Details

analyze8.0ms (0.2%)

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)

sample1.5s (30.5%)

Results

1.4s	8256×	body	256	valid
3.0ms	17×	body	256	invalid

Bogosity

preprocess157.0ms (3.3%)

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)

simplify145.0ms (3.1%)

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)

localize23.0ms (0.5%)

Local error

Found 3 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))
✓	0.0b	(sqrt.f64 (-.f64 1 (*.f64 x x)))

Compiler

Compiled 53 to 29 computations (45.3% saved)

series5.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

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

rewrite286.0ms (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	39
1	208	39
2	3113	39

Stop Event

1×	node limit

Counts

3 → 172

Calls

Call 1

Inputs
(sqrt.f64 (-.f64 1 (*.f64 x x)))
(+.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 0 (sqrt.f64 (-.f64 1 (.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (-.f64 1 (.f64 x x))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (-.f64 1 (.f64 x x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (-.f64 1 (.f64 x x)))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (-.f64 1 (.f64 x x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (.f64 x x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (sqrt.f64 (-.f64 1 (.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (-.f64 1 (.f64 x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (-.f64 1 (.f64 x x))) (pow.f64 (-.f64 1 (.f64 x x)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (-.f64 1 (.f64 x x)) 1/6) (cbrt.f64 (-.f64 1 (.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (-.f64 1 (.f64 x x)) 1/4) (pow.f64 (-.f64 1 (.f64 x x)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 6))) (hypot.f64 1 (hypot.f64 x (.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 4))) (hypot.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 1 (.f64 x x)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 1 (.f64 x x)) 2) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 1 (.f64 x x)) 3) 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 1 (.f64 x x)) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (-.f64 1 (.f64 x x))) 3/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 1 (.f64 x x)) 1/6) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 1 (.f64 x x)) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (-.f64 1 (.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (-.f64 1 (.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (-.f64 1 (.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 1 (.f64 x x)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 1 (sqrt.f64 (.f64 x (neg.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (-.f64 1 (.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 1/2 (log1p.f64 (.f64 x (neg.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log1p.f64 (.f64 x (neg.f64 x))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 1/2 (log1p.f64 (.f64 x (neg.f64 x)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 3/2 (log1p.f64 (.f64 x (neg.f64 x)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (pow.f64 (-.f64 1 (.f64 x x)) 1/6)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 1/4 (log1p.f64 (.f64 x (neg.f64 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (log1p.f64 (.f64 x (neg.f64 x))) 1) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (log1p.f64 (.f64 x (neg.f64 x))) 1/2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (.f64 1/2 (log1p.f64 (.f64 x (neg.f64 x)))) 1) 1))))))
((#(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 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Outputs

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x))) (*.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 1/6) (/.f64 1 x)) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (pow.f64 x -2)) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.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 (sqrt.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)) (sqrt.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)) (/.f64 1 x))))) (#(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) (/.f64 1 x)) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x -1/2) (pow.f64 x -1/2) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x -1/2) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (sqrt.f64 x)) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x 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(#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 1/4) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 1/4) (cbrt.f64 x)) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (cbrt.f64 (-.f64 1 (*.f64 x x))) (sqrt.f64 x)) (/.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 1/6) (sqrt.f64 x)) (/.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 0 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 x) (sqrt.f64 (-.f64 1 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)) (cbrt.f64 (*.f64 (-.f64 1 (*.f64 x x)) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (-.f64 1 (*.f64 x x)) (pow.f64 x -2))) (cbrt.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (-.f64 1 (*.f64 x x))) (*.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 1/6) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)) (sqrt.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 1/4) (*.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 1/4) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -1/2) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) (/.f64 1 (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 x) -2) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (-.f64 1 (*.f64 x x))) 1) (/.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 1/6) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 1/4) 1) (/.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 1/4) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (-.f64 1 (*.f64 x x))) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 1/4) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 1/4) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (-.f64 1 (*.f64 x x))) (sqrt.f64 x)) (/.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 1/6) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (cbrt.f64 (pow.f64 x -2))) (cbrt.f64 (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (pow.f64 x -1/2)) (pow.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (-.f64 1 (*.f64 x x)) (pow.f64 x -2)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 x (sqrt.f64 (-.f64 1 (*.f64 x x)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 x (sqrt.f64 (-.f64 1 (*.f64 x x)))) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 x -3) (pow.f64 (-.f64 1 (*.f64 x x)) 3/2)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (cbrt.f64 (/.f64 1 x)) (pow.f64 (-.f64 1 (*.f64 x x)) 1/6)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 x -1/2) (pow.f64 (-.f64 1 (*.f64 x x)) 1/4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (-.f64 1 (*.f64 x x)) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x 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))))))

simplify338.0ms (7.1%)

Algorithm

1×	egg-herbie

Rules

488×	`associate-/l/_binary64`
467×	`times-frac_binary64`
423×	`associate-*r/_binary64`
417×	`cancel-sign-sub-inv_binary64`
411×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	94	751
1	286	712
2	866	688
3	3148	682

Stop Event

1×	node limit

Counts

208 → 235

Calls

Call 1

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

eval139.0ms (2.9%)

Compiler: Compiled 4633 to 3208 computations (30.8% saved)

prune65.0ms (1.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	232	3	235
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	233	3	236

