y 4) (*.f64 z z)))))))
(fma.f64 (/.f64 x (/.f64 (pow.f64 y 3) x)) (sqrt.f64 (/.f64 1 (pow.f64 z 3))) (-.f64 (-.f64 (/.f64 (sqrt.f64 (/.f64 1 z)) y) (/.f64 x (.f64 y (.f64 y z)))) (/.f64 (pow.f64 x 3) (.f64 z (.f64 z (pow.f64 y 4))))))
(-.f64 (-.f64 (fma.f64 (.f64 (/.f64 x (pow.f64 y 3)) x) (sqrt.f64 (/.f64 1 (pow.f64 z 3))) (/.f64 (sqrt.f64 (/.f64 1 z)) y)) (/.f64 (pow.f64 x 3) (.f64 (pow.f64 y 4) (.f64 z z)))) (/.f64 x (.f64 y (*.f64 y z))))
(+.f64 (/.f64 (sqrt.f64 (/.f64 1 z)) y) (-.f64 (.f64 (/.f64 x (.f64 y y)) (+.f64 (/.f64 -1 z) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 z 3))) (/.f64 x y)))) (/.f64 (pow.f64 x 3) (.f64 z (*.f64 z (pow.f64 y 4))))))
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z)))
(/.f64 (sqrt.f64 (/.f64 1 z)) y)
(+.f64 (.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z))) (.f64 -1 (/.f64 x (*.f64 (pow.f64 y 2) z))))
(fma.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z)) (neg.f64 (/.f64 x (.f64 z (.f64 y y)))))
(-.f64 (/.f64 (sqrt.f64 (/.f64 1 z)) y) (/.f64 x (.f64 y (.f64 y z))))
(-.f64 (/.f64 (sqrt.f64 (/.f64 1 z)) y) (/.f64 (/.f64 x (*.f64 y y)) z))
(+.f64 (.f64 (/.f64 (pow.f64 x 2) (pow.f64 y 3)) (sqrt.f64 (/.f64 1 (pow.f64 z 3)))) (+.f64 (.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z))) (.f64 -1 (/.f64 x (.f64 (pow.f64 y 2) z)))))
(fma.f64 (/.f64 (.f64 x x) (pow.f64 y 3)) (sqrt.f64 (/.f64 1 (pow.f64 z 3))) (fma.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z)) (neg.f64 (/.f64 x (.f64 z (*.f64 y y))))))
(fma.f64 (/.f64 x (/.f64 (pow.f64 y 3) x)) (sqrt.f64 (/.f64 1 (pow.f64 z 3))) (-.f64 (/.f64 (sqrt.f64 (/.f64 1 z)) y) (/.f64 x (.f64 y (.f64 y z)))))
(-.f64 (fma.f64 (.f64 (/.f64 x (pow.f64 y 3)) x) (sqrt.f64 (/.f64 1 (pow.f64 z 3))) (/.f64 (sqrt.f64 (/.f64 1 z)) y)) (/.f64 x (.f64 y (*.f64 y z))))
(+.f64 (/.f64 (sqrt.f64 (/.f64 1 z)) y) (.f64 (/.f64 x (.f64 y y)) (+.f64 (/.f64 -1 z) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 z 3))) (/.f64 x y)))))
(+.f64 (.f64 (/.f64 (pow.f64 x 2) (pow.f64 y 3)) (sqrt.f64 (/.f64 1 (pow.f64 z 3)))) (+.f64 (.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z))) (+.f64 (.f64 -1 (/.f64 x (.f64 (pow.f64 y 2) z))) (.f64 -1 (/.f64 (pow.f64 x 3) (.f64 (pow.f64 y 4) (pow.f64 z 2)))))))
(fma.f64 (/.f64 (.f64 x x) (pow.f64 y 3)) (sqrt.f64 (/.f64 1 (pow.f64 z 3))) (fma.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z)) (fma.f64 -1 (/.f64 x (.f64 z (.f64 y y))) (neg.f64 (/.f64 (pow.f64 x 3) (.f64 (pow.f64 y 4) (*.f64 z z)))))))
(fma.f64 (/.f64 x (/.f64 (pow.f64 y 3) x)) (sqrt.f64 (/.f64 1 (pow.f64 z 3))) (-.f64 (-.f64 (/.f64 (sqrt.f64 (/.f64 1 z)) y) (/.f64 x (.f64 y (.f64 y z)))) (/.f64 (pow.f64 x 3) (.f64 z (.f64 z (pow.f64 y 4))))))
(-.f64 (-.f64 (fma.f64 (.f64 (/.f64 x (pow.f64 y 3)) x) (sqrt.f64 (/.f64 1 (pow.f64 z 3))) (/.f64 (sqrt.f64 (/.f64 1 z)) y)) (/.f64 (pow.f64 x 3) (.f64 (pow.f64 y 4) (.f64 z z)))) (/.f64 x (.f64 y (*.f64 y z))))
(+.f64 (/.f64 (sqrt.f64 (/.f64 1 z)) y) (-.f64 (.f64 (/.f64 x (.f64 y y)) (+.f64 (/.f64 -1 z) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 z 3))) (/.f64 x y)))) (/.f64 (pow.f64 x 3) (.f64 z (*.f64 z (pow.f64 y 4))))))
(/.f64 1 x)
(.f64 -1 (.f64 (pow.f64 y 2) z))
(neg.f64 (.f64 z (.f64 y y)))
(.f64 z (neg.f64 (.f64 y y)))
(.f64 z (.f64 y (neg.f64 y)))
(+.f64 (.f64 -1 (.f64 (pow.f64 y 2) z)) (pow.f64 x 2))
(fma.f64 -1 (.f64 z (.f64 y y)) (*.f64 x x))
(-.f64 (.f64 x x) (.f64 y (*.f64 y z)))
(fma.f64 z (.f64 y (neg.f64 y)) (.f64 x x))
(+.f64 (.f64 -1 (.f64 (pow.f64 y 2) z)) (pow.f64 x 2))
(fma.f64 -1 (.f64 z (.f64 y y)) (*.f64 x x))
(-.f64 (.f64 x x) (.f64 y (*.f64 y z)))
(fma.f64 z (.f64 y (neg.f64 y)) (.f64 x x))
(+.f64 (.f64 -1 (.f64 (pow.f64 y 2) z)) (pow.f64 x 2))
(fma.f64 -1 (.f64 z (.f64 y y)) (*.f64 x x))
(-.f64 (.f64 x x) (.f64 y (*.f64 y z)))
(fma.f64 z (.f64 y (neg.f64 y)) (.f64 x x))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (.f64 -1 (.f64 (pow.f64 y 2) z)) (pow.f64 x 2))
(fma.f64 -1 (.f64 z (.f64 y y)) (*.f64 x x))
(-.f64 (.f64 x x) (.f64 y (*.f64 y z)))
(fma.f64 z (.f64 y (neg.f64 y)) (.f64 x x))
(+.f64 (.f64 -1 (.f64 (pow.f64 y 2) z)) (pow.f64 x 2))
(fma.f64 -1 (.f64 z (.f64 y y)) (*.f64 x x))
(-.f64 (.f64 x x) (.f64 y (*.f64 y z)))
(fma.f64 z (.f64 y (neg.f64 y)) (.f64 x x))
(+.f64 (.f64 -1 (.f64 (pow.f64 y 2) z)) (pow.f64 x 2))
(fma.f64 -1 (.f64 z (.f64 y y)) (*.f64 x x))
(-.f64 (.f64 x x) (.f64 y (*.f64 y z)))
(fma.f64 z (.f64 y (neg.f64 y)) (.f64 x x))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (.f64 -1 (.f64 (pow.f64 y 2) z)) (pow.f64 x 2))
(fma.f64 -1 (.f64 z (.f64 y y)) (*.f64 x x))
(-.f64 (.f64 x x) (.f64 y (*.f64 y z)))
(fma.f64 z (.f64 y (neg.f64 y)) (.f64 x x))
(+.f64 (.f64 -1 (.f64 (pow.f64 y 2) z)) (pow.f64 x 2))
(fma.f64 -1 (.f64 z (.f64 y y)) (*.f64 x x))
(-.f64 (.f64 x x) (.f64 y (*.f64 y z)))
(fma.f64 z (.f64 y (neg.f64 y)) (.f64 x x))
(+.f64 (.f64 -1 (.f64 (pow.f64 y 2) z)) (pow.f64 x 2))
(fma.f64 -1 (.f64 z (.f64 y y)) (*.f64 x x))
(-.f64 (.f64 x x) (.f64 y (*.f64 y z)))
(fma.f64 z (.f64 y (neg.f64 y)) (.f64 x x))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (.f64 -1 (.f64 (pow.f64 y 2) z)) (pow.f64 x 2))
(fma.f64 -1 (.f64 z (.f64 y y)) (*.f64 x x))
(-.f64 (.f64 x x) (.f64 y (*.f64 y z)))
(fma.f64 z (.f64 y (neg.f64 y)) (.f64 x x))
(+.f64 (.f64 -1 (.f64 (pow.f64 y 2) z)) (pow.f64 x 2))
(fma.f64 -1 (.f64 z (.f64 y y)) (*.f64 x x))
(-.f64 (.f64 x x) (.f64 y (*.f64 y z)))
(fma.f64 z (.f64 y (neg.f64 y)) (.f64 x x))
(+.f64 (.f64 -1 (.f64 (pow.f64 y 2) z)) (pow.f64 x 2))
(fma.f64 -1 (.f64 z (.f64 y y)) (*.f64 x x))
(-.f64 (.f64 x x) (.f64 y (*.f64 y z)))
(fma.f64 z (.f64 y (neg.f64 y)) (.f64 x x))
(.f64 -1 (.f64 (pow.f64 y 2) z))
(neg.f64 (.f64 z (.f64 y y)))
(.f64 z (neg.f64 (.f64 y y)))
(.f64 z (.f64 y (neg.f64 y)))
(+.f64 (.f64 -1 (.f64 (pow.f64 y 2) z)) (pow.f64 x 2))
(fma.f64 -1 (.f64 z (.f64 y y)) (*.f64 x x))
(-.f64 (.f64 x x) (.f64 y (*.f64 y z)))
(fma.f64 z (.f64 y (neg.f64 y)) (.f64 x x))
(+.f64 (.f64 -1 (.f64 (pow.f64 y 2) z)) (pow.f64 x 2))
(fma.f64 -1 (.f64 z (.f64 y y)) (*.f64 x x))
(-.f64 (.f64 x x) (.f64 y (*.f64 y z)))
(fma.f64 z (.f64 y (neg.f64 y)) (.f64 x x))
(+.f64 (.f64 -1 (.f64 (pow.f64 y 2) z)) (pow.f64 x 2))
(fma.f64 -1 (.f64 z (.f64 y y)) (*.f64 x x))
(-.f64 (.f64 x x) (.f64 y (*.f64 y z)))
(fma.f64 z (.f64 y (neg.f64 y)) (.f64 x x))
(.f64 -1 (.f64 (pow.f64 y 2) z))
(neg.f64 (.f64 z (.f64 y y)))
(.f64 z (neg.f64 (.f64 y y)))
(.f64 z (.f64 y (neg.f64 y)))
(+.f64 (.f64 -1 (.f64 (pow.f64 y 2) z)) (pow.f64 x 2))
(fma.f64 -1 (.f64 z (.f64 y y)) (*.f64 x x))
(-.f64 (.f64 x x) (.f64 y (*.f64 y z)))
(fma.f64 z (.f64 y (neg.f64 y)) (.f64 x x))
(+.f64 (.f64 -1 (.f64 (pow.f64 y 2) z)) (pow.f64 x 2))
(fma.f64 -1 (.f64 z (.f64 y y)) (*.f64 x x))
(-.f64 (.f64 x x) (.f64 y (*.f64 y z)))
(fma.f64 z (.f64 y (neg.f64 y)) (.f64 x x))
(+.f64 (.f64 -1 (.f64 (pow.f64 y 2) z)) (pow.f64 x 2))
(fma.f64 -1 (.f64 z (.f64 y y)) (*.f64 x x))
(-.f64 (.f64 x x) (.f64 y (*.f64 y z)))
(fma.f64 z (.f64 y (neg.f64 y)) (.f64 x x))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (.f64 -1 (.f64 (pow.f64 y 2) z)) (pow.f64 x 2))
(fma.f64 -1 (.f64 z (.f64 y y)) (*.f64 x x))
(-.f64 (.f64 x x) (.f64 y (*.f64 y z)))
(fma.f64 z (.f64 y (neg.f64 y)) (.f64 x x))
(+.f64 (.f64 -1 (.f64 (pow.f64 y 2) z)) (pow.f64 x 2))
(fma.f64 -1 (.f64 z (.f64 y y)) (*.f64 x x))
(-.f64 (.f64 x x) (.f64 y (*.f64 y z)))
(fma.f64 z (.f64 y (neg.f64 y)) (.f64 x x))
(+.f64 (.f64 -1 (.f64 (pow.f64 y 2) z)) (pow.f64 x 2))
(fma.f64 -1 (.f64 z (.f64 y y)) (*.f64 x x))
(-.f64 (.f64 x x) (.f64 y (*.f64 y z)))
(fma.f64 z (.f64 y (neg.f64 y)) (.f64 x x))
(.f64 -1 (.f64 (pow.f64 y 2) z))
(neg.f64 (.f64 z (.f64 y y)))
(.f64 z (neg.f64 (.f64 y y)))
(.f64 z (.f64 y (neg.f64 y)))
(+.f64 (.f64 -1 (.f64 (pow.f64 y 2) z)) (pow.f64 x 2))
(fma.f64 -1 (.f64 z (.f64 y y)) (*.f64 x x))
(-.f64 (.f64 x x) (.f64 y (*.f64 y z)))
(fma.f64 z (.f64 y (neg.f64 y)) (.f64 x x))
(+.f64 (.f64 -1 (.f64 (pow.f64 y 2) z)) (pow.f64 x 2))
(fma.f64 -1 (.f64 z (.f64 y y)) (*.f64 x x))
(-.f64 (.f64 x x) (.f64 y (*.f64 y z)))
(fma.f64 z (.f64 y (neg.f64 y)) (.f64 x x))
(+.f64 (.f64 -1 (.f64 (pow.f64 y 2) z)) (pow.f64 x 2))
(fma.f64 -1 (.f64 z (.f64 y y)) (*.f64 x x))
(-.f64 (.f64 x x) (.f64 y (*.f64 y z)))
(fma.f64 z (.f64 y (neg.f64 y)) (.f64 x x))
(.f64 -1 (.f64 (pow.f64 y 2) z))
(neg.f64 (.f64 z (.f64 y y)))
(.f64 z (neg.f64 (.f64 y y)))
(.f64 z (.f64 y (neg.f64 y)))
(+.f64 (.f64 -1 (.f64 (pow.f64 y 2) z)) (pow.f64 x 2))
(fma.f64 -1 (.f64 z (.f64 y y)) (*.f64 x x))
(-.f64 (.f64 x x) (.f64 y (*.f64 y z)))
(fma.f64 z (.f64 y (neg.f64 y)) (.f64 x x))
(+.f64 (.f64 -1 (.f64 (pow.f64 y 2) z)) (pow.f64 x 2))
(fma.f64 -1 (.f64 z (.f64 y y)) (*.f64 x x))
(-.f64 (.f64 x x) (.f64 y (*.f64 y z)))
(fma.f64 z (.f64 y (neg.f64 y)) (.f64 x x))
(+.f64 (.f64 -1 (.f64 (pow.f64 y 2) z)) (pow.f64 x 2))
(fma.f64 -1 (.f64 z (.f64 y y)) (*.f64 x x))
(-.f64 (.f64 x x) (.f64 y (*.f64 y z)))
(fma.f64 z (.f64 y (neg.f64 y)) (.f64 x x))

