Details

analyze0.0ms (0%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	25%	75%	0%	0%	0%	0
100%	25%	0%	75%	0%	0%	0%	1

Compiler

Compiled 6 to 4 computations (33.3% saved)

sample2.5s (50.4%)

Results

2.5s

8256×

body

256

valid

Bogosity

preprocess11.0ms (0.2%)

Algorithm

2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	5
0	1	1

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0

Outputs
0

Call 2

Inputs
(acosh.f32 x)

Outputs
(acosh.f32 x)

Compiler

Compiled 11 to 8 computations (27.3% saved)

simplify141.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

1814×	`rational.json-simplify-35`
1350×	`rational.json-simplify-53`
1016×	`rational.json-simplify-39`
864×	`rational.json-simplify-59`
750×	`rational.json-simplify-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	27
1	14	27
2	19	27
3	37	27
4	185	27
5	1957	27
6	5904	27
7	7843	27

Stop Event

1×	node limit

Counts

1 → 2

Calls

Call 1

Inputs
(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) 1))))

Outputs
(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) 1))))
(log.f32 (+.f32 x (sqrt.f32 (+.f32 (*.f32 x x) -1))))

eval1.0ms (0%)

Compiler: Compiled 19 to 12 computations (36.8% saved)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

16.6b

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	16.6b	(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) 1))))

Compiler

Compiled 10 to 7 computations (30% saved)

localize30.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) 1))))
✓	0.0b	(-.f32 (*.f32 x x) 1)
✓	0.0b	(+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) 1)))
✓	14.5b	(sqrt.f32 (-.f32 (*.f32 x x) 1))

Compiler

Compiled 34 to 17 computations (50% saved)

series4.0ms (0.1%)

Counts

4 → 48

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) 1))))
1.0ms	x	@	0	(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) 1))))
0.0ms	x	@	0	(sqrt.f32 (-.f32 (*.f32 x x) 1))
0.0ms	x	@	-inf	(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) 1))))
0.0ms	x	@	inf	(sqrt.f32 (-.f32 (*.f32 x x) 1))

rewrite75.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

1424×	`rational.json-1`
1424×	`rational.json-2`
1424×	`rational.json-3`
1422×	`rational.json-4`
1416×	`exponential.json-3`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	80
1	75	80
2	167	80
3	361	80
4	1254	80
5	4677	80