Error

Counts

236 → 3

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.5b	(log.f64 (+.f64 (.f64 -1/2 x) (.f64 2 (/.f64 1 x))))
▶	1.0b	(log.f64 (/.f64 2 x))
▶	0b	(log.f64 (.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) 1)))

Compiler

Compiled 30 to 24 computations (20% saved)

localize25.0ms (0.5%)

Local error

Found 3 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))
	0.0b	(sqrt.f64 (-.f64 1 (*.f64 x x)))

Compiler

Compiled 53 to 32 computations (39.6% saved)

series2.0ms (0%)

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 (/.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 (/.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)

rewrite74.0ms (1.6%)

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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Outputs

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(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)))))

simplify61.0ms (1.3%)

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))

localize16.0ms (0.3%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 35 to 27 computations (22.9% saved)

series4.0ms (0.1%)

Counts

2 → 15

Calls

6 calls:

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

rewrite152.0ms (3.2%)

Algorithm

1×	batch-egg-rewrite

Rules

981×	`pow1_binary64`
913×	`add-log-exp_binary64`
912×	`log1p-expm1-u_binary64`
912×	`expm1-log1p-u_binary64`
102×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	18
1	211	18
2	2583	18

Stop Event

1×	node limit

Counts

2 → 61

Calls

Call 1

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

Outputs

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

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

simplify54.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

671×	`fma-def_binary64`
585×	`times-frac_binary64`
384×	`associate-+l-_binary64`
313×	`associate-+r+_binary64`
285×	`unswap-sqr_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	57	298
1	155	276
2	461	274
3	1574	270
4	6285	270

Stop Event

1×	node limit

Counts

76 → 88

Calls

Call 1

Inputs
(/.f64 2 x)
(*.f64 -1/2 x)
(*.f64 -1/2 x)
(+.f64 (log.f64 2) (*.f64 -1 (log.f64 x)))
(+.f64 (log.f64 2) (+.f64 (.f64 -1/4 (pow.f64 x 2)) (.f64 -1 (log.f64 x))))
(+.f64 (log.f64 2) (+.f64 (.f64 -1/4 (pow.f64 x 2)) (+.f64 (.f64 -1/32 (pow.f64 x 4)) (*.f64 -1 (log.f64 x)))))
(+.f64 (.f64 -1/192 (pow.f64 x 6)) (+.f64 (log.f64 2) (+.f64 (.f64 -1/4 (pow.f64 x 2)) (+.f64 (.f64 -1/32 (pow.f64 x 4)) (.f64 -1 (log.f64 x))))))
(+.f64 (log.f64 -1/2) (*.f64 -1 (log.f64 (/.f64 1 x))))
(-.f64 (+.f64 (log.f64 -1/2) (.f64 -1 (log.f64 (/.f64 1 x)))) (.f64 4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (log.f64 -1/2) (.f64 -1 (log.f64 (/.f64 1 x)))) (+.f64 (.f64 8 (/.f64 1 (pow.f64 x 4))) (*.f64 4 (/.f64 1 (pow.f64 x 2)))))
(-.f64 (+.f64 (log.f64 -1/2) (.f64 -1 (log.f64 (/.f64 1 x)))) (+.f64 (.f64 8 (/.f64 1 (pow.f64 x 4))) (+.f64 (.f64 64/3 (/.f64 1 (pow.f64 x 6))) (.f64 4 (/.f64 1 (pow.f64 x 2))))))
(+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 1/2))
(-.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 1/2)) (.f64 4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 1/2)) (+.f64 (.f64 8 (/.f64 1 (pow.f64 x 4))) (*.f64 4 (/.f64 1 (pow.f64 x 2)))))
(-.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 1/2)) (+.f64 (.f64 8 (/.f64 1 (pow.f64 x 4))) (+.f64 (.f64 64/3 (/.f64 1 (pow.f64 x 6))) (.f64 4 (/.f64 1 (pow.f64 x 2))))))

