Details

analyze0.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	0%	50%	2

Compiler

Compiled 13 to 11 computations (15.4% saved)

sample1.8s (47.5%)

Results

892.0ms	2363×	body	1024	valid
471.0ms	4302×	body	128	valid
326.0ms	1077×	body	512	valid
95.0ms	514×	body	256	valid

preprocess28.0ms (0.7%)

Algorithm

2×	egg-herbie

Rules

566×	`fma-neg_binary64`
270×	`rule--a-bc--c-ba_binary64`
248×	`rule---abc---acb_binary64`
245×	`rule--+abc-+a-bc_binary64`
238×	`rule-+a-bc--+abc_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	60	17
2	191	17
3	846	17
0	1	1

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0

Outputs
0

Call 2

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

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

Compiler

Compiled 12 to 10 computations (16.7% saved)

simplify18.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

566×	`fma-neg_binary64`
270×	`rule--a-bc--c-ba_binary64`
248×	`rule---abc---acb_binary64`
245×	`rule--+abc-+a-bc_binary64`
238×	`rule-+a-bc--+abc_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	60	17
2	191	17
3	846	17

Stop Event

1×	node limit

Counts

1 → 2

Calls

Call 1

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

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

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

21.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	21.8b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

Compiler

Compiled 47 to 38 computations (19.1% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 x 1))
✓	0.1b	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
✓	0.3b	(/.f64 1 (sqrt.f64 x))
✓	3.4b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

series10.0ms (0.3%)

Counts

4 → 8

Calls

12 calls:

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

rewrite65.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

243×	`rule-/ab-*+aa/1/2b_binary64`
223×	`rule-aa-fabsaa_binary64`
173×	`rule--ab--+aa+ab_binary64`
173×	`rule-nega-/a-1_binary64`
171×	`rule-nega--0a_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	38
1	240	30
2	3351	30

Stop Event

1×	node limit

Counts

4 → 194

Calls

Call 1

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

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

simplify30.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

449×	`rule-a-*a1_binary64`
449×	`rule-a--a0_binary64`
449×	`rule-a-+a0_binary64`
449×	`rule-a-/a1_binary64`
404×	`rule--ab--+aa+ab_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	30	80
1	203	76
2	574	74
3	2572	74

Stop Event

1×	node limit

Counts

202 → 207

Calls

Call 1

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

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

prune454.0ms (12%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	196	11	207
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	197	11	208

Error

21.2b

Counts

208 → 11

Alt Table

Status	Error	Program
	26.6b	(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (pow.f64 (sqrt.f64 (+.f64 1 x)) -1/2) 2))
	32.7b	(fma.f64 (pow.f64 (sqrt.f64 x) -1/2) (pow.f64 (sqrt.f64 x) -1/2) (neg.f64 (pow.f64 (+.f64 1 x) -1/2)))
	24.1b	(*.f64 (-.f64 (pow.f64 (pow.f64 x 1/4) -1) (pow.f64 (sqrt.f64 (+.f64 1 x)) -1/2)) (+.f64 (pow.f64 (pow.f64 x 1/4) -1) (pow.f64 (sqrt.f64 (+.f64 1 x)) -1/2)))
	25.0b	(+.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (fma.f64 (neg.f64 (/.f64 1/2 (sqrt.f64 (+.f64 1 x)))) 2 (pow.f64 (+.f64 1 x) -1/2)))
	33.0b	(fma.f64 (cbrt.f64 (pow.f64 x -1)) (cbrt.f64 (pow.f64 x -1/2)) (neg.f64 (pow.f64 (+.f64 1 x) -1/2)))
	25.1b	(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (+.f64 1 x) -1/2))
	29.4b	(-.f64 (/.f64 1 (sqrt.f64 x)) (*.f64 (cbrt.f64 (pow.f64 (+.f64 1 x) -1/2)) (cbrt.f64 (pow.f64 (+.f64 1 x) -1))))
	32.6b	(pow.f64 (pow.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) 3) 1/3)
	32.4b	(+.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (fma.f64 (neg.f64 (pow.f64 (sqrt.f64 (+.f64 1 x)) -1/2)) (pow.f64 (sqrt.f64 (+.f64 1 x)) -1/2) (pow.f64 (+.f64 1 x) -1/2)))
	32.3b	(+.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (fma.f64 (neg.f64 (cbrt.f64 (pow.f64 (+.f64 1 x) -1/2))) (cbrt.f64 (pow.f64 (+.f64 1 x) -1)) (pow.f64 (+.f64 1 x) -1/2)))
▶	23.9b	(exp.f64 (log.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))))