Stop Event

1×	node limit

Counts

4 → 64

Calls

Call 1

Inputs
(sqrt.f32 (-.f32 (*.f32 x x) 1))
(+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) 1)))
(-.f32 (*.f32 x x) 1)
(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) 1))))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f32 (sqrt.f32 (+.f32 (.f32 x x) -1)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 0 (sqrt.f32 (+.f32 (.f32 x x) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (sqrt.f32 (+.f32 (.f32 x x) -1)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 1 (sqrt.f32 (+.f32 (.f32 x x) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (sqrt.f32 (+.f32 (.f32 x x) -1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 2 (/.f32 (sqrt.f32 (+.f32 (.f32 x x) -1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 2 (.f32 (/.f32 (sqrt.f32 (+.f32 (.f32 x x) -1)) 2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (.f32 (sqrt.f32 (+.f32 (.f32 x x) -1)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 1/2 (.f32 (sqrt.f32 (+.f32 (.f32 x x) -1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 (sqrt.f32 (+.f32 (.f32 x x) -1)) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (sqrt.f32 (+.f32 (.f32 x x) -1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (.f32 (sqrt.f32 (+.f32 (.f32 x x) -1)) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (.f32 (sqrt.f32 (+.f32 (.f32 x x) -1)) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (.f32 2 (.f32 (sqrt.f32 (+.f32 (.f32 x x) -1)) 4)) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (+.f32 (.f32 2 (.f32 (sqrt.f32 (+.f32 (.f32 x x) -1)) 4)) (.f32 2 (.f32 (sqrt.f32 (+.f32 (.f32 x x) -1)) 4))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (+.f32 (*.f32 x x) -1)) 1)))))
((#(struct:change #<rule egg-rr> (2) ((x -.f32 (+.f32 x (sqrt.f32 (+.f32 (.f32 x x) -1))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 1 (+.f32 x (sqrt.f32 (+.f32 (.f32 x x) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (+.f32 x (sqrt.f32 (+.f32 (.f32 x x) -1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 2 (/.f32 (+.f32 x (sqrt.f32 (+.f32 (.f32 x x) -1))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 2 (.f32 (/.f32 (+.f32 x (sqrt.f32 (+.f32 (.f32 x x) -1))) 2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (.f32 (+.f32 x (sqrt.f32 (+.f32 (.f32 x x) -1))) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 1/2 (.f32 (+.f32 x (sqrt.f32 (+.f32 (.f32 x x) -1))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 (+.f32 x (sqrt.f32 (+.f32 (.f32 x x) -1))) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (+.f32 x (sqrt.f32 (+.f32 (.f32 x x) -1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (.f32 (+.f32 x (sqrt.f32 (+.f32 (.f32 x x) -1))) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (.f32 (+.f32 x (sqrt.f32 (+.f32 (.f32 x x) -1))) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (.f32 2 (.f32 (+.f32 x (sqrt.f32 (+.f32 (.f32 x x) -1))) 4)) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (+.f32 (.f32 2 (.f32 (+.f32 x (sqrt.f32 (+.f32 (.f32 x x) -1))) 4)) (.f32 2 (.f32 (+.f32 x (sqrt.f32 (+.f32 (.f32 x x) -1))) 4))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (+.f32 x (sqrt.f32 (+.f32 (*.f32 x x) -1))) 1)))))
((#(struct:change #<rule egg-rr> (2) ((x +.f32 (.f32 x x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (+.f32 (.f32 x x) -1) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 0 (+.f32 (.f32 x x) -1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 -1 (.f32 x x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 -2 (-.f32 1 (.f32 x (neg.f32 x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 1 (+.f32 (.f32 x x) -1))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (+.f32 (.f32 x x) -1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 2 (/.f32 (+.f32 (.f32 x x) -1) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 2 (.f32 (/.f32 (+.f32 (.f32 x x) -1) 2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (.f32 (+.f32 (.f32 x x) -1) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 1/2 (.f32 (+.f32 (.f32 x x) -1) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 (+.f32 (.f32 x x) -1) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (+.f32 (.f32 x x) -1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (.f32 (+.f32 (.f32 x x) -1) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (.f32 (+.f32 (.f32 x x) -1) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (.f32 2 (.f32 (+.f32 (.f32 x x) -1) 4)) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (+.f32 (.f32 2 (.f32 (+.f32 (.f32 x x) -1) 4)) (.f32 2 (.f32 (+.f32 (.f32 x x) -1) 4))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (+.f32 (*.f32 x x) -1) 1)))))
((#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (+.f32 x (sqrt.f32 (+.f32 (.f32 x x) -1)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 0 (log.f32 (+.f32 x (sqrt.f32 (+.f32 (.f32 x x) -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (log.f32 (+.f32 x (sqrt.f32 (+.f32 (.f32 x x) -1)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 1 (log.f32 (+.f32 x (sqrt.f32 (+.f32 (.f32 x x) -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (log.f32 (+.f32 x (sqrt.f32 (+.f32 (.f32 x x) -1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 2 (/.f32 (log.f32 (+.f32 x (sqrt.f32 (+.f32 (.f32 x x) -1)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 2 (.f32 (/.f32 (log.f32 (+.f32 x (sqrt.f32 (+.f32 (.f32 x x) -1)))) 2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (.f32 (log.f32 (+.f32 x (sqrt.f32 (+.f32 (.f32 x x) -1)))) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 1/2 (.f32 (log.f32 (+.f32 x (sqrt.f32 (+.f32 (.f32 x x) -1)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 (log.f32 (+.f32 x (sqrt.f32 (+.f32 (.f32 x x) -1)))) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (log.f32 (+.f32 x (sqrt.f32 (+.f32 (.f32 x x) -1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (.f32 (log.f32 (+.f32 x (sqrt.f32 (+.f32 (.f32 x x) -1)))) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (.f32 (log.f32 (+.f32 x (sqrt.f32 (+.f32 (.f32 x x) -1)))) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (.f32 2 (.f32 (log.f32 (+.f32 x (sqrt.f32 (+.f32 (.f32 x x) -1)))) 4)) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (+.f32 (.f32 2 (.f32 (log.f32 (+.f32 x (sqrt.f32 (+.f32 (.f32 x x) -1)))) 4)) (.f32 2 (.f32 (log.f32 (+.f32 x (sqrt.f32 (+.f32 (.f32 x x) -1)))) 4))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (log.f32 (+.f32 x (sqrt.f32 (+.f32 (*.f32 x x) -1)))) 1)))))

