Details

analyze0.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
100%	0%	0%	1

Compiler

Compiled 14 to 13 computations (7.1% saved)

sample2.1s (59.1%)

Results

1.0s	2172×	body	2048	valid
429.0ms	4283×	body	128	valid
405.0ms	1042×	body	1024	valid
130.0ms	492×	body	512	valid
50.0ms	267×	body	256	valid

Compiler

Compiled 28 to 26 computations (7.1% saved)

preprocess17.0ms (0.5%)

Algorithm

2×	egg-herbie

Rules

8×	`sub-neg_binary64`
8×	`fma-def_binary64`
5×	`+-commutative_binary64`
3×	`*-commutative_binary64`
3×	`associate-+l-_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	18
1	22	15
2	29	15
3	37	15
4	44	15
5	54	15
6	65	15
7	77	15
8	80	15
0	1	1

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0

Outputs
0

Call 2

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

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

Compiler

Compiled 13 to 12 computations (7.7% saved)

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

8×	`sub-neg_binary64`
8×	`fma-def_binary64`
5×	`+-commutative_binary64`
3×	`*-commutative_binary64`
3×	`associate-+l-_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	18
1	22	15
2	29	15
3	37	15
4	44	15
5	54	15
6	65	15
7	77	15
8	80	15

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

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

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

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

17.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	17.7b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

Compiler

Compiled 45 to 41 computations (8.9% saved)

localize6.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
✓	0.0b	(/.f64 1/2 (hypot.f64 1 x))
✓	0.0b	(hypot.f64 1 x)
✓	2.5b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

series7.0ms (0.2%)

Counts

4 → 48

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
1.0ms	x	@	0	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
1.0ms	x	@	-inf	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
1.0ms	x	@	inf	(hypot.f64 1 x)
0.0ms	x	@	inf	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))

rewrite59.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

406×	`log-prod_binary64`
387×	`prod-diff_binary64`
205×	`fma-def_binary64`
170×	`expm1-udef_binary64`
169×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	38
1	201	38
2	2591	38

Stop Event

1×	node limit

Counts

4 → 119

Calls

Call 1

Inputs
(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
(hypot.f64 1 x)
(/.f64 1/2 (hypot.f64 1 x))
(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (.f64 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) (cbrt.f64 (exp.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))) (log.f64 (cbrt.f64 (exp.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) (log.f64 (sqrt.f64 (exp.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (pow.f64 (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 2) (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2)) (/.f64 1 (+.f64 (+.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (+.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2)) (+.f64 (+.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2))) (neg.f64 (+.f64 (+.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (neg.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 3)) (+.f64 1 (-.f64 (.f64 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (.f64 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) (-.f64 1 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (neg.f64 (cbrt.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4) (neg.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (cbrt.f64 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (cbrt.f64 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) (cbrt.f64 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (sqrt.f64 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (cbrt.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4)) (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4) 1)))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log1p.f64 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log1p.f64 (neg.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (hypot.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (hypot.f64 1 x))) (cbrt.f64 (exp.f64 (hypot.f64 1 x))))) (log.f64 (cbrt.f64 (exp.f64 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 1 x)))) (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (hypot.f64 1 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (hypot.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (hypot.f64 1 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (hypot.f64 1 x)) (cbrt.f64 (fma.f64 x x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (fma.f64 x x 1)) (cbrt.f64 (hypot.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (hypot.f64 1 x)) (sqrt.f64 (hypot.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 1 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 x x 1) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (hypot.f64 1 x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (hypot.f64 1 x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (hypot.f64 1 x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (fma.f64 x x 1))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (hypot.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (hypot.f64 1 x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (hypot.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (hypot.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (hypot.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (hypot.f64 1 x)) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 1/2 (hypot.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (/.f64 1/2 (hypot.f64 1 x)))) (cbrt.f64 (exp.f64 (/.f64 1/2 (hypot.f64 1 x)))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 1/2 (hypot.f64 1 x))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 1/2 (hypot.f64 1 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (/.f64 1/2 (hypot.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/2 (/.f64 1 (hypot.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1/2 (hypot.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 1/2 (hypot.f64 1 x))) (cbrt.f64 (/.f64 1/4 (fma.f64 x x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 1/4 (fma.f64 x x 1))) (cbrt.f64 (/.f64 1/2 (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x))) (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -1/2 (/.f64 1 (neg.f64 (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (hypot.f64 1 x)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 1/2 (hypot.f64 1 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1/8 (pow.f64 (hypot.f64 1 x) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (hypot.f64 1 x) 2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 1/4 (fma.f64 x x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1/2 (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 1/2 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 1/8 (pow.f64 (hypot.f64 1 x) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1/2 (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1/2 (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 1/2 (hypot.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 1/2 (hypot.f64 1 x))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (cbrt.f64 (exp.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (cbrt.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4) (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 2)) (sqrt.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 1 1/2) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 2) 1/2) (pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (-.f64 1/4 (/.f64 1/4 (fma.f64 x x 1)))) (sqrt.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (+.f64 1/8 (/.f64 1/8 (pow.f64 (hypot.f64 1 x) 3)))) (sqrt.f64 (-.f64 (+.f64 1/4 (/.f64 1/4 (fma.f64 x x 1))) (/.f64 1/4 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4)) (hypot.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 1/4)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 1))))))

simplify51.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

891×	`fma-neg_binary64`
442×	`fma-def_binary64`
232×	`associate--l+_binary64`
220×	`cancel-sign-sub-inv_binary64`
194×	`+-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	128	942
1	428	918
2	1343	892
3	4750	892

Stop Event

1×	node limit

Counts

167 → 202

Calls

Call 1

Inputs
(*.f64 1/8 (pow.f64 x 2))
(-.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 11/128 (pow.f64 x 4)))
(-.f64 (+.f64 (.f64 69/1024 (pow.f64 x 6)) (.f64 1/8 (pow.f64 x 2))) (*.f64 11/128 (pow.f64 x 4)))
(-.f64 (+.f64 (.f64 69/1024 (pow.f64 x 6)) (.f64 1/8 (pow.f64 x 2))) (+.f64 (.f64 11/128 (pow.f64 x 4)) (.f64 1843/32768 (pow.f64 x 8))))
(-.f64 1 (sqrt.f64 1/2))
(-.f64 1 (+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x)))))
(-.f64 (+.f64 (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))) 1) (+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x)))))
(-.f64 (+.f64 (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))) (+.f64 1 (.f64 1/8 (/.f64 1 (.f64 (sqrt.f64 1/2) (pow.f64 x 3)))))) (+.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/128 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3)))) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))))))
(-.f64 1 (sqrt.f64 1/2))
(-.f64 (+.f64 1 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x)))) (sqrt.f64 1/2))
(-.f64 (+.f64 (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))) (+.f64 1 (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))))) (sqrt.f64 1/2))
(-.f64 (+.f64 (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))) (+.f64 1 (+.f64 (.f64 1/128 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3)))) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x)))))) (+.f64 (sqrt.f64 1/2) (.f64 1/8 (/.f64 1 (.f64 (sqrt.f64 1/2) (pow.f64 x 3))))))
1
(+.f64 1 (*.f64 1/2 (pow.f64 x 2)))
(-.f64 (+.f64 1 (.f64 1/2 (pow.f64 x 2))) (.f64 1/8 (pow.f64 x 4)))
(-.f64 (+.f64 1 (+.f64 (.f64 1/16 (pow.f64 x 6)) (.f64 1/2 (pow.f64 x 2)))) (*.f64 1/8 (pow.f64 x 4)))
x
(+.f64 (*.f64 1/2 (/.f64 1 x)) x)
(-.f64 (+.f64 (.f64 1/2 (/.f64 1 x)) x) (.f64 1/8 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 5))) (+.f64 (.f64 1/2 (/.f64 1 x)) x)) (*.f64 1/8 (/.f64 1 (pow.f64 x 3))))
(*.f64 -1 x)
(neg.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) x))
(-.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 1 x)) x))
(-.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 5))) (+.f64 (*.f64 1/2 (/.f64 1 x)) x)))
1/2
(-.f64 1/2 (*.f64 1/4 (pow.f64 x 2)))
(-.f64 (+.f64 (.f64 3/16 (pow.f64 x 4)) 1/2) (.f64 1/4 (pow.f64 x 2)))
(-.f64 (+.f64 (.f64 3/16 (pow.f64 x 4)) 1/2) (+.f64 (.f64 5/32 (pow.f64 x 6)) (*.f64 1/4 (pow.f64 x 2))))
(/.f64 1/2 x)
(-.f64 (.f64 1/2 (/.f64 1 x)) (.f64 1/4 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 (.f64 3/16 (/.f64 1 (pow.f64 x 5))) (.f64 1/2 (/.f64 1 x))) (*.f64 1/4 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 (.f64 3/16 (/.f64 1 (pow.f64 x 5))) (.f64 1/2 (/.f64 1 x))) (+.f64 (.f64 5/32 (/.f64 1 (pow.f64 x 7))) (.f64 1/4 (/.f64 1 (pow.f64 x 3)))))
(/.f64 -1/2 x)
(-.f64 (.f64 1/4 (/.f64 1 (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(-.f64 (.f64 1/4 (/.f64 1 (pow.f64 x 3))) (+.f64 (.f64 3/16 (/.f64 1 (pow.f64 x 5))) (*.f64 1/2 (/.f64 1 x))))
(-.f64 (+.f64 (.f64 5/32 (/.f64 1 (pow.f64 x 7))) (.f64 1/4 (/.f64 1 (pow.f64 x 3)))) (+.f64 (.f64 3/16 (/.f64 1 (pow.f64 x 5))) (.f64 1/2 (/.f64 1 x))))
1
(-.f64 1 (*.f64 1/8 (pow.f64 x 2)))
(-.f64 (+.f64 (.f64 11/128 (pow.f64 x 4)) 1) (.f64 1/8 (pow.f64 x 2)))
(-.f64 (+.f64 (.f64 11/128 (pow.f64 x 4)) 1) (+.f64 (.f64 69/1024 (pow.f64 x 6)) (*.f64 1/8 (pow.f64 x 2))))
(sqrt.f64 1/2)
(+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))))
(-.f64 (+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x)))) (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))))
(-.f64 (+.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/128 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3)))) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))))) (+.f64 (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))) (.f64 1/8 (/.f64 1 (.f64 (sqrt.f64 1/2) (pow.f64 x 3))))))
(sqrt.f64 1/2)
(-.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))))
(-.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x)))))
(-.f64 (+.f64 (sqrt.f64 1/2) (.f64 1/8 (/.f64 1 (.f64 (sqrt.f64 1/2) (pow.f64 x 3))))) (+.f64 (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))) (+.f64 (.f64 1/128 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3)))) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))))))