Outputs
(/.f64 2 x)
(*.f64 -1/2 x)
(*.f64 x -1/2)
(*.f64 -1/2 x)
(*.f64 x -1/2)
(+.f64 (log.f64 2) (*.f64 -1 (log.f64 x)))
(+.f64 (log.f64 2) (neg.f64 (log.f64 x)))
(-.f64 (log.f64 2) (log.f64 x))
(+.f64 (log.f64 2) (+.f64 (.f64 -1/4 (pow.f64 x 2)) (.f64 -1 (log.f64 x))))
(+.f64 (log.f64 2) (fma.f64 -1/4 (*.f64 x x) (neg.f64 (log.f64 x))))
(+.f64 (log.f64 2) (-.f64 (.f64 (.f64 -1/4 x) x) (log.f64 x)))
(-.f64 (fma.f64 x (*.f64 x -1/4) (log.f64 2)) (log.f64 x))
(+.f64 (log.f64 2) (+.f64 (.f64 -1/4 (pow.f64 x 2)) (+.f64 (.f64 -1/32 (pow.f64 x 4)) (*.f64 -1 (log.f64 x)))))
(+.f64 (log.f64 2) (fma.f64 -1/4 (*.f64 x x) (fma.f64 -1/32 (pow.f64 x 4) (neg.f64 (log.f64 x)))))
(+.f64 (log.f64 2) (-.f64 (fma.f64 x (.f64 x -1/4) (.f64 -1/32 (pow.f64 x 4))) (log.f64 x)))
(-.f64 (fma.f64 x (*.f64 x -1/4) (fma.f64 -1/32 (pow.f64 x 4) (log.f64 2))) (log.f64 x))
(+.f64 (.f64 -1/192 (pow.f64 x 6)) (+.f64 (log.f64 2) (+.f64 (.f64 -1/4 (pow.f64 x 2)) (+.f64 (.f64 -1/32 (pow.f64 x 4)) (.f64 -1 (log.f64 x))))))
(fma.f64 -1/192 (pow.f64 x 6) (+.f64 (log.f64 2) (fma.f64 -1/4 (*.f64 x x) (fma.f64 -1/32 (pow.f64 x 4) (neg.f64 (log.f64 x))))))
(+.f64 (fma.f64 -1/4 (*.f64 x x) (fma.f64 -1/32 (pow.f64 x 4) (neg.f64 (log.f64 x)))) (fma.f64 -1/192 (pow.f64 x 6) (log.f64 2)))
(+.f64 (-.f64 (.f64 -1/32 (pow.f64 x 4)) (log.f64 x)) (fma.f64 -1/192 (pow.f64 x 6) (fma.f64 x (.f64 x -1/4) (log.f64 2))))
(-.f64 (fma.f64 (.f64 x x) (fma.f64 x (.f64 x -1/32) -1/4) (fma.f64 -1/192 (pow.f64 x 6) (log.f64 2))) (log.f64 x))
(+.f64 (log.f64 -1/2) (*.f64 -1 (log.f64 (/.f64 1 x))))
(+.f64 (log.f64 -1/2) (neg.f64 (neg.f64 (log.f64 x))))
(+.f64 (log.f64 x) (log.f64 -1/2))
(-.f64 (+.f64 (log.f64 -1/2) (.f64 -1 (log.f64 (/.f64 1 x)))) (.f64 4 (/.f64 1 (pow.f64 x 2))))
(+.f64 (log.f64 -1/2) (-.f64 (neg.f64 (neg.f64 (log.f64 x))) (/.f64 4 (*.f64 x x))))
(+.f64 (log.f64 x) (-.f64 (log.f64 -1/2) (/.f64 4 (*.f64 x x))))
(+.f64 (+.f64 (log.f64 x) (log.f64 -1/2)) (/.f64 -4 (*.f64 x x)))
(+.f64 (log.f64 x) (+.f64 (log.f64 -1/2) (/.f64 -4 (*.f64 x x))))
(-.f64 (+.f64 (log.f64 -1/2) (.f64 -1 (log.f64 (/.f64 1 x)))) (+.f64 (.f64 8 (/.f64 1 (pow.f64 x 4))) (*.f64 4 (/.f64 1 (pow.f64 x 2)))))
(-.f64 (+.f64 (log.f64 -1/2) (neg.f64 (neg.f64 (log.f64 x)))) (+.f64 (/.f64 4 (*.f64 x x)) (/.f64 8 (pow.f64 x 4))))
(+.f64 (log.f64 x) (-.f64 (log.f64 -1/2) (+.f64 (/.f64 4 (*.f64 x x)) (/.f64 8 (pow.f64 x 4)))))
(+.f64 (log.f64 x) (+.f64 (log.f64 -1/2) (+.f64 (/.f64 -4 (*.f64 x x)) (/.f64 -8 (pow.f64 x 4)))))
(-.f64 (+.f64 (log.f64 -1/2) (.f64 -1 (log.f64 (/.f64 1 x)))) (+.f64 (.f64 8 (/.f64 1 (pow.f64 x 4))) (+.f64 (.f64 64/3 (/.f64 1 (pow.f64 x 6))) (.f64 4 (/.f64 1 (pow.f64 x 2))))))
(+.f64 (log.f64 -1/2) (-.f64 (neg.f64 (neg.f64 (log.f64 x))) (+.f64 (/.f64 8 (pow.f64 x 4)) (+.f64 (/.f64 4 (*.f64 x x)) (/.f64 64/3 (pow.f64 x 6))))))
(+.f64 (log.f64 x) (-.f64 (log.f64 -1/2) (+.f64 (/.f64 4 (*.f64 x x)) (+.f64 (/.f64 8 (pow.f64 x 4)) (/.f64 64/3 (pow.f64 x 6))))))
(+.f64 (+.f64 (log.f64 x) (log.f64 -1/2)) (-.f64 (+.f64 (/.f64 -4 (*.f64 x x)) (/.f64 -8 (pow.f64 x 4))) (/.f64 64/3 (pow.f64 x 6))))
(+.f64 (+.f64 (log.f64 x) (log.f64 -1/2)) (+.f64 (+.f64 (/.f64 -4 (*.f64 x x)) (/.f64 -8 (pow.f64 x 4))) (/.f64 -64/3 (pow.f64 x 6))))
(+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 1/2))
(fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 1/2))
(-.f64 (log.f64 1/2) (log.f64 (/.f64 -1 x)))
(-.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 1/2)) (.f64 4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 1/2)) (/.f64 4 (*.f64 x x)))
(+.f64 (-.f64 (log.f64 1/2) (log.f64 (/.f64 -1 x))) (/.f64 -4 (*.f64 x x)))
(+.f64 (log.f64 1/2) (-.f64 (/.f64 -4 (*.f64 x x)) (log.f64 (/.f64 -1 x))))
(-.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 1/2)) (+.f64 (.f64 8 (/.f64 1 (pow.f64 x 4))) (*.f64 4 (/.f64 1 (pow.f64 x 2)))))
(-.f64 (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 1/2)) (+.f64 (/.f64 4 (*.f64 x x)) (/.f64 8 (pow.f64 x 4))))
(+.f64 (-.f64 (-.f64 (log.f64 1/2) (log.f64 (/.f64 -1 x))) (/.f64 8 (pow.f64 x 4))) (/.f64 -4 (*.f64 x x)))
(+.f64 (-.f64 (log.f64 1/2) (log.f64 (/.f64 -1 x))) (+.f64 (/.f64 -4 (*.f64 x x)) (/.f64 -8 (pow.f64 x 4))))
(+.f64 (log.f64 1/2) (+.f64 (/.f64 -8 (pow.f64 x 4)) (-.f64 (/.f64 -4 (*.f64 x x)) (log.f64 (/.f64 -1 x)))))
(+.f64 (log.f64 1/2) (+.f64 (/.f64 -4 (*.f64 x x)) (-.f64 (/.f64 -8 (pow.f64 x 4)) (log.f64 (/.f64 -1 x)))))
(-.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 1/2)) (+.f64 (.f64 8 (/.f64 1 (pow.f64 x 4))) (+.f64 (.f64 64/3 (/.f64 1 (pow.f64 x 6))) (.f64 4 (/.f64 1 (pow.f64 x 2))))))
(-.f64 (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 1/2)) (+.f64 (/.f64 8 (pow.f64 x 4)) (+.f64 (/.f64 4 (*.f64 x x)) (/.f64 64/3 (pow.f64 x 6)))))
(-.f64 (-.f64 (log.f64 1/2) (log.f64 (/.f64 -1 x))) (+.f64 (/.f64 4 (*.f64 x x)) (+.f64 (/.f64 8 (pow.f64 x 4)) (/.f64 64/3 (pow.f64 x 6)))))
(+.f64 (-.f64 (log.f64 1/2) (log.f64 (/.f64 -1 x))) (-.f64 (+.f64 (/.f64 -4 (*.f64 x x)) (/.f64 -8 (pow.f64 x 4))) (/.f64 64/3 (pow.f64 x 6))))
(+.f64 (log.f64 1/2) (+.f64 (+.f64 (/.f64 -8 (pow.f64 x 4)) (-.f64 (/.f64 -4 (*.f64 x x)) (log.f64 (/.f64 -1 x)))) (/.f64 -64/3 (pow.f64 x 6))))
(+.f64 (log.f64 1/2) (+.f64 (/.f64 -8 (pow.f64 x 4)) (-.f64 (+.f64 (/.f64 -4 (*.f64 x x)) (/.f64 -64/3 (pow.f64 x 6))) (log.f64 (/.f64 -1 x)))))