simplify203.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

1032×	`rational.json-simplify-2`
858×	`rational.json-simplify-35`
846×	`rational.json-simplify-41`
748×	`rational.json-simplify-59`
692×	`rational.json-simplify-51`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	213	2980
1	435	2972
2	825	2972
3	1958	2972
4	4098	2972
5	6287	2968

Stop Event

1×	node limit

Counts

112 → 168

Calls

Call 1

Inputs
(sqrt.f32 -1)
(+.f32 (sqrt.f32 -1) (*.f32 1/2 (/.f32 (pow.f32 x 2) (sqrt.f32 -1))))
(+.f32 (.f32 -1/8 (/.f32 (pow.f32 x 4) (pow.f32 (sqrt.f32 -1) 3))) (+.f32 (sqrt.f32 -1) (.f32 1/2 (/.f32 (pow.f32 x 2) (sqrt.f32 -1)))))
(+.f32 (.f32 -1/8 (/.f32 (pow.f32 x 4) (pow.f32 (sqrt.f32 -1) 3))) (+.f32 (sqrt.f32 -1) (+.f32 (.f32 1/2 (/.f32 (pow.f32 x 2) (sqrt.f32 -1))) (*.f32 1/16 (/.f32 (pow.f32 x 6) (pow.f32 (sqrt.f32 -1) 5))))))
x
(-.f32 x (*.f32 1/2 (/.f32 1 x)))
(-.f32 x (+.f32 (.f32 1/2 (/.f32 1 x)) (.f32 1/8 (/.f32 1 (pow.f32 x 3)))))
(-.f32 x (+.f32 (.f32 1/2 (/.f32 1 x)) (+.f32 (.f32 1/16 (/.f32 1 (pow.f32 x 5))) (*.f32 1/8 (/.f32 1 (pow.f32 x 3))))))
(*.f32 -1 x)
(+.f32 (.f32 -1 x) (.f32 1/2 (/.f32 1 x)))
(+.f32 (.f32 1/2 (/.f32 1 x)) (+.f32 (.f32 1/8 (/.f32 1 (pow.f32 x 3))) (*.f32 -1 x)))
(+.f32 (.f32 1/2 (/.f32 1 x)) (+.f32 (.f32 1/16 (/.f32 1 (pow.f32 x 5))) (+.f32 (.f32 1/8 (/.f32 1 (pow.f32 x 3))) (.f32 -1 x))))
(sqrt.f32 -1)
(+.f32 (sqrt.f32 -1) x)
(+.f32 (sqrt.f32 -1) (+.f32 (*.f32 1/2 (/.f32 (pow.f32 x 2) (sqrt.f32 -1))) x))
(+.f32 (.f32 -1/8 (/.f32 (pow.f32 x 4) (pow.f32 (sqrt.f32 -1) 3))) (+.f32 (sqrt.f32 -1) (+.f32 (.f32 1/2 (/.f32 (pow.f32 x 2) (sqrt.f32 -1))) x)))
(*.f32 2 x)
(-.f32 (.f32 2 x) (.f32 1/2 (/.f32 1 x)))
(-.f32 (.f32 2 x) (+.f32 (.f32 1/2 (/.f32 1 x)) (*.f32 1/8 (/.f32 1 (pow.f32 x 3)))))
(-.f32 (.f32 2 x) (+.f32 (.f32 1/2 (/.f32 1 x)) (+.f32 (.f32 1/16 (/.f32 1 (pow.f32 x 5))) (.f32 1/8 (/.f32 1 (pow.f32 x 3))))))
(/.f32 1/2 x)
