Details

analyze395.0ms (4.2%)

Algorithm

1×

Search

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

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample2.0s (21.4%)

Results

1.6s	8256×	body	256	valid
394.0ms	2793×	body	256	invalid

preprocess37.0ms (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)

simplify13.0ms (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)

prune3.0ms (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 1/2 (fma.f64 y (sqrt.f64 z) x))
▶	0.1b	(.f64 (/.f64 1 2) (+.f64 x (.f64 y (sqrt.f64 z))))

Compiler

Compiled 23 to 17 computations (26.1% saved)

localize18.0ms (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)

series10.0ms (0.1%)

Counts

1 → 25

Calls

9 calls:

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

rewrite72.0ms (0.8%)

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)))))))

simplify15.0ms (0.2%)

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)

localize13.0ms (0.1%)

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)

series7.0ms (0.1%)

Counts

2 → 25

Calls

15 calls:

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

rewrite80.0ms (0.9%)

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)))))

simplify11.0ms (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

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

eval17.0ms (0.2%)

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

prune19.0ms (0.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	65	8	73
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	66	9	75

Error

0.0b

Counts

75 → 9

Alt Table

Click to see full alt table

Status	Error	Program
▶	21.0b	(.f64 (/.f64 1 2) (+.f64 x (cbrt.f64 (pow.f64 (.f64 y (sqrt.f64 z)) 3))))
	33.8b	(.f64 1/2 (.f64 y (sqrt.f64 z)))
▶	27.2b	(.f64 (/.f64 1 2) (+.f64 x (sqrt.f64 (.f64 z (*.f64 y y)))))
▶	0.1b	(.f64 1/2 (+.f64 (.f64 y (sqrt.f64 z)) x))
✓	0.1b	(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
	33.6b	(.f64 (/.f64 1 2) (/.f64 (-.f64 (.f64 z (.f64 y y)) (.f64 x x)) (-.f64 (*.f64 y (sqrt.f64 z)) x)))
▶	44.2b	(.f64 (/.f64 1 2) (/.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)))))
▶	28.9b	(*.f64 1/2 x)
	32.3b	(.f64 (/.f64 1 2) (+.f64 x (pow.f64 (sqrt.f64 (.f64 y (sqrt.f64 z))) 2)))

Compiler

Compiled 266 to 187 computations (29.7% saved)

localize9.0ms (0.1%)

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	z	@	0	(+.f64 (*.f64 y (sqrt.f64 z)) x)
0.0ms	y	@	inf	(+.f64 (*.f64 y (sqrt.f64 z)) x)

rewrite60.0ms (0.6%)

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)))))

simplify11.0ms (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%)

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

localize14.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	6.1b	(.f64 z (.f64 y y))
✓	24.7b	(sqrt.f64 (.f64 z (.f64 y y)))

Compiler

Compiled 45 to 16 computations (64.4% saved)

series10.0ms (0.1%)

Counts

2 → 36

Calls

12 calls:

Time	Variable		Point	Expression
4.0ms	y	@	0	(sqrt.f64 (.f64 z (.f64 y y)))
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))

rewrite66.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

537×	`pow1_binary64`
511×	`add-sqr-sqrt_binary64`
496×	`add-log-exp_binary64`
496×	`log1p-expm1-u_binary64`
496×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	16
1	121	13
2	1448	13

Stop Event

1×	node limit

Counts

2 → 36

Calls

Call 1

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

simplify114.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

974×	`fma-def_binary64`
404×	`distribute-rgt-neg-out_binary64`
365×	`fma-neg_binary64`
337×	`distribute-rgt-neg-in_binary64`
318×	`fabs-mul_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	248
1	21	248
2	44	248
3	86	248
4	204	248
5	634	248
6	988	248
7	1635	248
8	2039	248
9	2929	248
10	3766	248
11	4633	248
12	5763	248

Stop Event

1×	node limit

Counts

72 → 40

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)

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)))
(neg.f64 (*.f64 y (sqrt.f64 z)))
(*.f64 y (neg.f64 (sqrt.f64 z)))
(.f64 -1 (.f64 y (sqrt.f64 z)))
(neg.f64 (*.f64 y (sqrt.f64 z)))
(*.f64 y (neg.f64 (sqrt.f64 z)))
(.f64 -1 (.f64 y (sqrt.f64 z)))
(neg.f64 (*.f64 y (sqrt.f64 z)))
(*.f64 y (neg.f64 (sqrt.f64 z)))
(.f64 -1 (.f64 y (sqrt.f64 z)))
(neg.f64 (*.f64 y (sqrt.f64 z)))
(*.f64 y (neg.f64 (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))

localize40.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (cbrt.f64 (pow.f64 (*.f64 y (sqrt.f64 z)) 3)))
✓	0.2b	(pow.f64 (*.f64 y (sqrt.f64 z)) 3)
	0.2b	(*.f64 y (sqrt.f64 z))
✓	35.7b	(cbrt.f64 (pow.f64 (*.f64 y (sqrt.f64 z)) 3))

Compiler

Compiled 53 to 28 computations (47.2% saved)

series30.0ms (0.3%)

Counts

3 → 49

Calls

21 calls:

