Details

analyze5.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	50%	25%	3
50%	25%	25%	4
62.5%	12.5%	25%	5
68.7%	6.2%	25%	6
71.8%	3.1%	25%	7
73.4%	1.6%	25%	8
74.2%	0.8%	25%	9
74.6%	0.4%	25%	10
74.8%	0.2%	25%	11
74.9%	0.1%	25%	12
74.9%	0%	25%	13
74.9%	0%	25%	14

Compiler

Compiled 10 to 8 computations (20% saved)

sample763.0ms (30.3%)

Results

751.0ms	8252×	body	128	valid
1.0ms	4×	body	2048	valid

preprocess18.0ms (0.7%)

Algorithm

2×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	11	12
0	1	1

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0

Outputs
0

Call 2

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

Outputs
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))

Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	11	12

Stop Event

1×

saturated

Counts

1 → 1

Calls

Call 1

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

Outputs
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))

eval0.0ms (0%)

Compiler: Compiled 9 to 7 computations (22.2% saved)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.2b

Counts

2 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.2b	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))

Compiler

Compiled 18 to 14 computations (22.2% saved)

localize5.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
✓	0.0b	(sqrt.f64 (+.f64 x 1))
✓	0.2b	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))

series8.0ms (0.3%)

Counts

3 → 12

Calls

9 calls:

Time	Variable		Point	Expression
3.0ms	x	@	inf	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
2.0ms	x	@	-inf	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
1.0ms	x	@	0	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
0.0ms	x	@	inf	(sqrt.f64 (+.f64 x 1))
0.0ms	x	@	-inf	(sqrt.f64 (+.f64 x 1))

rewrite48.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

804×	`log1p-expm1-u_binary64`
804×	`expm1-log1p-u_binary64`
81×	`add-sqr-sqrt_binary64`
78×	`*-un-lft-identity_binary64`
78×	`pow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	27
1	157	27
2	2258	27

Stop Event

1×	node limit

Counts

3 → 93

Calls

Call 1

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

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

Outputs

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

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

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

simplify48.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

803×	`unswap-sqr_binary64`
571×	`distribute-lft-out_binary64`
504×	`fma-def_binary64`
349×	`*-commutative_binary64`
197×	`distribute-rgt-out_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	33	136
1	92	132
2	210	130
3	601	109
4	1607	109
5	2610	109
6	4589	109
7	4732	109
8	4996	109

Stop Event

1×	node limit

Counts

105 → 114

Calls

Call 1

Inputs
(*.f64 1/2 x)
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (.f64 1/2 x))
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) (*.f64 1/16 (pow.f64 x 3))))
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) (+.f64 (.f64 -5/128 (pow.f64 x 4)) (.f64 1/16 (pow.f64 x 3)))))
1
(+.f64 (*.f64 1/2 x) 1)
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) 1))
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) (+.f64 1 (*.f64 1/16 (pow.f64 x 3)))))
2
(+.f64 (*.f64 1/2 x) 2)
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) 2))
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) (+.f64 2 (*.f64 1/16 (pow.f64 x 3)))))

Outputs
(*.f64 1/2 x)
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (.f64 1/2 x))
(fma.f64 -1/8 (.f64 x x) (.f64 1/2 x))
(fma.f64 1/2 x (.f64 -1/8 (.f64 x x)))
(.f64 x (+.f64 1/2 (.f64 x -1/8)))
(*.f64 x (fma.f64 x -1/8 1/2))
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) (*.f64 1/16 (pow.f64 x 3))))
(fma.f64 -1/8 (.f64 x x) (fma.f64 1/2 x (.f64 1/16 (pow.f64 x 3))))
(fma.f64 1/2 x (.f64 (.f64 x x) (+.f64 -1/8 (*.f64 x 1/16))))
(.f64 x (+.f64 1/2 (.f64 x (fma.f64 x 1/16 -1/8))))
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) (+.f64 (.f64 -5/128 (pow.f64 x 4)) (.f64 1/16 (pow.f64 x 3)))))
(fma.f64 -1/8 (.f64 x x) (fma.f64 1/2 x (fma.f64 -5/128 (pow.f64 x 4) (.f64 1/16 (pow.f64 x 3)))))
(fma.f64 -1/8 (.f64 x x) (fma.f64 1/2 x (fma.f64 1/16 (pow.f64 x 3) (.f64 -5/128 (pow.f64 x 4)))))
(fma.f64 1/2 x (fma.f64 x (.f64 x -1/8) (fma.f64 1/16 (pow.f64 x 3) (.f64 -5/128 (pow.f64 x 4)))))
(fma.f64 x (fma.f64 x -1/8 1/2) (.f64 (pow.f64 x 3) (+.f64 (.f64 x -5/128) 1/16)))
(fma.f64 x (fma.f64 x -1/8 1/2) (.f64 (pow.f64 x 3) (+.f64 1/16 (.f64 x -5/128))))
1
(+.f64 (*.f64 1/2 x) 1)
(fma.f64 1/2 x 1)
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) 1))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 1/2 x 1))
(fma.f64 1/2 x (fma.f64 -1/8 (*.f64 x x) 1))
(fma.f64 x (fma.f64 x -1/8 1/2) 1)
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) (+.f64 1 (*.f64 1/16 (pow.f64 x 3)))))
(fma.f64 -1/8 (.f64 x x) (+.f64 (fma.f64 1/2 x 1) (.f64 1/16 (pow.f64 x 3))))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 1/2 x (fma.f64 1/16 (pow.f64 x 3) 1)))
(fma.f64 x (*.f64 x -1/8) (fma.f64 1/2 x (fma.f64 1/16 (pow.f64 x 3) 1)))
(fma.f64 x (fma.f64 x -1/8 1/2) (fma.f64 1/16 (pow.f64 x 3) 1))
(fma.f64 1/2 x (fma.f64 x (*.f64 x (fma.f64 x 1/16 -1/8)) 1))
2
(+.f64 (*.f64 1/2 x) 2)
(fma.f64 1/2 x 2)
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) 2))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 1/2 x 2))
(fma.f64 1/2 x (fma.f64 x (*.f64 x -1/8) 2))
(fma.f64 x (fma.f64 x -1/8 1/2) 2)
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) (+.f64 2 (*.f64 1/16 (pow.f64 x 3)))))
(fma.f64 -1/8 (.f64 x x) (+.f64 (fma.f64 1/2 x 2) (.f64 1/16 (pow.f64 x 3))))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 1/2 x (fma.f64 1/16 (pow.f64 x 3) 2)))
(fma.f64 1/2 x (fma.f64 x (*.f64 x -1/8) (fma.f64 1/16 (pow.f64 x 3) 2)))
(fma.f64 x (fma.f64 x -1/8 1/2) (fma.f64 1/16 (pow.f64 x 3) 2))
(fma.f64 (*.f64 x x) (fma.f64 x 1/16 -1/8) (fma.f64 1/2 x 2))

eval34.0ms (1.3%)

Compiler: Compiled 1464 to 1146 computations (21.7% saved)

prune174.0ms (6.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	110	4	114
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	111	4	115

Error

Counts

115 → 4

Alt Table

Click to see full alt table

Status	Error	Program
	0.3b	(pow.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x) -1)
	21.2b	(*.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
	19.8b	(+.f64 (.f64 -1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) (*.f64 1/16 (pow.f64 x 3))))
▶	0.2b	(/.f64 x (fma.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4) 1))

Compiler

Compiled 114 to 90 computations (21.1% saved)

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (+.f64 x 1) 1/4)
✓	0.2b	(/.f64 x (fma.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4) 1))
✓	0.2b	(fma.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4) 1)

series15.0ms (0.6%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
4.0ms	x	@	-inf	(/.f64 x (fma.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4) 1))
3.0ms	x	@	-inf	(fma.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4) 1)
3.0ms	x	@	inf	(/.f64 x (fma.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4) 1))
2.0ms	x	@	inf	(fma.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4) 1)
1.0ms	x	@	inf	(pow.f64 (+.f64 x 1) 1/4)

rewrite48.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

803×	`log1p-expm1-u_binary64`
803×	`expm1-log1p-u_binary64`
86×	`add-sqr-sqrt_binary64`
83×	`add-log-exp_binary64`
82×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	44
1	177	28
2	2213	28