localize37.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (pow.f64 (cbrt.f64 (*.f64 y (sqrt.f64 z))) 3))
	0.2b	(*.f64 y (sqrt.f64 z))
✓	0.6b	(pow.f64 (cbrt.f64 (*.f64 y (sqrt.f64 z))) 3)
✓	4.2b	(cbrt.f64 (*.f64 y (sqrt.f64 z)))

Compiler

Compiled 52 to 24 computations (53.8% saved)

series82.0ms (1.3%)

Counts

3 → 51

Calls

21 calls:

Time	Variable		Point	Expression
32.0ms	z	@	0	(cbrt.f64 (*.f64 y (sqrt.f64 z)))
12.0ms	z	@	inf	(cbrt.f64 (*.f64 y (sqrt.f64 z)))
12.0ms	z	@	inf	(pow.f64 (cbrt.f64 (*.f64 y (sqrt.f64 z))) 3)
4.0ms	x	@	0	(+.f64 x (pow.f64 (cbrt.f64 (*.f64 y (sqrt.f64 z))) 3))
3.0ms	y	@	-inf	(pow.f64 (cbrt.f64 (*.f64 y (sqrt.f64 z))) 3)

rewrite75.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

957×	`pow1_binary64`
896×	`add-log-exp_binary64`
896×	`log1p-expm1-u_binary64`
896×	`expm1-log1p-u_binary64`
98×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	23
1	217	21
2	2515	21

Stop Event

1×	node limit

Counts

3 → 91

Calls

Call 1

Inputs
(cbrt.f64 (*.f64 y (sqrt.f64 z)))
(pow.f64 (cbrt.f64 (*.f64 y (sqrt.f64 z))) 3)
(+.f64 x (pow.f64 (cbrt.f64 (*.f64 y (sqrt.f64 z))) 3))

Outputs

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

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

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

simplify141.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

756×	`sqr-pow_binary64`
712×	`fma-neg_binary64`
705×	`fma-def_binary64`
508×	`unswap-sqr_binary64`
380×	`*-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	31	488
1	83	390
2	174	382
3	389	382
4	1295	382
5	2322	382
6	2460	382
7	2719	382
8	3030	382
9	3393	382
10	4378	382
11	5227	382
12	6274	382
13	7478	382

Stop Event

1×	node limit

Counts

142 → 102

Calls

Call 1

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

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

eval170.0ms (2.7%)

Compiler: Compiled 12465 to 4812 computations (61.4% saved)

prune107.0ms (1.7%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	494	8	502
Fresh	2	2	4
Picked	1	0	1
Done	2	3	5
Total	499	13	512

Error

0.0b

Counts

512 → 13

Alt Table

Click to see full alt table

Status	Error	Program
	32.2b	(.f64 (/.f64 1 2) (/.f64 1 (/.f64 (-.f64 x (.f64 y (sqrt.f64 z))) (-.f64 (.f64 x x) (.f64 y (*.f64 y z))))))
▶	33.6b	(*.f64 (/.f64 1 2) (/.f64 1 (/.f64 (sqrt.f64 (/.f64 1 z)) y)))
▶	29.8b	(*.f64 (/.f64 1 2) (/.f64 1 (/.f64 1 x)))
	33.7b	(.f64 (/.f64 1 2) (/.f64 1 (.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z)))))
▶	0.3b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (pow.f64 z 1/4) (*.f64 (pow.f64 z 1/4) y))))
	26.5b	(.f64 (/.f64 1 2) (+.f64 x (sqrt.f64 (.f64 y (*.f64 y z)))))
✓	0.1b	(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
	36.0b	(*.f64 1/2 (pow.f64 (sqrt.f64 (fma.f64 y (sqrt.f64 z) x)) 2))
▶	37.2b	(.f64 1/2 (/.f64 (-.f64 (.f64 z (.f64 y y)) (.f64 x x)) (-.f64 (*.f64 y (sqrt.f64 z)) x)))
✓	0.1b	(.f64 1/2 (+.f64 (.f64 y (sqrt.f64 z)) x))
▶	29.9b	(.f64 1/2 (+.f64 (sqrt.f64 (.f64 z (*.f64 y y))) x))
	33.5b	(.f64 1/2 (.f64 y (sqrt.f64 z)))
✓	29.7b	(*.f64 1/2 x)

Compiler

Compiled 343 to 260 computations (24.2% saved)

localize47.0ms (0.7%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (.f64 (pow.f64 z 1/4) (.f64 (pow.f64 z 1/4) y)))
✓	0.3b	(*.f64 (pow.f64 z 1/4) y)
✓	0.3b	(.f64 (pow.f64 z 1/4) (.f64 (pow.f64 z 1/4) y))

Compiler

Compiled 55 to 38 computations (30.9% saved)

series79.0ms (1.2%)

Counts

3 → 61

Calls

21 calls:

Time	Variable		Point	Expression
45.0ms	y	@	0	(*.f64 (pow.f64 z 1/4) y)
16.0ms	z	@	-inf	(*.f64 (pow.f64 z 1/4) y)
9.0ms	z	@	0	(*.f64 (pow.f64 z 1/4) y)
1.0ms	z	@	inf	(*.f64 (pow.f64 z 1/4) y)
1.0ms	z	@	0	(.f64 (pow.f64 z 1/4) (.f64 (pow.f64 z 1/4) y))

rewrite77.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

939×	`prod-diff_binary64`
471×	`log-prod_binary64`
328×	`pow-prod-down_binary64`
255×	`fma-def_binary64`
251×	`pow2_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	36
1	197	20
2	2565	20

Stop Event

1×	node limit

Counts

3 → 98

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 y (sqrt.f64 z)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 y) (sqrt.f64 z))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 y) (sqrt.f64 z)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 y) (sqrt.f64 z)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 y) (sqrt.f64 z)))))))) (#(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 (*.f64 z (*.f64 y y)) 1/2)))) (#(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 pow.f64 (*.f64 (sqrt.f64 y) (pow.f64 z 1/4)) 2)))) (#(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 expm1.f64 (log1p.f64 (*.f64 y (sqrt.f64 z))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 y (sqrt.f64 z))))))) (#(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 +.f64 0 (*.f64 (pow.f64 z 1/4) y))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 y) (pow.f64 z 1/4))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 y) (pow.f64 z 1/4)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 y) (pow.f64 z 1/4)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 y) (pow.f64 z 1/4)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 z 1/4) y))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 z 1/4) y) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 y (*.f64 y (sqrt.f64 z))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 y 3) (pow.f64 z 3/4)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (cbrt.f64 y) (pow.f64 z 1/12)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (pow.f64 z 1/4) y)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 y (*.f64 y (sqrt.f64 z))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 y) (pow.f64 z 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (pow.f64 z 1/4) y))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 y 3) (pow.f64 z 3/4)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (pow.f64 z 1/4) y)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (pow.f64 z 1/4) y)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (pow.f64 z 1/4) y)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 z 1/4) y)) 1))))))

((#(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 (fma.f64 y (sqrt.f64 z) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 y (sqrt.f64 z) x))))) (#(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 (fma.f64 (pow.f64 z 3/2) (pow.f64 y 3) (pow.f64 x 3)) (/.f64 1 (fma.f64 (*.f64 y (sqrt.f64 z)) (fma.f64 y (sqrt.f64 z) (neg.f64 x)) (*.f64 x 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 (*.f64 y (sqrt.f64 z)) (fma.f64 y (sqrt.f64 z) (neg.f64 x)) (*.f64 x x)) (fma.f64 (pow.f64 z 3/2) (pow.f64 y 3) (pow.f64 x 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 (fma.f64 (pow.f64 z 3/2) (pow.f64 y 3) (pow.f64 x 3)) (fma.f64 (*.f64 y (sqrt.f64 z)) (fma.f64 y (sqrt.f64 z) (neg.f64 x)) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 (pow.f64 z 3/2) (pow.f64 y 3) (pow.f64 x 3)) (fma.f64 z (*.f64 y y) (-.f64 (*.f64 x x) (*.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 x (*.f64 y (sqrt.f64 z))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (fma.f64 (pow.f64 z 3/2) (pow.f64 y 3) (pow.f64 x 3))) (neg.f64 (fma.f64 (*.f64 y (sqrt.f64 z)) (fma.f64 y (sqrt.f64 z) (neg.f64 x)) (*.f64 x 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 (fma.f64 z (*.f64 y y) (neg.f64 (*.f64 x x))) (fma.f64 y (sqrt.f64 z) (neg.f64 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) 2) 1/2)))) (#(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 pow.f64 (/.f64 (fma.f64 (*.f64 y (sqrt.f64 z)) (fma.f64 y (sqrt.f64 z) (neg.f64 x)) (*.f64 x x)) (fma.f64 (pow.f64 z 3/2) (pow.f64 y 3) (pow.f64 x 3))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 x (*.f64 y (sqrt.f64 z))) (-.f64 (*.f64 x x) (*.f64 z (*.f64 y y)))) -1)))) (#(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 log.f64 (*.f64 (+.f64 1 (expm1.f64 (*.f64 y (sqrt.f64 z)))) (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (pow.f64 (exp.f64 y) (sqrt.f64 z)) (+.f64 1 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (*.f64 y (sqrt.f64 z)))) (+.f64 1 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 x)) (pow.f64 (exp.f64 y) (sqrt.f64 z))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 x) (+.f64 1 (expm1.f64 (*.f64 y (sqrt.f64 z))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 x)) (+.f64 1 (expm1.f64 (*.f64 y (sqrt.f64 z))))))))) (#(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 expm1.f64 (log1p.f64 (fma.f64 y (sqrt.f64 z) x)))))) (#(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 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 fma.f64 (pow.f64 z 1/4) (*.f64 (pow.f64 z 1/4) y) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 y (sqrt.f64 z) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (pow.f64 z 1/4) y) (pow.f64 z 1/4) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 y (sqrt.f64 z)) 1 x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x 1 (*.f64 y (sqrt.f64 z)))))) (#(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 (sqrt.f64 z) y x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 x) (pow.f64 (cbrt.f64 x) 2) (*.f64 y (sqrt.f64 z)))))) (#(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 (cbrt.f64 (*.f64 y (*.f64 y (sqrt.f64 z)))) (*.f64 (*.f64 (cbrt.f64 y) (pow.f64 z 1/12)) (pow.f64 z 1/4)) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 y (sqrt.f64 z))) (cbrt.f64 (*.f64 z (*.f64 y y))) x)))) (#(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 (cbrt.f64 (sqrt.f64 z)) (*.f64 (pow.f64 z 1/12) (*.f64 (pow.f64 z 1/4) y)) 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 fma.f64 (sqrt.f64 (*.f64 (pow.f64 z 1/4) y)) (*.f64 (sqrt.f64 (*.f64 (pow.f64 z 1/4) y)) (pow.f64 z 1/4)) x)))) (#(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 (pow.f64 z 1/8) (*.f64 (pow.f64 z 1/8) (*.f64 (pow.f64 z 1/4) y)) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (sqrt.f64 z) 1) y x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (pow.f64 z 1/4) (cbrt.f64 (*.f64 y (*.f64 y (sqrt.f64 z))))) (*.f64 (cbrt.f64 y) (pow.f64 z 1/12)) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (pow.f64 z 1/4) (sqrt.f64 (*.f64 (pow.f64 z 1/4) y))) (sqrt.f64 (*.f64 (pow.f64 z 1/4) y)) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 (pow.f64 z 1/4) y) (cbrt.f64 (sqrt.f64 z))) (pow.f64 z 1/12) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 (pow.f64 z 1/4) y) (pow.f64 z 1/8)) (pow.f64 z 1/8) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (sqrt.f64 z) (pow.f64 (cbrt.f64 y) 2)) (cbrt.f64 y) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (*.f64 z y) 1/2) (sqrt.f64 y) x)))))

simplify62.0ms (1%)