Time	Variable		Point	Expression
6.0ms	z	@	-inf	(pow.f64 (*.f64 y (sqrt.f64 z)) 3)
5.0ms	z	@	0	(pow.f64 (*.f64 y (sqrt.f64 z)) 3)
5.0ms	y	@	-inf	(cbrt.f64 (pow.f64 (*.f64 y (sqrt.f64 z)) 3))
2.0ms	z	@	inf	(pow.f64 (*.f64 y (sqrt.f64 z)) 3)
1.0ms	y	@	-inf	(pow.f64 (*.f64 y (sqrt.f64 z)) 3)

rewrite79.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

956×	`pow1_binary64`
895×	`add-log-exp_binary64`
895×	`log1p-expm1-u_binary64`
895×	`expm1-log1p-u_binary64`
99×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	24
1	218	22
2	2534	22

Stop Event

1×	node limit

Counts

3 → 92

Calls

Call 1

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

Outputs

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

simplify131.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

789×	`fma-def_binary64`
546×	`unswap-sqr_binary64`
510×	`fma-neg_binary64`
392×	`sqr-pow_binary64`
303×	`*-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	18	423
1	45	420
2	98	396
3	197	396
4	339	396
5	1071	396
6	2256	396
7	2442	396
8	2748	396
9	3611	396
10	4174	396
11	4902	396
12	6238	396
13	7651	396

Stop Event

1×	node limit

Counts

141 → 99

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

localize36.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(fma.f64 x x (.f64 (.f64 y (sqrt.f64 z)) (-.f64 (*.f64 y (sqrt.f64 z)) x)))
✓	1.9b	(.f64 (.f64 y (sqrt.f64 z)) (-.f64 (*.f64 y (sqrt.f64 z)) x))
✓	2.9b	(+.f64 (pow.f64 x 3) (pow.f64 (*.f64 y (sqrt.f64 z)) 3))
✓	42.8b	(/.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))))

Compiler

Compiled 122 to 39 computations (68% saved)

series47.0ms (0.5%)

Counts

4 → 99

Calls

36 calls:

Time	Variable		Point	Expression
11.0ms	z	@	-inf	(/.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))))
9.0ms	z	@	inf	(/.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))))
3.0ms	z	@	inf	(.f64 (.f64 y (sqrt.f64 z)) (-.f64 (*.f64 y (sqrt.f64 z)) x))
2.0ms	z	@	0	(/.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))))
1.0ms	x	@	0	(/.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))))

rewrite114.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

845×	`fma-def_binary64`
819×	`log-prod_binary64`
327×	`fma-neg_binary64`
269×	`expm1-udef_binary64`
269×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	91
1	327	59
2	4725	59

Stop Event

1×	node limit

Counts

4 → 260

Calls

Call 1

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

simplify90.0ms (1%)

Algorithm

1×	egg-herbie

Rules

793×	`fma-neg_binary64`
723×	`fma-def_binary64`
528×	`associate-/l/_binary64`
331×	`associate-l_binary64`
282×	`associate-+l+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	104	1326
1	376	1266
2	1484	1116
3	5809	1116

Stop Event

1×	node limit

Counts

359 → 290

Calls

Call 1

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

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

eval254.0ms (2.7%)

Compiler: Compiled 12605 to 5136 computations (59.3% saved)

prune264.0ms (2.8%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	480	8	488
Fresh	2	1	3
Picked	1	0	1
Done	2	3	5
Total	485	12	497

Error

0.0b

Counts

497 → 12

Alt Table

Click to see full alt table

Status	Error	Program
	0.6b	(.f64 (/.f64 1 2) (fma.f64 (.f64 (sqrt.f64 z) (pow.f64 (cbrt.f64 y) 2)) (cbrt.f64 y) x))
	32.3b	(.f64 1/2 (+.f64 (pow.f64 (sqrt.f64 (.f64 y (sqrt.f64 z))) 2) x))
▶	33.8b	(.f64 1/2 (.f64 y (sqrt.f64 z)))
▶	24.5b	(.f64 (/.f64 1 2) (+.f64 x (sqrt.f64 (.f64 y (*.f64 y z)))))
▶	0.3b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (pow.f64 z 1/4) (*.f64 (pow.f64 z 1/4) y))))
✓	0.1b	(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
	27.2b	(.f64 1/2 (+.f64 (sqrt.f64 (.f64 z (*.f64 y y))) x))
✓	0.1b	(.f64 1/2 (+.f64 (.f64 y (sqrt.f64 z)) x))
✓	28.9b	(*.f64 1/2 x)
▶	0.4b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (*.f64 y (cbrt.f64 z)) (cbrt.f64 (sqrt.f64 z)))))
▶	36.6b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (sqrt.f64 (*.f64 z y)) (sqrt.f64 y))))
	33.6b	(.f64 1/2 (/.f64 (-.f64 (.f64 z (.f64 y y)) (.f64 x x)) (-.f64 (*.f64 y (sqrt.f64 z)) x)))

Compiler

Compiled 309 to 226 computations (26.9% saved)

localize105.0ms (1.1%)

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)))
✓	0.2b	(*.f64 (pow.f64 z 1/4) y)
✓	0.4b	(.f64 (pow.f64 z 1/4) (.f64 (pow.f64 z 1/4) y))

Compiler

Compiled 55 to 38 computations (30.9% saved)

series207.0ms (2.2%)

Counts

3 → 61

Calls

21 calls:

Time	Variable		Point	Expression
85.0ms	y	@	0	(*.f64 (pow.f64 z 1/4) y)
63.0ms	z	@	0	(*.f64 (pow.f64 z 1/4) y)
29.0ms	z	@	-inf	(*.f64 (pow.f64 z 1/4) y)
15.0ms	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))

rewrite672.0ms (7.2%)

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)))))

simplify69.0ms (0.7%)

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)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 18 to 8 computations (55.6% saved)

series7.0ms (0.1%)