Stop Event

1×	node limit

Counts

3 → 73

Calls

Call 1

Inputs
(fma.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4) 1)
(/.f64 x (fma.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4) 1))
(pow.f64 (+.f64 x 1) 1/4)

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

Outputs

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

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

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

simplify51.0ms (2%)

Algorithm

1×	egg-herbie

Rules

612×	`times-frac_binary64`
432×	`associate-/l*_binary64`
217×	`cancel-sign-sub-inv_binary64`
196×	`fma-def_binary64`
156×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	208	1935
1	627	1813
2	2157	1562

Stop Event

1×	node limit

Counts

109 → 139

Calls

Call 1

Inputs
2
(+.f64 (*.f64 1/2 x) 2)
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) 2))
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) (+.f64 2 (*.f64 1/16 (pow.f64 x 3)))))
(+.f64 1 (sqrt.f64 x))
(+.f64 1 (+.f64 (sqrt.f64 x) (*.f64 1/2 (sqrt.f64 (/.f64 1 x)))))
(+.f64 1 (+.f64 (.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (+.f64 (sqrt.f64 x) (+.f64 (.f64 1/2 (sqrt.f64 (/.f64 1 x))) (*.f64 -3/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))))
(+.f64 (.f64 7/64 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 1 (+.f64 (.f64 -3/64 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (+.f64 (sqrt.f64 x) (+.f64 (.f64 1/2 (sqrt.f64 (/.f64 1 x))) (*.f64 -3/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))))))
(+.f64 1 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2))
(+.f64 (.f64 1/2 (/.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) x)) (+.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) 1))
(+.f64 (.f64 1/2 (/.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) x)) (+.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (+.f64 1 (+.f64 (.f64 -3/16 (/.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (pow.f64 x 2))) (.f64 1/16 (/.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (pow.f64 x 2)))))))
(+.f64 (.f64 1/2 (/.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) x)) (+.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (+.f64 1 (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 -7/64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) (.f64 3/64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2))) (pow.f64 x 3))) (+.f64 (.f64 -3/16 (/.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (pow.f64 x 2))) (.f64 1/16 (/.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (pow.f64 x 2))))))))
(*.f64 1/2 x)
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (.f64 1/2 x))
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) (*.f64 1/16 (pow.f64 x 3))))
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) (+.f64 (.f64 -5/128 (pow.f64 x 4)) (.f64 1/16 (pow.f64 x 3)))))
(/.f64 x (+.f64 1 (sqrt.f64 x)))
(+.f64 (/.f64 x (+.f64 1 (sqrt.f64 x))) (.f64 -1/2 (.f64 (/.f64 1 (pow.f64 (+.f64 1 (sqrt.f64 x)) 2)) (sqrt.f64 x))))
(-.f64 (+.f64 (/.f64 x (+.f64 1 (sqrt.f64 x))) (+.f64 (.f64 1/4 (/.f64 1 (pow.f64 (+.f64 1 (sqrt.f64 x)) 3))) (.f64 -1/2 (.f64 (/.f64 1 (pow.f64 (+.f64 1 (sqrt.f64 x)) 2)) (sqrt.f64 x))))) (+.f64 (.f64 -3/16 (.f64 (/.f64 1 (pow.f64 (+.f64 1 (sqrt.f64 x)) 2)) (sqrt.f64 (/.f64 1 x)))) (.f64 1/16 (*.f64 (/.f64 1 (pow.f64 (+.f64 1 (sqrt.f64 x)) 2)) (sqrt.f64 (/.f64 1 x))))))
(-.f64 (+.f64 (/.f64 x (+.f64 1 (sqrt.f64 x))) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 1/2 (.f64 (/.f64 (-.f64 (.f64 1/4 (/.f64 x (pow.f64 (+.f64 1 (sqrt.f64 x)) 3))) (+.f64 (.f64 -3/16 (.f64 (/.f64 1 (pow.f64 (+.f64 1 (sqrt.f64 x)) 2)) (sqrt.f64 x))) (.f64 1/16 (.f64 (/.f64 1 (pow.f64 (+.f64 1 (sqrt.f64 x)) 2)) (sqrt.f64 x))))) (+.f64 1 (sqrt.f64 x))) (sqrt.f64 x))) (+.f64 (.f64 -3/64 (.f64 (/.f64 1 (pow.f64 (+.f64 1 (sqrt.f64 x)) 2)) (sqrt.f64 x))) (+.f64 (.f64 -1/2 (.f64 (/.f64 (+.f64 (.f64 -3/16 (sqrt.f64 x)) (.f64 1/16 (sqrt.f64 x))) (pow.f64 (+.f64 1 (sqrt.f64 x)) 3)) (sqrt.f64 x))) (.f64 7/64 (.f64 (/.f64 1 (pow.f64 (+.f64 1 (sqrt.f64 x)) 2)) (sqrt.f64 x)))))) (pow.f64 x 2))) (+.f64 (.f64 -1/2 (.f64 (/.f64 1 (pow.f64 (+.f64 1 (sqrt.f64 x)) 2)) (sqrt.f64 x))) (.f64 1/4 (/.f64 1 (pow.f64 (+.f64 1 (sqrt.f64 x)) 3)))))) (+.f64 (.f64 -3/16 (.f64 (/.f64 1 (pow.f64 (+.f64 1 (sqrt.f64 x)) 2)) (sqrt.f64 (/.f64 1 x)))) (.f64 1/16 (*.f64 (/.f64 1 (pow.f64 (+.f64 1 (sqrt.f64 x)) 2)) (sqrt.f64 (/.f64 1 x))))))
(/.f64 x (+.f64 1 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)))
(+.f64 (/.f64 x (+.f64 1 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2))) (.f64 -1/2 (/.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (pow.f64 (+.f64 1 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) 2))))
(+.f64 (/.f64 x (+.f64 1 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2))) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 1/16 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) (.f64 -3/16 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2))) (.f64 (pow.f64 (+.f64 1 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) 2) x))) (+.f64 (.f64 1/4 (/.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 4) (.f64 (pow.f64 (+.f64 1 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) 3) x))) (.f64 -1/2 (/.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (pow.f64 (+.f64 1 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) 2))))))
(+.f64 (/.f64 x (+.f64 1 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2))) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 1/16 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) (.f64 -3/16 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2))) (.f64 (pow.f64 (+.f64 1 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) 2) x))) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (+.f64 (.f64 1/4 (/.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 4) (pow.f64 (+.f64 1 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) 3))) (.f64 -1 (/.f64 (+.f64 (.f64 1/16 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) (.f64 -3/16 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2))) (pow.f64 (+.f64 1 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) 2))))) (+.f64 1 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)))) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 -7/64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) (.f64 3/64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2))) (pow.f64 (+.f64 1 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) 2))) (.f64 -1/2 (/.f64 (.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (+.f64 (.f64 1/16 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) (.f64 -3/16 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)))) (pow.f64 (+.f64 1 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) 3))))) (pow.f64 x 2))) (+.f64 (.f64 1/4 (/.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 4) (.f64 (pow.f64 (+.f64 1 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) 3) x))) (.f64 -1/2 (/.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (pow.f64 (+.f64 1 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) 2)))))))
1
(+.f64 1 (*.f64 1/4 x))
(+.f64 1 (+.f64 (.f64 -3/32 (pow.f64 x 2)) (.f64 1/4 x)))
(+.f64 1 (+.f64 (.f64 7/128 (pow.f64 x 3)) (+.f64 (.f64 -3/32 (pow.f64 x 2)) (*.f64 1/4 x))))
(pow.f64 x 1/4)
(+.f64 (pow.f64 x 1/4) (*.f64 1/4 (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4)))
(+.f64 (pow.f64 x 1/4) (+.f64 (.f64 1/4 (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4)) (.f64 -3/32 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/4))))
(+.f64 (.f64 7/128 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/4)) (+.f64 (pow.f64 x 1/4) (+.f64 (.f64 1/4 (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4)) (*.f64 -3/32 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/4)))))
(exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))
(+.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (.f64 1/4 (/.f64 (exp.f64 (.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)))
(+.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (+.f64 (.f64 1/4 (/.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)) (.f64 -3/32 (/.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2)))))
(+.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (+.f64 (.f64 7/128 (/.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3))) (+.f64 (.f64 1/4 (/.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)) (.f64 -3/32 (/.f64 (exp.f64 (.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))))))