Algorithm

1×	egg-herbie

Rules

674×	`fma-def_binary64`
634×	`div-sub_binary64`
610×	`fma-neg_binary64`
362×	`times-frac_binary64`
232×	`unswap-sqr_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	388
1	49	388
2	99	388
3	213	388
4	593	388
5	1744	388
6	5484	388

Stop Event

1×	node limit

Counts

159 → 104

Calls

Call 1

Inputs
(*.f64 y (sqrt.f64 z))
(*.f64 y (sqrt.f64 z))
(*.f64 y (sqrt.f64 z))
(*.f64 y (sqrt.f64 z))
(*.f64 y (sqrt.f64 z))
(*.f64 y (sqrt.f64 z))
(*.f64 y (sqrt.f64 z))
(*.f64 y (sqrt.f64 z))
(*.f64 y (sqrt.f64 z))
(*.f64 y (sqrt.f64 z))
(*.f64 y (sqrt.f64 z))
(*.f64 y (sqrt.f64 z))
(.f64 (pow.f64 (.f64 1 z) 1/4) y)
(.f64 (pow.f64 (.f64 1 z) 1/4) y)
(.f64 (pow.f64 (.f64 1 z) 1/4) y)
(.f64 (pow.f64 (.f64 1 z) 1/4) y)
(.f64 (pow.f64 (.f64 1 z) 1/4) y)
(.f64 (pow.f64 (.f64 1 z) 1/4) y)
(.f64 (pow.f64 (.f64 1 z) 1/4) y)
(.f64 (pow.f64 (.f64 1 z) 1/4) y)
(.f64 y (exp.f64 (.f64 1/4 (+.f64 (log.f64 -1) (*.f64 -1 (log.f64 (/.f64 -1 z)))))))
(.f64 y (exp.f64 (.f64 1/4 (+.f64 (log.f64 -1) (*.f64 -1 (log.f64 (/.f64 -1 z)))))))
(.f64 y (exp.f64 (.f64 1/4 (+.f64 (log.f64 -1) (*.f64 -1 (log.f64 (/.f64 -1 z)))))))
(.f64 y (exp.f64 (.f64 1/4 (+.f64 (log.f64 -1) (*.f64 -1 (log.f64 (/.f64 -1 z)))))))
(.f64 (pow.f64 (.f64 1 z) 1/4) y)
(.f64 (pow.f64 (.f64 1 z) 1/4) y)
(.f64 (pow.f64 (.f64 1 z) 1/4) y)
(.f64 (pow.f64 (.f64 1 z) 1/4) y)
(.f64 (pow.f64 (.f64 1 z) 1/4) y)
(.f64 (pow.f64 (.f64 1 z) 1/4) y)
(.f64 (pow.f64 (.f64 1 z) 1/4) y)
(.f64 (pow.f64 (.f64 1 z) 1/4) y)
(.f64 (pow.f64 (.f64 1 z) 1/4) y)
(.f64 (pow.f64 (.f64 1 z) 1/4) y)
(.f64 (pow.f64 (.f64 1 z) 1/4) y)
(.f64 (pow.f64 (.f64 1 z) 1/4) y)
(*.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
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)

Outputs
(*.f64 y (sqrt.f64 z))
(*.f64 y (sqrt.f64 z))
(*.f64 y (sqrt.f64 z))
(*.f64 y (sqrt.f64 z))
(*.f64 y (sqrt.f64 z))
(*.f64 y (sqrt.f64 z))
(*.f64 y (sqrt.f64 z))
(*.f64 y (sqrt.f64 z))
(*.f64 y (sqrt.f64 z))
(*.f64 y (sqrt.f64 z))
(*.f64 y (sqrt.f64 z))
(*.f64 y (sqrt.f64 z))
(.f64 (pow.f64 (.f64 1 z) 1/4) y)
(*.f64 y (pow.f64 z 1/4))
(.f64 (pow.f64 (.f64 1 z) 1/4) y)
(*.f64 y (pow.f64 z 1/4))
(.f64 (pow.f64 (.f64 1 z) 1/4) y)
(*.f64 y (pow.f64 z 1/4))
(.f64 (pow.f64 (.f64 1 z) 1/4) y)
(*.f64 y (pow.f64 z 1/4))
(.f64 (pow.f64 (.f64 1 z) 1/4) y)
(*.f64 y (pow.f64 z 1/4))
(.f64 (pow.f64 (.f64 1 z) 1/4) y)
(*.f64 y (pow.f64 z 1/4))
(.f64 (pow.f64 (.f64 1 z) 1/4) y)
(*.f64 y (pow.f64 z 1/4))
(.f64 (pow.f64 (.f64 1 z) 1/4) y)
(*.f64 y (pow.f64 z 1/4))
(.f64 y (exp.f64 (.f64 1/4 (+.f64 (log.f64 -1) (*.f64 -1 (log.f64 (/.f64 -1 z)))))))
(*.f64 y (pow.f64 z 1/4))
(.f64 y (exp.f64 (.f64 1/4 (+.f64 (log.f64 -1) (*.f64 -1 (log.f64 (/.f64 -1 z)))))))
(*.f64 y (pow.f64 z 1/4))
(.f64 y (exp.f64 (.f64 1/4 (+.f64 (log.f64 -1) (*.f64 -1 (log.f64 (/.f64 -1 z)))))))
(*.f64 y (pow.f64 z 1/4))
(.f64 y (exp.f64 (.f64 1/4 (+.f64 (log.f64 -1) (*.f64 -1 (log.f64 (/.f64 -1 z)))))))
(*.f64 y (pow.f64 z 1/4))
(.f64 (pow.f64 (.f64 1 z) 1/4) y)
(*.f64 y (pow.f64 z 1/4))
(.f64 (pow.f64 (.f64 1 z) 1/4) y)
(*.f64 y (pow.f64 z 1/4))
(.f64 (pow.f64 (.f64 1 z) 1/4) y)
(*.f64 y (pow.f64 z 1/4))
(.f64 (pow.f64 (.f64 1 z) 1/4) y)
(*.f64 y (pow.f64 z 1/4))
(.f64 (pow.f64 (.f64 1 z) 1/4) y)
(*.f64 y (pow.f64 z 1/4))
(.f64 (pow.f64 (.f64 1 z) 1/4) y)
(*.f64 y (pow.f64 z 1/4))
(.f64 (pow.f64 (.f64 1 z) 1/4) y)
(*.f64 y (pow.f64 z 1/4))
(.f64 (pow.f64 (.f64 1 z) 1/4) y)
(*.f64 y (pow.f64 z 1/4))
(.f64 (pow.f64 (.f64 1 z) 1/4) y)
(*.f64 y (pow.f64 z 1/4))
(.f64 (pow.f64 (.f64 1 z) 1/4) y)
(*.f64 y (pow.f64 z 1/4))
(.f64 (pow.f64 (.f64 1 z) 1/4) y)
(*.f64 y (pow.f64 z 1/4))
(.f64 (pow.f64 (.f64 1 z) 1/4) y)
(*.f64 y (pow.f64 z 1/4))
(*.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
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)

localize12.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1 (/.f64 1 x))

Compiler

Compiled 26 to 22 computations (15.4% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite46.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

348×	`pow1_binary64`
336×	`add-sqr-sqrt_binary64`
328×	`*-un-lft-identity_binary64`
323×	`add-log-exp_binary64`
323×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	1
1	105	1
2	997	1

Stop Event

1×	node limit

Counts

1 → 47

Calls

Call 1

Inputs
(/.f64 1 (/.f64 1 x))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 x)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 x))) (log.f64 (sqrt.f64 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 2) x))) (log.f64 (cbrt.f64 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 x)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 x) (cbrt.f64 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 x x)) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 x x)) (neg.f64 (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (neg.f64 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x 1/4) (sqrt.f64 (pow.f64 x 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (cbrt.f64 (*.f64 x x))) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 x 5/2)) (pow.f64 x 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (*.f64 x (cbrt.f64 x)) 2)) (cbrt.f64 (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 x) 5)) (pow.f64 x 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 x 3/2)) (pow.f64 x 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (*.f64 x (cbrt.f64 x)) 2) 1/3) (cbrt.f64 (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 x 5/2) 1/3) (pow.f64 x 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 x 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (log.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x x) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x -2) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x -3) -1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 x) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (cbrt.f64 x)) -3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 x) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x -1/2) -2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 -1) (neg.f64 (log.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 x)) 2)) (cbrt.f64 (log.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 x))) (sqrt.f64 (log.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 x)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 x 3))))) (#(struct:change #<rule egg-rr> (2) ((x . x)))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 x)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 x)) 2))))))

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1	12

Stop Event

1×

saturated

Counts

59 → 48

Calls

Call 1

Inputs
x
x
x
x
x
x
x
x
x
x
x
x

Outputs
x
x
x
x
x
x
x
x
x
x
x
x

localize12.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (sqrt.f64 (.f64 z (.f64 y y))) x)
	9.3b	(.f64 z (.f64 y y))
	27.4b	(sqrt.f64 (.f64 z (.f64 y y)))

Compiler

Compiled 39 to 10 computations (74.4% saved)

series3.0ms (0%)

Counts

1 → 25

Calls

9 calls:

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

rewrite59.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

877×	`pow1_binary64`
814×	`add-log-exp_binary64`
814×	`log1p-expm1-u_binary64`
814×	`expm1-log1p-u_binary64`
792×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	171	7
2	2324	7

Stop Event

1×	node limit

Counts

1 → 34

Calls

Call 1

Inputs
(+.f64 (sqrt.f64 (.f64 z (.f64 y y))) x)

Outputs

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

simplify28.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

106×	`fma-def_binary64`
82×	`fma-neg_binary64`
29×	`cancel-sign-sub-inv_binary64`
19×	`sub-neg_binary64`
16×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	159
1	19	156
2	36	156
3	49	156
4	61	156
5	98	156
6	155	156
7	206	156
8	277	156
9	372	156
10	448	156
11	462	156
12	464	156

Stop Event

1×

saturated

Counts

59 → 42

Calls

Call 1

Inputs
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 -1 (.f64 y (sqrt.f64 z)))
(+.f64 (.f64 -1 (.f64 y (sqrt.f64 z))) x)
(+.f64 (.f64 -1 (.f64 y (sqrt.f64 z))) x)
(+.f64 (.f64 -1 (.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
(+.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)

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

localize19.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (/.f64 1 z))
✓	0.3b	(/.f64 (sqrt.f64 (/.f64 1 z)) y)
✓	0.3b	(/.f64 1 (/.f64 (sqrt.f64 (/.f64 1 z)) y))

Compiler

Compiled 43 to 33 computations (23.3% saved)

series8.0ms (0.1%)

Counts

3 → 24

Calls

15 calls:

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

rewrite74.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

796×	`pow1_binary64`
737×	`add-log-exp_binary64`
737×	`log1p-expm1-u_binary64`
737×	`expm1-log1p-u_binary64`
717×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	27
1	170	17
2	2192	17

Stop Event

1×	node limit

Counts

3 → 94

Calls

Call 1

Inputs
(/.f64 1 (/.f64 (sqrt.f64 (/.f64 1 z)) y))
(/.f64 (sqrt.f64 (/.f64 1 z)) y)
(sqrt.f64 (/.f64 1 z))

Outputs

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

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

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

simplify18.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

4×	`associate-/l*_binary64`
3×	`*-commutative_binary64`
3×	`associate-*l/_binary64`
3×	`associate-/r*_binary64`
3×	`*-lft-identity_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	216
1	16	180
2	21	180
3	32	180
4	32	180
5	33	180
6	36	180
7	43	180
8	43	180