Counts

1 → 0

Calls

6 calls:

Time	Variable		Point	Expression
4.0ms	z	@	inf	(.f64 1/2 (.f64 y (sqrt.f64 z)))
1.0ms	z	@	-inf	(.f64 1/2 (.f64 y (sqrt.f64 z)))
1.0ms	z	@	0	(.f64 1/2 (.f64 y (sqrt.f64 z)))
1.0ms	y	@	0	(.f64 1/2 (.f64 y (sqrt.f64 z)))
0.0ms	y	@	inf	(.f64 1/2 (.f64 y (sqrt.f64 z)))

rewrite56.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

621×	`pow1_binary64`
571×	`add-log-exp_binary64`
571×	`log1p-expm1-u_binary64`
571×	`expm1-log1p-u_binary64`
558×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	140	9
2	1587	9

Stop Event

1×	node limit

Counts

1 → 11

Calls

Call 1

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

Outputs

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

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

11 → 11

Calls

Call 1

Inputs

Outputs

localize14.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 y (.f64 y z))
✓	24.7b	(sqrt.f64 (.f64 y (.f64 y z)))

Compiler

Compiled 45 to 16 computations (64.4% saved)

series7.0ms (0.1%)

Counts

2 → 36

Calls

12 calls:

Time	Variable		Point	Expression
4.0ms	z	@	0	(.f64 y (.f64 y z))
0.0ms	z	@	-inf	(sqrt.f64 (.f64 y (.f64 y z)))
0.0ms	z	@	0	(sqrt.f64 (.f64 y (.f64 y z)))
0.0ms	y	@	0	(sqrt.f64 (.f64 y (.f64 y z)))
0.0ms	z	@	inf	(sqrt.f64 (.f64 y (.f64 y z)))

rewrite55.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

551×	`pow1_binary64`
507×	`add-log-exp_binary64`
507×	`log1p-expm1-u_binary64`
507×	`expm1-log1p-u_binary64`
494×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	16
1	120	13
2	1429	13

Stop Event

1×	node limit

Counts

2 → 36

Calls

Call 1

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

simplify112.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

974×	`fma-def_binary64`
404×	`distribute-rgt-neg-out_binary64`
365×	`fma-neg_binary64`
337×	`distribute-rgt-neg-in_binary64`
318×	`fabs-mul_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	248
1	21	248
2	44	248
3	86	248
4	204	248
5	634	248
6	988	248
7	1635	248
8	2039	248
9	2929	248
10	3766	248
11	4633	248
12	5763	248

Stop Event

1×	node limit

Counts

72 → 40

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)

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)))
(neg.f64 (*.f64 y (sqrt.f64 z)))
(*.f64 y (neg.f64 (sqrt.f64 z)))
(.f64 -1 (.f64 y (sqrt.f64 z)))
(neg.f64 (*.f64 y (sqrt.f64 z)))
(*.f64 y (neg.f64 (sqrt.f64 z)))
(.f64 -1 (.f64 y (sqrt.f64 z)))
(neg.f64 (*.f64 y (sqrt.f64 z)))
(*.f64 y (neg.f64 (sqrt.f64 z)))
(.f64 -1 (.f64 y (sqrt.f64 z)))
(neg.f64 (*.f64 y (sqrt.f64 z)))
(*.f64 y (neg.f64 (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))

localize32.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (sqrt.f64 (.f64 z y)) (sqrt.f64 y))
✓	10.9b	(sqrt.f64 (*.f64 z y))

Compiler

Compiled 49 to 17 computations (65.3% saved)

series14.0ms (0.1%)

Counts

2 → 12

Calls

12 calls:

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

rewrite64.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

619×	`pow1_binary64`
569×	`add-log-exp_binary64`
569×	`log1p-expm1-u_binary64`
569×	`expm1-log1p-u_binary64`
552×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	15
1	140	12
2	1641	12

Stop Event

1×	node limit

Counts

2 → 37

Calls

Call 1

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

Outputs

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

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

simplify79.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

899×	`fma-def_binary64`
445×	`cube-prod_binary64`
388×	`distribute-rgt-neg-in_binary64`
388×	`fma-neg_binary64`
330×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	72
1	25	72
2	74	72
3	179	72
4	706	72
5	1548	72
6	2571	72
7	3718	72
8	4857	72
9	6712	72

Stop Event

1×

unsound

Counts

49 → 39

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

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 y (cbrt.f64 z))
✓	0.3b	(.f64 (.f64 y (cbrt.f64 z)) (cbrt.f64 (sqrt.f64 z)))
✓	0.6b	(cbrt.f64 z)
✓	0.6b	(cbrt.f64 (sqrt.f64 z))

Compiler

Compiled 54 to 18 computations (66.7% saved)

series43.0ms (0.5%)

Counts

4 → 36

Calls

18 calls:

Time	Variable		Point	Expression
22.0ms	z	@	-inf	(.f64 (.f64 y (cbrt.f64 z)) (cbrt.f64 (sqrt.f64 z)))
9.0ms	z	@	0	(cbrt.f64 (sqrt.f64 z))
2.0ms	z	@	-inf	(cbrt.f64 (sqrt.f64 z))
2.0ms	y	@	0	(*.f64 y (cbrt.f64 z))
1.0ms	z	@	-inf	(*.f64 y (cbrt.f64 z))

rewrite60.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

662×	`pow1_binary64`
611×	`add-log-exp_binary64`
611×	`log1p-expm1-u_binary64`
611×	`expm1-log1p-u_binary64`
593×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	27
1	155	19
2	1815	19