Outputs
2
(+.f64 (*.f64 1/2 x) 2)
(fma.f64 1/2 x 2)
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) 2))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 1/2 x 2))
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) (+.f64 2 (*.f64 1/16 (pow.f64 x 3)))))
(fma.f64 -1/8 (.f64 x x) (+.f64 (fma.f64 1/2 x 2) (.f64 1/16 (pow.f64 x 3))))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 1/2 x (fma.f64 1/16 (pow.f64 x 3) 2)))
(+.f64 1 (sqrt.f64 x))
(+.f64 1 (+.f64 (sqrt.f64 x) (*.f64 1/2 (sqrt.f64 (/.f64 1 x)))))
(+.f64 (+.f64 1 (sqrt.f64 x)) (*.f64 1/2 (sqrt.f64 (/.f64 1 x))))
(+.f64 1 (fma.f64 1/2 (sqrt.f64 (/.f64 1 x)) (sqrt.f64 x)))
(+.f64 1 (+.f64 (.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (+.f64 (sqrt.f64 x) (+.f64 (.f64 1/2 (sqrt.f64 (/.f64 1 x))) (*.f64 -3/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))))
(+.f64 1 (fma.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (+.f64 (sqrt.f64 x) (fma.f64 1/2 (sqrt.f64 (/.f64 1 x)) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -3/16)))))
(+.f64 (fma.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (sqrt.f64 x)) (+.f64 (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -3/16 (*.f64 1/2 (sqrt.f64 (/.f64 1 x)))) 1))
(+.f64 1 (+.f64 (fma.f64 1/2 (sqrt.f64 (/.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -1/8)))
(+.f64 (.f64 7/64 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 1 (+.f64 (.f64 -3/64 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (+.f64 (sqrt.f64 x) (+.f64 (.f64 1/2 (sqrt.f64 (/.f64 1 x))) (*.f64 -3/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))))))
(fma.f64 7/64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (+.f64 1 (fma.f64 -3/64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (fma.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (+.f64 (sqrt.f64 x) (fma.f64 1/2 (sqrt.f64 (/.f64 1 x)) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -3/16)))))))
(+.f64 (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) -3/64 (+.f64 (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -3/16 (*.f64 1/2 (sqrt.f64 (/.f64 1 x)))) (fma.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (sqrt.f64 x)))) (fma.f64 7/64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) 1))
(+.f64 (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) -3/64 (+.f64 (fma.f64 1/2 (sqrt.f64 (/.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -1/8))) (fma.f64 7/64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) 1))
(+.f64 1 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2))
(+.f64 1 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2))
(+.f64 1 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2))
(+.f64 1 (pow.f64 (*.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2))
(+.f64 (.f64 1/2 (/.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) x)) (+.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) 1))
(fma.f64 1/2 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2) x) (+.f64 1 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2)))
(+.f64 1 (fma.f64 1/2 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2) x) (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2)))
(+.f64 1 (fma.f64 1/2 (/.f64 (pow.f64 (.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2) x) (pow.f64 (.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2)))
(+.f64 (.f64 1/2 (/.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) x)) (+.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (+.f64 1 (+.f64 (.f64 -3/16 (/.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (pow.f64 x 2))) (.f64 1/16 (/.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (pow.f64 x 2)))))))
(fma.f64 1/2 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2) x) (+.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2) (+.f64 1 (.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2) (.f64 x x)) -1/8))))
(+.f64 (fma.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2) (*.f64 x x)) -1/8 1) (fma.f64 1/2 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2) x) (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2)))
(+.f64 (fma.f64 (/.f64 (pow.f64 (.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2) (.f64 x x)) -1/8 1) (fma.f64 1/2 (/.f64 (pow.f64 (.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2) x) (pow.f64 (.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2)))
(+.f64 (.f64 1/2 (/.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) x)) (+.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (+.f64 1 (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 -7/64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) (.f64 3/64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2))) (pow.f64 x 3))) (+.f64 (.f64 -3/16 (/.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (pow.f64 x 2))) (.f64 1/16 (/.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (pow.f64 x 2))))))))
(fma.f64 1/2 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2) x) (+.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2) (+.f64 1 (fma.f64 -1 (/.f64 (.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2) -1/16) (pow.f64 x 3)) (.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2) (*.f64 x x)) -1/8)))))
(+.f64 (+.f64 1 (-.f64 (/.f64 (.f64 -1/8 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2)) (.f64 x x)) (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2) (/.f64 (pow.f64 x 3) -1/16)))) (fma.f64 1/2 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2) x) (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2)))
(+.f64 (+.f64 1 (.f64 (/.f64 (pow.f64 (.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2) (.f64 x x)) (-.f64 -1/8 (/.f64 -1/16 x)))) (fma.f64 1/2 (/.f64 (pow.f64 (.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2) x) (pow.f64 (*.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2)))
(*.f64 1/2 x)
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (.f64 1/2 x))
(fma.f64 -1/8 (.f64 x x) (.f64 1/2 x))
(fma.f64 1/2 x (.f64 (.f64 -1/8 x) x))
(.f64 x (+.f64 (.f64 -1/8 x) 1/2))
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) (*.f64 1/16 (pow.f64 x 3))))
(fma.f64 -1/8 (.f64 x x) (fma.f64 1/2 x (.f64 1/16 (pow.f64 x 3))))
(fma.f64 -1/8 (.f64 x x) (fma.f64 1/16 (pow.f64 x 3) (.f64 1/2 x)))
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) (+.f64 (.f64 -5/128 (pow.f64 x 4)) (.f64 1/16 (pow.f64 x 3)))))
(fma.f64 -1/8 (.f64 x x) (fma.f64 1/2 x (fma.f64 -5/128 (pow.f64 x 4) (.f64 1/16 (pow.f64 x 3)))))
(fma.f64 -1/8 (.f64 x x) (fma.f64 1/2 x (fma.f64 1/16 (pow.f64 x 3) (.f64 -5/128 (pow.f64 x 4)))))
(/.f64 x (+.f64 1 (sqrt.f64 x)))
(+.f64 (/.f64 x (+.f64 1 (sqrt.f64 x))) (.f64 -1/2 (.f64 (/.f64 1 (pow.f64 (+.f64 1 (sqrt.f64 x)) 2)) (sqrt.f64 x))))
(+.f64 (/.f64 x (+.f64 1 (sqrt.f64 x))) (.f64 -1/2 (/.f64 (.f64 1 (sqrt.f64 x)) (pow.f64 (+.f64 1 (sqrt.f64 x)) 2))))
(fma.f64 -1/2 (/.f64 (sqrt.f64 x) (pow.f64 (+.f64 1 (sqrt.f64 x)) 2)) (/.f64 x (+.f64 1 (sqrt.f64 x))))
(-.f64 (+.f64 (/.f64 x (+.f64 1 (sqrt.f64 x))) (+.f64 (.f64 1/4 (/.f64 1 (pow.f64 (+.f64 1 (sqrt.f64 x)) 3))) (.f64 -1/2 (.f64 (/.f64 1 (pow.f64 (+.f64 1 (sqrt.f64 x)) 2)) (sqrt.f64 x))))) (+.f64 (.f64 -3/16 (.f64 (/.f64 1 (pow.f64 (+.f64 1 (sqrt.f64 x)) 2)) (sqrt.f64 (/.f64 1 x)))) (.f64 1/16 (*.f64 (/.f64 1 (pow.f64 (+.f64 1 (sqrt.f64 x)) 2)) (sqrt.f64 (/.f64 1 x))))))
(+.f64 (/.f64 x (+.f64 1 (sqrt.f64 x))) (-.f64 (fma.f64 -1/2 (/.f64 (.f64 1 (sqrt.f64 x)) (pow.f64 (+.f64 1 (sqrt.f64 x)) 2)) (/.f64 1/4 (pow.f64 (+.f64 1 (sqrt.f64 x)) 3))) (.f64 (/.f64 (*.f64 1 (sqrt.f64 (/.f64 1 x))) (pow.f64 (+.f64 1 (sqrt.f64 x)) 2)) -1/8)))
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(+.f64 (-.f64 (fma.f64 1/4 (/.f64 (pow.f64 (.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 4) (.f64 x (pow.f64 (+.f64 1 (pow.f64 (.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2)) 3))) (.f64 -1/2 (/.f64 (pow.f64 (.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2) (pow.f64 (+.f64 1 (pow.f64 (.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2)) 2)))) (/.f64 (fma.f64 1/2 (.f64 (/.f64 (pow.f64 (.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2) (+.f64 1 (pow.f64 (.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2))) (fma.f64 1/4 (/.f64 (pow.f64 (.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 4) (pow.f64 (+.f64 1 (pow.f64 (.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2)) 3)) (/.f64 (.f64 (pow.f64 (.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2) 1/8) (pow.f64 (+.f64 1 (pow.f64 (.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2)) 2)))) (fma.f64 -1/2 (.f64 (/.f64 (pow.f64 (.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 4) (pow.f64 (+.f64 1 (pow.f64 (.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2)) 3)) -1/8) (/.f64 (.f64 1/16 (pow.f64 (.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2)) (pow.f64 (+.f64 1 (pow.f64 (.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2)) 2)))) (.f64 x x))) (+.f64 (/.f64 x (+.f64 1 (pow.f64 (.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2))) (/.f64 (/.f64 (.f64 (pow.f64 (.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2) 1/8) (pow.f64 (+.f64 1 (pow.f64 (*.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2)) 2)) x)))
1
(+.f64 1 (*.f64 1/4 x))
(+.f64 1 (*.f64 x 1/4))
(fma.f64 x 1/4 1)
(+.f64 1 (+.f64 (.f64 -3/32 (pow.f64 x 2)) (.f64 1/4 x)))
(+.f64 1 (fma.f64 -3/32 (.f64 x x) (.f64 x 1/4)))
(+.f64 (.f64 x (.f64 x -3/32)) (fma.f64 x 1/4 1))
(+.f64 1 (.f64 x (+.f64 1/4 (.f64 -3/32 x))))
(+.f64 1 (+.f64 (.f64 7/128 (pow.f64 x 3)) (+.f64 (.f64 -3/32 (pow.f64 x 2)) (*.f64 1/4 x))))
(+.f64 1 (fma.f64 7/128 (pow.f64 x 3) (fma.f64 -3/32 (.f64 x x) (.f64 x 1/4))))
(+.f64 (fma.f64 (pow.f64 x 3) 7/128 (.f64 x (.f64 x -3/32))) (fma.f64 x 1/4 1))
(+.f64 1 (fma.f64 (pow.f64 x 3) 7/128 (.f64 x (+.f64 1/4 (.f64 -3/32 x)))))
(pow.f64 x 1/4)
(+.f64 (pow.f64 x 1/4) (*.f64 1/4 (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4)))
(fma.f64 1/4 (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4) (pow.f64 x 1/4))
(+.f64 (pow.f64 x 1/4) (+.f64 (.f64 1/4 (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4)) (.f64 -3/32 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/4))))
(+.f64 (pow.f64 x 1/4) (fma.f64 1/4 (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4) (*.f64 -3/32 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/4))))
(+.f64 (fma.f64 1/4 (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4) (pow.f64 x 1/4)) (*.f64 -3/32 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/4)))
(+.f64 (.f64 7/128 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/4)) (+.f64 (pow.f64 x 1/4) (+.f64 (.f64 1/4 (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4)) (*.f64 -3/32 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/4)))))
(fma.f64 7/128 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/4) (+.f64 (pow.f64 x 1/4) (fma.f64 1/4 (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4) (*.f64 -3/32 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/4)))))
(+.f64 (fma.f64 1/4 (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4) (*.f64 -3/32 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/4))) (fma.f64 7/128 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/4) (pow.f64 x 1/4)))
(exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))
(pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)))
(pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))
(*.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4))
(+.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (.f64 1/4 (/.f64 (exp.f64 (.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)))
(+.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (*.f64 1/4 (/.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) x)))
(fma.f64 1/4 (/.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x) (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))
(fma.f64 1/4 (/.f64 (.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) x) (.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)))
(+.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (+.f64 (.f64 1/4 (/.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)) (.f64 -3/32 (/.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2)))))
(+.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (fma.f64 1/4 (/.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) x) (.f64 -3/32 (/.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (.f64 x x)))))
(+.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (fma.f64 -3/32 (/.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (*.f64 x x)) (/.f64 1/4 (/.f64 x (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))))))
(+.f64 (.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) (.f64 (/.f64 (*.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) x) (+.f64 1/4 (/.f64 -3/32 x))))
(+.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (+.f64 (.f64 7/128 (/.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3))) (+.f64 (.f64 1/4 (/.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)) (.f64 -3/32 (/.f64 (exp.f64 (.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))))))
(+.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (fma.f64 7/128 (/.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (pow.f64 x 3)) (fma.f64 1/4 (/.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) x) (.f64 -3/32 (/.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (.f64 x x))))))
(+.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (fma.f64 7/128 (/.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (pow.f64 x 3)) (fma.f64 -3/32 (/.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (*.f64 x x)) (/.f64 1/4 (/.f64 x (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))))))
(+.f64 (.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) (fma.f64 7/128 (/.f64 (.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) (pow.f64 x 3)) (.f64 (/.f64 (.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) x) (+.f64 1/4 (/.f64 -3/32 x)))))

