Details

analyze5.0ms (0.1%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
0%	0%	100%	0%	0%	0%	0%	2
0%	0%	50%	0%	0%	50%	0%	3
33.3%	12.5%	25%	0%	0%	62.5%	0%	4
60%	18.7%	12.5%	0%	0%	68.7%	0%	5
77.8%	21.9%	6.2%	0%	0%	71.8%	0%	6
88.2%	23.4%	3.1%	0%	0%	73.4%	0%	7
93.9%	24.2%	1.6%	0%	0%	74.2%	0%	8
96.9%	24.6%	0.8%	0%	0%	74.6%	0%	9
98.4%	24.8%	0.4%	0%	0%	74.8%	0%	10
99.2%	24.9%	0.2%	0%	0%	74.9%	0%	11
99.6%	24.9%	0.1%	0%	0%	74.9%	0%	12

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample1.7s (53.7%)

Results

1.7s	8256×	body	256	valid
3.0ms	23×	body	256	invalid

Bogosity

preprocess156.0ms (4.9%)

Algorithm

2×	egg-herbie

Rules

600×	`unsub-neg_binary64`
587×	`distribute-rgt-out--_binary64`
492×	`fma-neg_binary64`
438×	`distribute-neg-in_binary64`
411×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	18	20
2	25	20
3	36	20
4	53	20
5	81	20
6	128	20
7	345	20
8	713	20
9	1518	20
10	2898	20
11	4338	20
12	5312	20
13	5623	20
14	5927	20
15	6028	20
16	6106	20
17	6374	20
18	7320	20
0	1	1

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0

Outputs
0

Call 2

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

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

Compiler

Compiled 15 to 11 computations (26.7% saved)

simplify139.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

600×	`unsub-neg_binary64`
587×	`distribute-rgt-out--_binary64`
492×	`fma-neg_binary64`
438×	`distribute-neg-in_binary64`
411×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	18	20
2	25	20
3	36	20
4	53	20
5	81	20
6	128	20
7	345	20
8	713	20
9	1518	20
10	2898	20
11	4338	20
12	5312	20
13	5623	20
14	5927	20
15	6028	20
16	6106	20
17	6374	20
18	7320	20

Stop Event

1×	node limit

Counts

1 → 1

Calls

Call 1

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

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

eval1.0ms (0%)

Compiler: Compiled 14 to 10 computations (28.6% saved)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.0b

Counts

2 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.0b	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))

Compiler

Compiled 14 to 10 computations (28.6% saved)

localize46.0ms (1.5%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 53 to 29 computations (45.3% saved)

series4.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

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

rewrite191.0ms (6%)

Algorithm

1×	batch-egg-rewrite

Rules

481×	`log-prod_binary64`
394×	`fma-def_binary64`
349×	`pow-prod-down_binary64`
262×	`pow2_binary64`
192×	`fma-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	30
1	208	30
2	3114	30

Stop Event

1×	node limit

Counts

2 → 137

Calls

Call 1

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

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

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

simplify60.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

795×	`fma-def_binary64`
724×	`distribute-neg-frac_binary64`
327×	`times-frac_binary64`
271×	`associate-/l/_binary64`
269×	`sub-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	66	475
1	195	456
2	545	444
3	1943	432
4	6154	432

Stop Event

1×	node limit

Counts

161 → 178

Calls

Call 1

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

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

eval239.0ms (7.6%)

Compiler: Compiled 3503 to 2382 computations (32% saved)

prune22.0ms (0.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	175	3	178
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	175	4	179

Error

Counts

179 → 4

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.6b	(log.f64 (/.f64 2 x))
▶	0.0b	(log.f64 (.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) 1)))
✓	0.0b	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
▶	0.2b	(log.f64 (+.f64 (.f64 -1/2 x) (.f64 2 (/.f64 1 x))))

Compiler

Compiled 44 to 34 computations (22.7% saved)

localize22.0ms (0.7%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 53 to 32 computations (39.6% saved)

series3.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

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

rewrite94.0ms (3%)

Algorithm

1×	batch-egg-rewrite

Rules

508×	`prod-diff_binary64`
448×	`log-prod_binary64`
318×	`pow-prod-down_binary64`
291×	`fma-def_binary64`
242×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	27
1	206	27
2	2918	27