Stop Event

1×	node limit

Counts

4 → 68

Calls

Call 1

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

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

simplify166.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

2124×	`unswap-sqr_binary64`
1124×	`sqr-pow_binary64`
478×	`pow-sqr_binary64`
465×	`fabs-mul_binary64`
462×	`cube-prod_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	228
1	44	228
2	81	228
3	182	228
4	697	228
5	1327	228
6	1409	228
7	1534	228
8	1700	228
9	1899	228
10	2164	228
11	2502	228
12	2919	228
13	3430	228
14	4055	228
15	4439	228
16	4709	228
17	4909	228
18	5103	228
19	5201	228
20	5778	228

Stop Event

1×	node limit

Counts

104 → 73

Calls

Call 1

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

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

eval78.0ms (0.8%)

Compiler: Compiled 4282 to 2391 computations (44.2% saved)

prune48.0ms (0.5%)

Pruning

12 alts after pruning (5 fresh and 7 done)

	Pruned	Kept	Total
New	274	4	278
Fresh	3	1	4
Picked	1	0	1
Done	0	7	7
Total	278	12	290

Error

Counts

290 → 12

Alt Table

Click to see full alt table

Status	Error	Program
✓	33.8b	(.f64 1/2 (.f64 y (sqrt.f64 z)))
✓	24.5b	(.f64 (/.f64 1 2) (+.f64 x (sqrt.f64 (.f64 y (*.f64 y z)))))
✓	0.3b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (pow.f64 z 1/4) (*.f64 (pow.f64 z 1/4) y))))
✓	0.1b	(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
▶	34.2b	(pow.f64 (cbrt.f64 (.f64 1/2 (.f64 y (sqrt.f64 z)))) 3)
▶	51.2b	(.f64 1/2 (pow.f64 (sqrt.f64 (.f64 y (sqrt.f64 z))) 2))
▶	0.4b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (*.f64 y (cbrt.f64 z)) (sqrt.f64 (cbrt.f64 z)))))
▶	57.5b	(.f64 1/2 (sqrt.f64 (.f64 z (*.f64 y y))))
✓	0.1b	(.f64 1/2 (+.f64 (.f64 y (sqrt.f64 z)) x))
✓	28.9b	(*.f64 1/2 x)
✓	36.6b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (sqrt.f64 (*.f64 z y)) (sqrt.f64 y))))
▶	33.6b	(.f64 1/2 (/.f64 (-.f64 (.f64 z (.f64 y y)) (.f64 x x)) (-.f64 (*.f64 y (sqrt.f64 z)) x)))

Compiler

Compiled 231 to 170 computations (26.4% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (cbrt.f64 z))
	0.3b	(*.f64 y (cbrt.f64 z))
✓	0.3b	(.f64 (.f64 y (cbrt.f64 z)) (sqrt.f64 (cbrt.f64 z)))
	0.6b	(cbrt.f64 z)

Compiler

Compiled 52 to 17 computations (67.3% saved)

series5.0ms (0.1%)

Counts

2 → 24

Calls

9 calls:

Time	Variable		Point	Expression
2.0ms	z	@	-inf	(sqrt.f64 (cbrt.f64 z))
1.0ms	z	@	-inf	(.f64 (.f64 y (cbrt.f64 z)) (sqrt.f64 (cbrt.f64 z)))
0.0ms	z	@	0	(sqrt.f64 (cbrt.f64 z))
0.0ms	z	@	0	(.f64 (.f64 y (cbrt.f64 z)) (sqrt.f64 (cbrt.f64 z)))
0.0ms	y	@	0	(.f64 (.f64 y (cbrt.f64 z)) (sqrt.f64 (cbrt.f64 z)))

rewrite66.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

609×	`pow1_binary64`
563×	`add-log-exp_binary64`
563×	`log1p-expm1-u_binary64`
563×	`expm1-log1p-u_binary64`
547×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	18
1	138	10
2	1615	10

Stop Event

1×	node limit

Counts

2 → 32

Calls

Call 1

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

simplify151.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

1002×	`sqr-pow_binary64`
724×	`unswap-sqr_binary64`
588×	`associate-l_binary64`
504×	`cube-prod_binary64`
428×	`pow-sqr_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	156
1	24	156
2	37	156
3	64	156
4	142	156
5	440	156
6	1700	156
7	3040	156
8	3200	156
9	3480	156
10	3796	156
11	4247	156
12	4860	156
13	5670	156
14	6158	156
15	6627	156
16	6898	156
17	7153	156
18	7293	156

Stop Event

1×	node limit

Counts

56 → 35

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))
(pow.f64 z 1/6)
(pow.f64 z 1/6)
(pow.f64 z 1/6)
(pow.f64 z 1/6)
(pow.f64 z 1/6)
(pow.f64 z 1/6)
(pow.f64 z 1/6)
(pow.f64 z 1/6)
(.f64 (pow.f64 (.f64 -1 z) 1/6) (sqrt.f64 (cbrt.f64 -1)))
(.f64 (pow.f64 (.f64 -1 z) 1/6) (sqrt.f64 (cbrt.f64 -1)))
(.f64 (pow.f64 (.f64 -1 z) 1/6) (sqrt.f64 (cbrt.f64 -1)))
(.f64 (pow.f64 (.f64 -1 z) 1/6) (sqrt.f64 (cbrt.f64 -1)))