eval107.0ms (4.3%)

Compiler: Compiled 4834 to 4027 computations (16.7% saved)

prune270.0ms (10.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	174	4	178
Fresh	2	1	3
Picked	0	1	1
Done	0	0	0
Total	176	6	182

Error

Counts

182 → 6

Alt Table

Click to see full alt table

Status	Error	Program
	0.2b	(/.f64 x (fma.f64 (pow.f64 (+.f64 x 1) 1/4) (*.f64 (pow.f64 (+.f64 x 1) 1/8) (pow.f64 (+.f64 x 1) 1/8)) 1))
	19.8b	(fma.f64 -1/8 (.f64 x x) (fma.f64 1/16 (pow.f64 x 3) (.f64 1/2 x)))
	0.3b	(pow.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x) -1)
▶	0.1b	(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
	0.2b	(/.f64 x (fma.f64 (*.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2) 1/4) (pow.f64 (cbrt.f64 (+.f64 x 1)) 1/4)) (pow.f64 (+.f64 x 1) 1/4) 1))
✓	0.2b	(/.f64 x (fma.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4) 1))

Compiler

Compiled 179 to 144 computations (19.6% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
	0.0b	(sqrt.f64 (+.f64 x 1))
✓	0.1b	(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
✓	0.1b	(/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))

series4.0ms (0.1%)

Counts

2 → 8

Calls

6 calls:

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

rewrite45.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

853×	`log1p-expm1-u_binary64`
853×	`expm1-log1p-u_binary64`
90×	`add-sqr-sqrt_binary64`
86×	`*-un-lft-identity_binary64`
86×	`pow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	24
1	179	24
2	2448	24