(+.f32 (.f32 1/8 (/.f32 1 (pow.f32 x 3))) (.f32 1/2 (/.f32 1 x)))
(+.f32 (.f32 1/16 (/.f32 1 (pow.f32 x 5))) (+.f32 (.f32 1/8 (/.f32 1 (pow.f32 x 3))) (*.f32 1/2 (/.f32 1 x))))
(+.f32 (.f32 1/16 (/.f32 1 (pow.f32 x 5))) (+.f32 (.f32 1/8 (/.f32 1 (pow.f32 x 3))) (+.f32 (.f32 1/2 (/.f32 1 x)) (.f32 5/128 (/.f32 1 (pow.f32 x 7))))))
-1
(-.f32 (pow.f32 x 2) 1)
(-.f32 (pow.f32 x 2) 1)
(-.f32 (pow.f32 x 2) 1)
(pow.f32 x 2)
(-.f32 (pow.f32 x 2) 1)
(-.f32 (pow.f32 x 2) 1)
(-.f32 (pow.f32 x 2) 1)
(pow.f32 x 2)
(-.f32 (pow.f32 x 2) 1)
(-.f32 (pow.f32 x 2) 1)
(-.f32 (pow.f32 x 2) 1)
(log.f32 (sqrt.f32 -1))
(+.f32 (/.f32 x (sqrt.f32 -1)) (log.f32 (sqrt.f32 -1)))
(+.f32 (*.f32 -1/6 (/.f32 (pow.f32 x 3) (pow.f32 (sqrt.f32 -1) 3))) (+.f32 (/.f32 x (sqrt.f32 -1)) (log.f32 (sqrt.f32 -1))))
(+.f32 (.f32 3/40 (/.f32 (pow.f32 x 5) (pow.f32 (sqrt.f32 -1) 5))) (+.f32 (.f32 -1/6 (/.f32 (pow.f32 x 3) (pow.f32 (sqrt.f32 -1) 3))) (+.f32 (/.f32 x (sqrt.f32 -1)) (log.f32 (sqrt.f32 -1)))))
(+.f32 (log.f32 2) (*.f32 -1 (log.f32 (/.f32 1 x))))
(-.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 1 x))) (log.f32 2)) (.f32 1/4 (/.f32 1 (pow.f32 x 2))))
(-.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 1 x))) (log.f32 2)) (+.f32 (.f32 3/32 (/.f32 1 (pow.f32 x 4))) (*.f32 1/4 (/.f32 1 (pow.f32 x 2)))))
(-.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 1 x))) (log.f32 2)) (+.f32 (.f32 3/32 (/.f32 1 (pow.f32 x 4))) (+.f32 (.f32 5/96 (/.f32 1 (pow.f32 x 6))) (.f32 1/4 (/.f32 1 (pow.f32 x 2))))))
(+.f32 (log.f32 -1/2) (log.f32 (/.f32 -1 x)))
(+.f32 (log.f32 (/.f32 -1 x)) (+.f32 (log.f32 -1/2) (*.f32 1/4 (/.f32 1 (pow.f32 x 2)))))
(+.f32 (log.f32 (/.f32 -1 x)) (+.f32 (log.f32 -1/2) (+.f32 (.f32 3/32 (/.f32 1 (pow.f32 x 4))) (.f32 1/4 (/.f32 1 (pow.f32 x 2))))))
(+.f32 (log.f32 (/.f32 -1 x)) (+.f32 (log.f32 -1/2) (+.f32 (.f32 3/32 (/.f32 1 (pow.f32 x 4))) (+.f32 (.f32 5/96 (/.f32 1 (pow.f32 x 6))) (*.f32 1/4 (/.f32 1 (pow.f32 x 2)))))))
