Details

analyze4.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	50%	50%	3
12.5%	25%	62.5%	4
18.7%	12.5%	68.8%	5
21.9%	6.2%	71.9%	6
23.4%	3.1%	73.5%	7
24.2%	1.6%	74.2%	8
24.6%	0.8%	74.6%	9
24.8%	0.4%	74.8%	10
24.9%	0.2%	74.9%	11
24.9%	0.1%	75%	12

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample995.0ms (37.1%)

Results

981.0ms	8252×	body	64	valid
2.0ms	17×	body	64	invalid
1.0ms	4×	body	128	valid

preprocess110.0ms (4.1%)

Algorithm

2×	egg-herbie

Rules

597×	`unsub-neg_binary64`
579×	`distribute-rgt-out--_binary64`
492×	`fma-neg_binary64`
435×	`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	323	20
8	664	20
9	1447	20
10	2776	20
11	4161	20
12	5093	20
13	5405	20
14	5708	20
15	5804	20
16	5882	20
17	6150	20
18	7096	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 14 to 10 computations (28.6% saved)

simplify96.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

597×	`unsub-neg_binary64`
579×	`distribute-rgt-out--_binary64`
492×	`fma-neg_binary64`
435×	`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	323	20
8	664	20
9	1447	20
10	2776	20
11	4161	20
12	5093	20
13	5405	20
14	5708	20
15	5804	20
16	5882	20
17	6150	20
18	7096	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)))

prune2.0ms (0.1%)

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

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

Compiler

Compiled 42 to 30 computations (28.6% saved)

localize9.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

series7.0ms (0.3%)

Counts

3 → 36

Calls

9 calls:

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

rewrite84.0ms (3.1%)

Algorithm

1×	batch-egg-rewrite

Rules

519×	`log-prod_binary64`
399×	`fma-def_binary64`
365×	`pow-prod-down_binary64`
282×	`pow2_binary64`
203×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	47
1	225	47
2	3285	45

Stop Event

1×	node limit

Counts

3 → 195

Calls

Call 1

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

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

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((#(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 (pow.f64 1 1/2) (sqrt.f64 (-.f64 1 (*.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 /.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 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 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 log1p.f64 (expm1.f64 (sqrt.f64 (-.f64 1 (*.f64 x 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 hypot.f64 1 (sqrt.f64 (*.f64 x (neg.f64 x))))))))

simplify46.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

526×	`times-frac_binary64`
503×	`associate-/l/_binary64`
437×	`fma-neg_binary64`
434×	`associate-*l/_binary64`
393×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	110	782
1	323	745
2	974	721
3	3477	705