Stop Event

1×	node limit

Counts

2 → 51

Calls

Call 1

Inputs
(/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))
(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))

Outputs

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

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

simplify48.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

803×	`unswap-sqr_binary64`
504×	`distribute-lft-out_binary64`
434×	`fma-def_binary64`
369×	`*-commutative_binary64`
209×	`distribute-rgt-out_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	30	99
1	81	95
2	196	88
3	570	74
4	1516	74
5	2437	74
6	4453	74
7	4601	74
8	4895	74

Stop Event

1×	node limit

Counts

59 → 65

Calls

Call 1

Inputs
1/2
(+.f64 (*.f64 -1/8 x) 1/2)
(+.f64 (.f64 -1/8 x) (+.f64 1/2 (.f64 1/16 (pow.f64 x 2))))
(+.f64 (.f64 -1/8 x) (+.f64 (.f64 -5/128 (pow.f64 x 3)) (+.f64 1/2 (*.f64 1/16 (pow.f64 x 2)))))
(*.f64 1/2 x)
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (.f64 1/2 x))
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) (*.f64 1/16 (pow.f64 x 3))))
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) (+.f64 (.f64 -5/128 (pow.f64 x 4)) (.f64 1/16 (pow.f64 x 3)))))

Outputs
1/2
(+.f64 (*.f64 -1/8 x) 1/2)
(fma.f64 -1/8 x 1/2)
(+.f64 (.f64 -1/8 x) (+.f64 1/2 (.f64 1/16 (pow.f64 x 2))))
(+.f64 (fma.f64 -1/8 x 1/2) (.f64 1/16 (.f64 x x)))
(fma.f64 -1/8 x (fma.f64 1/16 (*.f64 x x) 1/2))
(fma.f64 x (*.f64 x 1/16) (fma.f64 -1/8 x 1/2))
(fma.f64 x (fma.f64 x 1/16 -1/8) 1/2)
(+.f64 (.f64 -1/8 x) (+.f64 (.f64 -5/128 (pow.f64 x 3)) (+.f64 1/2 (*.f64 1/16 (pow.f64 x 2)))))
(fma.f64 -1/8 x (fma.f64 -5/128 (pow.f64 x 3) (+.f64 1/2 (.f64 1/16 (.f64 x x)))))
(fma.f64 -1/8 x (fma.f64 -5/128 (pow.f64 x 3) (fma.f64 1/16 (*.f64 x x) 1/2)))
(fma.f64 -1/8 x (fma.f64 x (*.f64 x 1/16) (fma.f64 -5/128 (pow.f64 x 3) 1/2)))
(fma.f64 -1/8 x (fma.f64 x (*.f64 x (fma.f64 x -5/128 1/16)) 1/2))
(fma.f64 x (fma.f64 x 1/16 -1/8) (fma.f64 -5/128 (pow.f64 x 3) 1/2))
(fma.f64 -1/8 x (fma.f64 (*.f64 x x) (fma.f64 x -5/128 1/16) 1/2))
(*.f64 1/2 x)
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (.f64 1/2 x))
(fma.f64 -1/8 (.f64 x x) (.f64 1/2 x))
(fma.f64 1/2 x (.f64 x (.f64 -1/8 x)))
(*.f64 x (fma.f64 -1/8 x 1/2))
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) (*.f64 1/16 (pow.f64 x 3))))
(fma.f64 -1/8 (.f64 x x) (fma.f64 1/2 x (.f64 1/16 (pow.f64 x 3))))
(fma.f64 1/16 (pow.f64 x 3) (*.f64 x (fma.f64 -1/8 x 1/2)))
(*.f64 x (fma.f64 x (fma.f64 x 1/16 -1/8) 1/2))
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) (+.f64 (.f64 -5/128 (pow.f64 x 4)) (.f64 1/16 (pow.f64 x 3)))))
(fma.f64 -1/8 (.f64 x x) (fma.f64 1/2 x (fma.f64 -5/128 (pow.f64 x 4) (.f64 1/16 (pow.f64 x 3)))))
(fma.f64 -1/8 (.f64 x x) (fma.f64 1/2 x (fma.f64 1/16 (pow.f64 x 3) (.f64 -5/128 (pow.f64 x 4)))))
(+.f64 (fma.f64 -5/128 (pow.f64 x 4) (.f64 1/16 (pow.f64 x 3))) (.f64 x (fma.f64 -1/8 x 1/2)))
(fma.f64 x (fma.f64 -1/8 x 1/2) (*.f64 (pow.f64 x 3) (fma.f64 x -5/128 1/16)))
(*.f64 x (fma.f64 x (fma.f64 x 1/16 -1/8) (fma.f64 -5/128 (pow.f64 x 3) 1/2)))
(.f64 x (fma.f64 -1/8 x (fma.f64 (.f64 x x) (fma.f64 x -5/128 1/16) 1/2)))

eval44.0ms (1.7%)

Compiler: Compiled 1852 to 1498 computations (19.1% saved)

prune271.0ms (10.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	135	2	137
Fresh	2	2	4
Picked	0	1	1
Done	0	1	1
Total	137	6	143

Error

Counts

143 → 6

Alt Table

Click to see full alt table

Status	Error	Program
	1.4b	(*.f64 x (exp.f64 (neg.f64 (log1p.f64 (sqrt.f64 (+.f64 1 x))))))
✓	0.1b	(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
	0.2b	(/.f64 x (fma.f64 (*.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2) 1/4) (pow.f64 (cbrt.f64 (+.f64 x 1)) 1/4)) (pow.f64 (+.f64 x 1) 1/4) 1))
	0.3b	(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x))
▶	0.2b	(/.f64 x (fma.f64 (pow.f64 (+.f64 x 1) 1/4) (*.f64 (pow.f64 (+.f64 x 1) 1/8) (pow.f64 (+.f64 x 1) 1/8)) 1))
✓	0.2b	(/.f64 x (fma.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4) 1))

Compiler

Compiled 160 to 131 computations (18.1% saved)

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(pow.f64 (+.f64 x 1) 1/4)
✓	0.2b	(/.f64 x (fma.f64 (pow.f64 (+.f64 x 1) 1/4) (*.f64 (pow.f64 (+.f64 x 1) 1/8) (pow.f64 (+.f64 x 1) 1/8)) 1))
✓	0.2b	(fma.f64 (pow.f64 (+.f64 x 1) 1/4) (*.f64 (pow.f64 (+.f64 x 1) 1/8) (pow.f64 (+.f64 x 1) 1/8)) 1)
✓	0.2b	(*.f64 (pow.f64 (+.f64 x 1) 1/8) (pow.f64 (+.f64 x 1) 1/8))

series5.0ms (0.2%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(/.f64 x (fma.f64 (pow.f64 (+.f64 x 1) 1/4) (*.f64 (pow.f64 (+.f64 x 1) 1/8) (pow.f64 (+.f64 x 1) 1/8)) 1))
1.0ms	x	@	-inf	(/.f64 x (fma.f64 (pow.f64 (+.f64 x 1) 1/4) (*.f64 (pow.f64 (+.f64 x 1) 1/8) (pow.f64 (+.f64 x 1) 1/8)) 1))
0.0ms	x	@	-inf	(fma.f64 (pow.f64 (+.f64 x 1) 1/4) (*.f64 (pow.f64 (+.f64 x 1) 1/8) (pow.f64 (+.f64 x 1) 1/8)) 1)
0.0ms	x	@	0	(*.f64 (pow.f64 (+.f64 x 1) 1/8) (pow.f64 (+.f64 x 1) 1/8))
0.0ms	x	@	-inf	(*.f64 (pow.f64 (+.f64 x 1) 1/8) (pow.f64 (+.f64 x 1) 1/8))

rewrite47.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

914×	`log1p-expm1-u_binary64`
914×	`expm1-log1p-u_binary64`
103×	`add-sqr-sqrt_binary64`
100×	`add-log-exp_binary64`
100×	`pow1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	44
1	245	28
2	2612	28