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(log.f64 (/.f64 2 x))

Compiler

Compiled 10 to 7 computations (30% saved)

series46.0ms (1%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
21.0ms	x	@	0	(log.f64 (/.f64 2 x))
15.0ms	x	@	-inf	(log.f64 (/.f64 2 x))
9.0ms	x	@	inf	(log.f64 (/.f64 2 x))

rewrite45.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

476×	`pow1_binary64`
465×	`add-sqr-sqrt_binary64`
454×	`*-un-lft-identity_binary64`
443×	`add-log-exp_binary64`
443×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	105	6
2	1210	6

Stop Event

1×	node limit

Counts

1 → 25

Calls

Call 1

Inputs
(log.f64 (/.f64 2 x))

Outputs

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

simplify39.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

155×	`fma-neg_binary64`
118×	`fma-def_binary64`
56×	`cancel-sign-sub-inv_binary64`
44×	`sub-neg_binary64`
39×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	124
1	27	108
2	40	108
3	60	108
4	109	108
5	204	108
6	336	108
7	510	108
8	658	108
9	779	108
10	799	108

Stop Event

1×

saturated

Counts

37 → 28

Calls

Call 1

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

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

eval218.0ms (4.6%)

Compiler: Compiled 5617 to 4164 computations (25.9% saved)

prune81.0ms (1.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	335	2	337
Fresh	0	0	0
Picked	0	1	1
Done	1	1	2
Total	336	4	340

Error

Counts

340 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.5b	(log.f64 (+.f64 (.f64 -1/2 x) (.f64 2 (/.f64 1 x))))
✓	1.0b	(log.f64 (/.f64 2 x))
▶	0b	(log.f64 (/.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) x))
▶	1.0b	(neg.f64 (log.f64 (/.f64 x 2)))

Compiler

Compiled 34 to 27 computations (20.6% saved)

localize34.0ms (0.7%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 46 to 26 computations (43.5% saved)

series3.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

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

rewrite237.0ms (5%)

Algorithm

1×	batch-egg-rewrite

Rules

967×	`pow1_binary64`
906×	`add-log-exp_binary64`
905×	`log1p-expm1-u_binary64`
905×	`expm1-log1p-u_binary64`
92×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	27
1	179	27
2	2532	27