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))
(pow.f64 z 1/6)
(pow.f64 z 1/6)
(pow.f64 z 1/6)
(pow.f64 z 1/6)
(pow.f64 z 1/6)
(pow.f64 z 1/6)
(pow.f64 z 1/6)
(pow.f64 z 1/6)
(.f64 (pow.f64 (.f64 -1 z) 1/6) (sqrt.f64 (cbrt.f64 -1)))
(*.f64 (pow.f64 (neg.f64 z) 1/6) (sqrt.f64 (cbrt.f64 -1)))
(*.f64 (sqrt.f64 (cbrt.f64 -1)) (pow.f64 (neg.f64 z) 1/6))
(.f64 (pow.f64 (.f64 -1 z) 1/6) (sqrt.f64 (cbrt.f64 -1)))
(*.f64 (pow.f64 (neg.f64 z) 1/6) (sqrt.f64 (cbrt.f64 -1)))
(*.f64 (sqrt.f64 (cbrt.f64 -1)) (pow.f64 (neg.f64 z) 1/6))
(.f64 (pow.f64 (.f64 -1 z) 1/6) (sqrt.f64 (cbrt.f64 -1)))
(*.f64 (pow.f64 (neg.f64 z) 1/6) (sqrt.f64 (cbrt.f64 -1)))
(*.f64 (sqrt.f64 (cbrt.f64 -1)) (pow.f64 (neg.f64 z) 1/6))
(.f64 (pow.f64 (.f64 -1 z) 1/6) (sqrt.f64 (cbrt.f64 -1)))
(*.f64 (pow.f64 (neg.f64 z) 1/6) (sqrt.f64 (cbrt.f64 -1)))
(*.f64 (sqrt.f64 (cbrt.f64 -1)) (pow.f64 (neg.f64 z) 1/6))

localize13.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 1/2 (sqrt.f64 (.f64 z (*.f64 y y))))
	6.1b	(.f64 z (.f64 y y))
	24.7b	(sqrt.f64 (.f64 z (.f64 y y)))

Compiler

Compiled 28 to 9 computations (67.9% saved)

series2.0ms (0%)

Counts

1 → 12

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	z	@	0	(.f64 1/2 (sqrt.f64 (.f64 z (*.f64 y y))))
0.0ms	z	@	-inf	(.f64 1/2 (sqrt.f64 (.f64 z (*.f64 y y))))
0.0ms	z	@	inf	(.f64 1/2 (sqrt.f64 (.f64 z (*.f64 y y))))
0.0ms	y	@	-inf	(.f64 1/2 (sqrt.f64 (.f64 z (*.f64 y y))))
0.0ms	y	@	inf	(.f64 1/2 (sqrt.f64 (.f64 z (*.f64 y y))))

rewrite52.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

700×	`pow1_binary64`
645×	`add-log-exp_binary64`
645×	`log1p-expm1-u_binary64`
645×	`expm1-log1p-u_binary64`
628×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	161	9
2	1853	9

Stop Event

1×	node limit

Counts

1 → 11

Calls

Call 1

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

Outputs

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

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

9×	`*-commutative_binary64`
6×	`associate-r_binary64`
6×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	108
1	16	108
2	30	108
3	34	108

Stop Event

1×

saturated

Counts

23 → 15

Calls

Call 1

Inputs
(.f64 1/2 (.f64 y (sqrt.f64 z)))
(.f64 1/2 (.f64 y (sqrt.f64 z)))
(.f64 1/2 (.f64 y (sqrt.f64 z)))
(.f64 1/2 (.f64 y (sqrt.f64 z)))
(.f64 1/2 (.f64 y (sqrt.f64 z)))
(.f64 1/2 (.f64 y (sqrt.f64 z)))
(.f64 1/2 (.f64 y (sqrt.f64 z)))
(.f64 1/2 (.f64 y (sqrt.f64 z)))
(.f64 -1/2 (.f64 y (sqrt.f64 z)))
(.f64 -1/2 (.f64 y (sqrt.f64 z)))
(.f64 -1/2 (.f64 y (sqrt.f64 z)))
(.f64 -1/2 (.f64 y (sqrt.f64 z)))

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

localize48.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(*.f64 y (sqrt.f64 z))
✓	2.9b	(-.f64 (.f64 z (.f64 y y)) (*.f64 x x))
	6.1b	(.f64 z (.f64 y y))
✓	28.0b	(/.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)

series14.0ms (0.1%)

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))
2.0ms	z	@	inf	(/.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	x	@	0	(/.f64 (-.f64 (.f64 z (.f64 y y)) (.f64 x x)) (-.f64 (.f64 y (sqrt.f64 z)) x))
1.0ms	x	@	inf	(/.f64 (-.f64 (.f64 z (.f64 y y)) (.f64 x x)) (-.f64 (.f64 y (sqrt.f64 z)) x))

rewrite203.0ms (2.2%)

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

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

simplify137.0ms (1.5%)

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)))

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 1/2 (pow.f64 (sqrt.f64 (.f64 y (sqrt.f64 z))) 2))
✓	0.2b	(pow.f64 (sqrt.f64 (*.f64 y (sqrt.f64 z))) 2)
	0.2b	(*.f64 y (sqrt.f64 z))
✓	4.6b	(sqrt.f64 (*.f64 y (sqrt.f64 z)))

Compiler

Compiled 34 to 14 computations (58.8% saved)

series14.0ms (0.2%)

Counts

3 → 36

Calls

18 calls:

Time	Variable		Point	Expression
2.0ms	y	@	0	(pow.f64 (sqrt.f64 (*.f64 y (sqrt.f64 z))) 2)
1.0ms	y	@	-inf	(pow.f64 (sqrt.f64 (*.f64 y (sqrt.f64 z))) 2)
1.0ms	y	@	0	(sqrt.f64 (*.f64 y (sqrt.f64 z)))
1.0ms	z	@	-inf	(sqrt.f64 (*.f64 y (sqrt.f64 z)))
1.0ms	z	@	0	(sqrt.f64 (*.f64 y (sqrt.f64 z)))

rewrite65.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

748×	`pow1_binary64`
689×	`add-log-exp_binary64`
689×	`log1p-expm1-u_binary64`
689×	`expm1-log1p-u_binary64`
672×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	23
1	204	23
2	1968	23

Stop Event

1×	node limit

Counts

3 → 63

Calls

Call 1

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

Outputs

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

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

simplify175.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

754×	`fma-def_binary64`
683×	`associate-l_binary64`
636×	`sqr-pow_binary64`
492×	`*-commutative_binary64`
455×	`cube-prod_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	26	348
1	55	328
2	112	324
3	235	324
4	612	324
5	1601	324
6	2215	324
7	3087	324
8	3371	324
9	3840	324
10	4393	324
11	4950	324
12	5614	324
13	6434	324
14	7025	324

Stop Event

1×	node limit

Counts

99 → 71

Calls

Call 1

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

Outputs
(.f64 (pow.f64 (.f64 1 z) 1/4) (sqrt.f64 y))
(*.f64 (pow.f64 z 1/4) (sqrt.f64 y))
(.f64 (pow.f64 (.f64 1 z) 1/4) (sqrt.f64 y))
(*.f64 (pow.f64 z 1/4) (sqrt.f64 y))
(.f64 (pow.f64 (.f64 1 z) 1/4) (sqrt.f64 y))
(*.f64 (pow.f64 z 1/4) (sqrt.f64 y))
(.f64 (pow.f64 (.f64 1 z) 1/4) (sqrt.f64 y))
(*.f64 (pow.f64 z 1/4) (sqrt.f64 y))
(.f64 (pow.f64 (.f64 1 z) 1/4) (sqrt.f64 y))
(*.f64 (pow.f64 z 1/4) (sqrt.f64 y))
(.f64 (pow.f64 (.f64 1 z) 1/4) (sqrt.f64 y))
(*.f64 (pow.f64 z 1/4) (sqrt.f64 y))
(.f64 (pow.f64 (.f64 1 z) 1/4) (sqrt.f64 y))
(*.f64 (pow.f64 z 1/4) (sqrt.f64 y))
(.f64 (pow.f64 (.f64 1 z) 1/4) (sqrt.f64 y))
(*.f64 (pow.f64 z 1/4) (sqrt.f64 y))
(.f64 (pow.f64 (.f64 -1 z) 1/4) (sqrt.f64 (*.f64 (sqrt.f64 -1) y)))
(.f64 (pow.f64 (neg.f64 z) 1/4) (sqrt.f64 (.f64 y (sqrt.f64 -1))))
(.f64 (pow.f64 (.f64 -1 z) 1/4) (sqrt.f64 (*.f64 (sqrt.f64 -1) y)))
(.f64 (pow.f64 (neg.f64 z) 1/4) (sqrt.f64 (.f64 y (sqrt.f64 -1))))
(.f64 (pow.f64 (.f64 -1 z) 1/4) (sqrt.f64 (*.f64 (sqrt.f64 -1) y)))
(.f64 (pow.f64 (neg.f64 z) 1/4) (sqrt.f64 (.f64 y (sqrt.f64 -1))))
(.f64 (pow.f64 (.f64 -1 z) 1/4) (sqrt.f64 (*.f64 (sqrt.f64 -1) y)))
(.f64 (pow.f64 (neg.f64 z) 1/4) (sqrt.f64 (.f64 y (sqrt.f64 -1))))
(*.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 (pow.f64 (sqrt.f64 -1) 2) y) (sqrt.f64 z))
(.f64 (sqrt.f64 z) (.f64 y (pow.f64 (sqrt.f64 -1) 2)))
(.f64 (sqrt.f64 z) (.f64 y -1))
(*.f64 y (neg.f64 (sqrt.f64 z)))
(.f64 (.f64 (pow.f64 (sqrt.f64 -1) 2) y) (sqrt.f64 z))
(.f64 (sqrt.f64 z) (.f64 y (pow.f64 (sqrt.f64 -1) 2)))
(.f64 (sqrt.f64 z) (.f64 y -1))
(*.f64 y (neg.f64 (sqrt.f64 z)))
(.f64 (.f64 (pow.f64 (sqrt.f64 -1) 2) y) (sqrt.f64 z))
(.f64 (sqrt.f64 z) (.f64 y (pow.f64 (sqrt.f64 -1) 2)))
(.f64 (sqrt.f64 z) (.f64 y -1))
(*.f64 y (neg.f64 (sqrt.f64 z)))
(.f64 (.f64 (pow.f64 (sqrt.f64 -1) 2) y) (sqrt.f64 z))
(.f64 (sqrt.f64 z) (.f64 y (pow.f64 (sqrt.f64 -1) 2)))
(.f64 (sqrt.f64 z) (.f64 y -1))
(*.f64 y (neg.f64 (sqrt.f64 z)))
(.f64 1/2 (.f64 y (sqrt.f64 z)))
(.f64 (.f64 1/2 y) (sqrt.f64 z))
(.f64 y (.f64 (sqrt.f64 z) 1/2))
(.f64 (.f64 y (sqrt.f64 z)) 1/2)
(.f64 1/2 (.f64 y (sqrt.f64 z)))
(.f64 (.f64 1/2 y) (sqrt.f64 z))
(.f64 y (.f64 (sqrt.f64 z) 1/2))
(.f64 (.f64 y (sqrt.f64 z)) 1/2)
(.f64 1/2 (.f64 y (sqrt.f64 z)))
(.f64 (.f64 1/2 y) (sqrt.f64 z))
(.f64 y (.f64 (sqrt.f64 z) 1/2))
(.f64 (.f64 y (sqrt.f64 z)) 1/2)
(.f64 1/2 (.f64 y (sqrt.f64 z)))
(.f64 (.f64 1/2 y) (sqrt.f64 z))
(.f64 y (.f64 (sqrt.f64 z) 1/2))
(.f64 (.f64 y (sqrt.f64 z)) 1/2)
(.f64 1/2 (.f64 y (sqrt.f64 z)))
(.f64 (.f64 1/2 y) (sqrt.f64 z))
(.f64 y (.f64 (sqrt.f64 z) 1/2))
(.f64 (.f64 y (sqrt.f64 z)) 1/2)
(.f64 1/2 (.f64 y (sqrt.f64 z)))
(.f64 (.f64 1/2 y) (sqrt.f64 z))
(.f64 y (.f64 (sqrt.f64 z) 1/2))
(.f64 (.f64 y (sqrt.f64 z)) 1/2)
(.f64 1/2 (.f64 y (sqrt.f64 z)))
(.f64 (.f64 1/2 y) (sqrt.f64 z))
(.f64 y (.f64 (sqrt.f64 z) 1/2))
(.f64 (.f64 y (sqrt.f64 z)) 1/2)
(.f64 1/2 (.f64 y (sqrt.f64 z)))
(.f64 (.f64 1/2 y) (sqrt.f64 z))
(.f64 y (.f64 (sqrt.f64 z) 1/2))
(.f64 (.f64 y (sqrt.f64 z)) 1/2)
(.f64 -1/2 (.f64 (*.f64 (pow.f64 (sqrt.f64 -1) 2) y) (sqrt.f64 z)))
(.f64 (.f64 1/2 y) (sqrt.f64 z))
(.f64 y (.f64 (sqrt.f64 z) 1/2))
(.f64 (.f64 y (sqrt.f64 z)) 1/2)
(.f64 -1/2 (.f64 (*.f64 (pow.f64 (sqrt.f64 -1) 2) y) (sqrt.f64 z)))
(.f64 (.f64 1/2 y) (sqrt.f64 z))
(.f64 y (.f64 (sqrt.f64 z) 1/2))
(.f64 (.f64 y (sqrt.f64 z)) 1/2)
(.f64 -1/2 (.f64 (*.f64 (pow.f64 (sqrt.f64 -1) 2) y) (sqrt.f64 z)))
(.f64 (.f64 1/2 y) (sqrt.f64 z))
(.f64 y (.f64 (sqrt.f64 z) 1/2))
(.f64 (.f64 y (sqrt.f64 z)) 1/2)
(.f64 -1/2 (.f64 (*.f64 (pow.f64 (sqrt.f64 -1) 2) y) (sqrt.f64 z)))
(.f64 (.f64 1/2 y) (sqrt.f64 z))
(.f64 y (.f64 (sqrt.f64 z) 1/2))
(.f64 (.f64 y (sqrt.f64 z)) 1/2)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(.f64 1/2 (.f64 y (sqrt.f64 z)))
	0.2b	(*.f64 y (sqrt.f64 z))
✓	0.7b	(pow.f64 (cbrt.f64 (.f64 1/2 (.f64 y (sqrt.f64 z)))) 3)
✓	5.3b	(cbrt.f64 (.f64 1/2 (.f64 y (sqrt.f64 z))))