Stop Event

1×	node limit

Counts

3 → 73

Calls

Call 1

Inputs

(*.f64 (pow.f64 (+.f64 x 1) 1/8) (pow.f64 (+.f64 x 1) 1/8))

(fma.f64 (pow.f64 (+.f64 x 1) 1/4) (*.f64 (pow.f64 (+.f64 x 1) 1/8) (pow.f64 (+.f64 x 1) 1/8)) 1)

(/.f64 x (fma.f64 (pow.f64 (+.f64 x 1) 1/4) (*.f64 (pow.f64 (+.f64 x 1) 1/8) (pow.f64 (+.f64 x 1) 1/8)) 1))

Outputs

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

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

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

simplify48.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

612×	`times-frac_binary64`
433×	`associate-/l*_binary64`
217×	`cancel-sign-sub-inv_binary64`
196×	`fma-def_binary64`
156×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	208	1935
1	627	1813
2	2157	1562

Stop Event

1×	node limit

Counts

109 → 140

Calls

Call 1

Inputs
1
(+.f64 1 (*.f64 1/4 x))
(+.f64 1 (+.f64 (.f64 -3/32 (pow.f64 x 2)) (.f64 1/4 x)))
(+.f64 1 (+.f64 (.f64 7/128 (pow.f64 x 3)) (+.f64 (.f64 -3/32 (pow.f64 x 2)) (*.f64 1/4 x))))
(pow.f64 x 1/4)
(+.f64 (pow.f64 x 1/4) (*.f64 1/4 (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4)))
(+.f64 (pow.f64 x 1/4) (+.f64 (.f64 1/4 (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4)) (.f64 -3/32 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/4))))
(+.f64 (.f64 7/128 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/4)) (+.f64 (pow.f64 x 1/4) (+.f64 (.f64 1/4 (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4)) (*.f64 -3/32 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/4)))))
(exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))
(+.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (.f64 1/4 (/.f64 (exp.f64 (.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)))
(+.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (+.f64 (.f64 1/4 (/.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)) (.f64 -3/32 (/.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2)))))
(+.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (+.f64 (.f64 7/128 (/.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3))) (+.f64 (.f64 1/4 (/.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)) (.f64 -3/32 (/.f64 (exp.f64 (.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))))))
2
(+.f64 (*.f64 1/2 x) 2)
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) 2))
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) (+.f64 2 (*.f64 1/16 (pow.f64 x 3)))))
(+.f64 1 (sqrt.f64 x))
(+.f64 1 (+.f64 (sqrt.f64 x) (*.f64 1/2 (sqrt.f64 (/.f64 1 x)))))
(+.f64 1 (+.f64 (.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (+.f64 (sqrt.f64 x) (+.f64 (.f64 1/2 (sqrt.f64 (/.f64 1 x))) (*.f64 -3/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))))
(+.f64 (.f64 7/64 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 1 (+.f64 (.f64 -3/64 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (+.f64 (sqrt.f64 x) (+.f64 (.f64 1/2 (sqrt.f64 (/.f64 1 x))) (*.f64 -3/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))))))
(+.f64 1 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2))
(+.f64 (.f64 1/2 (/.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) x)) (+.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) 1))
(+.f64 (.f64 1/2 (/.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) x)) (+.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (+.f64 1 (+.f64 (.f64 -3/16 (/.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (pow.f64 x 2))) (.f64 1/16 (/.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (pow.f64 x 2)))))))
(+.f64 (.f64 1/2 (/.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) x)) (+.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (+.f64 1 (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 -7/64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) (.f64 3/64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2))) (pow.f64 x 3))) (+.f64 (.f64 -3/16 (/.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (pow.f64 x 2))) (.f64 1/16 (/.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (pow.f64 x 2))))))))
(*.f64 1/2 x)
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (.f64 1/2 x))
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) (*.f64 1/16 (pow.f64 x 3))))
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) (+.f64 (.f64 -5/128 (pow.f64 x 4)) (.f64 1/16 (pow.f64 x 3)))))
(/.f64 x (+.f64 1 (sqrt.f64 x)))
(+.f64 (/.f64 x (+.f64 1 (sqrt.f64 x))) (.f64 -1/2 (.f64 (/.f64 1 (pow.f64 (+.f64 1 (sqrt.f64 x)) 2)) (sqrt.f64 x))))
(-.f64 (+.f64 (/.f64 x (+.f64 1 (sqrt.f64 x))) (+.f64 (.f64 1/4 (/.f64 1 (pow.f64 (+.f64 1 (sqrt.f64 x)) 3))) (.f64 -1/2 (.f64 (/.f64 1 (pow.f64 (+.f64 1 (sqrt.f64 x)) 2)) (sqrt.f64 x))))) (+.f64 (.f64 -3/16 (.f64 (/.f64 1 (pow.f64 (+.f64 1 (sqrt.f64 x)) 2)) (sqrt.f64 (/.f64 1 x)))) (.f64 1/16 (*.f64 (/.f64 1 (pow.f64 (+.f64 1 (sqrt.f64 x)) 2)) (sqrt.f64 (/.f64 1 x))))))
(-.f64 (+.f64 (/.f64 x (+.f64 1 (sqrt.f64 x))) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 1/2 (.f64 (/.f64 (-.f64 (.f64 1/4 (/.f64 x (pow.f64 (+.f64 1 (sqrt.f64 x)) 3))) (+.f64 (.f64 -3/16 (.f64 (/.f64 1 (pow.f64 (+.f64 1 (sqrt.f64 x)) 2)) (sqrt.f64 x))) (.f64 1/16 (.f64 (/.f64 1 (pow.f64 (+.f64 1 (sqrt.f64 x)) 2)) (sqrt.f64 x))))) (+.f64 1 (sqrt.f64 x))) (sqrt.f64 x))) (+.f64 (.f64 -3/64 (.f64 (/.f64 1 (pow.f64 (+.f64 1 (sqrt.f64 x)) 2)) (sqrt.f64 x))) (+.f64 (.f64 -1/2 (.f64 (/.f64 (+.f64 (.f64 -3/16 (sqrt.f64 x)) (.f64 1/16 (sqrt.f64 x))) (pow.f64 (+.f64 1 (sqrt.f64 x)) 3)) (sqrt.f64 x))) (.f64 7/64 (.f64 (/.f64 1 (pow.f64 (+.f64 1 (sqrt.f64 x)) 2)) (sqrt.f64 x)))))) (pow.f64 x 2))) (+.f64 (.f64 -1/2 (.f64 (/.f64 1 (pow.f64 (+.f64 1 (sqrt.f64 x)) 2)) (sqrt.f64 x))) (.f64 1/4 (/.f64 1 (pow.f64 (+.f64 1 (sqrt.f64 x)) 3)))))) (+.f64 (.f64 -3/16 (.f64 (/.f64 1 (pow.f64 (+.f64 1 (sqrt.f64 x)) 2)) (sqrt.f64 (/.f64 1 x)))) (.f64 1/16 (*.f64 (/.f64 1 (pow.f64 (+.f64 1 (sqrt.f64 x)) 2)) (sqrt.f64 (/.f64 1 x))))))
(/.f64 x (+.f64 1 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)))
(+.f64 (/.f64 x (+.f64 1 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2))) (.f64 -1/2 (/.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (pow.f64 (+.f64 1 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) 2))))
(+.f64 (/.f64 x (+.f64 1 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2))) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 1/16 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) (.f64 -3/16 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2))) (.f64 (pow.f64 (+.f64 1 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) 2) x))) (+.f64 (.f64 1/4 (/.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 4) (.f64 (pow.f64 (+.f64 1 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) 3) x))) (.f64 -1/2 (/.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (pow.f64 (+.f64 1 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) 2))))))
(+.f64 (/.f64 x (+.f64 1 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2))) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 1/16 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) (.f64 -3/16 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2))) (.f64 (pow.f64 (+.f64 1 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) 2) x))) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (+.f64 (.f64 1/4 (/.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 4) (pow.f64 (+.f64 1 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) 3))) (.f64 -1 (/.f64 (+.f64 (.f64 1/16 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) (.f64 -3/16 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2))) (pow.f64 (+.f64 1 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) 2))))) (+.f64 1 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)))) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 -7/64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) (.f64 3/64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2))) (pow.f64 (+.f64 1 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) 2))) (.f64 -1/2 (/.f64 (.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (+.f64 (.f64 1/16 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) (.f64 -3/16 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)))) (pow.f64 (+.f64 1 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) 3))))) (pow.f64 x 2))) (+.f64 (.f64 1/4 (/.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 4) (.f64 (pow.f64 (+.f64 1 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) 3) x))) (.f64 -1/2 (/.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (pow.f64 (+.f64 1 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) 2)))))))