Stop Event

1×	node limit

Counts

231 → 263

Calls

Call 1

Inputs
(/.f64 2 x)
(+.f64 (.f64 -1/2 x) (.f64 2 (/.f64 1 x)))
(+.f64 (.f64 -1/8 (pow.f64 x 3)) (+.f64 (.f64 -1/2 x) (*.f64 2 (/.f64 1 x))))
(+.f64 (.f64 -1/8 (pow.f64 x 3)) (+.f64 (.f64 -1/2 x) (+.f64 (.f64 2 (/.f64 1 x)) (.f64 -1/16 (pow.f64 x 5)))))
(sqrt.f64 -1)
(+.f64 (sqrt.f64 -1) (/.f64 1 x))
(+.f64 (sqrt.f64 -1) (+.f64 (/.f64 1 x) (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 -1) (pow.f64 x 2))))))
(-.f64 (+.f64 (sqrt.f64 -1) (+.f64 (/.f64 1 x) (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 -1) (pow.f64 x 2)))))) (.f64 1/8 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 4)))))
(*.f64 -1 (sqrt.f64 -1))
(+.f64 (/.f64 1 x) (*.f64 -1 (sqrt.f64 -1)))
(-.f64 (+.f64 (/.f64 1 x) (.f64 -1 (sqrt.f64 -1))) (.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) (pow.f64 x 2)))))
(-.f64 (+.f64 (/.f64 1 x) (+.f64 (.f64 -1 (sqrt.f64 -1)) (.f64 1/8 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 4)))))) (.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) (pow.f64 x 2)))))
(+.f64 (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 -3/32 (pow.f64 x 4)) (*.f64 -1 (log.f64 x)))))
(+.f64 (.f64 -5/96 (pow.f64 x 6)) (+.f64 (log.f64 2) (+.f64 (.f64 -1/4 (pow.f64 x 2)) (+.f64 (.f64 -3/32 (pow.f64 x 4)) (.f64 -1 (log.f64 x))))))
(log.f64 (sqrt.f64 -1))
(+.f64 (/.f64 1 (*.f64 (sqrt.f64 -1) x)) (log.f64 (sqrt.f64 -1)))
(-.f64 (+.f64 (/.f64 1 (.f64 (sqrt.f64 -1) x)) (log.f64 (sqrt.f64 -1))) (.f64 1/6 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))))
(-.f64 (+.f64 (/.f64 1 (.f64 (sqrt.f64 -1) x)) (+.f64 (.f64 3/40 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5)))) (log.f64 (sqrt.f64 -1)))) (.f64 1/6 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))))
(log.f64 (*.f64 -1 (sqrt.f64 -1)))
(-.f64 (log.f64 (.f64 -1 (sqrt.f64 -1))) (/.f64 1 (.f64 (sqrt.f64 -1) x)))
(-.f64 (+.f64 (log.f64 (.f64 -1 (sqrt.f64 -1))) (.f64 1/6 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3))))) (/.f64 1 (.f64 (sqrt.f64 -1) x)))
(-.f64 (+.f64 (log.f64 (.f64 -1 (sqrt.f64 -1))) (.f64 1/6 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3))))) (+.f64 (/.f64 1 (.f64 (sqrt.f64 -1) x)) (.f64 3/40 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5))))))
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)))))