Outputs
(*.f64 1/8 (pow.f64 x 2))
(.f64 1/8 (.f64 x x))
(-.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 11/128 (pow.f64 x 4)))
(+.f64 (.f64 1/8 (.f64 x x)) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 1/8 (.f64 x x) (.f64 (pow.f64 x 4) -11/128))
(-.f64 (+.f64 (.f64 69/1024 (pow.f64 x 6)) (.f64 1/8 (pow.f64 x 2))) (*.f64 11/128 (pow.f64 x 4)))
(+.f64 (fma.f64 69/1024 (pow.f64 x 6) (.f64 1/8 (.f64 x x))) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 69/1024 (pow.f64 x 6) (fma.f64 1/8 (.f64 x x) (.f64 (pow.f64 x 4) -11/128)))
(fma.f64 (pow.f64 x 4) -11/128 (fma.f64 1/8 (.f64 x x) (.f64 69/1024 (pow.f64 x 6))))
(-.f64 (+.f64 (.f64 69/1024 (pow.f64 x 6)) (.f64 1/8 (pow.f64 x 2))) (+.f64 (.f64 11/128 (pow.f64 x 4)) (.f64 1843/32768 (pow.f64 x 8))))
(-.f64 (fma.f64 69/1024 (pow.f64 x 6) (.f64 1/8 (.f64 x x))) (fma.f64 11/128 (pow.f64 x 4) (*.f64 1843/32768 (pow.f64 x 8))))
(+.f64 (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 1/8 (.f64 x x) (.f64 (pow.f64 x 4) -11/128))) (*.f64 -1843/32768 (pow.f64 x 8)))
(fma.f64 1/8 (.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768))))
(-.f64 1 (sqrt.f64 1/2))
(-.f64 1 (+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x)))))
(-.f64 (-.f64 1 (sqrt.f64 1/2)) (/.f64 1/4 (*.f64 x (sqrt.f64 1/2))))
(+.f64 (-.f64 1 (sqrt.f64 1/2)) (/.f64 -1/4 (*.f64 x (sqrt.f64 1/2))))
(+.f64 1 (-.f64 (/.f64 (/.f64 -1/4 (sqrt.f64 1/2)) x) (sqrt.f64 1/2)))
(-.f64 (+.f64 (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))) 1) (+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x)))))
(+.f64 (/.f64 1/32 (.f64 (.f64 x x) (pow.f64 (sqrt.f64 1/2) 3))) (-.f64 (-.f64 1 (sqrt.f64 1/2)) (/.f64 1/4 (*.f64 x (sqrt.f64 1/2)))))
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(-.f64 1 (sqrt.f64 1/2))
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(-.f64 (+.f64 1 (/.f64 1/4 (*.f64 x (sqrt.f64 1/2)))) (sqrt.f64 1/2))
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(-.f64 (+.f64 1 (+.f64 (/.f64 1/4 (.f64 x (sqrt.f64 1/2))) (fma.f64 1/32 (/.f64 (/.f64 2 (sqrt.f64 1/2)) (.f64 x x)) (/.f64 1/128 (*.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 1/2) 5)))))) (+.f64 (sqrt.f64 1/2) (/.f64 (/.f64 1/8 (pow.f64 x 3)) (sqrt.f64 1/2))))
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1
(+.f64 1 (*.f64 1/2 (pow.f64 x 2)))
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(fma.f64 (*.f64 x x) 1/2 1)
(fma.f64 x (*.f64 x 1/2) 1)
(-.f64 (+.f64 1 (.f64 1/2 (pow.f64 x 2))) (.f64 1/8 (pow.f64 x 4)))
(+.f64 1 (-.f64 (.f64 (.f64 x x) 1/2) (*.f64 1/8 (pow.f64 x 4))))
(+.f64 1 (fma.f64 (.f64 x x) 1/2 (.f64 (pow.f64 x 4) -1/8)))
(fma.f64 (pow.f64 x 4) -1/8 (fma.f64 x (*.f64 x 1/2) 1))
(-.f64 (+.f64 1 (+.f64 (.f64 1/16 (pow.f64 x 6)) (.f64 1/2 (pow.f64 x 2)))) (*.f64 1/8 (pow.f64 x 4)))
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(+.f64 1 (+.f64 (fma.f64 (.f64 x x) 1/2 (.f64 (pow.f64 x 6) 1/16)) (*.f64 (pow.f64 x 4) -1/8)))
(fma.f64 (pow.f64 x 4) -1/8 (fma.f64 x (*.f64 x 1/2) (fma.f64 (pow.f64 x 6) 1/16 1)))
x
(+.f64 (*.f64 1/2 (/.f64 1 x)) x)
(+.f64 x (/.f64 1/2 x))
(-.f64 (+.f64 (.f64 1/2 (/.f64 1 x)) x) (.f64 1/8 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))
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(*.f64 -1 x)
(neg.f64 x)
(neg.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) x))
(neg.f64 (+.f64 x (/.f64 1/2 x)))
(-.f64 (/.f64 -1/2 x) x)
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(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 x (/.f64 1/2 x)))
(-.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)) x)
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(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/16 (pow.f64 x 5))))
(+.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/16 (pow.f64 x 5))) (-.f64 (/.f64 -1/2 x) x))
(+.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (-.f64 (/.f64 -1/2 x) x) (/.f64 -1/16 (pow.f64 x 5))))
1/2
(-.f64 1/2 (*.f64 1/4 (pow.f64 x 2)))
(+.f64 1/2 (.f64 -1/4 (.f64 x x)))
(+.f64 1/2 (.f64 (.f64 x x) -1/4))
(fma.f64 (*.f64 x x) -1/4 1/2)
(-.f64 (+.f64 (.f64 3/16 (pow.f64 x 4)) 1/2) (.f64 1/4 (pow.f64 x 2)))
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(+.f64 (fma.f64 (pow.f64 x 4) 3/16 1/2) (.f64 (.f64 x x) -1/4))
(fma.f64 (*.f64 x x) -1/4 (fma.f64 (pow.f64 x 4) 3/16 1/2))
(-.f64 (+.f64 (.f64 3/16 (pow.f64 x 4)) 1/2) (+.f64 (.f64 5/32 (pow.f64 x 6)) (*.f64 1/4 (pow.f64 x 2))))
(-.f64 (fma.f64 3/16 (pow.f64 x 4) 1/2) (fma.f64 5/32 (pow.f64 x 6) (.f64 (.f64 x x) 1/4)))
(-.f64 (fma.f64 (pow.f64 x 4) 3/16 1/2) (fma.f64 (.f64 x x) 1/4 (.f64 (pow.f64 x 6) 5/32)))
(+.f64 1/2 (fma.f64 (pow.f64 x 4) 3/16 (fma.f64 (.f64 x x) -1/4 (.f64 (pow.f64 x 6) -5/32))))
(+.f64 1/2 (fma.f64 (.f64 x x) (fma.f64 x (.f64 x 3/16) -1/4) (*.f64 (pow.f64 x 6) -5/32)))
(/.f64 1/2 x)
(-.f64 (.f64 1/2 (/.f64 1 x)) (.f64 1/4 (/.f64 1 (pow.f64 x 3))))
(-.f64 (/.f64 1/2 x) (/.f64 1/4 (pow.f64 x 3)))
(+.f64 (/.f64 1/2 x) (/.f64 -1/4 (pow.f64 x 3)))
(-.f64 (+.f64 (.f64 3/16 (/.f64 1 (pow.f64 x 5))) (.f64 1/2 (/.f64 1 x))) (*.f64 1/4 (/.f64 1 (pow.f64 x 3))))
(+.f64 (/.f64 3/16 (pow.f64 x 5)) (-.f64 (/.f64 1/2 x) (/.f64 1/4 (pow.f64 x 3))))
(+.f64 (/.f64 1/2 x) (-.f64 (/.f64 3/16 (pow.f64 x 5)) (/.f64 1/4 (pow.f64 x 3))))
(+.f64 (/.f64 3/16 (pow.f64 x 5)) (+.f64 (/.f64 1/2 x) (/.f64 -1/4 (pow.f64 x 3))))
(-.f64 (+.f64 (.f64 3/16 (/.f64 1 (pow.f64 x 5))) (.f64 1/2 (/.f64 1 x))) (+.f64 (.f64 5/32 (/.f64 1 (pow.f64 x 7))) (.f64 1/4 (/.f64 1 (pow.f64 x 3)))))
(+.f64 (/.f64 3/16 (pow.f64 x 5)) (-.f64 (/.f64 1/2 x) (+.f64 (/.f64 1/4 (pow.f64 x 3)) (/.f64 5/32 (pow.f64 x 7)))))
(+.f64 (/.f64 1/2 x) (-.f64 (/.f64 3/16 (pow.f64 x 5)) (+.f64 (/.f64 1/4 (pow.f64 x 3)) (/.f64 5/32 (pow.f64 x 7)))))
(+.f64 (/.f64 1/2 x) (+.f64 (/.f64 3/16 (pow.f64 x 5)) (+.f64 (/.f64 -1/4 (pow.f64 x 3)) (/.f64 -5/32 (pow.f64 x 7)))))
(/.f64 -1/2 x)
(-.f64 (.f64 1/4 (/.f64 1 (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(-.f64 (/.f64 1/4 (pow.f64 x 3)) (/.f64 1/2 x))
(+.f64 (/.f64 1/4 (pow.f64 x 3)) (/.f64 -1/2 x))
(-.f64 (.f64 1/4 (/.f64 1 (pow.f64 x 3))) (+.f64 (.f64 3/16 (/.f64 1 (pow.f64 x 5))) (*.f64 1/2 (/.f64 1 x))))
(-.f64 (/.f64 1/4 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 3/16 (pow.f64 x 5))))
(+.f64 (-.f64 (/.f64 1/4 (pow.f64 x 3)) (/.f64 3/16 (pow.f64 x 5))) (/.f64 -1/2 x))
(+.f64 (/.f64 1/4 (pow.f64 x 3)) (-.f64 (/.f64 -1/2 x) (/.f64 3/16 (pow.f64 x 5))))
(-.f64 (+.f64 (.f64 5/32 (/.f64 1 (pow.f64 x 7))) (.f64 1/4 (/.f64 1 (pow.f64 x 3)))) (+.f64 (.f64 3/16 (/.f64 1 (pow.f64 x 5))) (.f64 1/2 (/.f64 1 x))))
(+.f64 (/.f64 5/32 (pow.f64 x 7)) (-.f64 (/.f64 1/4 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 3/16 (pow.f64 x 5)))))
(-.f64 (+.f64 (/.f64 1/4 (pow.f64 x 3)) (/.f64 5/32 (pow.f64 x 7))) (+.f64 (/.f64 1/2 x) (/.f64 3/16 (pow.f64 x 5))))
(+.f64 (+.f64 (/.f64 1/4 (pow.f64 x 3)) (/.f64 5/32 (pow.f64 x 7))) (-.f64 (/.f64 -1/2 x) (/.f64 3/16 (pow.f64 x 5))))
1
(-.f64 1 (*.f64 1/8 (pow.f64 x 2)))
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(-.f64 1 (.f64 1/8 (.f64 x x)))
(fma.f64 (*.f64 x x) -1/8 1)
(-.f64 (+.f64 (.f64 11/128 (pow.f64 x 4)) 1) (.f64 1/8 (pow.f64 x 2)))
(+.f64 (fma.f64 11/128 (pow.f64 x 4) 1) (.f64 -1/8 (.f64 x x)))
(fma.f64 11/128 (pow.f64 x 4) (-.f64 1 (.f64 1/8 (.f64 x x))))
(fma.f64 (*.f64 x x) -1/8 (fma.f64 11/128 (pow.f64 x 4) 1))
(-.f64 (+.f64 (.f64 11/128 (pow.f64 x 4)) 1) (+.f64 (.f64 69/1024 (pow.f64 x 6)) (*.f64 1/8 (pow.f64 x 2))))
(-.f64 (fma.f64 11/128 (pow.f64 x 4) 1) (fma.f64 69/1024 (pow.f64 x 6) (.f64 1/8 (.f64 x x))))
(-.f64 (fma.f64 11/128 (pow.f64 x 4) 1) (fma.f64 1/8 (.f64 x x) (.f64 69/1024 (pow.f64 x 6))))
(+.f64 1 (fma.f64 11/128 (pow.f64 x 4) (fma.f64 (.f64 x x) -1/8 (.f64 (pow.f64 x 6) -69/1024))))
(+.f64 1 (fma.f64 (.f64 x x) (fma.f64 x (.f64 x 11/128) -1/8) (*.f64 (pow.f64 x 6) -69/1024)))
(sqrt.f64 1/2)
(+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))))
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(-.f64 (+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x)))) (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))))
(-.f64 (+.f64 (sqrt.f64 1/2) (/.f64 1/4 (.f64 x (sqrt.f64 1/2)))) (/.f64 1/32 (.f64 (*.f64 x x) (pow.f64 (sqrt.f64 1/2) 3))))
(+.f64 (sqrt.f64 1/2) (+.f64 (/.f64 1/4 (.f64 x (sqrt.f64 1/2))) (.f64 (/.f64 (/.f64 2 (sqrt.f64 1/2)) (*.f64 x x)) -1/32)))
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(-.f64 (+.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/128 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3)))) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))))) (+.f64 (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))) (.f64 1/8 (/.f64 1 (.f64 (sqrt.f64 1/2) (pow.f64 x 3))))))
(+.f64 (sqrt.f64 1/2) (-.f64 (+.f64 (/.f64 1/4 (.f64 x (sqrt.f64 1/2))) (/.f64 1/128 (.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 1/2) 5)))) (+.f64 (/.f64 1/32 (.f64 (.f64 x x) (pow.f64 (sqrt.f64 1/2) 3))) (/.f64 1/8 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3))))))
(+.f64 (sqrt.f64 1/2) (+.f64 (/.f64 1/4 (.f64 x (sqrt.f64 1/2))) (-.f64 (/.f64 1/128 (.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 1/2) 5))) (fma.f64 1/32 (/.f64 (/.f64 2 (sqrt.f64 1/2)) (*.f64 x x)) (/.f64 (/.f64 1/8 (pow.f64 x 3)) (sqrt.f64 1/2))))))
(+.f64 (sqrt.f64 1/2) (+.f64 (/.f64 1/128 (.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 1/2) 5))) (+.f64 (/.f64 1/4 (.f64 x (sqrt.f64 1/2))) (+.f64 (/.f64 -1/16 (.f64 (.f64 x x) (sqrt.f64 1/2))) (/.f64 -1/8 (*.f64 (sqrt.f64 1/2) (pow.f64 x 3)))))))
(sqrt.f64 1/2)
(-.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))))
(-.f64 (sqrt.f64 1/2) (/.f64 1/4 (*.f64 x (sqrt.f64 1/2))))
(+.f64 (sqrt.f64 1/2) (/.f64 -1/4 (*.f64 x (sqrt.f64 1/2))))
(+.f64 (sqrt.f64 1/2) (/.f64 (/.f64 -1/4 (sqrt.f64 1/2)) x))
(-.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x)))))
(-.f64 (sqrt.f64 1/2) (+.f64 (/.f64 1/4 (.f64 x (sqrt.f64 1/2))) (/.f64 1/32 (.f64 (*.f64 x x) (pow.f64 (sqrt.f64 1/2) 3)))))
(-.f64 (sqrt.f64 1/2) (fma.f64 1/32 (/.f64 (/.f64 2 (sqrt.f64 1/2)) (.f64 x x)) (/.f64 1/4 (.f64 x (sqrt.f64 1/2)))))
(+.f64 (sqrt.f64 1/2) (+.f64 (/.f64 (/.f64 -1/4 (sqrt.f64 1/2)) x) (/.f64 -1/16 (.f64 (.f64 x x) (sqrt.f64 1/2)))))
(-.f64 (+.f64 (sqrt.f64 1/2) (.f64 1/8 (/.f64 1 (.f64 (sqrt.f64 1/2) (pow.f64 x 3))))) (+.f64 (.f64 1/32 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 3) (pow.f64 x 2)))) (+.f64 (.f64 1/128 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 1/2) 5) (pow.f64 x 3)))) (.f64 1/4 (/.f64 1 (.f64 (sqrt.f64 1/2) x))))))
(-.f64 (+.f64 (sqrt.f64 1/2) (/.f64 1/8 (.f64 (sqrt.f64 1/2) (pow.f64 x 3)))) (+.f64 (/.f64 1/32 (.f64 (.f64 x x) (pow.f64 (sqrt.f64 1/2) 3))) (+.f64 (/.f64 1/4 (.f64 x (sqrt.f64 1/2))) (/.f64 1/128 (*.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 1/2) 5))))))
(+.f64 (sqrt.f64 1/2) (-.f64 (/.f64 (/.f64 1/8 (pow.f64 x 3)) (sqrt.f64 1/2)) (+.f64 (/.f64 1/4 (.f64 x (sqrt.f64 1/2))) (fma.f64 1/32 (/.f64 (/.f64 2 (sqrt.f64 1/2)) (.f64 x x)) (/.f64 1/128 (*.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 1/2) 5)))))))
(+.f64 (sqrt.f64 1/2) (-.f64 (+.f64 (/.f64 1/8 (.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (/.f64 -1/16 (.f64 (.f64 x x) (sqrt.f64 1/2)))) (+.f64 (/.f64 1/4 (.f64 x (sqrt.f64 1/2))) (/.f64 1/128 (*.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 1/2) 5))))))
(-.f64 (+.f64 (/.f64 1/8 (.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (/.f64 -1/16 (.f64 (.f64 x x) (sqrt.f64 1/2)))) (+.f64 (/.f64 1/128 (.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 1/2) 5))) (-.f64 (/.f64 1/4 (*.f64 x (sqrt.f64 1/2))) (sqrt.f64 1/2))))