Outputs
1
(+.f64 1 (*.f64 1/4 x))
(fma.f64 1/4 x 1)
(+.f64 1 (+.f64 (.f64 -3/32 (pow.f64 x 2)) (.f64 1/4 x)))
(+.f64 1 (fma.f64 -3/32 (.f64 x x) (.f64 1/4 x)))
(+.f64 1 (fma.f64 1/4 x (.f64 x (.f64 x -3/32))))
(+.f64 1 (.f64 x (+.f64 (.f64 -3/32 x) 1/4)))
(+.f64 1 (+.f64 (.f64 7/128 (pow.f64 x 3)) (+.f64 (.f64 -3/32 (pow.f64 x 2)) (*.f64 1/4 x))))
(+.f64 1 (fma.f64 7/128 (pow.f64 x 3) (fma.f64 -3/32 (.f64 x x) (.f64 1/4 x))))
(+.f64 (fma.f64 7/128 (pow.f64 x 3) (.f64 x (.f64 x -3/32))) (fma.f64 1/4 x 1))
(+.f64 (.f64 (.f64 x x) (+.f64 -3/32 (*.f64 7/128 x))) (fma.f64 1/4 x 1))
(pow.f64 x 1/4)
(+.f64 (pow.f64 x 1/4) (*.f64 1/4 (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4)))
(fma.f64 1/4 (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4) (pow.f64 x 1/4))
(+.f64 (pow.f64 x 1/4) (+.f64 (.f64 1/4 (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4)) (.f64 -3/32 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/4))))
(+.f64 (pow.f64 x 1/4) (fma.f64 1/4 (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4) (*.f64 -3/32 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/4))))
(+.f64 (pow.f64 x 1/4) (fma.f64 -3/32 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/4) (*.f64 1/4 (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4))))
(+.f64 (.f64 7/128 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/4)) (+.f64 (pow.f64 x 1/4) (+.f64 (.f64 1/4 (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4)) (*.f64 -3/32 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/4)))))
(fma.f64 7/128 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/4) (+.f64 (pow.f64 x 1/4) (fma.f64 1/4 (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4) (*.f64 -3/32 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/4)))))
(+.f64 (fma.f64 -3/32 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/4) (*.f64 1/4 (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4))) (fma.f64 7/128 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/4) (pow.f64 x 1/4)))
(+.f64 (fma.f64 1/4 (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4) (*.f64 -3/32 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/4))) (fma.f64 7/128 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/4) (pow.f64 x 1/4)))
(exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))
(pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)))
(pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))
(*.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4))
(+.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (.f64 1/4 (/.f64 (exp.f64 (.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)))
(+.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (*.f64 1/4 (/.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) x)))
(fma.f64 1/4 (/.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x) (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))
(fma.f64 1/4 (/.f64 (.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) x) (.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)))
(+.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (+.f64 (.f64 1/4 (/.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)) (.f64 -3/32 (/.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2)))))
(+.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (fma.f64 1/4 (/.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) x) (.f64 -3/32 (/.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (.f64 x x)))))
(+.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (fma.f64 -3/32 (/.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (.f64 x x)) (/.f64 (.f64 1/4 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) x)))
(+.f64 (.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) (.f64 (/.f64 (*.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) x) (+.f64 1/4 (/.f64 -3/32 x))))
(+.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (+.f64 (.f64 7/128 (/.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3))) (+.f64 (.f64 1/4 (/.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)) (.f64 -3/32 (/.f64 (exp.f64 (.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))))))
(+.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (fma.f64 7/128 (/.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (pow.f64 x 3)) (fma.f64 1/4 (/.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) x) (.f64 -3/32 (/.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (.f64 x x))))))
(+.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (fma.f64 7/128 (/.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (pow.f64 x 3)) (fma.f64 -3/32 (/.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (.f64 x x)) (/.f64 (.f64 1/4 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) x))))
(+.f64 (.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) (fma.f64 7/128 (/.f64 (pow.f64 (/.f64 -1 x) -1/4) (/.f64 (pow.f64 x 3) (pow.f64 -1 1/4))) (.f64 (/.f64 (*.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) x) (+.f64 1/4 (/.f64 -3/32 x)))))
2
(+.f64 (*.f64 1/2 x) 2)
(fma.f64 1/2 x 2)
(fma.f64 x 1/2 2)
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) 2))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 1/2 x 2))
(fma.f64 (*.f64 x x) -1/8 (fma.f64 x 1/2 2))
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) (+.f64 2 (*.f64 1/16 (pow.f64 x 3)))))
(fma.f64 -1/8 (.f64 x x) (+.f64 (fma.f64 1/2 x 2) (.f64 (pow.f64 x 3) 1/16)))
(fma.f64 (*.f64 x x) -1/8 (fma.f64 x 1/2 (fma.f64 (pow.f64 x 3) 1/16 2)))
(+.f64 1 (sqrt.f64 x))
(+.f64 1 (+.f64 (sqrt.f64 x) (*.f64 1/2 (sqrt.f64 (/.f64 1 x)))))
(+.f64 1 (fma.f64 1/2 (sqrt.f64 (/.f64 1 x)) (sqrt.f64 x)))
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(+.f64 1 (fma.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (+.f64 (sqrt.f64 x) (fma.f64 1/2 (sqrt.f64 (/.f64 1 x)) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -3/16)))))
(+.f64 1 (+.f64 (fma.f64 1/2 (sqrt.f64 (/.f64 1 x)) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -3/16)) (fma.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (sqrt.f64 x))))
(+.f64 1 (+.f64 (fma.f64 1/2 (sqrt.f64 (/.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -1/8)))
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(fma.f64 7/64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (+.f64 1 (fma.f64 -3/64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (fma.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (+.f64 (sqrt.f64 x) (fma.f64 1/2 (sqrt.f64 (/.f64 1 x)) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -3/16)))))))
(+.f64 (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) -3/64 (+.f64 (fma.f64 1/2 (sqrt.f64 (/.f64 1 x)) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -3/16)) (fma.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (sqrt.f64 x)))) (fma.f64 7/64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) 1))
(+.f64 (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) -3/64 (+.f64 (fma.f64 1/2 (sqrt.f64 (/.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -1/8))) (fma.f64 7/64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) 1))
(+.f64 1 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2))
(+.f64 1 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2))
(+.f64 1 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2))
(+.f64 1 (pow.f64 (*.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2))
(+.f64 (.f64 1/2 (/.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) x)) (+.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) 1))
(fma.f64 1/2 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2) x) (+.f64 1 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2)))
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(+.f64 (/.f64 x (+.f64 1 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2))) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 1/16 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) (.f64 -3/16 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2))) (.f64 (pow.f64 (+.f64 1 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) 2) x))) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (+.f64 (.f64 1/4 (/.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 4) (pow.f64 (+.f64 1 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) 3))) (.f64 -1 (/.f64 (+.f64 (.f64 1/16 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) (.f64 -3/16 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2))) (pow.f64 (+.f64 1 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) 2))))) (+.f64 1 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)))) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 -7/64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) (.f64 3/64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2))) (pow.f64 (+.f64 1 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) 2))) (.f64 -1/2 (/.f64 (.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (+.f64 (.f64 1/16 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) (.f64 -3/16 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)))) (pow.f64 (+.f64 1 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) 3))))) (pow.f64 x 2))) (+.f64 (.f64 1/4 (/.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 4) (.f64 (pow.f64 (+.f64 1 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) 3) x))) (.f64 -1/2 (/.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (pow.f64 (+.f64 1 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) 2)))))))
(+.f64 (/.f64 x (+.f64 1 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2))) (fma.f64 -1 (/.f64 (.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2) -1/8) (.f64 x (pow.f64 (+.f64 1 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2)) 2))) (fma.f64 -1 (/.f64 (fma.f64 1/2 (/.f64 (.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2) (fma.f64 1/4 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 4) (pow.f64 (+.f64 1 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2)) 3)) (neg.f64 (/.f64 (.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2) -1/8) (pow.f64 (+.f64 1 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2)) 2))))) (+.f64 1 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2))) (fma.f64 -1 (/.f64 (.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2) -1/16) (pow.f64 (+.f64 1 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2)) 2)) (.f64 -1/2 (/.f64 (.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2) (.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2) -1/8)) (pow.f64 (+.f64 1 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2)) 3))))) (.f64 x x)) (fma.f64 1/4 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 4) (.f64 x (pow.f64 (+.f64 1 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2)) 3))) (*.f64 -1/2 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2) (pow.f64 (+.f64 1 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2)) 2)))))))
(+.f64 (-.f64 (fma.f64 1/4 (/.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 4) x) (pow.f64 (+.f64 1 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2)) 3)) (/.f64 (.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2) -1/2) (pow.f64 (+.f64 1 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2)) 2))) (/.f64 (fma.f64 1/2 (.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2) (+.f64 1 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2))) (-.f64 (/.f64 (.f64 1/4 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 4)) (pow.f64 (+.f64 1 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2)) 3)) (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2) (/.f64 (pow.f64 (+.f64 1 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2)) 2) -1/8)))) (-.f64 (/.f64 (.f64 -1/2 (.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 4) -1/8)) (pow.f64 (+.f64 1 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2)) 3)) (/.f64 (.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2) -1/16) (pow.f64 (+.f64 1 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2)) 2)))) (.f64 x x))) (-.f64 (/.f64 x (+.f64 1 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2))) (/.f64 (/.f64 (.f64 -1/8 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2)) x) (pow.f64 (+.f64 1 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2)) 2))))
(+.f64 (-.f64 (fma.f64 1/4 (/.f64 (pow.f64 (.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 4) (.f64 x (pow.f64 (+.f64 1 (pow.f64 (.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2)) 3))) (.f64 -1/2 (/.f64 (pow.f64 (.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2) (pow.f64 (+.f64 1 (pow.f64 (.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2)) 2)))) (/.f64 (fma.f64 1/2 (.f64 (/.f64 (pow.f64 (.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2) (+.f64 1 (pow.f64 (.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2))) (fma.f64 1/4 (/.f64 (pow.f64 (.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 4) (pow.f64 (+.f64 1 (pow.f64 (.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2)) 3)) (/.f64 (.f64 (pow.f64 (.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2) 1/8) (pow.f64 (+.f64 1 (pow.f64 (.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2)) 2)))) (fma.f64 -1/2 (.f64 (/.f64 (pow.f64 (.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 4) (pow.f64 (+.f64 1 (pow.f64 (.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2)) 3)) -1/8) (/.f64 (.f64 1/16 (pow.f64 (.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2)) (pow.f64 (+.f64 1 (pow.f64 (.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2)) 2)))) (.f64 x x))) (+.f64 (/.f64 x (+.f64 1 (pow.f64 (.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2))) (/.f64 (/.f64 (.f64 (pow.f64 (.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2) 1/8) (pow.f64 (+.f64 1 (pow.f64 (*.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2)) 2)) x)))