Stop Event

1×

saturated

Counts

118 → 96

Calls

Call 1

Inputs
(*.f64 y (sqrt.f64 z))
(*.f64 y (sqrt.f64 z))
(*.f64 y (sqrt.f64 z))
(*.f64 y (sqrt.f64 z))
(*.f64 y (sqrt.f64 z))
(*.f64 y (sqrt.f64 z))
(*.f64 y (sqrt.f64 z))
(*.f64 y (sqrt.f64 z))
(*.f64 y (sqrt.f64 z))
(*.f64 y (sqrt.f64 z))
(*.f64 y (sqrt.f64 z))
(*.f64 y (sqrt.f64 z))
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z)))
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z)))
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z)))
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z)))
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z)))
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z)))
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z)))
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z)))
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z)))
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z)))
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z)))
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z)))

Outputs
(*.f64 y (sqrt.f64 z))
(*.f64 y (sqrt.f64 z))
(*.f64 y (sqrt.f64 z))
(*.f64 y (sqrt.f64 z))
(*.f64 y (sqrt.f64 z))
(*.f64 y (sqrt.f64 z))
(*.f64 y (sqrt.f64 z))
(*.f64 y (sqrt.f64 z))
(*.f64 y (sqrt.f64 z))
(*.f64 y (sqrt.f64 z))
(*.f64 y (sqrt.f64 z))
(*.f64 y (sqrt.f64 z))
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z)))
(/.f64 (sqrt.f64 (/.f64 1 z)) y)
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z)))
(/.f64 (sqrt.f64 (/.f64 1 z)) y)
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z)))
(/.f64 (sqrt.f64 (/.f64 1 z)) y)
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z)))
(/.f64 (sqrt.f64 (/.f64 1 z)) y)
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z)))
(/.f64 (sqrt.f64 (/.f64 1 z)) y)
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z)))
(/.f64 (sqrt.f64 (/.f64 1 z)) y)
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z)))
(/.f64 (sqrt.f64 (/.f64 1 z)) y)
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z)))
(/.f64 (sqrt.f64 (/.f64 1 z)) y)
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z)))
(/.f64 (sqrt.f64 (/.f64 1 z)) y)
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z)))
(/.f64 (sqrt.f64 (/.f64 1 z)) y)
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z)))
(/.f64 (sqrt.f64 (/.f64 1 z)) y)
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z)))
(/.f64 (sqrt.f64 (/.f64 1 z)) y)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(*.f64 y (sqrt.f64 z))
✓	2.7b	(-.f64 (.f64 z (.f64 y y)) (*.f64 x x))
	9.3b	(.f64 z (.f64 y y))
✓	30.2b	(/.f64 (-.f64 (.f64 z (.f64 y y)) (.f64 x x)) (-.f64 (.f64 y (sqrt.f64 z)) x))

Compiler

Compiled 73 to 14 computations (80.8% saved)

series15.0ms (0.2%)

Counts

2 → 61

Calls

18 calls:

Time	Variable		Point	Expression
3.0ms	z	@	-inf	(/.f64 (-.f64 (.f64 z (.f64 y y)) (.f64 x x)) (-.f64 (.f64 y (sqrt.f64 z)) x))
3.0ms	z	@	inf	(/.f64 (-.f64 (.f64 z (.f64 y y)) (.f64 x x)) (-.f64 (.f64 y (sqrt.f64 z)) x))
2.0ms	x	@	0	(/.f64 (-.f64 (.f64 z (.f64 y y)) (.f64 x x)) (-.f64 (.f64 y (sqrt.f64 z)) x))
2.0ms	z	@	0	(/.f64 (-.f64 (.f64 z (.f64 y y)) (.f64 x x)) (-.f64 (.f64 y (sqrt.f64 z)) x))
1.0ms	y	@	-inf	(/.f64 (-.f64 (.f64 z (.f64 y y)) (.f64 x x)) (-.f64 (.f64 y (sqrt.f64 z)) x))

rewrite109.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

759×	`fma-def_binary64`
737×	`log-prod_binary64`
402×	`fma-neg_binary64`
236×	`expm1-udef_binary64`
236×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	37
1	277	20
2	4251	20

Stop Event

1×	node limit

Counts

2 → 306

Calls

Call 1

Inputs
(/.f64 (-.f64 (.f64 z (.f64 y y)) (.f64 x x)) (-.f64 (.f64 y (sqrt.f64 z)) x))
(-.f64 (.f64 z (.f64 y y)) (*.f64 x x))

Outputs

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y y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 (sqrt.f64 (*.f64 x (neg.f64 x))) x) (hypot.f64 (sqrt.f64 (*.f64 x (neg.f64 x))) x) (-.f64 (*.f64 z (*.f64 y y)) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 x (neg.f64 x))) (sqrt.f64 (*.f64 x (neg.f64 x))) (*.f64 z (*.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1 (*.f64 x x) (*.f64 z (*.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (cbrt.f64 (pow.f64 x 4))) (pow.f64 (cbrt.f64 x) 2) (*.f64 z (*.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (neg.f64 x) 1) x (*.f64 z (*.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (neg.f64 x) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (*.f64 z (*.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (neg.f64 x) (sqrt.f64 x)) (sqrt.f64 x) (*.f64 z (*.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 z (cbrt.f64 (pow.f64 y 4))) (pow.f64 (cbrt.f64 y) 2) (*.f64 x (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 z (cbrt.f64 (pow.f64 y 4))) (pow.f64 (cbrt.f64 y) 2) (*.f64 (*.f64 x (neg.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 z (cbrt.f64 (pow.f64 y 4))) (pow.f64 (cbrt.f64 y) 2) (fma.f64 x (neg.f64 x) (fma.f64 x (neg.f64 x) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 z (cbrt.f64 (pow.f64 y 4))) (pow.f64 (cbrt.f64 y) 2) (neg.f64 (-.f64 (*.f64 x x) (fma.f64 x (neg.f64 x) (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 y y) (sqrt.f64 z)) (sqrt.f64 z) (*.f64 x (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 y y) (sqrt.f64 z)) (sqrt.f64 z) (*.f64 (*.f64 x (neg.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 y y) (sqrt.f64 z)) (sqrt.f64 z) (fma.f64 x (neg.f64 x) (fma.f64 x (neg.f64 x) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 y y) (sqrt.f64 z)) (sqrt.f64 z) (neg.f64 (-.f64 (*.f64 x x) (fma.f64 x (neg.f64 x) (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 y y) (cbrt.f64 (*.f64 z z))) (cbrt.f64 z) (*.f64 x (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 y y) (cbrt.f64 (*.f64 z z))) (cbrt.f64 z) (*.f64 (*.f64 x (neg.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 y y) (cbrt.f64 (*.f64 z z))) (cbrt.f64 z) (fma.f64 x (neg.f64 x) (fma.f64 x (neg.f64 x) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 y y) (cbrt.f64 (*.f64 z z))) (cbrt.f64 z) (neg.f64 (-.f64 (*.f64 x x) (fma.f64 x (neg.f64 x) (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 z y) 1) y (*.f64 x (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 z y) 1) y (*.f64 (*.f64 x (neg.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 z y) 1) y (fma.f64 x (neg.f64 x) (fma.f64 x (neg.f64 x) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 z y) 1) y (neg.f64 (-.f64 (*.f64 x x) (fma.f64 x (neg.f64 x) (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 z y) (pow.f64 (cbrt.f64 y) 2)) (cbrt.f64 y) (*.f64 x (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 z y) (pow.f64 (cbrt.f64 y) 2)) (cbrt.f64 y) (*.f64 (*.f64 x (neg.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 z y) (pow.f64 (cbrt.f64 y) 2)) (cbrt.f64 y) (fma.f64 x (neg.f64 x) (fma.f64 x (neg.f64 x) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 z y) (pow.f64 (cbrt.f64 y) 2)) (cbrt.f64 y) (neg.f64 (-.f64 (*.f64 x x) (fma.f64 x (neg.f64 x) (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 z y) (sqrt.f64 y)) (sqrt.f64 y) (*.f64 x (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 z y) (sqrt.f64 y)) (sqrt.f64 y) (*.f64 (*.f64 x (neg.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 z y) (sqrt.f64 y)) (sqrt.f64 y) (fma.f64 x (neg.f64 x) (fma.f64 x (neg.f64 x) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 z y) (sqrt.f64 y)) (sqrt.f64 y) (neg.f64 (-.f64 (*.f64 x x) (fma.f64 x (neg.f64 x) (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 y (sqrt.f64 z)) y) (sqrt.f64 z) (*.f64 x (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 y (sqrt.f64 z)) y) (sqrt.f64 z) (*.f64 (*.f64 x (neg.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 y (sqrt.f64 z)) y) (sqrt.f64 z) (fma.f64 x (neg.f64 x) (fma.f64 x (neg.f64 x) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 y (sqrt.f64 z)) y) (sqrt.f64 z) (neg.f64 (-.f64 (*.f64 x x) (fma.f64 x (neg.f64 x) (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 y (sqrt.f64 z)) (sqrt.f64 z)) y (*.f64 x (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 y (sqrt.f64 z)) (sqrt.f64 z)) y (*.f64 (*.f64 x (neg.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 y (sqrt.f64 z)) (sqrt.f64 z)) y (fma.f64 x (neg.f64 x) (fma.f64 x (neg.f64 x) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 y (sqrt.f64 z)) (sqrt.f64 z)) y (neg.f64 (-.f64 (*.f64 x x) (fma.f64 x (neg.f64 x) (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 y (sqrt.f64 z)) (cbrt.f64 (*.f64 z (*.f64 y y)))) (cbrt.f64 (*.f64 y (sqrt.f64 z))) (*.f64 x (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 y (sqrt.f64 z)) (cbrt.f64 (*.f64 z (*.f64 y y)))) (cbrt.f64 (*.f64 y (sqrt.f64 z))) (*.f64 (*.f64 x (neg.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 y (sqrt.f64 z)) (cbrt.f64 (*.f64 z (*.f64 y y)))) (cbrt.f64 (*.f64 y (sqrt.f64 z))) (fma.f64 x (neg.f64 x) (fma.f64 x (neg.f64 x) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 y (sqrt.f64 z)) (cbrt.f64 (*.f64 z (*.f64 y y)))) (cbrt.f64 (*.f64 y (sqrt.f64 z))) (neg.f64 (-.f64 (*.f64 x x) (fma.f64 x (neg.f64 x) (*.f64 x x)))))))))

simplify131.0ms (2%)

Algorithm

1×	egg-herbie

Rules

636×	`fma-def_binary64`
571×	`fma-neg_binary64`
484×	`unswap-sqr_binary64`
440×	`distribute-rgt-neg-in_binary64`
334×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	585
1	30	558
2	56	558
3	116	558
4	303	558
5	1028	558
6	2125	558
7	4222	558
8	5510	558
9	6554	558
10	7249	558
11	7925	558

Stop Event

1×	node limit

Counts

367 → 314

Calls

Call 1

Inputs
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)
(*.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)
(*.f64 -1 (pow.f64 x 2))
(+.f64 (.f64 -1 (pow.f64 x 2)) (.f64 (pow.f64 y 2) z))
(+.f64 (.f64 -1 (pow.f64 x 2)) (.f64 (pow.f64 y 2) z))
(+.f64 (.f64 -1 (pow.f64 x 2)) (.f64 (pow.f64 y 2) z))
(*.f64 (pow.f64 y 2) z)
(+.f64 (.f64 -1 (pow.f64 x 2)) (.f64 (pow.f64 y 2) z))
(+.f64 (.f64 -1 (pow.f64 x 2)) (.f64 (pow.f64 y 2) z))
(+.f64 (.f64 -1 (pow.f64 x 2)) (.f64 (pow.f64 y 2) z))
(*.f64 (pow.f64 y 2) z)
(+.f64 (.f64 -1 (pow.f64 x 2)) (.f64 (pow.f64 y 2) z))
(+.f64 (.f64 -1 (pow.f64 x 2)) (.f64 (pow.f64 y 2) z))
(+.f64 (.f64 -1 (pow.f64 x 2)) (.f64 (pow.f64 y 2) z))
(*.f64 -1 (pow.f64 x 2))
(+.f64 (.f64 -1 (pow.f64 x 2)) (.f64 (pow.f64 y 2) z))
(+.f64 (.f64 -1 (pow.f64 x 2)) (.f64 (pow.f64 y 2) z))
(+.f64 (.f64 -1 (pow.f64 x 2)) (.f64 (pow.f64 y 2) z))
(*.f64 (pow.f64 y 2) z)
(+.f64 (.f64 -1 (pow.f64 x 2)) (.f64 (pow.f64 y 2) z))
(+.f64 (.f64 -1 (pow.f64 x 2)) (.f64 (pow.f64 y 2) z))
(+.f64 (.f64 -1 (pow.f64 x 2)) (.f64 (pow.f64 y 2) z))
(*.f64 (pow.f64 y 2) z)
(+.f64 (.f64 -1 (pow.f64 x 2)) (.f64 (pow.f64 y 2) z))
(+.f64 (.f64 -1 (pow.f64 x 2)) (.f64 (pow.f64 y 2) z))
(+.f64 (.f64 -1 (pow.f64 x 2)) (.f64 (pow.f64 y 2) z))
(*.f64 (pow.f64 y 2) z)
(+.f64 (.f64 -1 (pow.f64 x 2)) (.f64 (pow.f64 y 2) z))
(+.f64 (.f64 -1 (pow.f64 x 2)) (.f64 (pow.f64 y 2) z))
(+.f64 (.f64 -1 (pow.f64 x 2)) (.f64 (pow.f64 y 2) z))
(*.f64 -1 (pow.f64 x 2))
(+.f64 (.f64 -1 (pow.f64 x 2)) (.f64 (pow.f64 y 2) z))
(+.f64 (.f64 -1 (pow.f64 x 2)) (.f64 (pow.f64 y 2) z))
(+.f64 (.f64 -1 (pow.f64 x 2)) (.f64 (pow.f64 y 2) z))
(*.f64 -1 (pow.f64 x 2))
(+.f64 (.f64 -1 (pow.f64 x 2)) (.f64 (pow.f64 y 2) z))
(+.f64 (.f64 -1 (pow.f64 x 2)) (.f64 (pow.f64 y 2) z))
(+.f64 (.f64 -1 (pow.f64 x 2)) (.f64 (pow.f64 y 2) z))