(+.f32 (sqrt.f32 (+.f32 (*.f32 x x) -1)) 0)
(+.f32 0 (sqrt.f32 (+.f32 (*.f32 x x) -1)))
(-.f32 (sqrt.f32 (+.f32 (*.f32 x x) -1)) 0)
(.f32 1 (sqrt.f32 (+.f32 (.f32 x x) -1)))
(.f32 (sqrt.f32 (+.f32 (.f32 x x) -1)) 1)
(.f32 2 (/.f32 (sqrt.f32 (+.f32 (.f32 x x) -1)) 2))
(.f32 2 (.f32 (/.f32 (sqrt.f32 (+.f32 (*.f32 x x) -1)) 2) 1))
(.f32 (.f32 (sqrt.f32 (+.f32 (*.f32 x x) -1)) 2) 1/2)
(.f32 1/2 (.f32 (sqrt.f32 (+.f32 (*.f32 x x) -1)) 2))
(.f32 (/.f32 (sqrt.f32 (+.f32 (.f32 x x) -1)) 2) 2)
(/.f32 (sqrt.f32 (+.f32 (*.f32 x x) -1)) 1)
(/.f32 (.f32 (sqrt.f32 (+.f32 (.f32 x x) -1)) 2) 2)
(/.f32 (.f32 (sqrt.f32 (+.f32 (.f32 x x) -1)) 4) 4)
(/.f32 (.f32 2 (.f32 (sqrt.f32 (+.f32 (*.f32 x x) -1)) 4)) 8)
(/.f32 (+.f32 (.f32 2 (.f32 (sqrt.f32 (+.f32 (.f32 x x) -1)) 4)) (.f32 2 (.f32 (sqrt.f32 (+.f32 (.f32 x x) -1)) 4))) 16)
(pow.f32 (sqrt.f32 (+.f32 (*.f32 x x) -1)) 1)
(-.f32 (+.f32 x (sqrt.f32 (+.f32 (*.f32 x x) -1))) 0)
(.f32 1 (+.f32 x (sqrt.f32 (+.f32 (.f32 x x) -1))))
(.f32 (+.f32 x (sqrt.f32 (+.f32 (.f32 x x) -1))) 1)
(.f32 2 (/.f32 (+.f32 x (sqrt.f32 (+.f32 (.f32 x x) -1))) 2))
(.f32 2 (.f32 (/.f32 (+.f32 x (sqrt.f32 (+.f32 (*.f32 x x) -1))) 2) 1))
(.f32 (.f32 (+.f32 x (sqrt.f32 (+.f32 (*.f32 x x) -1))) 2) 1/2)
(.f32 1/2 (.f32 (+.f32 x (sqrt.f32 (+.f32 (*.f32 x x) -1))) 2))
(.f32 (/.f32 (+.f32 x (sqrt.f32 (+.f32 (.f32 x x) -1))) 2) 2)
(/.f32 (+.f32 x (sqrt.f32 (+.f32 (*.f32 x x) -1))) 1)
(/.f32 (.f32 (+.f32 x (sqrt.f32 (+.f32 (.f32 x x) -1))) 2) 2)
(/.f32 (.f32 (+.f32 x (sqrt.f32 (+.f32 (.f32 x x) -1))) 4) 4)
(/.f32 (.f32 2 (.f32 (+.f32 x (sqrt.f32 (+.f32 (*.f32 x x) -1))) 4)) 8)
(/.f32 (+.f32 (.f32 2 (.f32 (+.f32 x (sqrt.f32 (+.f32 (.f32 x x) -1))) 4)) (.f32 2 (.f32 (+.f32 x (sqrt.f32 (+.f32 (.f32 x x) -1))) 4))) 16)
(pow.f32 (+.f32 x (sqrt.f32 (+.f32 (*.f32 x x) -1))) 1)
(+.f32 (*.f32 x x) -1)
(+.f32 (+.f32 (*.f32 x x) -1) 0)