prune131.0ms (3.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	200	2	202
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	200	3	203

Error

0.0b

Counts

203 → 3

Alt Table

Status	Error	Program
	33.0b	(fma.f64 1/8 (.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768))))
▶	17.2b	(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
✓	17.7b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

Status

Error

Program

33.0b

(fma.f64 1/8 (*.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -11/128 (*.f64 (pow.f64 x 8) -1843/32768))))

▶

17.2b

(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))

✓

17.7b

(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

Compiler

Compiled 3734 to 3306 computations (11.5% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
	0.0b	(/.f64 1/2 (hypot.f64 1 x))
	0.0b	(hypot.f64 1 x)
✓	1.9b	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

series2.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
0.0ms	x	@	inf	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
0.0ms	x	@	-inf	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

rewrite36.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

769×	`pow1_binary64`
717×	`log1p-expm1-u_binary64`
717×	`expm1-log1p-u_binary64`
77×	`add-sqr-sqrt_binary64`
72×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	153	10
2	1893	10

Stop Event

1×	node limit

Counts

1 → 30

Calls

Call 1

Inputs
(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

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

Outputs

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

simplify42.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

658×	`associate-l_binary64`
524×	`fma-def_binary64`
514×	`associate-r_binary64`
323×	`cancel-sign-sub-inv_binary64`
234×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	44	174
1	134	170
2	357	168
3	1111	168

Stop Event

1×	node limit

Counts

42 → 51

Calls

Call 1

Inputs
(*.f64 1/4 (pow.f64 x 2))
(-.f64 (.f64 1/4 (pow.f64 x 2)) (.f64 3/16 (pow.f64 x 4)))
(-.f64 (+.f64 (.f64 5/32 (pow.f64 x 6)) (.f64 1/4 (pow.f64 x 2))) (*.f64 3/16 (pow.f64 x 4)))
(-.f64 (+.f64 (.f64 5/32 (pow.f64 x 6)) (.f64 1/4 (pow.f64 x 2))) (+.f64 (.f64 3/16 (pow.f64 x 4)) (.f64 35/256 (pow.f64 x 8))))
1/2
(-.f64 1/2 (*.f64 1/2 (/.f64 1 x)))
(-.f64 (+.f64 1/2 (.f64 1/4 (/.f64 1 (pow.f64 x 3)))) (.f64 1/2 (/.f64 1 x)))
(-.f64 (+.f64 1/2 (.f64 1/4 (/.f64 1 (pow.f64 x 3)))) (+.f64 (.f64 3/16 (/.f64 1 (pow.f64 x 5))) (*.f64 1/2 (/.f64 1 x))))
1/2
(+.f64 1/2 (*.f64 1/2 (/.f64 1 x)))
(-.f64 (+.f64 1/2 (.f64 1/2 (/.f64 1 x))) (.f64 1/4 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 (.f64 3/16 (/.f64 1 (pow.f64 x 5))) (+.f64 1/2 (.f64 1/2 (/.f64 1 x)))) (*.f64 1/4 (/.f64 1 (pow.f64 x 3))))