Stop Event

1×	node limit

Counts

2 → 63

Calls

Call 1

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

Outputs

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

simplify80.0ms (1.7%)

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

87 → 108

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))

localize17.0ms (0.4%)

Compiler: Compiled 15 to 11 computations (26.7% saved)

eval578.0ms (12.1%)

Compiler: Compiled 2815 to 2080 computations (26.1% saved)

prune56.0ms (1.2%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	165	1	166
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	165	5	170

Error

Counts

170 → 5

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.5b	(log.f64 (+.f64 (.f64 -1/2 x) (.f64 2 (/.f64 1 x))))
✓	1.0b	(log.f64 (/.f64 2 x))
▶	0.5b	(log.f64 (/.f64 (fma.f64 x (*.f64 x -1/2) 2) x))
✓	0b	(log.f64 (/.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) x))
✓	1.0b	(neg.f64 (log.f64 (/.f64 x 2)))

Compiler

Compiled 44 to 34 computations (22.7% saved)

localize34.0ms (0.7%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(log.f64 (/.f64 (fma.f64 x (*.f64 x -1/2) 2) x))
✓	0.0b	(/.f64 (fma.f64 x (*.f64 x -1/2) 2) x)

Compiler

Compiled 30 to 20 computations (33.3% saved)

series7.0ms (0.2%)

Counts

2 → 24

Calls

6 calls:

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

rewrite80.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

807×	`pow1_binary64`
750×	`add-log-exp_binary64`
750×	`log1p-expm1-u_binary64`
750×	`expm1-log1p-u_binary64`
736×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	24
1	166	24
2	1982	24

Stop Event

1×	node limit

Counts

2 → 60

Calls

Call 1

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

Outputs

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

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

simplify57.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

677×	`fma-def_binary64`
587×	`times-frac_binary64`
383×	`associate-+l-_binary64`
334×	`associate-+r+_binary64`
285×	`unswap-sqr_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	59	370
1	160	348
2	469	346
3	1583	342
4	6310	342

Stop Event

1×	node limit

Counts

84 → 89

Calls

Call 1

Inputs
(/.f64 2 x)
(+.f64 (.f64 -1/2 x) (.f64 2 (/.f64 1 x)))
(+.f64 (.f64 -1/2 x) (.f64 2 (/.f64 1 x)))
(+.f64 (.f64 -1/2 x) (.f64 2 (/.f64 1 x)))
(*.f64 -1/2 x)
(+.f64 (.f64 -1/2 x) (.f64 2 (/.f64 1 x)))
(+.f64 (.f64 -1/2 x) (.f64 2 (/.f64 1 x)))
(+.f64 (.f64 -1/2 x) (.f64 2 (/.f64 1 x)))
(*.f64 -1/2 x)
(+.f64 (.f64 -1/2 x) (.f64 2 (/.f64 1 x)))
(+.f64 (.f64 -1/2 x) (.f64 2 (/.f64 1 x)))
(+.f64 (.f64 -1/2 x) (.f64 2 (/.f64 1 x)))
(+.f64 (log.f64 2) (*.f64 -1 (log.f64 x)))
(+.f64 (log.f64 2) (+.f64 (.f64 -1/4 (pow.f64 x 2)) (.f64 -1 (log.f64 x))))
(+.f64 (log.f64 2) (+.f64 (.f64 -1/4 (pow.f64 x 2)) (+.f64 (.f64 -1/32 (pow.f64 x 4)) (*.f64 -1 (log.f64 x)))))
(+.f64 (.f64 -1/192 (pow.f64 x 6)) (+.f64 (log.f64 2) (+.f64 (.f64 -1/4 (pow.f64 x 2)) (+.f64 (.f64 -1/32 (pow.f64 x 4)) (.f64 -1 (log.f64 x))))))
(+.f64 (log.f64 -1/2) (*.f64 -1 (log.f64 (/.f64 1 x))))
(-.f64 (+.f64 (log.f64 -1/2) (.f64 -1 (log.f64 (/.f64 1 x)))) (.f64 4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (log.f64 -1/2) (.f64 -1 (log.f64 (/.f64 1 x)))) (+.f64 (.f64 8 (/.f64 1 (pow.f64 x 4))) (*.f64 4 (/.f64 1 (pow.f64 x 2)))))
(-.f64 (+.f64 (log.f64 -1/2) (.f64 -1 (log.f64 (/.f64 1 x)))) (+.f64 (.f64 8 (/.f64 1 (pow.f64 x 4))) (+.f64 (.f64 64/3 (/.f64 1 (pow.f64 x 6))) (.f64 4 (/.f64 1 (pow.f64 x 2))))))
(+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 1/2))
(-.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 1/2)) (.f64 4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 1/2)) (+.f64 (.f64 8 (/.f64 1 (pow.f64 x 4))) (*.f64 4 (/.f64 1 (pow.f64 x 2)))))
(-.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 1/2)) (+.f64 (.f64 8 (/.f64 1 (pow.f64 x 4))) (+.f64 (.f64 64/3 (/.f64 1 (pow.f64 x 6))) (.f64 4 (/.f64 1 (pow.f64 x 2))))))