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 (+.f64 (/.f64 1 x) (sqrt.f64 -1)) (/.f64 1/2 (.f64 (sqrt.f64 -1) (.f64 x x))))
(+.f64 (/.f64 1 x) (+.f64 (/.f64 1/2 (.f64 x (.f64 x (sqrt.f64 -1)))) (sqrt.f64 -1)))
(+.f64 (sqrt.f64 -1) (+.f64 (/.f64 1 x) (/.f64 (/.f64 1/2 (*.f64 x (sqrt.f64 -1))) x)))
(+.f64 (/.f64 1 x) (-.f64 (sqrt.f64 -1) (/.f64 -1/2 (.f64 (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 (/.f64 1 x) (sqrt.f64 -1)) (/.f64 1/2 (.f64 (sqrt.f64 -1) (.f64 x x)))) (/.f64 1/8 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 4))))
(+.f64 (+.f64 (/.f64 1 x) (/.f64 1/2 (.f64 x (.f64 x (sqrt.f64 -1))))) (-.f64 (sqrt.f64 -1) (/.f64 (/.f64 1/8 (neg.f64 (sqrt.f64 -1))) (pow.f64 x 4))))
(+.f64 (/.f64 1 x) (+.f64 (sqrt.f64 -1) (+.f64 (/.f64 (/.f64 1/2 (*.f64 x (sqrt.f64 -1))) x) (/.f64 (/.f64 1/8 (sqrt.f64 -1)) (pow.f64 x 4)))))
(+.f64 (/.f64 1 x) (+.f64 (-.f64 (sqrt.f64 -1) (/.f64 -1/2 (.f64 (sqrt.f64 -1) (.f64 x x)))) (/.f64 (/.f64 1/8 (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 (sqrt.f64 -1) (.f64 x x)))))
(+.f64 (-.f64 (/.f64 1 x) (sqrt.f64 -1)) (/.f64 -1/2 (.f64 x (.f64 x (sqrt.f64 -1)))))
(-.f64 (/.f64 1 x) (+.f64 (sqrt.f64 -1) (/.f64 (/.f64 1/2 (*.f64 x (sqrt.f64 -1))) x)))
(+.f64 (/.f64 1 x) (-.f64 (/.f64 -1/2 (.f64 (sqrt.f64 -1) (.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 (sqrt.f64 -1) 3) (pow.f64 x 4)))) (/.f64 1/2 (.f64 (sqrt.f64 -1) (*.f64 x x)))))
(+.f64 (/.f64 1 x) (+.f64 (-.f64 (/.f64 (/.f64 1/8 (neg.f64 (sqrt.f64 -1))) (pow.f64 x 4)) (sqrt.f64 -1)) (/.f64 -1/2 (.f64 x (.f64 x (sqrt.f64 -1))))))
(+.f64 (/.f64 1 x) (-.f64 (/.f64 -1/8 (.f64 (sqrt.f64 -1) (pow.f64 x 4))) (+.f64 (sqrt.f64 -1) (/.f64 (/.f64 1/2 (.f64 x (sqrt.f64 -1))) x))))
(+.f64 (-.f64 (/.f64 1 x) (sqrt.f64 -1)) (.f64 (/.f64 -1 (.f64 (sqrt.f64 -1) (.f64 x x))) (+.f64 1/2 (/.f64 1/8 (.f64 x 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 x (.f64 x -1/4)) (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 -3/32 (pow.f64 x 4)) (*.f64 -1 (log.f64 x)))))
(+.f64 (log.f64 2) (fma.f64 -1/4 (*.f64 x x) (fma.f64 -3/32 (pow.f64 x 4) (neg.f64 (log.f64 x)))))
(+.f64 (log.f64 2) (fma.f64 (*.f64 x x) -1/4 (fma.f64 (pow.f64 x 4) -3/32 (neg.f64 (log.f64 x)))))
(+.f64 (log.f64 2) (-.f64 (fma.f64 x (.f64 x -1/4) (.f64 (pow.f64 x 4) -3/32)) (log.f64 x)))
(fma.f64 x (*.f64 x -1/4) (fma.f64 (pow.f64 x 4) -3/32 (-.f64 (log.f64 2) (log.f64 x))))
(+.f64 (.f64 -5/96 (pow.f64 x 6)) (+.f64 (log.f64 2) (+.f64 (.f64 -1/4 (pow.f64 x 2)) (+.f64 (.f64 -3/32 (pow.f64 x 4)) (.f64 -1 (log.f64 x))))))
(fma.f64 -5/96 (pow.f64 x 6) (+.f64 (log.f64 2) (fma.f64 -1/4 (*.f64 x x) (fma.f64 -3/32 (pow.f64 x 4) (neg.f64 (log.f64 x))))))
(+.f64 (fma.f64 (*.f64 x x) -1/4 (fma.f64 (pow.f64 x 4) -3/32 (neg.f64 (log.f64 x)))) (fma.f64 -5/96 (pow.f64 x 6) (log.f64 2)))
(+.f64 (log.f64 2) (fma.f64 -5/96 (pow.f64 x 6) (-.f64 (fma.f64 x (.f64 x -1/4) (.f64 (pow.f64 x 4) -3/32)) (log.f64 x))))
(fma.f64 -5/96 (pow.f64 x 6) (fma.f64 x (*.f64 x -1/4) (fma.f64 (pow.f64 x 4) -3/32 (-.f64 (log.f64 2) (log.f64 x)))))
(log.f64 (sqrt.f64 -1))
(+.f64 (/.f64 1 (*.f64 (sqrt.f64 -1) x)) (log.f64 (sqrt.f64 -1)))
(+.f64 (log.f64 (sqrt.f64 -1)) (/.f64 1 (*.f64 x (sqrt.f64 -1))))
(+.f64 (log.f64 (sqrt.f64 -1)) (/.f64 (/.f64 1 x) (sqrt.f64 -1)))