Stop Event

1×	node limit

Counts

2 → 118

Calls

Call 1

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

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

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(pow.f64 (cbrt.f64 x) -2) (cbrt.f64 (/.f64 1 x)) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (/.f64 1 x) (cbrt.f64 (-.f64 1 (*.f64 x x)))) (pow.f64 (-.f64 1 (*.f64 x x)) 1/6) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (/.f64 1 x) (pow.f64 (-.f64 1 (*.f64 x x)) 1/4)) (pow.f64 (-.f64 1 (*.f64 x x)) 1/4) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (cbrt.f64 (pow.f64 x -2))) (cbrt.f64 (/.f64 1 x)) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (pow.f64 x -1/2)) (pow.f64 x -1/2) (/.f64 1 x))))))

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

simplify64.0ms (2%)

Algorithm

1×	egg-herbie

Rules

724×	`unswap-sqr_binary64`
345×	`associate-/l/_binary64`
299×	`times-frac_binary64`
295×	`associate-*r/_binary64`
292×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	73	412
1	214	387
2	630	373
3	2156	367
4	5956	367

Stop Event

1×	node limit

Counts

142 → 163

Calls

Call 1

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

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

localize18.0ms (0.6%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 35 to 27 computations (22.9% saved)

series2.0ms (0.1%)

Counts

1 → 3

Calls

3 calls:

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

rewrite61.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

913×	`pow1_binary64`
852×	`add-log-exp_binary64`
851×	`log1p-expm1-u_binary64`
851×	`expm1-log1p-u_binary64`
836×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	8
1	194	8
2	2404	8

Stop Event

1×	node limit

Counts

1 → 37

Calls

Call 1

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

Outputs

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

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	12
1	7	12

Stop Event

1×

saturated

Counts

40 → 40

Calls

Call 1

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

Outputs
(/.f64 2 x)
(*.f64 -1/2 x)
(*.f64 x -1/2)
(*.f64 -1/2 x)
(*.f64 x -1/2)

localize7.0ms (0.2%)

Compiler: Compiled 10 to 7 computations (30% saved)

eval85.0ms (2.7%)

Compiler: Compiled 3512 to 2545 computations (27.5% saved)

prune26.0ms (0.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	202	1	203
Fresh	0	0	0
Picked	0	1	1
Done	2	1	3
Total	204	3	207

Error

Counts

207 → 3

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.6b	(log.f64 (/.f64 2 x))
▶	0b	(log.f64 (/.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) x))
✓	0.2b	(log.f64 (+.f64 (.f64 -1/2 x) (.f64 2 (/.f64 1 x))))

Compiler

Compiled 28 to 22 computations (21.4% saved)

localize20.0ms (0.6%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 46 to 26 computations (43.5% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite57.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

777×	`pow1_binary64`
728×	`add-log-exp_binary64`
727×	`log1p-expm1-u_binary64`
727×	`expm1-log1p-u_binary64`
712×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	154	12
2	2077	12

Stop Event

1×	node limit

Counts

1 → 30

Calls

Call 1

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

Outputs

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

simplify50.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

860×	`fma-neg_binary64`
715×	`distribute-neg-frac_binary64`
664×	`fma-def_binary64`
636×	`associate-/r*_binary64`
596×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	44	204
1	128	188
2	377	178
3	1306	174
4	6469	174

Stop Event

1×	node limit

Counts

42 → 53

Calls

Call 1

Inputs
2
(+.f64 2 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 2 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 -1/8 (pow.f64 x 4))))
(+.f64 2 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (+.f64 (.f64 -1/16 (pow.f64 x 6)) (*.f64 -1/8 (pow.f64 x 4)))))
(*.f64 (sqrt.f64 -1) x)
(+.f64 1 (*.f64 (sqrt.f64 -1) x))
(+.f64 1 (+.f64 (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 -1) x))) (*.f64 (sqrt.f64 -1) x)))
(-.f64 (+.f64 1 (+.f64 (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 -1) x))) (.f64 (sqrt.f64 -1) x))) (.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))))
(.f64 -1 (.f64 (sqrt.f64 -1) x))
(+.f64 1 (.f64 -1 (.f64 (sqrt.f64 -1) x)))
(-.f64 (+.f64 1 (.f64 -1 (.f64 (sqrt.f64 -1) x))) (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 -1) x))))
(-.f64 (+.f64 1 (+.f64 (.f64 1/8 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))) (.f64 -1 (.f64 (sqrt.f64 -1) x)))) (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 -1) x))))