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 -1/2 x) (.f64 2 (/.f64 1 x)))
(fma.f64 -1/2 x (/.f64 2 x))
(fma.f64 x -1/2 (/.f64 2 x))
(+.f64 (.f64 -1/2 x) (.f64 2 (/.f64 1 x)))
(fma.f64 -1/2 x (/.f64 2 x))
(fma.f64 x -1/2 (/.f64 2 x))
(*.f64 -1/2 x)
(*.f64 x -1/2)
(+.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 -1/2 x) (.f64 2 (/.f64 1 x)))
(fma.f64 -1/2 x (/.f64 2 x))
(fma.f64 x -1/2 (/.f64 2 x))
(+.f64 (.f64 -1/2 x) (.f64 2 (/.f64 1 x)))
(fma.f64 -1/2 x (/.f64 2 x))
(fma.f64 x -1/2 (/.f64 2 x))
(*.f64 -1/2 x)
(*.f64 x -1/2)
(+.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 -1/2 x) (.f64 2 (/.f64 1 x)))
(fma.f64 -1/2 x (/.f64 2 x))
(fma.f64 x -1/2 (/.f64 2 x))
(+.f64 (.f64 -1/2 x) (.f64 2 (/.f64 1 x)))
(fma.f64 -1/2 x (/.f64 2 x))
(fma.f64 x -1/2 (/.f64 2 x))
(+.f64 (log.f64 2) (*.f64 -1 (log.f64 x)))
(+.f64 (log.f64 2) (neg.f64 (log.f64 x)))
(-.f64 (log.f64 2) (log.f64 x))
(+.f64 (log.f64 2) (+.f64 (.f64 -1/4 (pow.f64 x 2)) (.f64 -1 (log.f64 x))))
(+.f64 (log.f64 2) (fma.f64 -1/4 (*.f64 x x) (neg.f64 (log.f64 x))))
(+.f64 (log.f64 2) (-.f64 (.f64 -1/4 (.f64 x x)) (log.f64 x)))
(-.f64 (fma.f64 -1/4 (*.f64 x x) (log.f64 2)) (log.f64 x))
(-.f64 (fma.f64 x (*.f64 x -1/4) (log.f64 2)) (log.f64 x))
(+.f64 (log.f64 2) (+.f64 (.f64 -1/4 (pow.f64 x 2)) (+.f64 (.f64 -1/32 (pow.f64 x 4)) (*.f64 -1 (log.f64 x)))))
(+.f64 (log.f64 2) (fma.f64 -1/4 (*.f64 x x) (fma.f64 -1/32 (pow.f64 x 4) (neg.f64 (log.f64 x)))))
(+.f64 (fma.f64 -1/4 (.f64 x x) (.f64 -1/32 (pow.f64 x 4))) (-.f64 (log.f64 2) (log.f64 x)))
(+.f64 (log.f64 2) (fma.f64 x (.f64 x -1/4) (-.f64 (.f64 -1/32 (pow.f64 x 4)) (log.f64 x))))
(-.f64 (fma.f64 -1/32 (pow.f64 x 4) (fma.f64 x (*.f64 x -1/4) (log.f64 2))) (log.f64 x))
(+.f64 (.f64 -1/192 (pow.f64 x 6)) (+.f64 (log.f64 2) (+.f64 (.f64 -1/4 (pow.f64 x 2)) (+.f64 (.f64 -1/32 (pow.f64 x 4)) (.f64 -1 (log.f64 x))))))
(fma.f64 -1/192 (pow.f64 x 6) (+.f64 (log.f64 2) (fma.f64 -1/4 (*.f64 x x) (fma.f64 -1/32 (pow.f64 x 4) (neg.f64 (log.f64 x))))))
(+.f64 (-.f64 (fma.f64 -1/4 (.f64 x x) (.f64 -1/32 (pow.f64 x 4))) (log.f64 x)) (fma.f64 -1/192 (pow.f64 x 6) (log.f64 2)))
(+.f64 (-.f64 (.f64 -1/32 (pow.f64 x 4)) (log.f64 x)) (fma.f64 -1/192 (pow.f64 x 6) (fma.f64 -1/4 (.f64 x x) (log.f64 2))))
(-.f64 (fma.f64 -1/192 (pow.f64 x 6) (fma.f64 -1/32 (pow.f64 x 4) (fma.f64 x (*.f64 x -1/4) (log.f64 2)))) (log.f64 x))
(+.f64 (log.f64 -1/2) (*.f64 -1 (log.f64 (/.f64 1 x))))
(+.f64 (log.f64 -1/2) (neg.f64 (neg.f64 (log.f64 x))))
(+.f64 (log.f64 x) (log.f64 -1/2))
(-.f64 (+.f64 (log.f64 -1/2) (.f64 -1 (log.f64 (/.f64 1 x)))) (.f64 4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (log.f64 -1/2) (neg.f64 (neg.f64 (log.f64 x)))) (/.f64 4 (*.f64 x x)))
(+.f64 (log.f64 x) (-.f64 (log.f64 -1/2) (/.f64 4 (*.f64 x x))))
(+.f64 (log.f64 x) (+.f64 (log.f64 -1/2) (/.f64 -4 (*.f64 x x))))
(+.f64 (log.f64 x) (-.f64 (log.f64 -1/2) (/.f64 (/.f64 4 x) x)))
(-.f64 (+.f64 (log.f64 -1/2) (.f64 -1 (log.f64 (/.f64 1 x)))) (+.f64 (.f64 8 (/.f64 1 (pow.f64 x 4))) (*.f64 4 (/.f64 1 (pow.f64 x 2)))))