(-.f64 (+.f64 (/.f64 1 (.f64 (sqrt.f64 -1) x)) (log.f64 (sqrt.f64 -1))) (.f64 1/6 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))))
(+.f64 (/.f64 1 (.f64 x (sqrt.f64 -1))) (-.f64 (log.f64 (sqrt.f64 -1)) (/.f64 1/6 (.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 -1) 3)))))
(+.f64 (/.f64 1 (.f64 x (sqrt.f64 -1))) (+.f64 (log.f64 (sqrt.f64 -1)) (/.f64 -1/6 (.f64 (pow.f64 x 3) (neg.f64 (sqrt.f64 -1))))))
(+.f64 (log.f64 (sqrt.f64 -1)) (+.f64 (/.f64 1 (*.f64 x (sqrt.f64 -1))) (/.f64 (/.f64 1/6 (sqrt.f64 -1)) (pow.f64 x 3))))
(-.f64 (log.f64 (sqrt.f64 -1)) (.f64 (+.f64 (/.f64 1/6 (.f64 x x)) 1) (/.f64 (/.f64 -1 (sqrt.f64 -1)) x)))
(-.f64 (+.f64 (/.f64 1 (.f64 (sqrt.f64 -1) x)) (+.f64 (.f64 3/40 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5)))) (log.f64 (sqrt.f64 -1)))) (.f64 1/6 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))))
(+.f64 (/.f64 1 (.f64 x (sqrt.f64 -1))) (-.f64 (+.f64 (log.f64 (sqrt.f64 -1)) (/.f64 3/40 (.f64 (pow.f64 x 5) (pow.f64 (sqrt.f64 -1) 5)))) (/.f64 1/6 (*.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 -1) 3)))))
(+.f64 (+.f64 (log.f64 (sqrt.f64 -1)) (/.f64 3/40 (.f64 (pow.f64 x 5) (pow.f64 (sqrt.f64 -1) 5)))) (-.f64 (/.f64 1 (.f64 x (sqrt.f64 -1))) (/.f64 1/6 (*.f64 (pow.f64 x 3) (neg.f64 (sqrt.f64 -1))))))
(+.f64 (+.f64 (log.f64 (sqrt.f64 -1)) (/.f64 1 (*.f64 x (sqrt.f64 -1)))) (+.f64 (/.f64 (/.f64 3/40 (pow.f64 (sqrt.f64 -1) 5)) (pow.f64 x 5)) (/.f64 (/.f64 1/6 (sqrt.f64 -1)) (pow.f64 x 3))))
(+.f64 (/.f64 3/40 (.f64 (pow.f64 x 5) (pow.f64 (sqrt.f64 -1) 5))) (-.f64 (log.f64 (sqrt.f64 -1)) (.f64 (+.f64 (/.f64 1/6 (*.f64 x x)) 1) (/.f64 (/.f64 -1 (sqrt.f64 -1)) x))))
(log.f64 (*.f64 -1 (sqrt.f64 -1)))
(log.f64 (neg.f64 (sqrt.f64 -1)))
(-.f64 (log.f64 (.f64 -1 (sqrt.f64 -1))) (/.f64 1 (.f64 (sqrt.f64 -1) x)))
(-.f64 (log.f64 (neg.f64 (sqrt.f64 -1))) (/.f64 1 (*.f64 x (sqrt.f64 -1))))
(+.f64 (log.f64 (neg.f64 (sqrt.f64 -1))) (/.f64 -1 (*.f64 x (sqrt.f64 -1))))
(+.f64 (log.f64 (neg.f64 (sqrt.f64 -1))) (/.f64 (/.f64 -1 (sqrt.f64 -1)) x))
(fma.f64 3 (log.f64 (sqrt.f64 -1)) (/.f64 (/.f64 -1 (sqrt.f64 -1)) x))
(-.f64 (+.f64 (log.f64 (.f64 -1 (sqrt.f64 -1))) (.f64 1/6 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3))))) (/.f64 1 (.f64 (sqrt.f64 -1) x)))
(+.f64 (log.f64 (neg.f64 (sqrt.f64 -1))) (-.f64 (/.f64 1/6 (.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 -1) 3))) (/.f64 1 (.f64 x (sqrt.f64 -1)))))
(+.f64 (log.f64 (neg.f64 (sqrt.f64 -1))) (fma.f64 1/6 (/.f64 (/.f64 -1 (sqrt.f64 -1)) (pow.f64 x 3)) (/.f64 -1 (*.f64 x (sqrt.f64 -1)))))
(+.f64 (/.f64 -1/6 (*.f64 (pow.f64 x 3) (sqrt.f64 -1))) (+.f64 (log.f64 (neg.f64 (sqrt.f64 -1))) (/.f64 (/.f64 -1 (sqrt.f64 -1)) x)))
(+.f64 (log.f64 (neg.f64 (sqrt.f64 -1))) (.f64 (+.f64 (/.f64 1/6 (.f64 x x)) 1) (/.f64 (/.f64 -1 (sqrt.f64 -1)) x)))
(-.f64 (+.f64 (log.f64 (.f64 -1 (sqrt.f64 -1))) (.f64 1/6 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3))))) (+.f64 (/.f64 1 (.f64 (sqrt.f64 -1) x)) (.f64 3/40 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5))))))
(+.f64 (log.f64 (neg.f64 (sqrt.f64 -1))) (-.f64 (/.f64 1/6 (.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 -1) 3))) (+.f64 (/.f64 1 (.f64 x (sqrt.f64 -1))) (/.f64 3/40 (*.f64 (pow.f64 x 5) (pow.f64 (sqrt.f64 -1) 5))))))