Outputs
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)
(*.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)
(*.f64 -1 (pow.f64 x 2))
(neg.f64 (*.f64 x x))
(*.f64 x (neg.f64 x))
(+.f64 (.f64 -1 (pow.f64 x 2)) (.f64 (pow.f64 y 2) z))
(fma.f64 -1 (.f64 x x) (.f64 z (*.f64 y y)))
(-.f64 (.f64 y (.f64 y z)) (*.f64 x x))
(-.f64 (.f64 z (.f64 y y)) (*.f64 x x))
(neg.f64 (fma.f64 z (.f64 y y) (.f64 x x)))
(+.f64 (.f64 -1 (pow.f64 x 2)) (.f64 (pow.f64 y 2) z))
(fma.f64 -1 (.f64 x x) (.f64 z (*.f64 y y)))
(-.f64 (.f64 y (.f64 y z)) (*.f64 x x))
(-.f64 (.f64 z (.f64 y y)) (*.f64 x x))
(neg.f64 (fma.f64 z (.f64 y y) (.f64 x x)))
(+.f64 (.f64 -1 (pow.f64 x 2)) (.f64 (pow.f64 y 2) z))
(fma.f64 -1 (.f64 x x) (.f64 z (*.f64 y y)))
(-.f64 (.f64 y (.f64 y z)) (*.f64 x x))
(-.f64 (.f64 z (.f64 y y)) (*.f64 x x))
(neg.f64 (fma.f64 z (.f64 y y) (.f64 x x)))
(*.f64 (pow.f64 y 2) z)
(.f64 z (.f64 y y))
(.f64 y (.f64 y z))
(+.f64 (.f64 -1 (pow.f64 x 2)) (.f64 (pow.f64 y 2) z))
(fma.f64 -1 (.f64 x x) (.f64 z (*.f64 y y)))
(-.f64 (.f64 y (.f64 y z)) (*.f64 x x))
(-.f64 (.f64 z (.f64 y y)) (*.f64 x x))
(neg.f64 (fma.f64 z (.f64 y y) (.f64 x x)))
(+.f64 (.f64 -1 (pow.f64 x 2)) (.f64 (pow.f64 y 2) z))
(fma.f64 -1 (.f64 x x) (.f64 z (*.f64 y y)))
(-.f64 (.f64 y (.f64 y z)) (*.f64 x x))
(-.f64 (.f64 z (.f64 y y)) (*.f64 x x))
(neg.f64 (fma.f64 z (.f64 y y) (.f64 x x)))
(+.f64 (.f64 -1 (pow.f64 x 2)) (.f64 (pow.f64 y 2) z))
(fma.f64 -1 (.f64 x x) (.f64 z (*.f64 y y)))
(-.f64 (.f64 y (.f64 y z)) (*.f64 x x))
(-.f64 (.f64 z (.f64 y y)) (*.f64 x x))
(neg.f64 (fma.f64 z (.f64 y y) (.f64 x x)))
(*.f64 (pow.f64 y 2) z)
(.f64 z (.f64 y y))
(.f64 y (.f64 y z))
(+.f64 (.f64 -1 (pow.f64 x 2)) (.f64 (pow.f64 y 2) z))
(fma.f64 -1 (.f64 x x) (.f64 z (*.f64 y y)))
(-.f64 (.f64 y (.f64 y z)) (*.f64 x x))
(-.f64 (.f64 z (.f64 y y)) (*.f64 x x))
(neg.f64 (fma.f64 z (.f64 y y) (.f64 x x)))
(+.f64 (.f64 -1 (pow.f64 x 2)) (.f64 (pow.f64 y 2) z))
(fma.f64 -1 (.f64 x x) (.f64 z (*.f64 y y)))
(-.f64 (.f64 y (.f64 y z)) (*.f64 x x))
(-.f64 (.f64 z (.f64 y y)) (*.f64 x x))
(neg.f64 (fma.f64 z (.f64 y y) (.f64 x x)))
(+.f64 (.f64 -1 (pow.f64 x 2)) (.f64 (pow.f64 y 2) z))
(fma.f64 -1 (.f64 x x) (.f64 z (*.f64 y y)))
(-.f64 (.f64 y (.f64 y z)) (*.f64 x x))
(-.f64 (.f64 z (.f64 y y)) (*.f64 x x))
(neg.f64 (fma.f64 z (.f64 y y) (.f64 x x)))
(*.f64 -1 (pow.f64 x 2))
(neg.f64 (*.f64 x x))
(*.f64 x (neg.f64 x))
(+.f64 (.f64 -1 (pow.f64 x 2)) (.f64 (pow.f64 y 2) z))
(fma.f64 -1 (.f64 x x) (.f64 z (*.f64 y y)))
(-.f64 (.f64 y (.f64 y z)) (*.f64 x x))
(-.f64 (.f64 z (.f64 y y)) (*.f64 x x))
(neg.f64 (fma.f64 z (.f64 y y) (.f64 x x)))
(+.f64 (.f64 -1 (pow.f64 x 2)) (.f64 (pow.f64 y 2) z))
(fma.f64 -1 (.f64 x x) (.f64 z (*.f64 y y)))
(-.f64 (.f64 y (.f64 y z)) (*.f64 x x))
(-.f64 (.f64 z (.f64 y y)) (*.f64 x x))
(neg.f64 (fma.f64 z (.f64 y y) (.f64 x x)))
(+.f64 (.f64 -1 (pow.f64 x 2)) (.f64 (pow.f64 y 2) z))
(fma.f64 -1 (.f64 x x) (.f64 z (*.f64 y y)))
(-.f64 (.f64 y (.f64 y z)) (*.f64 x x))
(-.f64 (.f64 z (.f64 y y)) (*.f64 x x))
(neg.f64 (fma.f64 z (.f64 y y) (.f64 x x)))
(*.f64 (pow.f64 y 2) z)
(.f64 z (.f64 y y))
(.f64 y (.f64 y z))
(+.f64 (.f64 -1 (pow.f64 x 2)) (.f64 (pow.f64 y 2) z))
(fma.f64 -1 (.f64 x x) (.f64 z (*.f64 y y)))
(-.f64 (.f64 y (.f64 y z)) (*.f64 x x))
(-.f64 (.f64 z (.f64 y y)) (*.f64 x x))
(neg.f64 (fma.f64 z (.f64 y y) (.f64 x x)))
(+.f64 (.f64 -1 (pow.f64 x 2)) (.f64 (pow.f64 y 2) z))
(fma.f64 -1 (.f64 x x) (.f64 z (*.f64 y y)))
(-.f64 (.f64 y (.f64 y z)) (*.f64 x x))
(-.f64 (.f64 z (.f64 y y)) (*.f64 x x))
(neg.f64 (fma.f64 z (.f64 y y) (.f64 x x)))
(+.f64 (.f64 -1 (pow.f64 x 2)) (.f64 (pow.f64 y 2) z))
(fma.f64 -1 (.f64 x x) (.f64 z (*.f64 y y)))
(-.f64 (.f64 y (.f64 y z)) (*.f64 x x))
(-.f64 (.f64 z (.f64 y y)) (*.f64 x x))
(neg.f64 (fma.f64 z (.f64 y y) (.f64 x x)))
(*.f64 (pow.f64 y 2) z)
(.f64 z (.f64 y y))
(.f64 y (.f64 y z))
(+.f64 (.f64 -1 (pow.f64 x 2)) (.f64 (pow.f64 y 2) z))
(fma.f64 -1 (.f64 x x) (.f64 z (*.f64 y y)))
(-.f64 (.f64 y (.f64 y z)) (*.f64 x x))
(-.f64 (.f64 z (.f64 y y)) (*.f64 x x))
(neg.f64 (fma.f64 z (.f64 y y) (.f64 x x)))
(+.f64 (.f64 -1 (pow.f64 x 2)) (.f64 (pow.f64 y 2) z))
(fma.f64 -1 (.f64 x x) (.f64 z (*.f64 y y)))
(-.f64 (.f64 y (.f64 y z)) (*.f64 x x))
(-.f64 (.f64 z (.f64 y y)) (*.f64 x x))
(neg.f64 (fma.f64 z (.f64 y y) (.f64 x x)))
(+.f64 (.f64 -1 (pow.f64 x 2)) (.f64 (pow.f64 y 2) z))
(fma.f64 -1 (.f64 x x) (.f64 z (*.f64 y y)))
(-.f64 (.f64 y (.f64 y z)) (*.f64 x x))
(-.f64 (.f64 z (.f64 y y)) (*.f64 x x))
(neg.f64 (fma.f64 z (.f64 y y) (.f64 x x)))
(*.f64 (pow.f64 y 2) z)
(.f64 z (.f64 y y))
(.f64 y (.f64 y z))
(+.f64 (.f64 -1 (pow.f64 x 2)) (.f64 (pow.f64 y 2) z))
(fma.f64 -1 (.f64 x x) (.f64 z (*.f64 y y)))
(-.f64 (.f64 y (.f64 y z)) (*.f64 x x))
(-.f64 (.f64 z (.f64 y y)) (*.f64 x x))
(neg.f64 (fma.f64 z (.f64 y y) (.f64 x x)))
(+.f64 (.f64 -1 (pow.f64 x 2)) (.f64 (pow.f64 y 2) z))
(fma.f64 -1 (.f64 x x) (.f64 z (*.f64 y y)))
(-.f64 (.f64 y (.f64 y z)) (*.f64 x x))
(-.f64 (.f64 z (.f64 y y)) (*.f64 x x))
(neg.f64 (fma.f64 z (.f64 y y) (.f64 x x)))
(+.f64 (.f64 -1 (pow.f64 x 2)) (.f64 (pow.f64 y 2) z))
(fma.f64 -1 (.f64 x x) (.f64 z (*.f64 y y)))
(-.f64 (.f64 y (.f64 y z)) (*.f64 x x))
(-.f64 (.f64 z (.f64 y y)) (*.f64 x x))
(neg.f64 (fma.f64 z (.f64 y y) (.f64 x x)))
(*.f64 -1 (pow.f64 x 2))
(neg.f64 (*.f64 x x))
(*.f64 x (neg.f64 x))
(+.f64 (.f64 -1 (pow.f64 x 2)) (.f64 (pow.f64 y 2) z))
(fma.f64 -1 (.f64 x x) (.f64 z (*.f64 y y)))
(-.f64 (.f64 y (.f64 y z)) (*.f64 x x))
(-.f64 (.f64 z (.f64 y y)) (*.f64 x x))
(neg.f64 (fma.f64 z (.f64 y y) (.f64 x x)))
(+.f64 (.f64 -1 (pow.f64 x 2)) (.f64 (pow.f64 y 2) z))
(fma.f64 -1 (.f64 x x) (.f64 z (*.f64 y y)))
(-.f64 (.f64 y (.f64 y z)) (*.f64 x x))
(-.f64 (.f64 z (.f64 y y)) (*.f64 x x))
(neg.f64 (fma.f64 z (.f64 y y) (.f64 x x)))
(+.f64 (.f64 -1 (pow.f64 x 2)) (.f64 (pow.f64 y 2) z))
(fma.f64 -1 (.f64 x x) (.f64 z (*.f64 y y)))
(-.f64 (.f64 y (.f64 y z)) (*.f64 x x))
(-.f64 (.f64 z (.f64 y y)) (*.f64 x x))
(neg.f64 (fma.f64 z (.f64 y y) (.f64 x x)))
(*.f64 -1 (pow.f64 x 2))
(neg.f64 (*.f64 x x))
(*.f64 x (neg.f64 x))
(+.f64 (.f64 -1 (pow.f64 x 2)) (.f64 (pow.f64 y 2) z))
(fma.f64 -1 (.f64 x x) (.f64 z (*.f64 y y)))
(-.f64 (.f64 y (.f64 y z)) (*.f64 x x))
(-.f64 (.f64 z (.f64 y y)) (*.f64 x x))
(neg.f64 (fma.f64 z (.f64 y y) (.f64 x x)))
(+.f64 (.f64 -1 (pow.f64 x 2)) (.f64 (pow.f64 y 2) z))
(fma.f64 -1 (.f64 x x) (.f64 z (*.f64 y y)))
(-.f64 (.f64 y (.f64 y z)) (*.f64 x x))
(-.f64 (.f64 z (.f64 y y)) (*.f64 x x))
(neg.f64 (fma.f64 z (.f64 y y) (.f64 x x)))
(+.f64 (.f64 -1 (pow.f64 x 2)) (.f64 (pow.f64 y 2) z))
(fma.f64 -1 (.f64 x x) (.f64 z (*.f64 y y)))
(-.f64 (.f64 y (.f64 y z)) (*.f64 x x))
(-.f64 (.f64 z (.f64 y y)) (*.f64 x x))
(neg.f64 (fma.f64 z (.f64 y y) (.f64 x x)))

eval193.0ms (3%)