(+.f32 0 (+.f32 (*.f32 x x) -1))
(+.f32 -1 (*.f32 x x))
(+.f32 -2 (-.f32 1 (*.f32 x (neg.f32 x))))
(.f32 1 (+.f32 (.f32 x x) -1))
(.f32 (+.f32 (.f32 x x) -1) 1)
(.f32 2 (/.f32 (+.f32 (.f32 x x) -1) 2))
(.f32 2 (.f32 (/.f32 (+.f32 (*.f32 x x) -1) 2) 1))
(.f32 (.f32 (+.f32 (*.f32 x x) -1) 2) 1/2)
(.f32 1/2 (.f32 (+.f32 (*.f32 x x) -1) 2))
(.f32 (/.f32 (+.f32 (.f32 x x) -1) 2) 2)
(/.f32 (+.f32 (*.f32 x x) -1) 1)
(/.f32 (.f32 (+.f32 (.f32 x x) -1) 2) 2)
(/.f32 (.f32 (+.f32 (.f32 x x) -1) 4) 4)
(/.f32 (.f32 2 (.f32 (+.f32 (*.f32 x x) -1) 4)) 8)
(/.f32 (+.f32 (.f32 2 (.f32 (+.f32 (.f32 x x) -1) 4)) (.f32 2 (.f32 (+.f32 (.f32 x x) -1) 4))) 16)
(pow.f32 (+.f32 (*.f32 x x) -1) 1)
(+.f32 (log.f32 (+.f32 x (sqrt.f32 (+.f32 (*.f32 x x) -1)))) 0)
(+.f32 0 (log.f32 (+.f32 x (sqrt.f32 (+.f32 (*.f32 x x) -1)))))
(-.f32 (log.f32 (+.f32 x (sqrt.f32 (+.f32 (*.f32 x x) -1)))) 0)
(.f32 1 (log.f32 (+.f32 x (sqrt.f32 (+.f32 (.f32 x x) -1)))))
(.f32 (log.f32 (+.f32 x (sqrt.f32 (+.f32 (.f32 x x) -1)))) 1)
(.f32 2 (/.f32 (log.f32 (+.f32 x (sqrt.f32 (+.f32 (.f32 x x) -1)))) 2))
(.f32 2 (.f32 (/.f32 (log.f32 (+.f32 x (sqrt.f32 (+.f32 (*.f32 x x) -1)))) 2) 1))
(.f32 (.f32 (log.f32 (+.f32 x (sqrt.f32 (+.f32 (*.f32 x x) -1)))) 2) 1/2)
(.f32 1/2 (.f32 (log.f32 (+.f32 x (sqrt.f32 (+.f32 (*.f32 x x) -1)))) 2))
(.f32 (/.f32 (log.f32 (+.f32 x (sqrt.f32 (+.f32 (.f32 x x) -1)))) 2) 2)
(/.f32 (log.f32 (+.f32 x (sqrt.f32 (+.f32 (*.f32 x x) -1)))) 1)
(/.f32 (.f32 (log.f32 (+.f32 x (sqrt.f32 (+.f32 (.f32 x x) -1)))) 2) 2)
(/.f32 (.f32 (log.f32 (+.f32 x (sqrt.f32 (+.f32 (.f32 x x) -1)))) 4) 4)
(/.f32 (.f32 2 (.f32 (log.f32 (+.f32 x (sqrt.f32 (+.f32 (*.f32 x x) -1)))) 4)) 8)
(/.f32 (+.f32 (.f32 2 (.f32 (log.f32 (+.f32 x (sqrt.f32 (+.f32 (.f32 x x) -1)))) 4)) (.f32 2 (.f32 (log.f32 (+.f32 x (sqrt.f32 (+.f32 (.f32 x x) -1)))) 4))) 16)
(pow.f32 (log.f32 (+.f32 x (sqrt.f32 (+.f32 (*.f32 x x) -1)))) 1)