Compiler

Compiled 3935 to 3108 computations (21% saved)

localize12.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(log.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
✓	2.5b	(exp.f64 (log.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))))
✓	3.4b	(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))

series10.0ms (0.3%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
3.0ms	x	@	inf	(log.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
2.0ms	x	@	-inf	(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))
1.0ms	x	@	0	(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))
1.0ms	x	@	inf	(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))
1.0ms	x	@	0	(log.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))

rewrite67.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

218×	`rule-aa-fabsaa_binary64`
190×	`rule-/ab-*+aa/1/2b_binary64`
175×	`rule-nega--0a_binary64`
175×	`rule-nega-/a-1_binary64`
175×	`rule-nega-*a-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	41
1	256	41
2	3343	41

Stop Event

1×	node limit

Counts

3 → 189

Calls

Call 1

Inputs
(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))
(exp.f64 (log.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))))
(log.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))

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

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

simplify50.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

598×	`rule-a-*a1_binary64`
598×	`rule-a--a0_binary64`
598×	`rule-a-+a0_binary64`
589×	`rule-a-/a1_binary64`
240×	`fma-def_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	129	1362
1	928	1328
2	3408	1328

Stop Event

1×	node limit

Counts

225 → 171

Calls

Call 1

Inputs
(-.f64 (pow.f64 x -1/2) 1)
(-.f64 (+.f64 (*.f64 1/2 x) (pow.f64 x -1/2)) 1)
(-.f64 (+.f64 (.f64 1/2 x) (+.f64 (pow.f64 x -1/2) (.f64 -3/8 (pow.f64 x 2)))) 1)
(-.f64 (+.f64 (.f64 1/2 x) (+.f64 (pow.f64 x -1/2) (+.f64 (.f64 5/16 (pow.f64 x 3)) (*.f64 -3/8 (pow.f64 x 2))))) 1)
(*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))
(+.f64 (.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (.f64 -3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))))
(+.f64 (.f64 5/16 (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (+.f64 (.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 -3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))))))
(+.f64 (.f64 5/16 (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (+.f64 (.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (+.f64 (.f64 -35/128 (sqrt.f64 (/.f64 1 (pow.f64 x 9)))) (.f64 -3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))))))
(.f64 1/2 (/.f64 (exp.f64 (.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x))
(+.f64 (.f64 1/2 (/.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)) (.f64 -3/8 (/.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))))
(+.f64 (.f64 5/16 (/.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)) (.f64 -3/8 (/.f64 (exp.f64 (.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2)))))
(+.f64 (.f64 -35/128 (/.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 4))) (+.f64 (.f64 5/16 (/.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)) (.f64 -3/8 (/.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))))))
(-.f64 (pow.f64 x -1/2) 1)
(-.f64 (+.f64 (*.f64 1/2 x) (pow.f64 x -1/2)) 1)
(-.f64 (+.f64 (.f64 1/2 x) (+.f64 (pow.f64 x -1/2) (.f64 -3/8 (pow.f64 x 2)))) 1)
(-.f64 (+.f64 (.f64 1/2 x) (+.f64 (pow.f64 x -1/2) (+.f64 (.f64 5/16 (pow.f64 x 3)) (*.f64 -3/8 (pow.f64 x 2))))) 1)