Outputs
2
(+.f64 2 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 2 (.f64 -1/2 (.f64 x x)))
(fma.f64 -1/2 (*.f64 x x) 2)
(+.f64 2 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 -1/8 (pow.f64 x 4))))
(+.f64 2 (fma.f64 -1/2 (.f64 x x) (.f64 -1/8 (pow.f64 x 4))))
(+.f64 2 (fma.f64 -1/8 (pow.f64 x 4) (.f64 (.f64 -1/2 x) x)))
(fma.f64 -1/2 (*.f64 x x) (fma.f64 -1/8 (pow.f64 x 4) 2))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x -1/8) -1/2) 2)
(+.f64 2 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (+.f64 (.f64 -1/16 (pow.f64 x 6)) (*.f64 -1/8 (pow.f64 x 4)))))
(+.f64 2 (fma.f64 -1/2 (.f64 x x) (fma.f64 -1/16 (pow.f64 x 6) (.f64 -1/8 (pow.f64 x 4)))))
(+.f64 (fma.f64 -1/2 (.f64 x x) 2) (fma.f64 -1/16 (pow.f64 x 6) (.f64 -1/8 (pow.f64 x 4))))
(+.f64 2 (fma.f64 -1/2 (.f64 x x) (fma.f64 -1/8 (pow.f64 x 4) (.f64 -1/16 (pow.f64 x 6)))))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x -1/8) -1/2) (fma.f64 -1/16 (pow.f64 x 6) 2))
(*.f64 (sqrt.f64 -1) x)
(*.f64 x (sqrt.f64 -1))
(+.f64 1 (*.f64 (sqrt.f64 -1) x))
(+.f64 (*.f64 x (sqrt.f64 -1)) 1)
(fma.f64 x (sqrt.f64 -1) 1)
(+.f64 1 (+.f64 (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 -1) x))) (*.f64 (sqrt.f64 -1) x)))
(+.f64 1 (+.f64 (.f64 x (sqrt.f64 -1)) (/.f64 1/2 (.f64 x (sqrt.f64 -1)))))
(+.f64 1 (fma.f64 x (sqrt.f64 -1) (/.f64 (/.f64 1/2 x) (sqrt.f64 -1))))
(+.f64 1 (fma.f64 x (sqrt.f64 -1) (/.f64 1/2 (*.f64 x (sqrt.f64 -1)))))
(-.f64 (+.f64 1 (+.f64 (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 -1) x))) (.f64 (sqrt.f64 -1) x))) (.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))))
(+.f64 1 (-.f64 (+.f64 (.f64 x (sqrt.f64 -1)) (/.f64 1/2 (.f64 x (sqrt.f64 -1)))) (/.f64 1/8 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))))
(+.f64 1 (+.f64 (fma.f64 x (sqrt.f64 -1) (/.f64 (/.f64 1/2 x) (sqrt.f64 -1))) (/.f64 -1/8 (*.f64 (pow.f64 x 3) (neg.f64 (sqrt.f64 -1))))))
(+.f64 1 (+.f64 (fma.f64 x (sqrt.f64 -1) (/.f64 1/2 (.f64 x (sqrt.f64 -1)))) (/.f64 1/8 (.f64 (sqrt.f64 -1) (pow.f64 x 3)))))
(-.f64 1 (fma.f64 (/.f64 -1 (.f64 x (sqrt.f64 -1))) (+.f64 (/.f64 1/8 (.f64 x x)) 1/2) (*.f64 x (neg.f64 (sqrt.f64 -1)))))
(.f64 -1 (.f64 (sqrt.f64 -1) x))
(neg.f64 (*.f64 x (sqrt.f64 -1)))
(*.f64 (sqrt.f64 -1) (neg.f64 x))
(*.f64 x (neg.f64 (sqrt.f64 -1)))
(+.f64 1 (.f64 -1 (.f64 (sqrt.f64 -1) x)))
(+.f64 1 (neg.f64 (*.f64 x (sqrt.f64 -1))))
(-.f64 1 (*.f64 x (sqrt.f64 -1)))
(-.f64 (+.f64 1 (.f64 -1 (.f64 (sqrt.f64 -1) x))) (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 -1) x))))
(-.f64 (+.f64 1 (neg.f64 (.f64 x (sqrt.f64 -1)))) (/.f64 1/2 (.f64 x (sqrt.f64 -1))))
(+.f64 1 (fma.f64 (neg.f64 (sqrt.f64 -1)) x (/.f64 -1/2 (*.f64 x (sqrt.f64 -1)))))
(-.f64 1 (fma.f64 x (sqrt.f64 -1) (/.f64 1/2 (*.f64 x (sqrt.f64 -1)))))
(-.f64 (/.f64 -1/2 (*.f64 x (sqrt.f64 -1))) (fma.f64 x (sqrt.f64 -1) -1))
(-.f64 (+.f64 1 (+.f64 (.f64 1/8 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))) (.f64 -1 (.f64 (sqrt.f64 -1) x)))) (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 -1) x))))
(-.f64 (+.f64 1 (+.f64 (/.f64 1/8 (.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3))) (neg.f64 (.f64 x (sqrt.f64 -1))))) (/.f64 1/2 (*.f64 x (sqrt.f64 -1))))
(+.f64 1 (+.f64 (/.f64 1/8 (.f64 (pow.f64 x 3) (neg.f64 (sqrt.f64 -1)))) (fma.f64 (neg.f64 (sqrt.f64 -1)) x (/.f64 -1/2 (.f64 x (sqrt.f64 -1))))))
(+.f64 1 (-.f64 (/.f64 -1/8 (.f64 (sqrt.f64 -1) (pow.f64 x 3))) (fma.f64 x (sqrt.f64 -1) (/.f64 1/2 (.f64 x (sqrt.f64 -1))))))
(-.f64 (.f64 (/.f64 -1 (.f64 x (sqrt.f64 -1))) (+.f64 (/.f64 1/8 (*.f64 x x)) 1/2)) (fma.f64 x (sqrt.f64 -1) -1))