Outputs
(*.f64 1/4 (pow.f64 x 2))
(.f64 1/4 (.f64 x x))
(-.f64 (.f64 1/4 (pow.f64 x 2)) (.f64 3/16 (pow.f64 x 4)))
(+.f64 (.f64 1/4 (.f64 x x)) (*.f64 -3/16 (pow.f64 x 4)))
(fma.f64 1/4 (.f64 x x) (.f64 (pow.f64 x 4) -3/16))
(fma.f64 (pow.f64 x 4) -3/16 (.f64 1/4 (.f64 x x)))
(.f64 (.f64 x x) (fma.f64 (*.f64 x x) -3/16 1/4))
(-.f64 (+.f64 (.f64 5/32 (pow.f64 x 6)) (.f64 1/4 (pow.f64 x 2))) (*.f64 3/16 (pow.f64 x 4)))
(+.f64 (fma.f64 5/32 (pow.f64 x 6) (.f64 1/4 (.f64 x x))) (*.f64 -3/16 (pow.f64 x 4)))
(fma.f64 5/32 (pow.f64 x 6) (fma.f64 1/4 (.f64 x x) (.f64 (pow.f64 x 4) -3/16)))
(fma.f64 (pow.f64 x 4) -3/16 (fma.f64 1/4 (.f64 x x) (.f64 5/32 (pow.f64 x 6))))
(-.f64 (+.f64 (.f64 5/32 (pow.f64 x 6)) (.f64 1/4 (pow.f64 x 2))) (+.f64 (.f64 3/16 (pow.f64 x 4)) (.f64 35/256 (pow.f64 x 8))))
(-.f64 (fma.f64 5/32 (pow.f64 x 6) (.f64 1/4 (.f64 x x))) (fma.f64 3/16 (pow.f64 x 4) (*.f64 35/256 (pow.f64 x 8))))
(fma.f64 1/4 (.f64 x x) (fma.f64 5/32 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -3/16 (.f64 (pow.f64 x 8) -35/256))))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) -3/16 1/4) (fma.f64 5/32 (pow.f64 x 6) (*.f64 (pow.f64 x 8) -35/256)))
1/2
(-.f64 1/2 (*.f64 1/2 (/.f64 1 x)))
(-.f64 1/2 (/.f64 1/2 x))
(+.f64 1/2 (/.f64 -1/2 x))
(-.f64 (+.f64 1/2 (.f64 1/4 (/.f64 1 (pow.f64 x 3)))) (.f64 1/2 (/.f64 1 x)))
(+.f64 1/2 (-.f64 (/.f64 1/4 (pow.f64 x 3)) (/.f64 1/2 x)))
(+.f64 (/.f64 1/4 (pow.f64 x 3)) (+.f64 1/2 (/.f64 -1/2 x)))
(-.f64 1/2 (+.f64 (/.f64 1/2 x) (/.f64 -1/4 (pow.f64 x 3))))
(-.f64 (+.f64 1/2 (.f64 1/4 (/.f64 1 (pow.f64 x 3)))) (+.f64 (.f64 3/16 (/.f64 1 (pow.f64 x 5))) (*.f64 1/2 (/.f64 1 x))))
(-.f64 (-.f64 (+.f64 1/2 (/.f64 1/4 (pow.f64 x 3))) (/.f64 3/16 (pow.f64 x 5))) (/.f64 1/2 x))
(+.f64 (+.f64 1/2 (-.f64 (/.f64 1/4 (pow.f64 x 3)) (/.f64 3/16 (pow.f64 x 5)))) (/.f64 -1/2 x))
(+.f64 (/.f64 -1/2 x) (+.f64 (+.f64 1/2 (/.f64 1/4 (pow.f64 x 3))) (/.f64 -3/16 (pow.f64 x 5))))
(+.f64 (/.f64 1/4 (pow.f64 x 3)) (-.f64 (+.f64 1/2 (/.f64 -1/2 x)) (/.f64 3/16 (pow.f64 x 5))))
1/2
(+.f64 1/2 (*.f64 1/2 (/.f64 1 x)))
(+.f64 1/2 (/.f64 1/2 x))
(-.f64 (+.f64 1/2 (.f64 1/2 (/.f64 1 x))) (.f64 1/4 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 1/2 (/.f64 1/2 x)) (/.f64 1/4 (pow.f64 x 3)))
(+.f64 1/2 (+.f64 (/.f64 1/2 x) (/.f64 -1/4 (pow.f64 x 3))))
(-.f64 (+.f64 (.f64 3/16 (/.f64 1 (pow.f64 x 5))) (+.f64 1/2 (.f64 1/2 (/.f64 1 x)))) (*.f64 1/4 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 (/.f64 3/16 (pow.f64 x 5)) (+.f64 1/2 (/.f64 1/2 x))) (/.f64 1/4 (pow.f64 x 3)))
(+.f64 (/.f64 3/16 (pow.f64 x 5)) (+.f64 1/2 (+.f64 (/.f64 1/2 x) (/.f64 -1/4 (pow.f64 x 3)))))
(+.f64 1/2 (-.f64 (+.f64 (/.f64 1/2 x) (/.f64 3/16 (pow.f64 x 5))) (/.f64 1/4 (pow.f64 x 3))))
(+.f64 1/2 (+.f64 (/.f64 3/16 (pow.f64 x 5)) (+.f64 (/.f64 1/2 x) (/.f64 -1/4 (pow.f64 x 3)))))

prune252.0ms (7.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	280	1	281
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	280	4	284

Error

0.0b

Counts

284 → 4

Alt Table

Status	Error	Program
▶	33.0b	(fma.f64 1/8 (.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768))))
✓	17.2b	(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
✓	17.7b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
	33.2b	(/.f64 (.f64 (.f64 x x) (fma.f64 (*.f64 x x) -3/16 1/4)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))

Compiler

Compiled 7097 to 6213 computations (12.5% saved)

localize32.0ms (0.9%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (pow.f64 x 4) -11/128 (*.f64 (pow.f64 x 8) -1843/32768))
✓	0.0b	(*.f64 (pow.f64 x 8) -1843/32768)
✓	17.0b	(fma.f64 1/8 (.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768))))
✓	26.8b	(fma.f64 69/1024 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -11/128 (*.f64 (pow.f64 x 8) -1843/32768)))

series6.0ms (0.2%)

Counts

4 → 48

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(fma.f64 69/1024 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -11/128 (*.f64 (pow.f64 x 8) -1843/32768)))
1.0ms	x	@	0	(fma.f64 69/1024 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -11/128 (*.f64 (pow.f64 x 8) -1843/32768)))
1.0ms	x	@	-inf	(fma.f64 69/1024 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -11/128 (*.f64 (pow.f64 x 8) -1843/32768)))
1.0ms	x	@	0	(*.f64 (pow.f64 x 8) -1843/32768)
0.0ms	x	@	-inf	(fma.f64 (pow.f64 x 4) -11/128 (*.f64 (pow.f64 x 8) -1843/32768))

rewrite55.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

259×	`expm1-udef_binary64`
259×	`log1p-udef_binary64`
201×	`prod-diff_binary64`
162×	`add-sqr-sqrt_binary64`
158×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	70
1	359	70
2	3663	70

Stop Event

1×	node limit

Counts

4 → 84

Calls

Call 1

Inputs
(fma.f64 69/1024 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -11/128 (*.f64 (pow.f64 x 8) -1843/32768)))
(fma.f64 1/8 (.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768))))
(*.f64 (pow.f64 x 8) -1843/32768)
(fma.f64 (pow.f64 x 4) -11/128 (*.f64 (pow.f64 x 8) -1843/32768))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768)) (.f64 69/1024 (pow.f64 x 6)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 69/1024 (pow.f64 x 6)) (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (.f64 69/1024 (pow.f64 x 6)) 1) (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (.f64 69/1024 (pow.f64 x 6)) (.f64 (pow.f64 x 4) -11/128)) (.f64 (pow.f64 x 8) -1843/32768))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768)))) (pow.f64 (cbrt.f64 (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768)))) 2) (cbrt.f64 (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768)))) (sqrt.f64 (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (.f64 69/1024 (pow.f64 x 6)) 3) (pow.f64 (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768)) 3)) (+.f64 (.f64 (.f64 69/1024 (pow.f64 x 6)) (.f64 69/1024 (pow.f64 x 6))) (-.f64 (pow.f64 (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768)) 2) (.f64 (.f64 69/1024 (pow.f64 x 6)) (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 (.f64 69/1024 (pow.f64 x 6)) (.f64 69/1024 (pow.f64 x 6))) (pow.f64 (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768)) 2)) (-.f64 (.f64 69/1024 (pow.f64 x 6)) (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768)))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768))) (.f64 1/8 (.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 1/8 (.f64 x x)) (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (.f64 1/8 (.f64 x x)) 1) (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (.f64 1/8 (.f64 x x)) (.f64 69/1024 (pow.f64 x 6))) (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 1/8 (.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fma.f64 1/8 (.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (fma.f64 1/8 (.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (fma.f64 1/8 (.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768))))) (pow.f64 (cbrt.f64 (fma.f64 1/8 (.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (fma.f64 1/8 (.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768))))) 2) (cbrt.f64 (fma.f64 1/8 (.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (fma.f64 1/8 (.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768))))) (sqrt.f64 (fma.f64 1/8 (.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (.f64 1/8 (.f64 x x)) 3) (pow.f64 (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768))) 3)) (+.f64 (.f64 (.f64 1/8 (.f64 x x)) (.f64 1/8 (.f64 x x))) (-.f64 (pow.f64 (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768))) 2) (.f64 (.f64 1/8 (.f64 x x)) (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 (.f64 1/8 (.f64 x x)) (.f64 1/8 (.f64 x x))) (pow.f64 (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768))) 2)) (-.f64 (.f64 1/8 (.f64 x x)) (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 1/8 (.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 1/8 (.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768)))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 1/8 (.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 1/8 (.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 1/8 (.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 1/8 (.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 1/8 (.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 1/8 (.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 1/8 (.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 1/8 (.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 1/8 (.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (fma.f64 1/8 (.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768))))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 (pow.f64 x 8) -1843/32768))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 x 8) -1843/32768) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 (pow.f64 x 8) -1843/32768) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 (pow.f64 x 8) -1843/32768)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 x 4) (sqrt.f64 -1843/32768)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (.f64 3396649/1073741824 (pow.f64 x 16)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 -1843/32768) (pow.f64 x 8)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 (pow.f64 x 8) -1843/32768))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 (pow.f64 x 8) -1843/32768) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 (pow.f64 x 8) -1843/32768)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 (pow.f64 x 8) -1843/32768)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 (pow.f64 x 8) -1843/32768)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (*.f64 (pow.f64 x 8) -1843/32768)) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (pow.f64 x 8) -1843/32768) (.f64 (pow.f64 x 4) -11/128))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (pow.f64 x 4) -11/128) (.f64 (pow.f64 x 8) -1843/32768))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (.f64 (pow.f64 x 4) -11/128) 1) (.f64 (pow.f64 x 8) -1843/32768))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768))) (pow.f64 (cbrt.f64 (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768))) 2) (cbrt.f64 (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768))) (sqrt.f64 (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (.f64 (pow.f64 x 4) -11/128) 3) (pow.f64 (.f64 (pow.f64 x 8) -1843/32768) 3)) (+.f64 (.f64 (.f64 (pow.f64 x 4) -11/128) (.f64 (pow.f64 x 4) -11/128)) (-.f64 (.f64 3396649/1073741824 (pow.f64 x 16)) (.f64 (.f64 (pow.f64 x 4) -11/128) (.f64 (pow.f64 x 8) -1843/32768)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 (.f64 (pow.f64 x 4) -11/128) (.f64 (pow.f64 x 4) -11/128)) (.f64 3396649/1073741824 (pow.f64 x 16))) (-.f64 (.f64 (pow.f64 x 4) -11/128) (.f64 (pow.f64 x 8) -1843/32768)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (fma.f64 (pow.f64 x 4) -11/128 (*.f64 (pow.f64 x 8) -1843/32768))) 1))))))

simplify41.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

633×	`associate-l_binary64`
479×	`fma-def_binary64`
426×	`associate-r_binary64`
413×	`unswap-sqr_binary64`
315×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	31	684
1	82	670
2	200	630
3	713	630
4	4398	630