(*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))
(+.f64 (.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (.f64 -3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))))
(+.f64 (.f64 5/16 (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (+.f64 (.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 -3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))))))
(+.f64 (.f64 5/16 (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (+.f64 (.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (+.f64 (.f64 -35/128 (sqrt.f64 (/.f64 1 (pow.f64 x 9)))) (.f64 -3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))))))
(.f64 1/2 (/.f64 (exp.f64 (.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x))
(+.f64 (.f64 1/2 (/.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)) (.f64 -3/8 (/.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))))
(+.f64 (.f64 5/16 (/.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)) (.f64 -3/8 (/.f64 (exp.f64 (.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2)))))
(+.f64 (.f64 -35/128 (/.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 4))) (+.f64 (.f64 5/16 (/.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)) (.f64 -3/8 (/.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))))))
(log.f64 (-.f64 (pow.f64 x -1/2) 1))
(+.f64 (log.f64 (-.f64 (pow.f64 x -1/2) 1)) (*.f64 1/2 (/.f64 x (-.f64 (pow.f64 x -1/2) 1))))
(+.f64 (log.f64 (-.f64 (pow.f64 x -1/2) 1)) (+.f64 (.f64 1/2 (/.f64 x (-.f64 (pow.f64 x -1/2) 1))) (.f64 -1/2 (.f64 (pow.f64 x 2) (+.f64 (.f64 3/4 (/.f64 1 (-.f64 (pow.f64 x -1/2) 1))) (*.f64 1/4 (/.f64 1 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2))))))))
(+.f64 (log.f64 (-.f64 (pow.f64 x -1/2) 1)) (+.f64 (.f64 1/2 (/.f64 x (-.f64 (pow.f64 x -1/2) 1))) (+.f64 (.f64 -1/2 (.f64 (pow.f64 x 2) (+.f64 (.f64 3/4 (/.f64 1 (-.f64 (pow.f64 x -1/2) 1))) (.f64 1/4 (/.f64 1 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)))))) (.f64 1/6 (.f64 (+.f64 (.f64 9/8 (/.f64 1 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2))) (+.f64 (.f64 1/4 (/.f64 1 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 3))) (.f64 15/8 (/.f64 1 (-.f64 (pow.f64 x -1/2) 1))))) (pow.f64 x 3))))))
(+.f64 (log.f64 (/.f64 1 x)) (log.f64 (neg.f64 (*.f64 -1/2 (sqrt.f64 (/.f64 1 x))))))
(-.f64 (+.f64 (log.f64 (/.f64 1 x)) (log.f64 (neg.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 x)))))) (.f64 3/4 (/.f64 1 x)))
(-.f64 (+.f64 (log.f64 (/.f64 1 x)) (+.f64 (.f64 11/32 (/.f64 1 (pow.f64 x 2))) (log.f64 (neg.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 x))))))) (*.f64 3/4 (/.f64 1 x)))
(-.f64 (+.f64 (log.f64 (/.f64 1 x)) (+.f64 (.f64 11/32 (/.f64 1 (pow.f64 x 2))) (log.f64 (neg.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 x))))))) (+.f64 (.f64 3/4 (/.f64 1 x)) (.f64 7/32 (/.f64 1 (pow.f64 x 3)))))
(+.f64 (log.f64 (/.f64 -1 x)) (log.f64 (neg.f64 (.f64 1/2 (exp.f64 (.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))))))
(-.f64 (+.f64 (log.f64 (/.f64 -1 x)) (log.f64 (neg.f64 (.f64 1/2 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))))) (.f64 3/4 (/.f64 1 x)))
(-.f64 (+.f64 (log.f64 (/.f64 -1 x)) (+.f64 (.f64 11/32 (/.f64 1 (pow.f64 x 2))) (log.f64 (neg.f64 (.f64 1/2 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))))))) (*.f64 3/4 (/.f64 1 x)))
(-.f64 (+.f64 (log.f64 (/.f64 -1 x)) (+.f64 (.f64 11/32 (/.f64 1 (pow.f64 x 2))) (log.f64 (neg.f64 (.f64 1/2 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))))))) (+.f64 (.f64 3/4 (/.f64 1 x)) (.f64 7/32 (/.f64 1 (pow.f64 x 3)))))