eval21.0ms (0.7%)

Compiler: Compiled 898 to 638 computations (29% saved)

prune7.0ms (0.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	53	0	53
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	53	3	56

Error

Counts

56 → 3

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.6b	(log.f64 (/.f64 2 x))
✓	0b	(log.f64 (/.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) x))
✓	0.2b	(log.f64 (+.f64 (.f64 -1/2 x) (.f64 2 (/.f64 1 x))))

Compiler

Compiled 28 to 22 computations (21.4% saved)

regimes15.0ms (0.5%)

Counts

5 → 1

Calls

Call 1

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

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

Calls

3 calls:

5.0ms	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
5.0ms	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
3.0ms	x

Results

Error	Segments	Branch
0b	1	`x`
0b	1	`(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))`
0b	1	`(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))`

Compiler

Compiled 81 to 57 computations (29.6% saved)

regimes4.0ms (0.1%)

Accuracy

Total -0.4b remaining (-251.6%)

Threshold costs -0.4b (-251.6%)

Counts

2 → 1

Calls

Call 1

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

Outputs
(log.f64 (+.f64 (.f64 -1/2 x) (.f64 2 (/.f64 1 x))))

Calls

1 calls:

3.0ms

Results

Error	Segments	Branch
0.2b	1	`x`

Compiler

Compiled 17 to 13 computations (23.5% saved)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
4×	`*-commutative_binary64`
3×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	38
1	29	38
2	36	38
3	40	38
4	42	38

Stop Event

1×	done
1×	saturated

Calls

Call 1

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

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

Compiler

Compiled 28 to 22 computations (21.4% saved)

soundness0.0ms (0%)

end27.0ms (0.9%)

Compiler: Compiled 26 to 20 computations (23.1% saved)

Details

analyze5.0ms (0.1%)

sample1.7s (53.7%)

preprocess156.0ms (4.9%)

simplify139.0ms (4.4%)

eval1.0ms (0%)

prune1.0ms (0%)

localize46.0ms (1.5%)

series4.0ms (0.1%)

rewrite191.0ms (6%)

simplify60.0ms (1.9%)

eval239.0ms (7.6%)

prune22.0ms (0.7%)

localize22.0ms (0.7%)

series3.0ms (0.1%)

rewrite94.0ms (3%)

simplify64.0ms (2%)

localize18.0ms (0.6%)

series2.0ms (0.1%)

rewrite61.0ms (1.9%)

simplify7.0ms (0.2%)

localize7.0ms (0.2%)

eval85.0ms (2.7%)

prune26.0ms (0.8%)

localize20.0ms (0.6%)

series1.0ms (0%)

rewrite57.0ms (1.8%)

simplify50.0ms (1.6%)

eval21.0ms (0.7%)

prune7.0ms (0.2%)

regimes15.0ms (0.5%)

regimes4.0ms (0.1%)

simplify7.0ms (0.2%)

soundness0.0ms (0%)

end27.0ms (0.9%)

Profiling