eval113.0ms (4.5%)

Compiler: Compiled 5044 to 4130 computations (18.1% saved)

prune237.0ms (9.4%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	179	0	179
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	179	6	185

Error

Counts

185 → 6

Alt Table

Click to see full alt table

Status	Error	Program
	1.4b	(*.f64 x (exp.f64 (neg.f64 (log1p.f64 (sqrt.f64 (+.f64 1 x))))))
✓	0.1b	(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
	0.2b	(/.f64 x (fma.f64 (*.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2) 1/4) (pow.f64 (cbrt.f64 (+.f64 x 1)) 1/4)) (pow.f64 (+.f64 x 1) 1/4) 1))
	0.3b	(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x))
✓	0.2b	(/.f64 x (fma.f64 (pow.f64 (+.f64 x 1) 1/4) (*.f64 (pow.f64 (+.f64 x 1) 1/8) (pow.f64 (+.f64 x 1) 1/8)) 1))
✓	0.2b	(/.f64 x (fma.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4) 1))

Compiler

Compiled 93 to 76 computations (18.3% saved)

regimes17.0ms (0.7%)

Accuracy

Total -40.6b remaining (-28420.4%)

Threshold costs -40.6b (-28420.4%)

Counts

11 → 1

Calls

Call 1

Inputs
(*.f64 x (exp.f64 (neg.f64 (log1p.f64 (sqrt.f64 (+.f64 1 x))))))
(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x))
(/.f64 x (fma.f64 (pow.f64 (+.f64 x 1) 1/4) (*.f64 (pow.f64 (+.f64 x 1) 1/8) (pow.f64 (+.f64 x 1) 1/8)) 1))
(fma.f64 -1/8 (.f64 x x) (fma.f64 1/16 (pow.f64 x 3) (.f64 1/2 x)))
(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
(/.f64 x (fma.f64 (*.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2) 1/4) (pow.f64 (cbrt.f64 (+.f64 x 1)) 1/4)) (pow.f64 (+.f64 x 1) 1/4) 1))
(pow.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x) -1)
(*.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) (*.f64 1/16 (pow.f64 x 3))))
(/.f64 x (fma.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4) 1))
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))

Outputs
(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))

Results

Time	Error	Segments	Branch
6.0ms	0.1b	1	`x`
6.0ms	0.1b	1	`(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))`

Compiler

Compiled 159 to 124 computations (22% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	13	15

Stop Event

1×

saturated

Calls

Call 1

Inputs
(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))

Outputs
(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))

end15.0ms (0.6%)

Stop Event

1×

fuel

Compiler

Compiled 22 to 18 computations (18.2% saved)

Details

analyze5.0ms (0.2%)

sample763.0ms (30.3%)

preprocess18.0ms (0.7%)

simplify6.0ms (0.2%)

eval0.0ms (0%)

prune1.0ms (0%)

localize5.0ms (0.2%)

series8.0ms (0.3%)

rewrite48.0ms (1.9%)

simplify48.0ms (1.9%)

eval34.0ms (1.3%)

prune174.0ms (6.9%)

localize7.0ms (0.3%)

series15.0ms (0.6%)

rewrite48.0ms (1.9%)

simplify51.0ms (2%)

eval107.0ms (4.3%)

prune270.0ms (10.7%)

localize9.0ms (0.3%)

series4.0ms (0.1%)

rewrite45.0ms (1.8%)

simplify48.0ms (1.9%)

eval44.0ms (1.7%)

prune271.0ms (10.8%)

localize10.0ms (0.4%)

series5.0ms (0.2%)

rewrite47.0ms (1.9%)

simplify48.0ms (1.9%)

eval113.0ms (4.5%)

prune237.0ms (9.4%)

regimes17.0ms (0.7%)

simplify2.0ms (0.1%)

end15.0ms (0.6%)

Profiling