Outputs
(-.f64 (pow.f64 x -1/2) 1)
(+.f64 (pow.f64 x -1/2) -1)
(-.f64 (+.f64 (*.f64 1/2 x) (pow.f64 x -1/2)) 1)
(+.f64 (fma.f64 1/2 x (pow.f64 x -1/2)) -1)
(+.f64 (fma.f64 x 1/2 (pow.f64 x -1/2)) -1)
(-.f64 (+.f64 (.f64 1/2 x) (+.f64 (pow.f64 x -1/2) (.f64 -3/8 (pow.f64 x 2)))) 1)
(+.f64 (fma.f64 1/2 x (+.f64 (pow.f64 x -1/2) (.f64 -3/8 (.f64 x x)))) -1)
(+.f64 (fma.f64 x 1/2 (fma.f64 -3/8 (*.f64 x x) (pow.f64 x -1/2))) -1)
(-.f64 (+.f64 (.f64 1/2 x) (+.f64 (pow.f64 x -1/2) (+.f64 (.f64 5/16 (pow.f64 x 3)) (*.f64 -3/8 (pow.f64 x 2))))) 1)
(+.f64 (fma.f64 1/2 x (+.f64 (pow.f64 x -1/2) (fma.f64 5/16 (pow.f64 x 3) (.f64 -3/8 (.f64 x x))))) -1)
(+.f64 (fma.f64 x 1/2 (fma.f64 5/16 (pow.f64 x 3) (fma.f64 -3/8 (*.f64 x x) (pow.f64 x -1/2)))) -1)
(*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))
(+.f64 (.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (.f64 -3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))))
(fma.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 -3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))))
(+.f64 (.f64 5/16 (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (+.f64 (.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 -3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))))))
(fma.f64 5/16 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (fma.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 -3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))))))
(fma.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (fma.f64 5/16 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (*.f64 -3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))))))
(+.f64 (.f64 5/16 (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (+.f64 (.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (+.f64 (.f64 -35/128 (sqrt.f64 (/.f64 1 (pow.f64 x 9)))) (.f64 -3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))))))
(fma.f64 5/16 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (fma.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (fma.f64 -35/128 (sqrt.f64 (/.f64 1 (pow.f64 x 9))) (*.f64 -3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))))))
(fma.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (fma.f64 5/16 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (fma.f64 -35/128 (sqrt.f64 (/.f64 1 (pow.f64 x 9))) (*.f64 -3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))))))
(.f64 1/2 (/.f64 (exp.f64 (.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x))
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(-.f64 (+.f64 (log.f64 (/.f64 -1 x)) (+.f64 (.f64 11/32 (/.f64 1 (pow.f64 x 2))) (log.f64 (neg.f64 (.f64 1/2 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))))))) (+.f64 (.f64 3/4 (/.f64 1 x)) (.f64 7/32 (/.f64 1 (pow.f64 x 3)))))
(+.f64 (log.f64 (/.f64 -1 x)) (-.f64 (+.f64 (/.f64 11/32 (.f64 x x)) (log.f64 (neg.f64 (.f64 1/2 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))))))) (+.f64 (/.f64 3/4 x) (/.f64 7/32 (pow.f64 x 3)))))
(+.f64 (log.f64 (/.f64 -1 x)) (+.f64 (log.f64 (.f64 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) -1/2)) (-.f64 (/.f64 11/32 (.f64 x x)) (+.f64 (/.f64 3/4 x) (/.f64 7/32 (pow.f64 x 3))))))

prune149.0ms (3.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	169	2	171
Fresh	8	2	10
Picked	1	0	1
Done	0	0	0
Total	178	4	182

Error

2.1b

Counts

182 → 4

Alt Table

Status	Error	Program
	33.0b	(fma.f64 (cbrt.f64 (pow.f64 x -1)) (cbrt.f64 (pow.f64 x -1/2)) (neg.f64 (pow.f64 (+.f64 1 x) -1/2)))
▶	25.0b	(+.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (fma.f64 (neg.f64 (/.f64 1/2 (sqrt.f64 (+.f64 1 x)))) 2 (pow.f64 (+.f64 1 x) -1/2)))
	31.1b	(exp.f64 (-.f64 (-.f64 (log.f64 (*.f64 (sqrt.f64 (/.f64 1 x)) 1/2)) (log.f64 x)) (/.f64 3/4 x)))
	43.0b	(exp.f64 (log.f64 (fma.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 -3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))))))

Compiler

Compiled 4295 to 3587 computations (16.5% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 1 x))
✓	0.1b	(/.f64 1/2 (sqrt.f64 (+.f64 1 x)))
	3.4b	(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))
✓	10.5b	(fma.f64 (neg.f64 (/.f64 1/2 (sqrt.f64 (+.f64 1 x)))) 2 (pow.f64 (+.f64 1 x) -1/2))

series167.0ms (4.4%)

Counts

3 → 14

Calls

9 calls:

Time	Variable		Point	Expression
162.0ms	x	@	0	(fma.f64 (neg.f64 (/.f64 1/2 (sqrt.f64 (+.f64 1 x)))) 2 (pow.f64 (+.f64 1 x) -1/2))
1.0ms	x	@	inf	(fma.f64 (neg.f64 (/.f64 1/2 (sqrt.f64 (+.f64 1 x)))) 2 (pow.f64 (+.f64 1 x) -1/2))
1.0ms	x	@	-inf	(fma.f64 (neg.f64 (/.f64 1/2 (sqrt.f64 (+.f64 1 x)))) 2 (pow.f64 (+.f64 1 x) -1/2))
1.0ms	x	@	-inf	(/.f64 1/2 (sqrt.f64 (+.f64 1 x)))
1.0ms	x	@	inf	(/.f64 1/2 (sqrt.f64 (+.f64 1 x)))

rewrite60.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

234×	`rule-aa-fabsaa_binary64`
199×	`rule-/ab-*+aa/1/2b_binary64`
180×	`rule-nega-*a-1_binary64`
179×	`rule-nega--0a_binary64`
175×	`rule-nega-/a-1_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	36
1	308	34
2	3685	33