(+.f64 (log.f64 (neg.f64 (sqrt.f64 -1))) (-.f64 (fma.f64 1/6 (/.f64 (/.f64 -1 (sqrt.f64 -1)) (pow.f64 x 3)) (/.f64 -1 (.f64 x (sqrt.f64 -1)))) (/.f64 3/40 (.f64 (pow.f64 x 5) (pow.f64 (sqrt.f64 -1) 5)))))
(+.f64 (log.f64 (neg.f64 (sqrt.f64 -1))) (+.f64 (-.f64 (/.f64 -1/6 (*.f64 (pow.f64 x 3) (sqrt.f64 -1))) (/.f64 (/.f64 3/40 (pow.f64 (sqrt.f64 -1) 5)) (pow.f64 x 5))) (/.f64 (/.f64 -1 (sqrt.f64 -1)) x)))
(+.f64 (.f64 (+.f64 (/.f64 1/6 (.f64 x x)) 1) (/.f64 (/.f64 -1 (sqrt.f64 -1)) x)) (fma.f64 3 (log.f64 (sqrt.f64 -1)) (/.f64 -3/40 (*.f64 (pow.f64 x 5) (pow.f64 (sqrt.f64 -1) 5)))))
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 x (*.f64 x -1/2) (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 x (.f64 x -1/2) (fma.f64 -1/8 (pow.f64 x 4) (.f64 -1/16 (pow.f64 x 6)))))
(+.f64 1 (fma.f64 -1/16 (pow.f64 x 6) (.f64 x (fma.f64 -1/8 (pow.f64 x 3) (.f64 x -1/2)))))
(*.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 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 x 3) (pow.f64 (sqrt.f64 -1) 3)))))
(-.f64 (fma.f64 x (sqrt.f64 -1) (/.f64 1/2 (.f64 x (sqrt.f64 -1)))) (/.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 (/.f64 1/8 (sqrt.f64 -1)) (pow.f64 x 3)))
(+.f64 (fma.f64 x (sqrt.f64 -1) (/.f64 (/.f64 1/2 x) (sqrt.f64 -1))) (/.f64 1/8 (*.f64 (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 (+.f64 (.f64 x (sqrt.f64 -1)) (/.f64 1/2 (.f64 x (sqrt.f64 -1)))) (/.f64 1/16 (.f64 (pow.f64 x 5) (pow.f64 (sqrt.f64 -1) 5)))) (/.f64 1/8 (.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 -1) 3))))
(+.f64 (fma.f64 x (sqrt.f64 -1) (/.f64 1/2 (.f64 x (sqrt.f64 -1)))) (-.f64 (/.f64 1/16 (.f64 (pow.f64 x 5) (pow.f64 (sqrt.f64 -1) 5))) (/.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 (/.f64 (/.f64 -1/8 (sqrt.f64 -1)) (pow.f64 x 3)) (/.f64 -1/16 (.f64 (pow.f64 x 5) (pow.f64 (sqrt.f64 -1) 5)))))
(+.f64 (/.f64 (/.f64 1/2 x) (sqrt.f64 -1)) (+.f64 (fma.f64 x (sqrt.f64 -1) (/.f64 1/8 (.f64 (pow.f64 x 3) (sqrt.f64 -1)))) (/.f64 1/16 (.f64 (pow.f64 x 5) (pow.f64 (sqrt.f64 -1) 5)))))
(.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 (.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 1/2 (*.f64 x (sqrt.f64 -1)))))
(-.f64 (/.f64 -1/2 (.f64 x (sqrt.f64 -1))) (.f64 x (sqrt.f64 -1)))
(fma.f64 x (neg.f64 (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 1/2 (/.f64 1 (.f64 (sqrt.f64 -1) x))))
(+.f64 (/.f64 1/8 (.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 -1) 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 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 1/2 (*.f64 x (sqrt.f64 -1)))))
(-.f64 (/.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 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 x 3) (pow.f64 (sqrt.f64 -1) 3))) (-.f64 (.f64 (neg.f64 (sqrt.f64 -1)) x) (+.f64 (/.f64 1/2 (.f64 x (sqrt.f64 -1))) (/.f64 1/16 (.f64 (pow.f64 x 5) (pow.f64 (sqrt.f64 -1) 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 1/2 (.f64 x (sqrt.f64 -1)))))) (/.f64 1/16 (.f64 (pow.f64 x 5) (pow.f64 (sqrt.f64 -1) 5))))
(+.f64 (/.f64 -1/16 (.f64 (pow.f64 x 5) (pow.f64 (sqrt.f64 -1) 5))) (-.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 -1/16 (.f64 (pow.f64 x 5) (pow.f64 (sqrt.f64 -1) 5))) (-.f64 (/.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)))))