Compiler: Compiled 13565 to 4986 computations (63.2% saved)

prune412.0ms (6.4%)

Pruning

14 alts after pruning (9 fresh and 5 done)

	Pruned	Kept	Total
New	664	8	672
Fresh	4	1	5
Picked	1	0	1
Done	2	5	7
Total	671	14	685

Error

Counts

685 → 14

Alt Table

Click to see full alt table

Status	Error	Program
	33.6b	(*.f64 (/.f64 1 2) (/.f64 1 (/.f64 (pow.f64 z -1/2) y)))
▶	33.7b	(*.f64 (/.f64 1 2) (/.f64 1 (/.f64 (/.f64 1 (sqrt.f64 z)) y)))
✓	29.8b	(*.f64 (/.f64 1 2) (/.f64 1 (/.f64 1 x)))
	38.5b	(*.f64 (/.f64 1 2) (-.f64 (+.f64 1 x) 1))
✓	0.3b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (pow.f64 z 1/4) (*.f64 (pow.f64 z 1/4) y))))
	33.7b	(.f64 (/.f64 1 2) (.f64 (/.f64 1 (sqrt.f64 (pow.f64 z -1/2))) (/.f64 y (sqrt.f64 (pow.f64 z -1/2)))))
▶	62.5b	(*.f64 (/.f64 1 2) (neg.f64 x))
✓	0.1b	(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
▶	36.0b	(*.f64 1/2 (pow.f64 (sqrt.f64 (fma.f64 (sqrt.f64 z) y x)) 2))
	47.9b	(.f64 1/2 (/.f64 (.f64 y (.f64 y z)) (-.f64 (.f64 y (sqrt.f64 z)) x)))
✓	0.1b	(.f64 1/2 (+.f64 (.f64 y (sqrt.f64 z)) x))
▶	26.5b	(.f64 1/2 (+.f64 (sqrt.f64 (.f64 y (*.f64 y z))) x))
▶	33.5b	(.f64 1/2 (.f64 y (sqrt.f64 z)))
✓	29.7b	(*.f64 1/2 x)

Compiler

Compiled 301 to 241 computations (19.9% saved)

localize12.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (sqrt.f64 (.f64 y (.f64 y z))) x)
✓	0.1b	(.f64 y (.f64 y z))
✓	27.4b	(sqrt.f64 (.f64 y (.f64 y z)))

Compiler

Compiled 39 to 10 computations (74.4% saved)

series6.0ms (0.1%)

Counts

3 → 61

Calls

21 calls:

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

rewrite65.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

892×	`pow1_binary64`
826×	`add-log-exp_binary64`
826×	`log1p-expm1-u_binary64`
826×	`expm1-log1p-u_binary64`
806×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	28
1	170	22
2	2301	22

Stop Event

1×	node limit

Counts

3 → 72

Calls

Call 1

Inputs
(sqrt.f64 (.f64 y (.f64 y z)))
(.f64 y (.f64 y z))
(+.f64 (sqrt.f64 (.f64 y (.f64 y z))) x)

Outputs

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

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

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

simplify113.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

855×	`fma-neg_binary64`
783×	`fma-def_binary64`
381×	`cube-prod_binary64`
379×	`distribute-rgt-neg-in_binary64`
322×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	388
1	28	388
2	55	388
3	106	388
4	245	388
5	698	388
6	1125	388
7	1825	388
8	2344	388
9	3509	388
10	4747	388
11	6201	388
12	7564	388

Stop Event

1×	node limit

Counts

133 → 79

Calls

Call 1

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

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

localize7.0ms (0.1%)

Compiler: Compiled 17 to 13 computations (23.5% saved)

localize8.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
	0.2b	(*.f64 y (sqrt.f64 z))

Compiler

Compiled 18 to 8 computations (55.6% saved)

localize17.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 1 (sqrt.f64 z))
✓	0.3b	(/.f64 (/.f64 1 (sqrt.f64 z)) y)
✓	0.3b	(/.f64 1 (/.f64 (/.f64 1 (sqrt.f64 z)) y))

Compiler

Compiled 42 to 28 computations (33.3% saved)

series8.0ms (0.1%)

Counts

3 → 24

Calls

15 calls:

Time	Variable		Point	Expression
3.0ms	z	@	-inf	(/.f64 (/.f64 1 (sqrt.f64 z)) y)
1.0ms	z	@	-inf	(/.f64 1 (sqrt.f64 z))
0.0ms	z	@	0	(/.f64 1 (/.f64 (/.f64 1 (sqrt.f64 z)) y))
0.0ms	z	@	-inf	(/.f64 1 (/.f64 (/.f64 1 (sqrt.f64 z)) y))
0.0ms	z	@	inf	(/.f64 1 (/.f64 (/.f64 1 (sqrt.f64 z)) y))

rewrite67.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

804×	`pow1_binary64`
745×	`add-log-exp_binary64`
745×	`log1p-expm1-u_binary64`
745×	`expm1-log1p-u_binary64`
724×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	27
1	171	17
2	2243	17

Stop Event

1×	node limit

Counts

3 → 95

Calls

Call 1

Inputs
(/.f64 1 (/.f64 (/.f64 1 (sqrt.f64 z)) y))
(/.f64 (/.f64 1 (sqrt.f64 z)) y)
(/.f64 1 (sqrt.f64 z))

Outputs

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

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

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

simplify33.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

4×	`associate-/l*_binary64`
3×	`*-commutative_binary64`
3×	`associate-*l/_binary64`
3×	`associate-/r*_binary64`
3×	`*-lft-identity_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	216
1	16	180
2	21	180
3	32	180
4	32	180
5	33	180
6	36	180
7	43	180
8	43	180

Stop Event

1×

saturated

Counts

119 → 97

Calls

Call 1

Inputs
(*.f64 y (sqrt.f64 z))
(*.f64 y (sqrt.f64 z))
(*.f64 y (sqrt.f64 z))
(*.f64 y (sqrt.f64 z))
(*.f64 y (sqrt.f64 z))
(*.f64 y (sqrt.f64 z))
(*.f64 y (sqrt.f64 z))
(*.f64 y (sqrt.f64 z))
(*.f64 y (sqrt.f64 z))
(*.f64 y (sqrt.f64 z))
(*.f64 y (sqrt.f64 z))
(*.f64 y (sqrt.f64 z))
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z)))
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z)))
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z)))
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z)))
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z)))
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z)))
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z)))
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z)))
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z)))
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z)))
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z)))
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z)))

Outputs
(*.f64 y (sqrt.f64 z))
(*.f64 y (sqrt.f64 z))
(*.f64 y (sqrt.f64 z))
(*.f64 y (sqrt.f64 z))
(*.f64 y (sqrt.f64 z))
(*.f64 y (sqrt.f64 z))
(*.f64 y (sqrt.f64 z))
(*.f64 y (sqrt.f64 z))
(*.f64 y (sqrt.f64 z))
(*.f64 y (sqrt.f64 z))
(*.f64 y (sqrt.f64 z))
(*.f64 y (sqrt.f64 z))
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z)))
(/.f64 (sqrt.f64 (/.f64 1 z)) y)
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z)))
(/.f64 (sqrt.f64 (/.f64 1 z)) y)
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z)))
(/.f64 (sqrt.f64 (/.f64 1 z)) y)
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z)))
(/.f64 (sqrt.f64 (/.f64 1 z)) y)
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z)))
(/.f64 (sqrt.f64 (/.f64 1 z)) y)
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z)))
(/.f64 (sqrt.f64 (/.f64 1 z)) y)
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z)))
(/.f64 (sqrt.f64 (/.f64 1 z)) y)
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z)))
(/.f64 (sqrt.f64 (/.f64 1 z)) y)
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z)))
(/.f64 (sqrt.f64 (/.f64 1 z)) y)
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z)))
(/.f64 (sqrt.f64 (/.f64 1 z)) y)
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z)))
(/.f64 (sqrt.f64 (/.f64 1 z)) y)
(*.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z)))
(/.f64 (sqrt.f64 (/.f64 1 z)) y)

localize13.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (fma.f64 (sqrt.f64 z) y x))
✓	0.1b	(fma.f64 (sqrt.f64 z) y x)
✓	0.2b	(pow.f64 (sqrt.f64 (fma.f64 (sqrt.f64 z) y x)) 2)

Compiler

Compiled 39 to 14 computations (64.1% saved)

series29.0ms (0.5%)

Counts

3 → 43

Calls

27 calls:

Time	Variable		Point	Expression
6.0ms	z	@	inf	(pow.f64 (sqrt.f64 (fma.f64 (sqrt.f64 z) y x)) 2)
2.0ms	z	@	-inf	(pow.f64 (sqrt.f64 (fma.f64 (sqrt.f64 z) y x)) 2)
2.0ms	y	@	inf	(pow.f64 (sqrt.f64 (fma.f64 (sqrt.f64 z) y x)) 2)
2.0ms	x	@	0	(pow.f64 (sqrt.f64 (fma.f64 (sqrt.f64 z) y x)) 2)
2.0ms	z	@	0	(pow.f64 (sqrt.f64 (fma.f64 (sqrt.f64 z) y x)) 2)

rewrite66.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

682×	`pow1_binary64`
627×	`add-log-exp_binary64`
627×	`log1p-expm1-u_binary64`
627×	`expm1-log1p-u_binary64`
609×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	182	23
2	1775	23

Stop Event

1×	node limit

Counts

3 → 68

Calls

Call 1

Inputs
(pow.f64 (sqrt.f64 (fma.f64 (sqrt.f64 z) y x)) 2)
(fma.f64 (sqrt.f64 z) y x)
(sqrt.f64 (fma.f64 (sqrt.f64 z) y x))

Outputs

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

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

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

simplify56.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

654×	`fma-def_binary64`
631×	`associate-l_binary64`
591×	`associate-r_binary64`
346×	`distribute-rgt-out_binary64`
253×	`*-commutative_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	113	600
1	335	579
2	1173	557
3	5538	539