Stop Event

1×	node limit

Counts

3 → 128

Calls

Call 1

Inputs
(fma.f64 (neg.f64 (/.f64 1/2 (sqrt.f64 (+.f64 1 x)))) 2 (pow.f64 (+.f64 1 x) -1/2))
(/.f64 1/2 (sqrt.f64 (+.f64 1 x)))
(sqrt.f64 (+.f64 1 x))

Outputs

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

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

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

simplify40.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

615×	`rule-a--a0_binary64`
615×	`rule-a-+a0_binary64`
615×	`rule-a-/a1_binary64`
407×	`fma-def_binary64`
170×	`fma-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	41	109
1	267	101
2	764	101
3	3518	101

Stop Event

1×	node limit

Counts

142 → 146

Calls

Call 1

Inputs
0
0
0
0
(sqrt.f64 (/.f64 1 x))
(exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))
1/2
(+.f64 1/2 (*.f64 -1/4 x))
(+.f64 1/2 (+.f64 (.f64 3/16 (pow.f64 x 2)) (.f64 -1/4 x)))
(+.f64 1/2 (+.f64 (.f64 -5/32 (pow.f64 x 3)) (+.f64 (.f64 3/16 (pow.f64 x 2)) (*.f64 -1/4 x))))
1
(+.f64 (*.f64 1/2 x) 1)
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) 1))
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) (+.f64 1 (*.f64 1/16 (pow.f64 x 3)))))

Outputs
0
0
0
0
(sqrt.f64 (/.f64 1 x))
(exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))
(pow.f64 (exp.f64 -1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)))
(.f64 (exp.f64 (.f64 (log.f64 (/.f64 -1 x)) 1/2)) (pow.f64 -1 -1/2))
1/2
(+.f64 1/2 (*.f64 -1/4 x))
(+.f64 1/2 (*.f64 x -1/4))
(fma.f64 x -1/4 1/2)
(+.f64 1/2 (+.f64 (.f64 3/16 (pow.f64 x 2)) (.f64 -1/4 x)))
(+.f64 1/2 (fma.f64 3/16 (.f64 x x) (.f64 x -1/4)))
(fma.f64 3/16 (*.f64 x x) (fma.f64 x -1/4 1/2))
(fma.f64 x -1/4 (fma.f64 x (*.f64 x 3/16) 1/2))
(+.f64 1/2 (+.f64 (.f64 -5/32 (pow.f64 x 3)) (+.f64 (.f64 3/16 (pow.f64 x 2)) (*.f64 -1/4 x))))
(+.f64 1/2 (fma.f64 -5/32 (pow.f64 x 3) (fma.f64 3/16 (.f64 x x) (.f64 x -1/4))))
(fma.f64 -5/32 (pow.f64 x 3) (fma.f64 3/16 (*.f64 x x) (fma.f64 x -1/4 1/2)))
(fma.f64 -5/32 (pow.f64 x 3) (fma.f64 x -1/4 (fma.f64 x (*.f64 x 3/16) 1/2)))
1
(+.f64 (*.f64 1/2 x) 1)
(fma.f64 1/2 x 1)
(fma.f64 x 1/2 1)
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) 1))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 1/2 x 1))
(fma.f64 x 1/2 (fma.f64 (*.f64 x x) -1/8 1))
(fma.f64 x 1/2 (fma.f64 x (*.f64 x -1/8) 1))
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) (+.f64 1 (*.f64 1/16 (pow.f64 x 3)))))
(fma.f64 -1/8 (.f64 x x) (fma.f64 1/2 x (+.f64 1 (.f64 (pow.f64 x 3) 1/16))))
(fma.f64 x 1/2 (fma.f64 (*.f64 x x) -1/8 (fma.f64 (pow.f64 x 3) 1/16 1)))
(fma.f64 x 1/2 (fma.f64 x (*.f64 x -1/8) (fma.f64 (pow.f64 x 3) 1/16 1)))

prune255.0ms (6.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	234	1	235
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	235	4	239