prune750.0ms (28%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	262	1	263
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	263	1	264

Error

Counts

264 → 1

Alt Table

Status	Error	Program
▶	0b	(log1p.f64 (fma.f64 (/.f64 1 x) (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) -1))

Compiler

Compiled 5523 to 3624 computations (34.4% saved)

localize9.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

series2.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

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

rewrite60.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

522×	`prod-diff_binary64`
426×	`log-prod_binary64`
306×	`fma-def_binary64`
275×	`pow-prod-down_binary64`
258×	`pow2_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	31
1	214	30
2	2774	30

Stop Event

1×	node limit

Counts

2 → 72

Calls

Call 1

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

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

Outputs

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

simplify53.0ms (2%)

Algorithm

1×	egg-herbie

Rules

692×	`unswap-sqr_binary64`
573×	`sub-neg_binary64`
291×	`fma-neg_binary64`
283×	`associate-/l/_binary64`
271×	`associate-+l-_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	77	422
1	224	400
2	671	386
3	2354	380
4	6643	380

Stop Event

1×	node limit

Counts

96 → 118

Calls

Call 1

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

prune426.0ms (15.9%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	171	0	171
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	171	1	172

Error

Counts

172 → 1

Alt Table

Status	Error	Program
✓	0b	(log1p.f64 (fma.f64 (/.f64 1 x) (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) -1))

Compiler

Compiled 3306 to 2571 computations (22.2% saved)

regimes10.0ms (0.4%)

Accuracy

Total -0.0b remaining (-∞%)

Threshold costs -0.0b (-∞%)

Counts

2 → 1

Calls

Call 1

Inputs
(log1p.f64 (fma.f64 (/.f64 1 x) (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) -1))
(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))

Outputs
(log1p.f64 (fma.f64 (/.f64 1 x) (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) -1))

Results

2.0ms	0b	`x`
3.0ms	0b	`(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))`
3.0ms	0b	`(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))`

Compiler

Compiled 57 to 40 computations (29.8% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	21
1	19	21
2	25	21
3	29	21
4	31	21

Stop Event

1×

saturated

Calls

Call 1

Inputs
(log1p.f64 (fma.f64 (/.f64 1 x) (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) -1))

Outputs
(log1p.f64 (fma.f64 (/.f64 1 x) (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) -1))

end18.0ms (0.7%)

Stop Event

1×

done

Compiler

Compiled 30 to 24 computations (20% saved)

Details

analyze4.0ms (0.2%)

sample995.0ms (37.1%)

preprocess110.0ms (4.1%)

simplify96.0ms (3.6%)

prune2.0ms (0.1%)

localize9.0ms (0.3%)

series7.0ms (0.3%)

rewrite84.0ms (3.1%)

simplify46.0ms (1.7%)

prune750.0ms (28%)

localize9.0ms (0.3%)

series2.0ms (0.1%)

rewrite60.0ms (2.2%)

simplify53.0ms (2%)

prune426.0ms (15.9%)

regimes10.0ms (0.4%)

simplify2.0ms (0.1%)

end18.0ms (0.7%)

Profiling