Compiler

Compiled 35 to 17 computations (51.4% saved)

series19.0ms (0.2%)

Counts

2 → 24

Calls

12 calls:

Time	Variable		Point	Expression
4.0ms	z	@	0	(cbrt.f64 (.f64 1/2 (.f64 y (sqrt.f64 z))))
2.0ms	y	@	-inf	(pow.f64 (cbrt.f64 (.f64 1/2 (.f64 y (sqrt.f64 z)))) 3)
2.0ms	y	@	0	(pow.f64 (cbrt.f64 (.f64 1/2 (.f64 y (sqrt.f64 z)))) 3)
2.0ms	z	@	-inf	(cbrt.f64 (.f64 1/2 (.f64 y (sqrt.f64 z))))
1.0ms	y	@	inf	(pow.f64 (cbrt.f64 (.f64 1/2 (.f64 y (sqrt.f64 z)))) 3)

rewrite66.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

797×	`pow1_binary64`
745×	`add-log-exp_binary64`
744×	`log1p-expm1-u_binary64`
744×	`expm1-log1p-u_binary64`
727×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	209	20
2	2112	20

Stop Event

1×	node limit

Counts

2 → 58

Calls

Call 1

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

Outputs

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

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

simplify165.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

763×	`unswap-sqr_binary64`
750×	`cube-prod_binary64`
746×	`sqr-pow_binary64`
585×	`fabs-mul_binary64`
448×	`fma-def_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	34	348
1	92	304
2	225	304
3	588	304
4	758	304
5	986	304
6	1532	304
7	2526	304
8	2685	304
9	2884	304
10	3397	304
11	3864	304
12	4352	304
13	4993	304
14	5810	304
15	6872	304
16	7698	304