Error

1.5b

Counts

239 → 4

Alt Table

Status	Error	Program
	33.0b	(fma.f64 (cbrt.f64 (pow.f64 x -1)) (cbrt.f64 (pow.f64 x -1/2)) (neg.f64 (pow.f64 (+.f64 1 x) -1/2)))
✓	25.0b	(+.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (fma.f64 (neg.f64 (/.f64 1/2 (sqrt.f64 (+.f64 1 x)))) 2 (pow.f64 (+.f64 1 x) -1/2)))
▶	31.1b	(exp.f64 (-.f64 (-.f64 (log.f64 (*.f64 (sqrt.f64 (/.f64 1 x)) 1/2)) (log.f64 x)) (/.f64 3/4 x)))
	46.7b	(+.f64 (fma.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 -3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))))) (fma.f64 (neg.f64 (/.f64 1/2 (sqrt.f64 (+.f64 1 x)))) 2 (pow.f64 (+.f64 1 x) -1/2)))

Compiler

Compiled 7826 to 6589 computations (15.8% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (-.f64 (log.f64 (*.f64 (sqrt.f64 (/.f64 1 x)) 1/2)) (log.f64 x)) (/.f64 3/4 x))
✓	0.1b	(sqrt.f64 (/.f64 1 x))
✓	0.3b	(-.f64 (log.f64 (*.f64 (sqrt.f64 (/.f64 1 x)) 1/2)) (log.f64 x))
✓	2.1b	(exp.f64 (-.f64 (-.f64 (log.f64 (*.f64 (sqrt.f64 (/.f64 1 x)) 1/2)) (log.f64 x)) (/.f64 3/4 x)))

series10.0ms (0.3%)

Counts

4 → 5

Calls

12 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	(exp.f64 (-.f64 (-.f64 (log.f64 (*.f64 (sqrt.f64 (/.f64 1 x)) 1/2)) (log.f64 x)) (/.f64 3/4 x)))
2.0ms	x	@	-inf	(exp.f64 (-.f64 (-.f64 (log.f64 (*.f64 (sqrt.f64 (/.f64 1 x)) 1/2)) (log.f64 x)) (/.f64 3/4 x)))
1.0ms	x	@	-inf	(sqrt.f64 (/.f64 1 x))
1.0ms	x	@	inf	(-.f64 (log.f64 (*.f64 (sqrt.f64 (/.f64 1 x)) 1/2)) (log.f64 x))
1.0ms	x	@	-inf	(-.f64 (log.f64 (*.f64 (sqrt.f64 (/.f64 1 x)) 1/2)) (log.f64 x))

rewrite77.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

159×	`add-sqr-sqrt_binary64`
152×	`add-log-exp_binary64`
151×	`add-exp-log_binary64`
149×	`pow1_binary64`
149×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	62
1	368	49
2	4987	49

Stop Event

1×	node limit

Counts

4 → 175

Calls

Call 1

Inputs
(exp.f64 (-.f64 (-.f64 (log.f64 (*.f64 (sqrt.f64 (/.f64 1 x)) 1/2)) (log.f64 x)) (/.f64 3/4 x)))
(-.f64 (log.f64 (*.f64 (sqrt.f64 (/.f64 1 x)) 1/2)) (log.f64 x))
(sqrt.f64 (/.f64 1 x))
(-.f64 (-.f64 (log.f64 (*.f64 (sqrt.f64 (/.f64 1 x)) 1/2)) (log.f64 x)) (/.f64 3/4 x))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (/.f64 (/.f64 1/2 x) (sqrt.f64 x)) (exp.f64 (/.f64 3/4 x))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (/.f64 (/.f64 1/2 x) (sqrt.f64 x)) (exp.f64 (/.f64 3/4 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (exp.f64 (log1p.f64 (/.f64 (/.f64 (/.f64 1/2 x) (sqrt.f64 x)) (exp.f64 (/.f64 3/4 x))))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (/.f64 (/.f64 1/2 x) (sqrt.f64 x)) (exp.f64 (/.f64 3/4 x))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (/.f64 (/.f64 (/.f64 1/2 x) (sqrt.f64 x)) (exp.f64 (/.f64 3/4 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (/.f64 (/.f64 1/2 x) (sqrt.f64 x)) (exp.f64 (/.f64 3/4 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (/.f64 (/.f64 (/.f64 1/2 x) (sqrt.f64 x)) (exp.f64 (/.f64 3/4 x))) (/.f64 (/.f64 (/.f64 1/2 x) (sqrt.f64 x)) (exp.f64 (/.f64 3/4 x)))) (/.f64 (/.f64 (/.f64 1/2 x) (sqrt.f64 x)) 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(#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (-.f64 (log.f64 (/.f64 (/.f64 1/2 x) (sqrt.f64 x))) (/.f64 3/4 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (/.f64 (/.f64 (/.f64 1/2 x) (sqrt.f64 x)) (exp.f64 (/.f64 3/4 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (-.f64 (log.f64 (/.f64 (/.f64 1/2 x) (sqrt.f64 x))) (/.f64 3/4 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 (log.f64 (/.f64 (/.f64 1/2 x) (sqrt.f64 x))) (/.f64 3/4 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (log.f64 (/.f64 (/.f64 1/2 x) (sqrt.f64 x))) 1 (neg.f64 (/.f64 3/4 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 (log.f64 (/.f64 (/.f64 1/2 x) (sqrt.f64 x))) (/.f64 3/4 x)) 1 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (-.f64 (log.f64 (/.f64 (/.f64 1/2 x) (sqrt.f64 x))) (/.f64 3/4 x))) 2) (cbrt.f64 (-.f64 (log.f64 (/.f64 (/.f64 1/2 x) (sqrt.f64 x))) (/.f64 3/4 x))) 0)))) (#(struct:change 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simplify25.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