Stop Event

1×	node limit

Counts

111 → 71

Calls

Call 1

Inputs
x
x
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(+.f64 (.f64 y (sqrt.f64 z)) (+.f64 (.f64 (pow.f64 y 2) (+.f64 (.f64 1/4 (/.f64 z x)) (.f64 -1/4 (/.f64 z x)))) x))
(+.f64 (.f64 y (sqrt.f64 z)) (+.f64 (.f64 (pow.f64 y 2) (+.f64 (.f64 1/4 (/.f64 z x)) (.f64 -1/4 (/.f64 z x)))) (+.f64 (.f64 (pow.f64 y 3) (+.f64 (.f64 1/8 (.f64 (sqrt.f64 (pow.f64 z 3)) (/.f64 1 (pow.f64 x 2)))) (.f64 -1/8 (*.f64 (sqrt.f64 (pow.f64 z 3)) (/.f64 1 (pow.f64 x 2)))))) x)))
(*.f64 y (sqrt.f64 z))
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(+.f64 (.f64 (+.f64 (.f64 -1/4 (.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z)))) (.f64 1/4 (.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z))))) (pow.f64 x 2)) (+.f64 (.f64 y (sqrt.f64 z)) x))
(+.f64 (.f64 (+.f64 (.f64 -1 (+.f64 (.f64 1/16 (.f64 (/.f64 1 (pow.f64 y 3)) (sqrt.f64 (/.f64 1 (pow.f64 z 3))))) (pow.f64 (.f64 -1/8 (.f64 (pow.f64 (/.f64 1 (pow.f64 z 3)) 1/4) (sqrt.f64 (/.f64 1 (pow.f64 y 3))))) 2))) (+.f64 (.f64 1/64 (.f64 (/.f64 1 (pow.f64 y 3)) (sqrt.f64 (/.f64 1 (pow.f64 z 3))))) (.f64 1/16 (.f64 (/.f64 1 (pow.f64 y 3)) (sqrt.f64 (/.f64 1 (pow.f64 z 3))))))) (pow.f64 x 4)) (+.f64 (.f64 (+.f64 (.f64 -1/4 (.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z)))) (.f64 1/4 (.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z))))) (pow.f64 x 2)) (+.f64 (.f64 y (sqrt.f64 z)) x)))
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)
(*.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)
(sqrt.f64 x)
(sqrt.f64 x)
(+.f64 (.f64 1/2 (.f64 y (sqrt.f64 (/.f64 z x)))) (sqrt.f64 x))
(+.f64 (.f64 1/2 (.f64 y (sqrt.f64 (/.f64 z x)))) (+.f64 (.f64 -1/8 (.f64 (*.f64 (pow.f64 y 2) z) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (sqrt.f64 x)))
(+.f64 (.f64 1/2 (.f64 y (sqrt.f64 (/.f64 z x)))) (+.f64 (.f64 1/16 (.f64 (pow.f64 y 3) (sqrt.f64 (/.f64 (pow.f64 z 3) (pow.f64 x 5))))) (+.f64 (.f64 -1/8 (.f64 (*.f64 (pow.f64 y 2) z) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (sqrt.f64 x))))
(.f64 (pow.f64 (.f64 1 z) 1/4) (sqrt.f64 y))
(+.f64 (.f64 1/2 (.f64 (pow.f64 (/.f64 1 z) 1/4) (.f64 (sqrt.f64 (/.f64 1 y)) x))) (.f64 (pow.f64 (*.f64 1 z) 1/4) (sqrt.f64 y)))
(+.f64 (.f64 1/2 (.f64 (pow.f64 (/.f64 1 z) 1/4) (.f64 (sqrt.f64 (/.f64 1 y)) x))) (+.f64 (.f64 (pow.f64 (.f64 1 z) 1/4) (sqrt.f64 y)) (.f64 -1/8 (.f64 (pow.f64 (/.f64 1 (pow.f64 z 3)) 1/4) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 2))))))
(+.f64 (.f64 1/16 (.f64 (pow.f64 (/.f64 1 (pow.f64 z 5)) 1/4) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 5))) (pow.f64 x 3)))) (+.f64 (.f64 1/2 (.f64 (pow.f64 (/.f64 1 z) 1/4) (.f64 (sqrt.f64 (/.f64 1 y)) x))) (+.f64 (.f64 (pow.f64 (.f64 1 z) 1/4) (sqrt.f64 y)) (.f64 -1/8 (.f64 (pow.f64 (/.f64 1 (pow.f64 z 3)) 1/4) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 2)))))))

Outputs
x
x
(+.f64 (*.f64 y (sqrt.f64 z)) x)
(fma.f64 y (sqrt.f64 z) x)
(+.f64 (.f64 y (sqrt.f64 z)) (+.f64 (.f64 (pow.f64 y 2) (+.f64 (.f64 1/4 (/.f64 z x)) (.f64 -1/4 (/.f64 z x)))) x))
(fma.f64 y (sqrt.f64 z) x)
(+.f64 (.f64 y (sqrt.f64 z)) (+.f64 (.f64 (pow.f64 y 2) (+.f64 (.f64 1/4 (/.f64 z x)) (.f64 -1/4 (/.f64 z x)))) (+.f64 (.f64 (pow.f64 y 3) (+.f64 (.f64 1/8 (.f64 (sqrt.f64 (pow.f64 z 3)) (/.f64 1 (pow.f64 x 2)))) (.f64 -1/8 (*.f64 (sqrt.f64 (pow.f64 z 3)) (/.f64 1 (pow.f64 x 2)))))) 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 (+.f64 (.f64 -1/4 (.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z)))) (.f64 1/4 (.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z))))) (pow.f64 x 2)) (+.f64 (.f64 y (sqrt.f64 z)) x))
(fma.f64 y (sqrt.f64 z) x)
(+.f64 (.f64 (+.f64 (.f64 -1 (+.f64 (.f64 1/16 (.f64 (/.f64 1 (pow.f64 y 3)) (sqrt.f64 (/.f64 1 (pow.f64 z 3))))) (pow.f64 (.f64 -1/8 (.f64 (pow.f64 (/.f64 1 (pow.f64 z 3)) 1/4) (sqrt.f64 (/.f64 1 (pow.f64 y 3))))) 2))) (+.f64 (.f64 1/64 (.f64 (/.f64 1 (pow.f64 y 3)) (sqrt.f64 (/.f64 1 (pow.f64 z 3))))) (.f64 1/16 (.f64 (/.f64 1 (pow.f64 y 3)) (sqrt.f64 (/.f64 1 (pow.f64 z 3))))))) (pow.f64 x 4)) (+.f64 (.f64 (+.f64 (.f64 -1/4 (.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z)))) (.f64 1/4 (.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z))))) (pow.f64 x 2)) (+.f64 (.f64 y (sqrt.f64 z)) x)))
(fma.f64 (fma.f64 -1 (fma.f64 1/16 (.f64 (/.f64 1 (pow.f64 y 3)) (sqrt.f64 (/.f64 1 (pow.f64 z 3)))) (pow.f64 (.f64 -1/8 (.f64 (pow.f64 (/.f64 1 (pow.f64 z 3)) 1/4) (sqrt.f64 (/.f64 1 (pow.f64 y 3))))) 2)) (.f64 (.f64 (/.f64 1 (pow.f64 y 3)) (sqrt.f64 (/.f64 1 (pow.f64 z 3)))) 5/64)) (pow.f64 x 4) (fma.f64 (.f64 (.f64 (/.f64 1 y) (sqrt.f64 (/.f64 1 z))) 0) (.f64 x x) (fma.f64 y (sqrt.f64 z) x)))
(fma.f64 (-.f64 (.f64 (/.f64 (sqrt.f64 (/.f64 1 (pow.f64 z 3))) (pow.f64 y 3)) 5/64) (fma.f64 1/16 (/.f64 (sqrt.f64 (/.f64 1 (pow.f64 z 3))) (pow.f64 y 3)) (pow.f64 (.f64 -1/8 (.f64 (pow.f64 (/.f64 1 (pow.f64 z 3)) 1/4) (sqrt.f64 (/.f64 1 (pow.f64 y 3))))) 2))) (pow.f64 x 4) (fma.f64 0 (.f64 x x) (fma.f64 y (sqrt.f64 z) x)))
(+.f64 x (fma.f64 (pow.f64 x 4) (-.f64 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 z 3))) (/.f64 1/64 (pow.f64 y 3))) (pow.f64 (.f64 -1/8 (*.f64 (pow.f64 (/.f64 1 (pow.f64 z 3)) 1/4) (sqrt.f64 (/.f64 1 (pow.f64 y 3))))) 2)) (fma.f64 y (sqrt.f64 z) 0)))
(fma.f64 (pow.f64 x 4) (.f64 (/.f64 1 (pow.f64 y 3)) (-.f64 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 z 3))) 1/64) (*.f64 1/64 (pow.f64 (/.f64 1 (pow.f64 z 3)) 1/2)))) (fma.f64 y (sqrt.f64 z) x))
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)
(*.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)
(sqrt.f64 x)
(sqrt.f64 x)
(+.f64 (.f64 1/2 (.f64 y (sqrt.f64 (/.f64 z x)))) (sqrt.f64 x))
(fma.f64 1/2 (*.f64 y (sqrt.f64 (/.f64 z x))) (sqrt.f64 x))
(fma.f64 y (*.f64 1/2 (sqrt.f64 (/.f64 z x))) (sqrt.f64 x))
(+.f64 (.f64 1/2 (.f64 y (sqrt.f64 (/.f64 z x)))) (+.f64 (.f64 -1/8 (.f64 (*.f64 (pow.f64 y 2) z) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (sqrt.f64 x)))
(fma.f64 1/2 (.f64 y (sqrt.f64 (/.f64 z x))) (fma.f64 -1/8 (.f64 (.f64 y y) (.f64 z (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (sqrt.f64 x)))
(fma.f64 1/2 (.f64 y (sqrt.f64 (/.f64 z x))) (fma.f64 -1/8 (.f64 z (.f64 (.f64 y y) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (sqrt.f64 x)))
(fma.f64 y (.f64 1/2 (sqrt.f64 (/.f64 z x))) (fma.f64 (.f64 y y) (.f64 z (.f64 -1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (sqrt.f64 x)))
(fma.f64 (.f64 y y) (.f64 -1/8 (.f64 z (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (fma.f64 y (.f64 1/2 (sqrt.f64 (/.f64 z x))) (sqrt.f64 x)))
(+.f64 (.f64 1/2 (.f64 y (sqrt.f64 (/.f64 z x)))) (+.f64 (.f64 1/16 (.f64 (pow.f64 y 3) (sqrt.f64 (/.f64 (pow.f64 z 3) (pow.f64 x 5))))) (+.f64 (.f64 -1/8 (.f64 (*.f64 (pow.f64 y 2) z) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (sqrt.f64 x))))
(fma.f64 1/2 (.f64 y (sqrt.f64 (/.f64 z x))) (fma.f64 1/16 (.f64 (pow.f64 y 3) (sqrt.f64 (/.f64 (pow.f64 z 3) (pow.f64 x 5)))) (fma.f64 -1/8 (.f64 (.f64 y y) (*.f64 z (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (sqrt.f64 x))))
(fma.f64 1/2 (.f64 y (sqrt.f64 (/.f64 z x))) (fma.f64 1/16 (.f64 (pow.f64 y 3) (sqrt.f64 (/.f64 (pow.f64 z 3) (pow.f64 x 5)))) (fma.f64 -1/8 (.f64 z (.f64 (*.f64 y y) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (sqrt.f64 x))))
(fma.f64 y (.f64 1/2 (sqrt.f64 (/.f64 z x))) (fma.f64 -1/8 (.f64 y (.f64 (.f64 y z) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (fma.f64 1/16 (*.f64 (pow.f64 y 3) (fabs.f64 (/.f64 (pow.f64 z 3/2) (pow.f64 x 5/2)))) (sqrt.f64 x))))
(fma.f64 y (.f64 1/2 (sqrt.f64 (/.f64 z x))) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (.f64 z (.f64 (.f64 y y) -1/8)) (fma.f64 (pow.f64 y 3) (*.f64 1/16 (/.f64 (pow.f64 z 3/2) (pow.f64 x 5/2))) (sqrt.f64 x))))
(.f64 (pow.f64 (.f64 1 z) 1/4) (sqrt.f64 y))
(*.f64 (pow.f64 z 1/4) (sqrt.f64 y))
(+.f64 (.f64 1/2 (.f64 (pow.f64 (/.f64 1 z) 1/4) (.f64 (sqrt.f64 (/.f64 1 y)) x))) (.f64 (pow.f64 (*.f64 1 z) 1/4) (sqrt.f64 y)))
(fma.f64 1/2 (.f64 (pow.f64 (/.f64 1 z) 1/4) (.f64 x (sqrt.f64 (/.f64 1 y)))) (*.f64 (pow.f64 z 1/4) (sqrt.f64 y)))
(fma.f64 1/2 (.f64 x (.f64 (pow.f64 (/.f64 1 z) 1/4) (sqrt.f64 (/.f64 1 y)))) (*.f64 (pow.f64 z 1/4) (sqrt.f64 y)))
(+.f64 (.f64 1/2 (.f64 (pow.f64 (/.f64 1 z) 1/4) (.f64 (sqrt.f64 (/.f64 1 y)) x))) (+.f64 (.f64 (pow.f64 (.f64 1 z) 1/4) (sqrt.f64 y)) (.f64 -1/8 (.f64 (pow.f64 (/.f64 1 (pow.f64 z 3)) 1/4) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 2))))))
(fma.f64 1/2 (.f64 (pow.f64 (/.f64 1 z) 1/4) (.f64 x (sqrt.f64 (/.f64 1 y)))) (fma.f64 (pow.f64 z 1/4) (sqrt.f64 y) (.f64 (.f64 -1/8 (pow.f64 (/.f64 1 (pow.f64 z 3)) 1/4)) (.f64 (.f64 x x) (sqrt.f64 (/.f64 1 (pow.f64 y 3)))))))
(fma.f64 1/2 (.f64 x (.f64 (pow.f64 (/.f64 1 z) 1/4) (sqrt.f64 (/.f64 1 y)))) (fma.f64 -1/8 (.f64 (.f64 x x) (.f64 (pow.f64 (/.f64 1 (pow.f64 z 3)) 1/4) (sqrt.f64 (/.f64 1 (pow.f64 y 3))))) (.f64 (pow.f64 z 1/4) (sqrt.f64 y))))
(fma.f64 (pow.f64 (/.f64 1 (pow.f64 z 3)) 1/4) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (.f64 x (.f64 x -1/8))) (fma.f64 1/2 (.f64 x (.f64 (pow.f64 (/.f64 1 z) 1/4) (sqrt.f64 (/.f64 1 y)))) (.f64 (pow.f64 z 1/4) (sqrt.f64 y))))
(fma.f64 (pow.f64 z 1/4) (sqrt.f64 y) (.f64 x (+.f64 (.f64 1/2 (.f64 (pow.f64 (/.f64 1 z) 1/4) (sqrt.f64 (/.f64 1 y)))) (.f64 (.f64 -1/8 (pow.f64 (/.f64 1 (pow.f64 z 3)) 1/4)) (.f64 x (sqrt.f64 (/.f64 1 (pow.f64 y 3))))))))
(+.f64 (.f64 1/16 (.f64 (pow.f64 (/.f64 1 (pow.f64 z 5)) 1/4) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 5))) (pow.f64 x 3)))) (+.f64 (.f64 1/2 (.f64 (pow.f64 (/.f64 1 z) 1/4) (.f64 (sqrt.f64 (/.f64 1 y)) x))) (+.f64 (.f64 (pow.f64 (.f64 1 z) 1/4) (sqrt.f64 y)) (.f64 -1/8 (.f64 (pow.f64 (/.f64 1 (pow.f64 z 3)) 1/4) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 2)))))))
(fma.f64 1/16 (.f64 (pow.f64 (/.f64 1 (pow.f64 z 5)) 1/4) (.f64 (pow.f64 x 3) (sqrt.f64 (/.f64 1 (pow.f64 y 5))))) (fma.f64 1/2 (.f64 (pow.f64 (/.f64 1 z) 1/4) (.f64 x (sqrt.f64 (/.f64 1 y)))) (fma.f64 (pow.f64 z 1/4) (sqrt.f64 y) (.f64 (.f64 -1/8 (pow.f64 (/.f64 1 (pow.f64 z 3)) 1/4)) (.f64 (.f64 x x) (sqrt.f64 (/.f64 1 (pow.f64 y 3))))))))
(fma.f64 1/16 (.f64 (pow.f64 x 3) (.f64 (pow.f64 (/.f64 1 (pow.f64 z 5)) 1/4) (sqrt.f64 (/.f64 1 (pow.f64 y 5))))) (fma.f64 1/2 (.f64 x (.f64 (pow.f64 (/.f64 1 z) 1/4) (sqrt.f64 (/.f64 1 y)))) (fma.f64 -1/8 (.f64 (.f64 x x) (.f64 (pow.f64 (/.f64 1 (pow.f64 z 3)) 1/4) (sqrt.f64 (/.f64 1 (pow.f64 y 3))))) (.f64 (pow.f64 z 1/4) (sqrt.f64 y)))))
(fma.f64 1/16 (.f64 (pow.f64 x 3) (.f64 (pow.f64 (/.f64 1 (pow.f64 z 5)) 1/4) (sqrt.f64 (/.f64 1 (pow.f64 y 5))))) (fma.f64 (pow.f64 (/.f64 1 (pow.f64 z 3)) 1/4) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (.f64 x (.f64 x -1/8))) (fma.f64 1/2 (.f64 x (.f64 (pow.f64 (/.f64 1 z) 1/4) (sqrt.f64 (/.f64 1 y)))) (.f64 (pow.f64 z 1/4) (sqrt.f64 y)))))
(fma.f64 1/16 (.f64 (pow.f64 x 3) (.f64 (pow.f64 (/.f64 1 (pow.f64 z 5)) 1/4) (sqrt.f64 (/.f64 1 (pow.f64 y 5))))) (fma.f64 (pow.f64 z 1/4) (sqrt.f64 y) (.f64 x (+.f64 (.f64 1/2 (.f64 (pow.f64 (/.f64 1 z) 1/4) (sqrt.f64 (/.f64 1 y)))) (.f64 (.f64 -1/8 (pow.f64 (/.f64 1 (pow.f64 z 3)) 1/4)) (.f64 x (sqrt.f64 (/.f64 1 (pow.f64 y 3)))))))))