Stop Event

1×	node limit

Counts

82 → 66

Calls

Call 1

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

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

eval973.0ms (10.4%)

Compiler: Compiled 13037 to 4486 computations (65.6% saved)

prune503.0ms (5.4%)

Pruning

12 alts after pruning (4 fresh and 8 done)

	Pruned	Kept	Total
New	654	4	658
Fresh	0	0	0
Picked	0	1	1
Done	4	7	11
Total	658	12	670

Error

Counts

670 → 12

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.4b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (*.f64 y (cbrt.f64 z)) (sqrt.f64 (cbrt.f64 z)))))
	56.0b	(.f64 1/2 (sqrt.f64 (.f64 y (*.f64 y z))))
✓	0.1b	(.f64 1/2 (+.f64 (.f64 y (sqrt.f64 z)) x))
	45.1b	(.f64 1/2 (/.f64 (.f64 y (.f64 y z)) (-.f64 (.f64 y (sqrt.f64 z)) x)))
✓	0.1b	(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
✓	34.2b	(pow.f64 (cbrt.f64 (.f64 1/2 (.f64 y (sqrt.f64 z)))) 3)
✓	51.2b	(.f64 1/2 (pow.f64 (sqrt.f64 (.f64 y (sqrt.f64 z))) 2))
✓	57.5b	(.f64 1/2 (sqrt.f64 (.f64 z (*.f64 y y))))
✓	33.8b	(.f64 1/2 (.f64 y (sqrt.f64 z)))
✓	28.9b	(*.f64 1/2 x)
	33.9b	(.f64 (.f64 (*.f64 1/2 y) (pow.f64 z 1/4)) (pow.f64 z 1/4))
	53.1b	(.f64 1/2 (.f64 (sqrt.f64 (*.f64 z y)) (sqrt.f64 y)))

Compiler

Compiled 142 to 106 computations (25.4% saved)

regimes221.0ms (2.4%)

Counts

26 → 1

Calls

Call 1

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

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

Calls

8 calls:

47.0ms	(*.f64 y (sqrt.f64 z))
33.0ms	(*.f64 y (sqrt.f64 z))
27.0ms	(.f64 (/.f64 1 2) (+.f64 x (.f64 y (sqrt.f64 z))))
26.0ms	(+.f64 x (*.f64 y (sqrt.f64 z)))
24.0ms	(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 367 to 192 computations (47.7% saved)

regimes63.0ms (0.7%)

Counts

12 → 1

Calls

Call 1

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

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

Calls

7 calls:

10.0ms	(sqrt.f64 z)
9.0ms	(+.f64 x (*.f64 y (sqrt.f64 z)))
9.0ms	(.f64 (/.f64 1 2) (+.f64 x (.f64 y (sqrt.f64 z))))
8.0ms	x
8.0ms	y

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 178 to 87 computations (51.1% saved)

regimes185.0ms (2%)

Accuracy

Total -49.5b remaining (-373.9%)

Threshold costs -49.5b (-373.9%)

Counts

4 → 5

Calls

Call 1

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

Calls

5 calls:

51.0ms	x
42.0ms	z
41.0ms	y
27.0ms	(*.f64 y (sqrt.f64 z))
20.0ms	(sqrt.f64 z)

Results

Error	Segments	Branch
13.2b	5	`x`
15.4b	5	`y`
19.2b	4	`z`
13.2b	3	`(*.f64 y (sqrt.f64 z))`
19.2b	4	`(sqrt.f64 z)`

Compiler

Compiled 52 to 37 computations (28.8% saved)

bsearch118.0ms (1.3%)

Algorithm

4×	binary-search

Steps

Time	Left	Right
23.0ms	3.565951790083735e+39	1.5145750245645158e+42
22.0ms	-1.9613047742396892e-119	-1.7508974787812316e-119
28.0ms	-1.9738482226346165e-97	-9.212262981962894e-107
45.0ms	-2.103389146901951e+48	-1.7953418697274284e+47

Compiler

Compiled 19 to 15 computations (21.1% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	80
1	32	80

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 -2103389146901951024128600022903170210421868068864) (.f64 1/2 x) (if (<=.f64 x -3797538081005439/19239260838083241802870625048898248928261591440656956380834127638791856333738872368854622194768025215237611323392) (.f64 1/2 (.f64 y (sqrt.f64 z))) (if (<=.f64 x -7127761300316295/363419362147803445274661903944002267176820680343659030140745099590319644056698961663095525356881782780381260803133088966767300814307328) (.f64 1/2 x) (if (<=.f64 x 3565951790083735029353485821428935688192) (.f64 1/2 (.f64 y (sqrt.f64 z))) (*.f64 1/2 x)))))
(*.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 -2103389146901951024128600022903170210421868068864) (.f64 1/2 x) (if (<=.f64 x -3797538081005439/19239260838083241802870625048898248928261591440656956380834127638791856333738872368854622194768025215237611323392) (.f64 1/2 (.f64 y (sqrt.f64 z))) (if (<=.f64 x -7127761300316295/363419362147803445274661903944002267176820680343659030140745099590319644056698961663095525356881782780381260803133088966767300814307328) (.f64 1/2 x) (if (<=.f64 x 3565951790083735029353485821428935688192) (.f64 1/2 (.f64 y (sqrt.f64 z))) (*.f64 1/2 x)))))
(*.f64 1/2 x)

Compiler

Compiled 67 to 47 computations (29.9% 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)

end46.0ms (0.5%)

Compiler: Compiled 58 to 35 computations (39.7% saved)