344×	`rule-+a-bc-+b-ac_binary64`
256×	`rule-a-*a1_binary64`
256×	`rule-a--a0_binary64`
256×	`rule-a-+a0_binary64`
253×	`rule-a-/a1_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	16	100
1	104	92
2	313	84
3	1491	84

Stop Event

1×	node limit

Counts

180 → 178

Calls

Call 1

Inputs
(exp.f64 (-.f64 (log.f64 (.f64 1/2 (sqrt.f64 (/.f64 1 x)))) (+.f64 (.f64 3/4 (/.f64 1 x)) (log.f64 x))))
(exp.f64 (-.f64 (log.f64 (.f64 1/2 (sqrt.f64 (/.f64 1 x)))) (+.f64 (.f64 3/4 (/.f64 1 x)) (log.f64 x))))
(exp.f64 (-.f64 (log.f64 (.f64 1/2 (sqrt.f64 (/.f64 1 x)))) (+.f64 (.f64 3/4 (/.f64 1 x)) (log.f64 x))))
(exp.f64 (-.f64 (log.f64 (.f64 1/2 (sqrt.f64 (/.f64 1 x)))) (+.f64 (.f64 3/4 (/.f64 1 x)) (log.f64 x))))
(/.f64 -3/4 x)

Outputs
(exp.f64 (-.f64 (log.f64 (.f64 1/2 (sqrt.f64 (/.f64 1 x)))) (+.f64 (.f64 3/4 (/.f64 1 x)) (log.f64 x))))
(exp.f64 (-.f64 (log.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 x)))) (+.f64 (/.f64 3/4 x) (log.f64 x))))
(/.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 x))) (exp.f64 (+.f64 (/.f64 3/4 x) (log.f64 x))))
(/.f64 (/.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 x))) (exp.f64 (/.f64 3/4 x))) x)
(exp.f64 (-.f64 (log.f64 (.f64 1/2 (sqrt.f64 (/.f64 1 x)))) (+.f64 (.f64 3/4 (/.f64 1 x)) (log.f64 x))))
(exp.f64 (-.f64 (log.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 x)))) (+.f64 (/.f64 3/4 x) (log.f64 x))))
(/.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 x))) (exp.f64 (+.f64 (/.f64 3/4 x) (log.f64 x))))
(/.f64 (/.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 x))) (exp.f64 (/.f64 3/4 x))) x)
(exp.f64 (-.f64 (log.f64 (.f64 1/2 (sqrt.f64 (/.f64 1 x)))) (+.f64 (.f64 3/4 (/.f64 1 x)) (log.f64 x))))
(exp.f64 (-.f64 (log.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 x)))) (+.f64 (/.f64 3/4 x) (log.f64 x))))
(/.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 x))) (exp.f64 (+.f64 (/.f64 3/4 x) (log.f64 x))))
(/.f64 (/.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 x))) (exp.f64 (/.f64 3/4 x))) x)
(exp.f64 (-.f64 (log.f64 (.f64 1/2 (sqrt.f64 (/.f64 1 x)))) (+.f64 (.f64 3/4 (/.f64 1 x)) (log.f64 x))))
(exp.f64 (-.f64 (log.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 x)))) (+.f64 (/.f64 3/4 x) (log.f64 x))))
(/.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 x))) (exp.f64 (+.f64 (/.f64 3/4 x) (log.f64 x))))
(/.f64 (/.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 x))) (exp.f64 (/.f64 3/4 x))) x)
(/.f64 -3/4 x)

prune136.0ms (3.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	174	4	178
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	175	7	182