(-.f64 (+.f64 (log.f64 -1/2) (neg.f64 (neg.f64 (log.f64 x)))) (+.f64 (/.f64 4 (*.f64 x x)) (/.f64 8 (pow.f64 x 4))))
(+.f64 (log.f64 x) (-.f64 (log.f64 -1/2) (+.f64 (/.f64 4 (*.f64 x x)) (/.f64 8 (pow.f64 x 4)))))
(+.f64 (log.f64 x) (+.f64 (+.f64 (log.f64 -1/2) (/.f64 -4 (*.f64 x x))) (/.f64 -8 (pow.f64 x 4))))
(+.f64 (log.f64 x) (+.f64 (log.f64 -1/2) (-.f64 (/.f64 -8 (pow.f64 x 4)) (/.f64 (/.f64 4 x) x))))
(-.f64 (+.f64 (log.f64 -1/2) (.f64 -1 (log.f64 (/.f64 1 x)))) (+.f64 (.f64 8 (/.f64 1 (pow.f64 x 4))) (+.f64 (.f64 64/3 (/.f64 1 (pow.f64 x 6))) (.f64 4 (/.f64 1 (pow.f64 x 2))))))
(-.f64 (+.f64 (log.f64 -1/2) (neg.f64 (neg.f64 (log.f64 x)))) (+.f64 (/.f64 8 (pow.f64 x 4)) (+.f64 (/.f64 4 (*.f64 x x)) (/.f64 64/3 (pow.f64 x 6)))))
(+.f64 (log.f64 x) (-.f64 (log.f64 -1/2) (+.f64 (+.f64 (/.f64 4 (*.f64 x x)) (/.f64 8 (pow.f64 x 4))) (/.f64 64/3 (pow.f64 x 6)))))
(+.f64 (log.f64 x) (-.f64 (+.f64 (log.f64 -1/2) (/.f64 -8 (pow.f64 x 4))) (+.f64 (/.f64 4 (*.f64 x x)) (/.f64 64/3 (pow.f64 x 6)))))
(+.f64 (log.f64 x) (+.f64 (+.f64 (log.f64 -1/2) (-.f64 (/.f64 -8 (pow.f64 x 4)) (/.f64 (/.f64 4 x) x))) (/.f64 -64/3 (pow.f64 x 6))))
(+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 1/2))
(fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 1/2))
(-.f64 (log.f64 1/2) (log.f64 (/.f64 -1 x)))
(-.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 1/2)) (.f64 4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 1/2)) (/.f64 4 (*.f64 x x)))
(+.f64 (-.f64 (log.f64 1/2) (log.f64 (/.f64 -1 x))) (/.f64 -4 (*.f64 x x)))
(-.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 1/2)) (+.f64 (.f64 8 (/.f64 1 (pow.f64 x 4))) (*.f64 4 (/.f64 1 (pow.f64 x 2)))))
(-.f64 (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 1/2)) (+.f64 (/.f64 4 (*.f64 x x)) (/.f64 8 (pow.f64 x 4))))
(-.f64 (-.f64 (log.f64 1/2) (log.f64 (/.f64 -1 x))) (+.f64 (/.f64 4 (*.f64 x x)) (/.f64 8 (pow.f64 x 4))))
(+.f64 (-.f64 (log.f64 1/2) (log.f64 (/.f64 -1 x))) (+.f64 (/.f64 -4 (*.f64 x x)) (/.f64 -8 (pow.f64 x 4))))
(+.f64 (log.f64 1/2) (+.f64 (/.f64 -8 (pow.f64 x 4)) (-.f64 (/.f64 -4 (*.f64 x x)) (log.f64 (/.f64 -1 x)))))
(+.f64 (log.f64 1/2) (+.f64 (/.f64 -4 (*.f64 x x)) (-.f64 (/.f64 -8 (pow.f64 x 4)) (log.f64 (/.f64 -1 x)))))
(-.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 1/2)) (+.f64 (.f64 8 (/.f64 1 (pow.f64 x 4))) (+.f64 (.f64 64/3 (/.f64 1 (pow.f64 x 6))) (.f64 4 (/.f64 1 (pow.f64 x 2))))))
(-.f64 (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 1/2)) (+.f64 (/.f64 8 (pow.f64 x 4)) (+.f64 (/.f64 4 (*.f64 x x)) (/.f64 64/3 (pow.f64 x 6)))))
(-.f64 (-.f64 (log.f64 1/2) (log.f64 (/.f64 -1 x))) (+.f64 (+.f64 (/.f64 4 (*.f64 x x)) (/.f64 8 (pow.f64 x 4))) (/.f64 64/3 (pow.f64 x 6))))
(+.f64 (+.f64 (/.f64 -4 (*.f64 x x)) (/.f64 -8 (pow.f64 x 4))) (-.f64 (-.f64 (log.f64 1/2) (log.f64 (/.f64 -1 x))) (/.f64 64/3 (pow.f64 x 6))))
(+.f64 (-.f64 (+.f64 (log.f64 1/2) (/.f64 -8 (pow.f64 x 4))) (log.f64 (/.f64 -1 x))) (+.f64 (/.f64 -4 (*.f64 x x)) (/.f64 -64/3 (pow.f64 x 6))))
(+.f64 (+.f64 (log.f64 1/2) (-.f64 (/.f64 -8 (pow.f64 x 4)) (log.f64 (/.f64 -1 x)))) (+.f64 (/.f64 -4 (*.f64 x x)) (/.f64 -64/3 (pow.f64 x 6))))