Stop Event

1×	node limit

Counts

132 → 103

Calls

Call 1

Inputs
(*.f64 -11/128 (pow.f64 x 4))
(-.f64 (.f64 69/1024 (pow.f64 x 6)) (.f64 11/128 (pow.f64 x 4)))
(-.f64 (.f64 69/1024 (pow.f64 x 6)) (+.f64 (.f64 11/128 (pow.f64 x 4)) (*.f64 1843/32768 (pow.f64 x 8))))
(-.f64 (.f64 69/1024 (pow.f64 x 6)) (+.f64 (.f64 11/128 (pow.f64 x 4)) (*.f64 1843/32768 (pow.f64 x 8))))
(*.f64 -1843/32768 (pow.f64 x 8))
(-.f64 (.f64 69/1024 (pow.f64 x 6)) (.f64 1843/32768 (pow.f64 x 8)))
(-.f64 (.f64 69/1024 (pow.f64 x 6)) (+.f64 (.f64 11/128 (pow.f64 x 4)) (*.f64 1843/32768 (pow.f64 x 8))))
(-.f64 (.f64 69/1024 (pow.f64 x 6)) (+.f64 (.f64 11/128 (pow.f64 x 4)) (*.f64 1843/32768 (pow.f64 x 8))))
(*.f64 -1843/32768 (pow.f64 x 8))
(-.f64 (.f64 69/1024 (pow.f64 x 6)) (.f64 1843/32768 (pow.f64 x 8)))
(-.f64 (.f64 69/1024 (pow.f64 x 6)) (+.f64 (.f64 11/128 (pow.f64 x 4)) (*.f64 1843/32768 (pow.f64 x 8))))
(-.f64 (.f64 69/1024 (pow.f64 x 6)) (+.f64 (.f64 11/128 (pow.f64 x 4)) (*.f64 1843/32768 (pow.f64 x 8))))
(*.f64 1/8 (pow.f64 x 2))
(-.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 11/128 (pow.f64 x 4)))
(-.f64 (+.f64 (.f64 69/1024 (pow.f64 x 6)) (.f64 1/8 (pow.f64 x 2))) (*.f64 11/128 (pow.f64 x 4)))
(-.f64 (+.f64 (.f64 69/1024 (pow.f64 x 6)) (.f64 1/8 (pow.f64 x 2))) (+.f64 (.f64 11/128 (pow.f64 x 4)) (.f64 1843/32768 (pow.f64 x 8))))
(*.f64 -1843/32768 (pow.f64 x 8))
(-.f64 (.f64 69/1024 (pow.f64 x 6)) (.f64 1843/32768 (pow.f64 x 8)))
(-.f64 (.f64 69/1024 (pow.f64 x 6)) (+.f64 (.f64 11/128 (pow.f64 x 4)) (*.f64 1843/32768 (pow.f64 x 8))))
(-.f64 (+.f64 (.f64 69/1024 (pow.f64 x 6)) (.f64 1/8 (pow.f64 x 2))) (+.f64 (.f64 11/128 (pow.f64 x 4)) (.f64 1843/32768 (pow.f64 x 8))))
(*.f64 -1843/32768 (pow.f64 x 8))
(-.f64 (.f64 69/1024 (pow.f64 x 6)) (.f64 1843/32768 (pow.f64 x 8)))
(-.f64 (.f64 69/1024 (pow.f64 x 6)) (+.f64 (.f64 11/128 (pow.f64 x 4)) (*.f64 1843/32768 (pow.f64 x 8))))
(-.f64 (+.f64 (.f64 69/1024 (pow.f64 x 6)) (.f64 1/8 (pow.f64 x 2))) (+.f64 (.f64 11/128 (pow.f64 x 4)) (.f64 1843/32768 (pow.f64 x 8))))
(*.f64 -1843/32768 (pow.f64 x 8))
(*.f64 -1843/32768 (pow.f64 x 8))
(*.f64 -1843/32768 (pow.f64 x 8))
(*.f64 -1843/32768 (pow.f64 x 8))
(*.f64 -1843/32768 (pow.f64 x 8))
(*.f64 -1843/32768 (pow.f64 x 8))
(*.f64 -1843/32768 (pow.f64 x 8))
(*.f64 -1843/32768 (pow.f64 x 8))
(*.f64 -1843/32768 (pow.f64 x 8))
(*.f64 -1843/32768 (pow.f64 x 8))
(*.f64 -1843/32768 (pow.f64 x 8))
(*.f64 -1843/32768 (pow.f64 x 8))
(*.f64 -11/128 (pow.f64 x 4))
(neg.f64 (+.f64 (.f64 11/128 (pow.f64 x 4)) (.f64 1843/32768 (pow.f64 x 8))))
(neg.f64 (+.f64 (.f64 11/128 (pow.f64 x 4)) (.f64 1843/32768 (pow.f64 x 8))))
(neg.f64 (+.f64 (.f64 11/128 (pow.f64 x 4)) (.f64 1843/32768 (pow.f64 x 8))))
(*.f64 -1843/32768 (pow.f64 x 8))
(neg.f64 (+.f64 (.f64 11/128 (pow.f64 x 4)) (.f64 1843/32768 (pow.f64 x 8))))
(neg.f64 (+.f64 (.f64 11/128 (pow.f64 x 4)) (.f64 1843/32768 (pow.f64 x 8))))
(neg.f64 (+.f64 (.f64 11/128 (pow.f64 x 4)) (.f64 1843/32768 (pow.f64 x 8))))
(*.f64 -1843/32768 (pow.f64 x 8))
(neg.f64 (+.f64 (.f64 11/128 (pow.f64 x 4)) (.f64 1843/32768 (pow.f64 x 8))))
(neg.f64 (+.f64 (.f64 11/128 (pow.f64 x 4)) (.f64 1843/32768 (pow.f64 x 8))))
(neg.f64 (+.f64 (.f64 11/128 (pow.f64 x 4)) (.f64 1843/32768 (pow.f64 x 8))))