eval204.0ms (3.2%)

Compiler: Compiled 3985 to 2381 computations (40.3% saved)

prune44.0ms (0.7%)

Pruning

16 alts after pruning (8 fresh and 8 done)

	Pruned	Kept	Total
New	253	5	258
Fresh	1	3	4
Picked	1	0	1
Done	1	8	9
Total	256	16	272

Error

Counts

272 → 16

Alt Table

Click to see full alt table

Status	Error	Program
	33.6b	(*.f64 (/.f64 1 2) (/.f64 1 (/.f64 (pow.f64 z -1/2) y)))
✓	33.7b	(*.f64 (/.f64 1 2) (/.f64 1 (/.f64 (/.f64 1 (sqrt.f64 z)) y)))
✓	29.8b	(*.f64 (/.f64 1 2) (/.f64 1 (/.f64 1 x)))
	38.5b	(*.f64 (/.f64 1 2) (-.f64 (+.f64 1 x) 1))
	33.7b	(.f64 (/.f64 1 2) (.f64 (/.f64 1 (sqrt.f64 (pow.f64 z -1/2))) (/.f64 y (sqrt.f64 (pow.f64 z -1/2)))))
	33.7b	(.f64 (/.f64 1 2) (.f64 (*.f64 y (pow.f64 z 1/4)) (pow.f64 z 1/4)))
✓	62.5b	(*.f64 (/.f64 1 2) (neg.f64 x))
✓	0.1b	(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
	36.0b	(.f64 1/2 (pow.f64 (sqrt.f64 (+.f64 (.f64 y (sqrt.f64 z)) x)) 2))
	47.9b	(.f64 1/2 (/.f64 (.f64 y (.f64 y z)) (-.f64 (.f64 y (sqrt.f64 z)) x)))
✓	0.1b	(.f64 1/2 (+.f64 (.f64 y (sqrt.f64 z)) x))
✓	26.5b	(.f64 1/2 (+.f64 (sqrt.f64 (.f64 y (*.f64 y z))) x))
	32.2b	(.f64 1/2 (.f64 (-.f64 (.f64 y (.f64 y z)) (.f64 x x)) (/.f64 1 (-.f64 (.f64 y (sqrt.f64 z)) x))))
✓	33.5b	(.f64 1/2 (.f64 y (sqrt.f64 z)))
	58.6b	(.f64 1/2 (sqrt.f64 (.f64 z (*.f64 y y))))
✓	29.7b	(*.f64 1/2 x)

Compiler

Compiled 212 to 166 computations (21.7% saved)

regimes204.0ms (3.2%)

Counts

32 → 1

Calls

Call 1

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

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

Calls

8 calls:

46.0ms	(.f64 (/.f64 1 2) (+.f64 x (.f64 y (sqrt.f64 z))))
39.0ms	(*.f64 y (sqrt.f64 z))
20.0ms	z
19.0ms	(+.f64 x (*.f64 y (sqrt.f64 z)))
18.0ms	(sqrt.f64 z)

Results

Error	Segments	Branch
0.1b	1	`x`
0.1b	1	`y`
0.1b	1	`z`
0.1b	1	`(.f64 (/.f64 1 2) (+.f64 x (.f64 y (sqrt.f64 z))))`
0.1b	1	`(+.f64 x (*.f64 y (sqrt.f64 z)))`
0.1b	1	`(*.f64 y (sqrt.f64 z))`
0.1b	1	`(*.f64 y (sqrt.f64 z))`
0.1b	1	`(sqrt.f64 z)`

Compiler

Compiled 450 to 261 computations (42% saved)

regimes127.0ms (2%)

Counts

22 → 1

Calls

Call 1

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

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

Calls

7 calls:

41.0ms	(sqrt.f64 z)
16.0ms	(*.f64 y (sqrt.f64 z))
13.0ms	y
12.0ms	(.f64 (/.f64 1 2) (+.f64 x (.f64 y (sqrt.f64 z))))
12.0ms	z

Results

Error	Segments	Branch
0.1b	1	`x`
0.1b	1	`y`
0.1b	1	`z`
0.1b	1	`(.f64 (/.f64 1 2) (+.f64 x (.f64 y (sqrt.f64 z))))`
0.1b	1	`(+.f64 x (*.f64 y (sqrt.f64 z)))`
0.1b	1	`(*.f64 y (sqrt.f64 z))`
0.1b	1	`(sqrt.f64 z)`

Compiler

Compiled 317 to 172 computations (45.7% saved)

regimes239.0ms (3.7%)

Counts

6 → 5

Calls

Call 1

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

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

Calls

5 calls:

103.0ms	z
47.0ms	(sqrt.f64 z)
32.0ms	x
30.0ms	(*.f64 y (sqrt.f64 z))
24.0ms	y

Results

Error	Segments	Branch
11.3b	5	`x`
16.2b	3	`y`
21.2b	10	`z`
13.6b	7	`(*.f64 y (sqrt.f64 z))`
21.2b	10	`(sqrt.f64 z)`

Compiler

Compiled 68 to 53 computations (22.1% saved)

bsearch143.0ms (2.2%)

Algorithm

4×	binary-search

Steps

Time	Left	Right
51.0ms	985550.1694290685	1984707.7885266945
22.0ms	3.7287496659406427e-75	1.9240238722949991e-72
22.0ms	8.857867291799999e-123	2.350423423851963e-116
47.0ms	-4.691216402372508e-138	-1.8734428317330715e-142

Compiler

Compiled 19 to 15 computations (21.1% saved)

regimes15.0ms (0.2%)

Accuracy

Total -33.2b remaining (-111.8%)

Threshold costs -33.2b (-111.8%)

Counts

4 → 1

Calls

Call 1

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

Outputs
(*.f64 1/2 x)

Calls

3 calls:

5.0ms	z
4.0ms	x
4.0ms	y

Results

Error	Segments	Branch
29.7b	1	`x`
29.7b	1	`y`
29.7b	1	`z`

Compiler

Compiled 42 to 35 computations (16.7% saved)

simplify101.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
3×	`+-commutative_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	86
1	45	86
2	46	86

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
(.f64 1/2 (+.f64 (.f64 y (sqrt.f64 z)) x))
(if (<=.f64 x -3931183030050431/837987995621412318723376562387865382967460363787024586107722590232610251879596686050117143635431464230626991136655378178359617675746660621652103062880256) (.f64 1/2 x) (if (<=.f64 x 3296379372724067/372141426839350727961253789638658321589064376671906846864122981980487315514059736743009817965446945567110411062408283101969716033850703872) (.f64 1/2 (.f64 y (sqrt.f64 z))) (if (<=.f64 x 3797798608133143/1018517988167243043134222844204689080525734196832968125318070224677190649881668353091698688) (.f64 1/2 x) (if (<=.f64 x 1058226436566277/1073741824) (.f64 1/2 (.f64 y (sqrt.f64 z))) (*.f64 (/.f64 1 2) (-.f64 (+.f64 1 x) 1))))))
(*.f64 1/2 x)

Outputs
(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
(.f64 1/2 (+.f64 (.f64 y (sqrt.f64 z)) x))
(.f64 1/2 (+.f64 x (.f64 y (sqrt.f64 z))))
(if (<=.f64 x -3931183030050431/837987995621412318723376562387865382967460363787024586107722590232610251879596686050117143635431464230626991136655378178359617675746660621652103062880256) (.f64 1/2 x) (if (<=.f64 x 3296379372724067/372141426839350727961253789638658321589064376671906846864122981980487315514059736743009817965446945567110411062408283101969716033850703872) (.f64 1/2 (.f64 y (sqrt.f64 z))) (if (<=.f64 x 3797798608133143/1018517988167243043134222844204689080525734196832968125318070224677190649881668353091698688) (.f64 1/2 x) (if (<=.f64 x 1058226436566277/1073741824) (.f64 1/2 (.f64 y (sqrt.f64 z))) (*.f64 (/.f64 1 2) (-.f64 (+.f64 1 x) 1))))))
(if (<=.f64 x -3931183030050431/837987995621412318723376562387865382967460363787024586107722590232610251879596686050117143635431464230626991136655378178359617675746660621652103062880256) (.f64 1/2 x) (if (<=.f64 x 3296379372724067/372141426839350727961253789638658321589064376671906846864122981980487315514059736743009817965446945567110411062408283101969716033850703872) (.f64 1/2 (.f64 y (sqrt.f64 z))) (if (<=.f64 x 3797798608133143/1018517988167243043134222844204689080525734196832968125318070224677190649881668353091698688) (.f64 1/2 x) (if (<=.f64 x 1058226436566277/1073741824) (.f64 1/2 (.f64 y (sqrt.f64 z))) (*.f64 1/2 (+.f64 (+.f64 x 1) -1))))))
(*.f64 1/2 x)

Compiler

Compiled 71 to 51 computations (28.2% saved)

soundness9.0ms (0.1%)

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

Compiler

Compiled 48 to 36 computations (25% saved)

end38.0ms (0.6%)

Compiler: Compiled 62 to 39 computations (37.1% saved)

Iter	Nodes	Cost
0	10	159
1	19	156
2	36	156
3	49	156
4	61	156
5	98	156
6	155	156
7	206	156
8	277	156
9	372	156
10	448	156
11	462	156
12	464	156

Iter	Nodes	Cost
0	10	159
1	19	156
2	36	156
3	49	156
4	61	156
5	98	156
6	155	156
7	206	156
8	277	156
9	372	156
10	448	156
11	462	156
12	464	156

Iter	Nodes	Cost
0	10	159
1	19	156
2	36	156
3	49	156
4	61	156
5	98	156
6	155	156
7	206	156
8	277	156
9	372	156
10	448	156
11	462	156
12	464	156