eval36.0ms (0.7%)

Compiler: Compiled 1376 to 1024 computations (25.6% saved)

prune18.0ms (0.4%)

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	89	0	89
Fresh	0	0	0
Picked	0	1	1
Done	0	4	4
Total	89	5	94

Error

Counts

94 → 5

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.5b	(log.f64 (+.f64 (.f64 -1/2 x) (.f64 2 (/.f64 1 x))))
✓	1.0b	(log.f64 (/.f64 2 x))
✓	0.5b	(log.f64 (/.f64 (fma.f64 x (*.f64 x -1/2) 2) x))
✓	0b	(log.f64 (/.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) x))
✓	1.0b	(neg.f64 (log.f64 (/.f64 x 2)))

Compiler

Compiled 44 to 34 computations (22.7% saved)

regimes18.0ms (0.4%)

Counts

7 → 1

Calls

Call 1

Inputs
(log.f64 (/.f64 2 x))
(neg.f64 (log.f64 (/.f64 x 2)))
(log.f64 (+.f64 (.f64 -1/2 x) (.f64 2 (/.f64 1 x))))
(log.f64 (/.f64 (fma.f64 x (*.f64 x -1/2) 2) 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:

6.0ms	(+.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 95 to 67 computations (29.5% saved)

regimes10.0ms (0.2%)

Counts

4 → 1

Calls

Call 1

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

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

Calls

1 calls:

9.0ms

Results

Error	Segments	Branch
0.5b	1	`x`

Compiler

Compiled 31 to 23 computations (25.8% saved)

regimes3.0ms (0.1%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0.0b (-0%)

Counts

2 → 1

Calls

Call 1

Inputs
(log.f64 (/.f64 2 x))
(neg.f64 (log.f64 (/.f64 x 2)))

Outputs
(neg.f64 (log.f64 (/.f64 x 2)))

Calls

1 calls:

3.0ms

Results

Error	Segments	Branch
1.0b	1	`x`

Compiler

Compiled 12 to 9 computations (25% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	46
1	35	46
2	43	46
3	48	46
4	50	46

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))))
(neg.f64 (log.f64 (/.f64 x 2)))
(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))))
(neg.f64 (log.f64 (/.f64 x 2)))
(log.f64 (/.f64 2 x))

Compiler

Compiled 34 to 27 computations (20.6% saved)

soundness0.0ms (0%)

end42.0ms (0.9%)

Compiler: Compiled 31 to 24 computations (22.6% saved)

Iter	Nodes	Cost
0	17	124
1	27	108
2	40	108
3	60	108
4	109	108
5	204	108
6	336	108
7	510	108
8	658	108
9	779	108
10	799	108

Iter	Nodes	Cost
0	17	124
1	27	108
2	40	108
3	60	108
4	109	108
5	204	108
6	336	108
7	510	108
8	658	108
9	779	108
10	799	108

Details

analyze8.0ms (0.2%)

sample1.5s (30.5%)

preprocess157.0ms (3.3%)

simplify145.0ms (3.1%)

eval1.0ms (0%)

prune1.0ms (0%)

localize23.0ms (0.5%)

series5.0ms (0.1%)

rewrite286.0ms (6%)

simplify338.0ms (7.1%)

eval139.0ms (2.9%)

prune65.0ms (1.4%)

localize25.0ms (0.5%)

series2.0ms (0%)

rewrite74.0ms (1.6%)

simplify61.0ms (1.3%)

localize16.0ms (0.3%)

series4.0ms (0.1%)

rewrite152.0ms (3.2%)

simplify54.0ms (1.1%)

localize6.0ms (0.1%)

series46.0ms (1%)

rewrite45.0ms (1%)

simplify39.0ms (0.8%)

eval218.0ms (4.6%)

prune81.0ms (1.7%)

localize34.0ms (0.7%)

series3.0ms (0.1%)

rewrite237.0ms (5%)

simplify80.0ms (1.7%)

localize17.0ms (0.4%)

eval578.0ms (12.1%)

prune56.0ms (1.2%)

localize34.0ms (0.7%)

series7.0ms (0.2%)

rewrite80.0ms (1.7%)

simplify57.0ms (1.2%)

eval36.0ms (0.7%)

prune18.0ms (0.4%)

regimes18.0ms (0.4%)

regimes10.0ms (0.2%)

regimes3.0ms (0.1%)

simplify6.0ms (0.1%)

soundness0.0ms (0%)

end42.0ms (0.9%)

Profiling

Iter	Nodes	Cost
0	17	124
1	27	108
2	40	108
3	60	108
4	109	108
5	204	108
6	336	108
7	510	108
8	658	108
9	779	108
10	799	108