Outputs
(*.f64 -11/128 (pow.f64 x 4))
(-.f64 (.f64 69/1024 (pow.f64 x 6)) (.f64 11/128 (pow.f64 x 4)))
(+.f64 (.f64 69/1024 (pow.f64 x 6)) (.f64 -11/128 (pow.f64 x 4)))
(fma.f64 69/1024 (pow.f64 x 6) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 -11/128 (pow.f64 x 4) (*.f64 69/1024 (pow.f64 x 6)))
(-.f64 (.f64 69/1024 (pow.f64 x 6)) (+.f64 (.f64 11/128 (pow.f64 x 4)) (*.f64 1843/32768 (pow.f64 x 8))))
(-.f64 (.f64 69/1024 (pow.f64 x 6)) (fma.f64 11/128 (pow.f64 x 4) (.f64 1843/32768 (pow.f64 x 8))))
(-.f64 (.f64 69/1024 (pow.f64 x 6)) (fma.f64 (pow.f64 x 4) 11/128 (.f64 1843/32768 (pow.f64 x 8))))
(fma.f64 69/1024 (pow.f64 x 6) (fma.f64 -11/128 (pow.f64 x 4) (*.f64 (pow.f64 x 8) -1843/32768)))
(fma.f64 -11/128 (pow.f64 x 4) (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 8) -1843/32768)))
(-.f64 (.f64 69/1024 (pow.f64 x 6)) (+.f64 (.f64 11/128 (pow.f64 x 4)) (*.f64 1843/32768 (pow.f64 x 8))))
(-.f64 (.f64 69/1024 (pow.f64 x 6)) (fma.f64 11/128 (pow.f64 x 4) (.f64 1843/32768 (pow.f64 x 8))))
(-.f64 (.f64 69/1024 (pow.f64 x 6)) (fma.f64 (pow.f64 x 4) 11/128 (.f64 1843/32768 (pow.f64 x 8))))
(fma.f64 69/1024 (pow.f64 x 6) (fma.f64 -11/128 (pow.f64 x 4) (*.f64 (pow.f64 x 8) -1843/32768)))
(fma.f64 -11/128 (pow.f64 x 4) (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 8) -1843/32768)))
(*.f64 -1843/32768 (pow.f64 x 8))
(*.f64 (pow.f64 x 8) -1843/32768)
(-.f64 (.f64 69/1024 (pow.f64 x 6)) (.f64 1843/32768 (pow.f64 x 8)))
(+.f64 (.f64 69/1024 (pow.f64 x 6)) (.f64 (pow.f64 x 8) -1843/32768))
(fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 8) -1843/32768))
(-.f64 (.f64 69/1024 (pow.f64 x 6)) (+.f64 (.f64 11/128 (pow.f64 x 4)) (*.f64 1843/32768 (pow.f64 x 8))))
(-.f64 (.f64 69/1024 (pow.f64 x 6)) (fma.f64 11/128 (pow.f64 x 4) (.f64 1843/32768 (pow.f64 x 8))))
(-.f64 (.f64 69/1024 (pow.f64 x 6)) (fma.f64 (pow.f64 x 4) 11/128 (.f64 1843/32768 (pow.f64 x 8))))
(fma.f64 69/1024 (pow.f64 x 6) (fma.f64 -11/128 (pow.f64 x 4) (*.f64 (pow.f64 x 8) -1843/32768)))
(fma.f64 -11/128 (pow.f64 x 4) (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 8) -1843/32768)))
(-.f64 (.f64 69/1024 (pow.f64 x 6)) (+.f64 (.f64 11/128 (pow.f64 x 4)) (*.f64 1843/32768 (pow.f64 x 8))))
(-.f64 (.f64 69/1024 (pow.f64 x 6)) (fma.f64 11/128 (pow.f64 x 4) (.f64 1843/32768 (pow.f64 x 8))))
(-.f64 (.f64 69/1024 (pow.f64 x 6)) (fma.f64 (pow.f64 x 4) 11/128 (.f64 1843/32768 (pow.f64 x 8))))
(fma.f64 69/1024 (pow.f64 x 6) (fma.f64 -11/128 (pow.f64 x 4) (*.f64 (pow.f64 x 8) -1843/32768)))
(fma.f64 -11/128 (pow.f64 x 4) (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 8) -1843/32768)))
(*.f64 -1843/32768 (pow.f64 x 8))
(*.f64 (pow.f64 x 8) -1843/32768)
(-.f64 (.f64 69/1024 (pow.f64 x 6)) (.f64 1843/32768 (pow.f64 x 8)))
(+.f64 (.f64 69/1024 (pow.f64 x 6)) (.f64 (pow.f64 x 8) -1843/32768))
(fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 8) -1843/32768))
(-.f64 (.f64 69/1024 (pow.f64 x 6)) (+.f64 (.f64 11/128 (pow.f64 x 4)) (*.f64 1843/32768 (pow.f64 x 8))))
(-.f64 (.f64 69/1024 (pow.f64 x 6)) (fma.f64 11/128 (pow.f64 x 4) (.f64 1843/32768 (pow.f64 x 8))))
(-.f64 (.f64 69/1024 (pow.f64 x 6)) (fma.f64 (pow.f64 x 4) 11/128 (.f64 1843/32768 (pow.f64 x 8))))
(fma.f64 69/1024 (pow.f64 x 6) (fma.f64 -11/128 (pow.f64 x 4) (*.f64 (pow.f64 x 8) -1843/32768)))
(fma.f64 -11/128 (pow.f64 x 4) (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 8) -1843/32768)))
(-.f64 (.f64 69/1024 (pow.f64 x 6)) (+.f64 (.f64 11/128 (pow.f64 x 4)) (*.f64 1843/32768 (pow.f64 x 8))))
(-.f64 (.f64 69/1024 (pow.f64 x 6)) (fma.f64 11/128 (pow.f64 x 4) (.f64 1843/32768 (pow.f64 x 8))))
(-.f64 (.f64 69/1024 (pow.f64 x 6)) (fma.f64 (pow.f64 x 4) 11/128 (.f64 1843/32768 (pow.f64 x 8))))
(fma.f64 69/1024 (pow.f64 x 6) (fma.f64 -11/128 (pow.f64 x 4) (*.f64 (pow.f64 x 8) -1843/32768)))
(fma.f64 -11/128 (pow.f64 x 4) (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 8) -1843/32768)))
(*.f64 1/8 (pow.f64 x 2))
(.f64 1/8 (.f64 x x))
(.f64 x (.f64 x 1/8))
(-.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 11/128 (pow.f64 x 4)))
(+.f64 (.f64 1/8 (.f64 x x)) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 1/8 (.f64 x x) (.f64 -11/128 (pow.f64 x 4)))
(fma.f64 -11/128 (pow.f64 x 4) (.f64 x (.f64 x 1/8)))
(.f64 (.f64 x x) (fma.f64 -11/128 (*.f64 x x) 1/8))
(-.f64 (+.f64 (.f64 69/1024 (pow.f64 x 6)) (.f64 1/8 (pow.f64 x 2))) (*.f64 11/128 (pow.f64 x 4)))
(+.f64 (fma.f64 69/1024 (pow.f64 x 6) (.f64 1/8 (.f64 x x))) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 69/1024 (pow.f64 x 6) (fma.f64 1/8 (.f64 x x) (.f64 -11/128 (pow.f64 x 4))))
(fma.f64 -11/128 (pow.f64 x 4) (fma.f64 x (.f64 x 1/8) (.f64 69/1024 (pow.f64 x 6))))
(fma.f64 -11/128 (pow.f64 x 4) (fma.f64 69/1024 (pow.f64 x 6) (.f64 x (.f64 x 1/8))))
(-.f64 (+.f64 (.f64 69/1024 (pow.f64 x 6)) (.f64 1/8 (pow.f64 x 2))) (+.f64 (.f64 11/128 (pow.f64 x 4)) (.f64 1843/32768 (pow.f64 x 8))))
(-.f64 (fma.f64 69/1024 (pow.f64 x 6) (.f64 1/8 (.f64 x x))) (fma.f64 11/128 (pow.f64 x 4) (*.f64 1843/32768 (pow.f64 x 8))))
(+.f64 (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 1/8 (.f64 x x) (.f64 -11/128 (pow.f64 x 4)))) (*.f64 (pow.f64 x 8) -1843/32768))
(fma.f64 x (.f64 x 1/8) (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 -11/128 (pow.f64 x 4) (.f64 (pow.f64 x 8) -1843/32768))))
(fma.f64 -11/128 (pow.f64 x 4) (fma.f64 (pow.f64 x 8) -1843/32768 (fma.f64 69/1024 (pow.f64 x 6) (.f64 x (.f64 x 1/8)))))
(*.f64 -1843/32768 (pow.f64 x 8))
(*.f64 (pow.f64 x 8) -1843/32768)
(-.f64 (.f64 69/1024 (pow.f64 x 6)) (.f64 1843/32768 (pow.f64 x 8)))
(+.f64 (.f64 69/1024 (pow.f64 x 6)) (.f64 (pow.f64 x 8) -1843/32768))
(fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 8) -1843/32768))
(-.f64 (.f64 69/1024 (pow.f64 x 6)) (+.f64 (.f64 11/128 (pow.f64 x 4)) (*.f64 1843/32768 (pow.f64 x 8))))
(-.f64 (.f64 69/1024 (pow.f64 x 6)) (fma.f64 11/128 (pow.f64 x 4) (.f64 1843/32768 (pow.f64 x 8))))
(-.f64 (.f64 69/1024 (pow.f64 x 6)) (fma.f64 (pow.f64 x 4) 11/128 (.f64 1843/32768 (pow.f64 x 8))))
(fma.f64 69/1024 (pow.f64 x 6) (fma.f64 -11/128 (pow.f64 x 4) (*.f64 (pow.f64 x 8) -1843/32768)))
(fma.f64 -11/128 (pow.f64 x 4) (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 8) -1843/32768)))
(-.f64 (+.f64 (.f64 69/1024 (pow.f64 x 6)) (.f64 1/8 (pow.f64 x 2))) (+.f64 (.f64 11/128 (pow.f64 x 4)) (.f64 1843/32768 (pow.f64 x 8))))
(-.f64 (fma.f64 69/1024 (pow.f64 x 6) (.f64 1/8 (.f64 x x))) (fma.f64 11/128 (pow.f64 x 4) (*.f64 1843/32768 (pow.f64 x 8))))
(+.f64 (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 1/8 (.f64 x x) (.f64 -11/128 (pow.f64 x 4)))) (*.f64 (pow.f64 x 8) -1843/32768))
(fma.f64 x (.f64 x 1/8) (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 -11/128 (pow.f64 x 4) (.f64 (pow.f64 x 8) -1843/32768))))
(fma.f64 -11/128 (pow.f64 x 4) (fma.f64 (pow.f64 x 8) -1843/32768 (fma.f64 69/1024 (pow.f64 x 6) (.f64 x (.f64 x 1/8)))))
(*.f64 -1843/32768 (pow.f64 x 8))
(*.f64 (pow.f64 x 8) -1843/32768)
(-.f64 (.f64 69/1024 (pow.f64 x 6)) (.f64 1843/32768 (pow.f64 x 8)))
(+.f64 (.f64 69/1024 (pow.f64 x 6)) (.f64 (pow.f64 x 8) -1843/32768))
(fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 8) -1843/32768))
(-.f64 (.f64 69/1024 (pow.f64 x 6)) (+.f64 (.f64 11/128 (pow.f64 x 4)) (*.f64 1843/32768 (pow.f64 x 8))))
(-.f64 (.f64 69/1024 (pow.f64 x 6)) (fma.f64 11/128 (pow.f64 x 4) (.f64 1843/32768 (pow.f64 x 8))))
(-.f64 (.f64 69/1024 (pow.f64 x 6)) (fma.f64 (pow.f64 x 4) 11/128 (.f64 1843/32768 (pow.f64 x 8))))
(fma.f64 69/1024 (pow.f64 x 6) (fma.f64 -11/128 (pow.f64 x 4) (*.f64 (pow.f64 x 8) -1843/32768)))
(fma.f64 -11/128 (pow.f64 x 4) (fma.f64 69/1024 (pow.f64 x 6) (*.f64 (pow.f64 x 8) -1843/32768)))
(-.f64 (+.f64 (.f64 69/1024 (pow.f64 x 6)) (.f64 1/8 (pow.f64 x 2))) (+.f64 (.f64 11/128 (pow.f64 x 4)) (.f64 1843/32768 (pow.f64 x 8))))
(-.f64 (fma.f64 69/1024 (pow.f64 x 6) (.f64 1/8 (.f64 x x))) (fma.f64 11/128 (pow.f64 x 4) (*.f64 1843/32768 (pow.f64 x 8))))
(+.f64 (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 1/8 (.f64 x x) (.f64 -11/128 (pow.f64 x 4)))) (*.f64 (pow.f64 x 8) -1843/32768))
(fma.f64 x (.f64 x 1/8) (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 -11/128 (pow.f64 x 4) (.f64 (pow.f64 x 8) -1843/32768))))
(fma.f64 -11/128 (pow.f64 x 4) (fma.f64 (pow.f64 x 8) -1843/32768 (fma.f64 69/1024 (pow.f64 x 6) (.f64 x (.f64 x 1/8)))))
(*.f64 -1843/32768 (pow.f64 x 8))
(*.f64 (pow.f64 x 8) -1843/32768)
(*.f64 -1843/32768 (pow.f64 x 8))
(*.f64 (pow.f64 x 8) -1843/32768)
(*.f64 -1843/32768 (pow.f64 x 8))
(*.f64 (pow.f64 x 8) -1843/32768)
(*.f64 -1843/32768 (pow.f64 x 8))
(*.f64 (pow.f64 x 8) -1843/32768)
(*.f64 -1843/32768 (pow.f64 x 8))
(*.f64 (pow.f64 x 8) -1843/32768)
(*.f64 -1843/32768 (pow.f64 x 8))
(*.f64 (pow.f64 x 8) -1843/32768)
(*.f64 -1843/32768 (pow.f64 x 8))
(*.f64 (pow.f64 x 8) -1843/32768)
(*.f64 -1843/32768 (pow.f64 x 8))
(*.f64 (pow.f64 x 8) -1843/32768)
(*.f64 -1843/32768 (pow.f64 x 8))
(*.f64 (pow.f64 x 8) -1843/32768)
(*.f64 -1843/32768 (pow.f64 x 8))
(*.f64 (pow.f64 x 8) -1843/32768)
(*.f64 -1843/32768 (pow.f64 x 8))
(*.f64 (pow.f64 x 8) -1843/32768)
(*.f64 -1843/32768 (pow.f64 x 8))
(*.f64 (pow.f64 x 8) -1843/32768)
(*.f64 -11/128 (pow.f64 x 4))
(neg.f64 (+.f64 (.f64 11/128 (pow.f64 x 4)) (.f64 1843/32768 (pow.f64 x 8))))
(neg.f64 (fma.f64 11/128 (pow.f64 x 4) (*.f64 1843/32768 (pow.f64 x 8))))
(neg.f64 (fma.f64 (pow.f64 x 4) 11/128 (*.f64 1843/32768 (pow.f64 x 8))))
(fma.f64 -11/128 (pow.f64 x 4) (*.f64 (pow.f64 x 8) -1843/32768))
(*.f64 (pow.f64 x 4) (fma.f64 (pow.f64 x 4) -1843/32768 -11/128))
(neg.f64 (+.f64 (.f64 11/128 (pow.f64 x 4)) (.f64 1843/32768 (pow.f64 x 8))))
(neg.f64 (fma.f64 11/128 (pow.f64 x 4) (*.f64 1843/32768 (pow.f64 x 8))))
(neg.f64 (fma.f64 (pow.f64 x 4) 11/128 (*.f64 1843/32768 (pow.f64 x 8))))
(fma.f64 -11/128 (pow.f64 x 4) (*.f64 (pow.f64 x 8) -1843/32768))
(*.f64 (pow.f64 x 4) (fma.f64 (pow.f64 x 4) -1843/32768 -11/128))
(neg.f64 (+.f64 (.f64 11/128 (pow.f64 x 4)) (.f64 1843/32768 (pow.f64 x 8))))
(neg.f64 (fma.f64 11/128 (pow.f64 x 4) (*.f64 1843/32768 (pow.f64 x 8))))
(neg.f64 (fma.f64 (pow.f64 x 4) 11/128 (*.f64 1843/32768 (pow.f64 x 8))))
(fma.f64 -11/128 (pow.f64 x 4) (*.f64 (pow.f64 x 8) -1843/32768))
(*.f64 (pow.f64 x 4) (fma.f64 (pow.f64 x 4) -1843/32768 -11/128))
(*.f64 -1843/32768 (pow.f64 x 8))
(*.f64 (pow.f64 x 8) -1843/32768)
(neg.f64 (+.f64 (.f64 11/128 (pow.f64 x 4)) (.f64 1843/32768 (pow.f64 x 8))))
(neg.f64 (fma.f64 11/128 (pow.f64 x 4) (*.f64 1843/32768 (pow.f64 x 8))))
(neg.f64 (fma.f64 (pow.f64 x 4) 11/128 (*.f64 1843/32768 (pow.f64 x 8))))
(fma.f64 -11/128 (pow.f64 x 4) (*.f64 (pow.f64 x 8) -1843/32768))
(*.f64 (pow.f64 x 4) (fma.f64 (pow.f64 x 4) -1843/32768 -11/128))
(neg.f64 (+.f64 (.f64 11/128 (pow.f64 x 4)) (.f64 1843/32768 (pow.f64 x 8))))
(neg.f64 (fma.f64 11/128 (pow.f64 x 4) (*.f64 1843/32768 (pow.f64 x 8))))
(neg.f64 (fma.f64 (pow.f64 x 4) 11/128 (*.f64 1843/32768 (pow.f64 x 8))))
(fma.f64 -11/128 (pow.f64 x 4) (*.f64 (pow.f64 x 8) -1843/32768))
(*.f64 (pow.f64 x 4) (fma.f64 (pow.f64 x 4) -1843/32768 -11/128))
(neg.f64 (+.f64 (.f64 11/128 (pow.f64 x 4)) (.f64 1843/32768 (pow.f64 x 8))))
(neg.f64 (fma.f64 11/128 (pow.f64 x 4) (*.f64 1843/32768 (pow.f64 x 8))))
(neg.f64 (fma.f64 (pow.f64 x 4) 11/128 (*.f64 1843/32768 (pow.f64 x 8))))
(fma.f64 -11/128 (pow.f64 x 4) (*.f64 (pow.f64 x 8) -1843/32768))
(*.f64 (pow.f64 x 4) (fma.f64 (pow.f64 x 4) -1843/32768 -11/128))
(*.f64 -1843/32768 (pow.f64 x 8))
(*.f64 (pow.f64 x 8) -1843/32768)
(neg.f64 (+.f64 (.f64 11/128 (pow.f64 x 4)) (.f64 1843/32768 (pow.f64 x 8))))
(neg.f64 (fma.f64 11/128 (pow.f64 x 4) (*.f64 1843/32768 (pow.f64 x 8))))
(neg.f64 (fma.f64 (pow.f64 x 4) 11/128 (*.f64 1843/32768 (pow.f64 x 8))))
(fma.f64 -11/128 (pow.f64 x 4) (*.f64 (pow.f64 x 8) -1843/32768))
(*.f64 (pow.f64 x 4) (fma.f64 (pow.f64 x 4) -1843/32768 -11/128))
(neg.f64 (+.f64 (.f64 11/128 (pow.f64 x 4)) (.f64 1843/32768 (pow.f64 x 8))))
(neg.f64 (fma.f64 11/128 (pow.f64 x 4) (*.f64 1843/32768 (pow.f64 x 8))))
(neg.f64 (fma.f64 (pow.f64 x 4) 11/128 (*.f64 1843/32768 (pow.f64 x 8))))
(fma.f64 -11/128 (pow.f64 x 4) (*.f64 (pow.f64 x 8) -1843/32768))
(*.f64 (pow.f64 x 4) (fma.f64 (pow.f64 x 4) -1843/32768 -11/128))
(neg.f64 (+.f64 (.f64 11/128 (pow.f64 x 4)) (.f64 1843/32768 (pow.f64 x 8))))
(neg.f64 (fma.f64 11/128 (pow.f64 x 4) (*.f64 1843/32768 (pow.f64 x 8))))
(neg.f64 (fma.f64 (pow.f64 x 4) 11/128 (*.f64 1843/32768 (pow.f64 x 8))))
(fma.f64 -11/128 (pow.f64 x 4) (*.f64 (pow.f64 x 8) -1843/32768))
(*.f64 (pow.f64 x 4) (fma.f64 (pow.f64 x 4) -1843/32768 -11/128))