Error

0.0b

Counts

182 → 7

Alt Table

Status	Error	Program
	29.0b	(/.f64 (/.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 x))) (exp.f64 (/.f64 3/4 x))) x)
	33.0b	(fma.f64 (cbrt.f64 (pow.f64 x -1)) (cbrt.f64 (pow.f64 x -1/2)) (neg.f64 (pow.f64 (+.f64 1 x) -1/2)))
	29.3b	(+.f64 (/.f64 (/.f64 (/.f64 1/2 x) (sqrt.f64 x)) (exp.f64 (/.f64 3/4 x))) 0)
✓	25.0b	(+.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (fma.f64 (neg.f64 (/.f64 1/2 (sqrt.f64 (+.f64 1 x)))) 2 (pow.f64 (+.f64 1 x) -1/2)))
	29.4b	(pow.f64 (sqrt.f64 (/.f64 (/.f64 (/.f64 1/2 x) (sqrt.f64 x)) (exp.f64 (/.f64 3/4 x)))) 2)
	29.6b	(pow.f64 (cbrt.f64 (/.f64 (/.f64 (/.f64 1/2 x) (sqrt.f64 x)) (exp.f64 (/.f64 3/4 x)))) 3)
	46.7b	(+.f64 (fma.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 -3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))))) (fma.f64 (neg.f64 (/.f64 1/2 (sqrt.f64 (+.f64 1 x)))) 2 (pow.f64 (+.f64 1 x) -1/2)))

Compiler

Compiled 3771 to 2701 computations (28.4% saved)

regimes109.0ms (2.9%)

Accuracy

Total -61.6b remaining (-13452%)

Threshold costs -61.6b (-13452%)

Counts

59 → 2

Compiler

Compiled 1105 to 870 computations (21.3% saved)

bsearch1.0ms (0%)

Algorithm

1×	left-value

Calls

1 calls:

0.0ms

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

Steps

Iters	Point		Range
5e-18	∈ [	3.4173544256974747e-18	,	4.753694733028093	]

Compiler

Compiled 16 to 13 computations (18.8% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	69
1	33	69

Stop Event

1×

saturated

Calls

Call 1

Inputs

(if (<=.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1)))) 6490371073168535/1298074214633706907132624082305024) (/.f64 (/.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 x))) (exp.f64 (/.f64 3/4 x))) x) (+.f64 (-.f64 (pow.f64 (+.f64 1 x) -1/2) (neg.f64 (pow.f64 x -1/2))) (*.f64 (pow.f64 (+.f64 1 x) -1/2) -2)))

Outputs

(if (<=.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1)))) 6490371073168535/1298074214633706907132624082305024) (/.f64 (/.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 x))) (exp.f64 (/.f64 3/4 x))) x) (+.f64 (-.f64 (pow.f64 (+.f64 1 x) -1/2) (neg.f64 (pow.f64 x -1/2))) (*.f64 (pow.f64 (+.f64 1 x) -1/2) -2)))

end178.0ms (4.7%)

Stop Event

1×

fuel

Compiler

Compiled 216 to 174 computations (19.4% saved)

Details

analyze0.0ms (0%)

sample1.8s (47.5%)

preprocess28.0ms (0.7%)

simplify18.0ms (0.5%)

prune2.0ms (0.1%)

localize7.0ms (0.2%)

series10.0ms (0.3%)

rewrite65.0ms (1.7%)

simplify30.0ms (0.8%)

prune454.0ms (12%)

localize12.0ms (0.3%)

series10.0ms (0.3%)

rewrite67.0ms (1.8%)

simplify50.0ms (1.3%)

prune149.0ms (3.9%)

localize14.0ms (0.4%)

series167.0ms (4.4%)

rewrite60.0ms (1.6%)

simplify40.0ms (1.1%)

prune255.0ms (6.7%)

localize12.0ms (0.3%)

series10.0ms (0.3%)

rewrite77.0ms (2%)

simplify25.0ms (0.7%)

prune136.0ms (3.6%)

regimes109.0ms (2.9%)

bsearch1.0ms (0%)

simplify2.0ms (0%)

end178.0ms (4.7%)

Profiling