prune87.0ms (2.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	102	1	103
Fresh	1	0	1
Picked	0	1	1
Done	0	2	2
Total	103	4	107

Error

0.0b

Counts

107 → 4

Alt Table

Status	Error	Program
✓	33.0b	(fma.f64 1/8 (.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768))))
▶	33.2b	(.f64 (.f64 x x) (fma.f64 -11/128 (*.f64 x x) 1/8))
✓	17.2b	(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
✓	17.7b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

Compiler

Compiled 2606 to 1926 computations (26.1% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (.f64 x x) (fma.f64 -11/128 (*.f64 x x) 1/8))
✓	0.3b	(fma.f64 -11/128 (*.f64 x x) 1/8)

series3.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(fma.f64 -11/128 (*.f64 x x) 1/8)
1.0ms	x	@	0	(fma.f64 -11/128 (*.f64 x x) 1/8)
0.0ms	x	@	inf	(.f64 (.f64 x x) (fma.f64 -11/128 (*.f64 x x) 1/8))
0.0ms	x	@	0	(.f64 (.f64 x x) (fma.f64 -11/128 (*.f64 x x) 1/8))
0.0ms	x	@	-inf	(fma.f64 -11/128 (*.f64 x x) 1/8)

rewrite40.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

635×	`pow1_binary64`
594×	`add-log-exp_binary64`
594×	`log1p-expm1-u_binary64`
594×	`expm1-log1p-u_binary64`
70×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	22
1	144	22
2	1626	22

Stop Event

1×	node limit

Counts

2 → 38

Calls

Call 1

Inputs
(fma.f64 -11/128 (*.f64 x x) 1/8)
(.f64 (.f64 x x) (fma.f64 -11/128 (*.f64 x x) 1/8))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 1/8 (*.f64 -11/128 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 -11/128 (*.f64 x x)) 1/8)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 -11/128 (*.f64 x x)) 1) 1/8)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 -11/128 (*.f64 x x) 1/8))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 -11/128 (*.f64 x x) 1/8) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 -11/128 (*.f64 x x) 1/8))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 -11/128 (*.f64 x x) 1/8)) (pow.f64 (cbrt.f64 (fma.f64 -11/128 (*.f64 x x) 1/8)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 -11/128 (*.f64 x x) 1/8)) 2) (cbrt.f64 (fma.f64 -11/128 (*.f64 x x) 1/8)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 -11/128 (*.f64 x x) 1/8)) (sqrt.f64 (fma.f64 -11/128 (*.f64 x x) 1/8)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 -11/128 (*.f64 x x)) 3) 1/512) (+.f64 (*.f64 (*.f64 -11/128 (*.f64 x x)) (*.f64 -11/128 (*.f64 x x))) (-.f64 1/64 (*.f64 (*.f64 -11/128 (*.f64 x x)) 1/8))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 -11/128 (*.f64 x x)) (*.f64 -11/128 (*.f64 x x))) 1/64) (-.f64 (*.f64 -11/128 (*.f64 x x)) 1/8))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 -11/128 (*.f64 x x) 1/8) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 -11/128 (*.f64 x x) 1/8) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 -11/128 (*.f64 x x) 1/8)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 -11/128 (*.f64 x x) 1/8)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 -11/128 (*.f64 x x) 1/8) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 -11/128 (*.f64 x x) 1/8)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 -11/128 (*.f64 x x) 1/8))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 -11/128 (*.f64 x x) 1/8) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 -11/128 (*.f64 x x) 1/8)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 -11/128 (*.f64 x x) 1/8)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 -11/128 (*.f64 x x) 1/8)))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 -11/128 (*.f64 x x)) (*.f64 x x)) (*.f64 1/8 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 x x) (*.f64 -11/128 (*.f64 x x))) (*.f64 (*.f64 x x) 1/8))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (*.f64 x x) (fma.f64 -11/128 (*.f64 x x) 1/8)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (*.f64 x x) (fma.f64 -11/128 (*.f64 x x) 1/8)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (*.f64 x x) (fma.f64 -11/128 (*.f64 x x) 1/8)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (*.f64 x x) (fma.f64 -11/128 (*.f64 x x) 1/8))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (sqrt.f64 (fma.f64 -11/128 (*.f64 x x) 1/8))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 (fma.f64 -11/128 (*.f64 x x) 1/8) 2) (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (fma.f64 -11/128 (*.f64 x x) 1/8)) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (*.f64 x x) (fma.f64 -11/128 (*.f64 x x) 1/8)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (*.f64 x x) (fma.f64 -11/128 (*.f64 x x) 1/8)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (*.f64 x x) 3) (pow.f64 (fma.f64 -11/128 (*.f64 x x) 1/8) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (fma.f64 -11/128 (*.f64 x x) 1/8) 3) (pow.f64 (*.f64 x x) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (*.f64 x x) (fma.f64 -11/128 (*.f64 x x) 1/8))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (*.f64 x x) (fma.f64 -11/128 (*.f64 x x) 1/8))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (*.f64 x x) (fma.f64 -11/128 (*.f64 x x) 1/8))))))))

simplify32.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

691×	`fma-def_binary64`
536×	`fma-neg_binary64`
416×	`distribute-rgt-neg-in_binary64`
403×	`cancel-sign-sub-inv_binary64`
351×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	16	270
1	36	252
2	82	234
3	237	234
4	916	234
5	2232	234
6	3769	234

Stop Event

1×	node limit

Counts

62 → 48

Calls

Call 1

Inputs
1/8
(-.f64 1/8 (*.f64 11/128 (pow.f64 x 2)))
(-.f64 1/8 (*.f64 11/128 (pow.f64 x 2)))
(-.f64 1/8 (*.f64 11/128 (pow.f64 x 2)))
(*.f64 -11/128 (pow.f64 x 2))
(-.f64 1/8 (*.f64 11/128 (pow.f64 x 2)))
(-.f64 1/8 (*.f64 11/128 (pow.f64 x 2)))
(-.f64 1/8 (*.f64 11/128 (pow.f64 x 2)))
(*.f64 -11/128 (pow.f64 x 2))
(-.f64 1/8 (*.f64 11/128 (pow.f64 x 2)))
(-.f64 1/8 (*.f64 11/128 (pow.f64 x 2)))
(-.f64 1/8 (*.f64 11/128 (pow.f64 x 2)))
(*.f64 1/8 (pow.f64 x 2))
(-.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 11/128 (pow.f64 x 4)))
(-.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 11/128 (pow.f64 x 4)))
(-.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 11/128 (pow.f64 x 4)))
(*.f64 -11/128 (pow.f64 x 4))
(-.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 11/128 (pow.f64 x 4)))
(-.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 11/128 (pow.f64 x 4)))
(-.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 11/128 (pow.f64 x 4)))
(*.f64 -11/128 (pow.f64 x 4))
(-.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 11/128 (pow.f64 x 4)))
(-.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 11/128 (pow.f64 x 4)))
(-.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 11/128 (pow.f64 x 4)))

Outputs
1/8
(-.f64 1/8 (*.f64 11/128 (pow.f64 x 2)))
(+.f64 1/8 (.f64 (.f64 x x) -11/128))
(+.f64 1/8 (.f64 x (.f64 x -11/128)))
(fma.f64 x (*.f64 x -11/128) 1/8)
(-.f64 1/8 (*.f64 11/128 (pow.f64 x 2)))
(+.f64 1/8 (.f64 (.f64 x x) -11/128))
(+.f64 1/8 (.f64 x (.f64 x -11/128)))
(fma.f64 x (*.f64 x -11/128) 1/8)
(-.f64 1/8 (*.f64 11/128 (pow.f64 x 2)))
(+.f64 1/8 (.f64 (.f64 x x) -11/128))
(+.f64 1/8 (.f64 x (.f64 x -11/128)))
(fma.f64 x (*.f64 x -11/128) 1/8)
(*.f64 -11/128 (pow.f64 x 2))
(.f64 (.f64 x x) -11/128)
(.f64 x (.f64 x -11/128))
(-.f64 1/8 (*.f64 11/128 (pow.f64 x 2)))
(+.f64 1/8 (.f64 (.f64 x x) -11/128))
(+.f64 1/8 (.f64 x (.f64 x -11/128)))
(fma.f64 x (*.f64 x -11/128) 1/8)
(-.f64 1/8 (*.f64 11/128 (pow.f64 x 2)))
(+.f64 1/8 (.f64 (.f64 x x) -11/128))
(+.f64 1/8 (.f64 x (.f64 x -11/128)))
(fma.f64 x (*.f64 x -11/128) 1/8)
(-.f64 1/8 (*.f64 11/128 (pow.f64 x 2)))
(+.f64 1/8 (.f64 (.f64 x x) -11/128))
(+.f64 1/8 (.f64 x (.f64 x -11/128)))
(fma.f64 x (*.f64 x -11/128) 1/8)
(*.f64 -11/128 (pow.f64 x 2))
(.f64 (.f64 x x) -11/128)
(.f64 x (.f64 x -11/128))
(-.f64 1/8 (*.f64 11/128 (pow.f64 x 2)))
(+.f64 1/8 (.f64 (.f64 x x) -11/128))
(+.f64 1/8 (.f64 x (.f64 x -11/128)))
(fma.f64 x (*.f64 x -11/128) 1/8)
(-.f64 1/8 (*.f64 11/128 (pow.f64 x 2)))
(+.f64 1/8 (.f64 (.f64 x x) -11/128))
(+.f64 1/8 (.f64 x (.f64 x -11/128)))
(fma.f64 x (*.f64 x -11/128) 1/8)
(-.f64 1/8 (*.f64 11/128 (pow.f64 x 2)))
(+.f64 1/8 (.f64 (.f64 x x) -11/128))
(+.f64 1/8 (.f64 x (.f64 x -11/128)))
(fma.f64 x (*.f64 x -11/128) 1/8)
(*.f64 1/8 (pow.f64 x 2))
(.f64 1/8 (.f64 x x))
(.f64 x (.f64 x 1/8))
(-.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 11/128 (pow.f64 x 4)))
(+.f64 (.f64 1/8 (.f64 x x)) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 1/8 (.f64 x x) (.f64 -11/128 (pow.f64 x 4)))
(.f64 (.f64 x x) (fma.f64 x (*.f64 x -11/128) 1/8))
(-.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 11/128 (pow.f64 x 4)))
(+.f64 (.f64 1/8 (.f64 x x)) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 1/8 (.f64 x x) (.f64 -11/128 (pow.f64 x 4)))
(.f64 (.f64 x x) (fma.f64 x (*.f64 x -11/128) 1/8))
(-.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 11/128 (pow.f64 x 4)))
(+.f64 (.f64 1/8 (.f64 x x)) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 1/8 (.f64 x x) (.f64 -11/128 (pow.f64 x 4)))
(.f64 (.f64 x x) (fma.f64 x (*.f64 x -11/128) 1/8))
(*.f64 -11/128 (pow.f64 x 4))
(-.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 11/128 (pow.f64 x 4)))
(+.f64 (.f64 1/8 (.f64 x x)) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 1/8 (.f64 x x) (.f64 -11/128 (pow.f64 x 4)))
(.f64 (.f64 x x) (fma.f64 x (*.f64 x -11/128) 1/8))
(-.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 11/128 (pow.f64 x 4)))
(+.f64 (.f64 1/8 (.f64 x x)) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 1/8 (.f64 x x) (.f64 -11/128 (pow.f64 x 4)))
(.f64 (.f64 x x) (fma.f64 x (*.f64 x -11/128) 1/8))
(-.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 11/128 (pow.f64 x 4)))
(+.f64 (.f64 1/8 (.f64 x x)) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 1/8 (.f64 x x) (.f64 -11/128 (pow.f64 x 4)))
(.f64 (.f64 x x) (fma.f64 x (*.f64 x -11/128) 1/8))
(*.f64 -11/128 (pow.f64 x 4))
(-.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 11/128 (pow.f64 x 4)))
(+.f64 (.f64 1/8 (.f64 x x)) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 1/8 (.f64 x x) (.f64 -11/128 (pow.f64 x 4)))
(.f64 (.f64 x x) (fma.f64 x (*.f64 x -11/128) 1/8))
(-.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 11/128 (pow.f64 x 4)))
(+.f64 (.f64 1/8 (.f64 x x)) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 1/8 (.f64 x x) (.f64 -11/128 (pow.f64 x 4)))
(.f64 (.f64 x x) (fma.f64 x (*.f64 x -11/128) 1/8))
(-.f64 (.f64 1/8 (pow.f64 x 2)) (.f64 11/128 (pow.f64 x 4)))
(+.f64 (.f64 1/8 (.f64 x x)) (*.f64 -11/128 (pow.f64 x 4)))
(fma.f64 1/8 (.f64 x x) (.f64 -11/128 (pow.f64 x 4)))
(.f64 (.f64 x x) (fma.f64 x (*.f64 x -11/128) 1/8))

prune34.0ms (1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	47	1	48
Fresh	0	0	0
Picked	1	0	1
Done	0	3	3
Total	48	4	52

Error

0.0b

Counts

52 → 4

Alt Table

Status	Error	Program
✓	33.0b	(fma.f64 1/8 (.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768))))
✓	17.2b	(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
✓	17.7b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
	40.9b	(sqrt.f64 (.f64 (pow.f64 (fma.f64 -11/128 (.f64 x x) 1/8) 2) (pow.f64 x 4)))

Compiler

Compiled 692 to 396 computations (42.8% saved)

regimes370.0ms (10.6%)

Accuracy

Total 0.0b remaining (31.8%)

Threshold costs 0.0b (31.8%)

Counts

69 → 2

Compiler

Compiled 1019 to 764 computations (25% saved)

bsearch1.0ms (0%)

Algorithm

1×	left-value

Calls

1 calls:

0.0ms

(hypot.f64 1 x)

Steps

Iters	Point		Range
1.002	∈ [	1.0000373450175308	,	1.0034741811879035	]

Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
2×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`distribute-neg-frac_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	64
1	37	64
2	44	64
3	46	64
4	47	64

Stop Event

1×

saturated

Calls

Call 1

Inputs

(if (<=.f64 (hypot.f64 1 x) 4512606826625237/4503599627370496) (fma.f64 1/8 (*.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -11/128 (*.f64 (pow.f64 x 8) -1843/32768)))) (/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))

Outputs

(if (<=.f64 (hypot.f64 1 x) 4512606826625237/4503599627370496) (fma.f64 1/8 (*.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -11/128 (*.f64 (pow.f64 x 8) -1843/32768)))) (/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))

(if (<=.f64 (hypot.f64 1 x) 4512606826625237/4503599627370496) (fma.f64 1/8 (*.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -11/128 (*.f64 (pow.f64 x 8) -1843/32768)))) (/.f64 (+.f64 1/2 (/.f64 -1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))

end100.0ms (2.9%)

Stop Event

1×

fuel

Compiler

Compiled 155 to 128 computations (17.4% saved)

Details

analyze0.0ms (0%)

sample2.1s (59.1%)

preprocess17.0ms (0.5%)

simplify8.0ms (0.2%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series7.0ms (0.2%)

rewrite59.0ms (1.7%)

simplify51.0ms (1.5%)

prune131.0ms (3.8%)

localize8.0ms (0.2%)

series2.0ms (0.1%)

rewrite36.0ms (1%)

simplify42.0ms (1.2%)

prune252.0ms (7.2%)

localize32.0ms (0.9%)

series6.0ms (0.2%)

rewrite55.0ms (1.6%)

simplify41.0ms (1.2%)

prune87.0ms (2.5%)

localize4.0ms (0.1%)

series3.0ms (0.1%)

rewrite40.0ms (1.1%)

simplify32.0ms (0.9%)

prune34.0ms (1%)

regimes370.0ms (10.6%)

bsearch1.0ms (0%)

simplify3.0ms (0.1%)

end100.0ms (2.9%)

Profiling