Outputs
(sqrt.f32 -1)
(+.f32 (sqrt.f32 -1) (*.f32 1/2 (/.f32 (pow.f32 x 2) (sqrt.f32 -1))))
(+.f32 (.f32 -1/8 (/.f32 (pow.f32 x 4) (pow.f32 (sqrt.f32 -1) 3))) (+.f32 (sqrt.f32 -1) (.f32 1/2 (/.f32 (pow.f32 x 2) (sqrt.f32 -1)))))
(+.f32 (+.f32 (sqrt.f32 -1) (.f32 1/2 (/.f32 (pow.f32 x 2) (sqrt.f32 -1)))) (.f32 -1/8 (/.f32 (pow.f32 x 4) (sqrt.f32 -1))))
(+.f32 (.f32 1/2 (/.f32 (pow.f32 x 2) (sqrt.f32 -1))) (+.f32 (sqrt.f32 -1) (.f32 -1/8 (/.f32 (pow.f32 x 4) (sqrt.f32 -1)))))
(+.f32 (sqrt.f32 -1) (+.f32 (.f32 1/2 (/.f32 (pow.f32 x 2) (sqrt.f32 -1))) (.f32 -1/8 (/.f32 (pow.f32 x 4) (sqrt.f32 -1)))))
(+.f32 (.f32 -1/8 (/.f32 (pow.f32 x 4) (pow.f32 (sqrt.f32 -1) 3))) (+.f32 (sqrt.f32 -1) (+.f32 (.f32 1/2 (/.f32 (pow.f32 x 2) (sqrt.f32 -1))) (*.f32 1/16 (/.f32 (pow.f32 x 6) (pow.f32 (sqrt.f32 -1) 5))))))
(+.f32 (.f32 -1/8 (/.f32 (pow.f32 x 4) (sqrt.f32 -1))) (+.f32 (sqrt.f32 -1) (+.f32 (.f32 1/2 (/.f32 (pow.f32 x 2) (sqrt.f32 -1))) (*.f32 1/16 (/.f32 (pow.f32 x 6) (sqrt.f32 -1))))))
(+.f32 (.f32 1/2 (/.f32 (pow.f32 x 2) (sqrt.f32 -1))) (+.f32 (+.f32 (sqrt.f32 -1) (.f32 1/16 (/.f32 (pow.f32 x 6) (sqrt.f32 -1)))) (*.f32 -1/8 (/.f32 (pow.f32 x 4) (sqrt.f32 -1)))))
(+.f32 (.f32 1/2 (/.f32 (pow.f32 x 2) (sqrt.f32 -1))) (+.f32 (.f32 -1/8 (/.f32 (pow.f32 x 4) (sqrt.f32 -1))) (+.f32 (sqrt.f32 -1) (*.f32 1/16 (/.f32 (pow.f32 x 6) (sqrt.f32 -1))))))
(+.f32 (.f32 1/2 (/.f32 (pow.f32 x 2) (sqrt.f32 -1))) (+.f32 (sqrt.f32 -1) (+.f32 (.f32 -1/8 (/.f32 (pow.f32 x 4) (sqrt.f32 -1))) (*.f32 1/16 (/.f32 (pow.f32 x 6) (sqrt.f32 -1))))))
x
(-.f32 x (*.f32 1/2 (/.f32 1 x)))
(-.f32 x (+.f32 (.f32 1/2 (/.f32 1 x)) (.f32 1/8 (/.f32 1 (pow.f32 x 3)))))
(-.f32 x (+.f32 (.f32 1/2 (/.f32 1 x)) (+.f32 (.f32 1/16 (/.f32 1 (pow.f32 x 5))) (*.f32 1/8 (/.f32 1 (pow.f32 x 3))))))
(-.f32 x (+.f32 (.f32 1/2 (/.f32 1 x)) (+.f32 (.f32 1/8 (/.f32 1 (pow.f32 x 3))) (*.f32 1/16 (/.f32 1 (pow.f32 x 5))))))
(*.f32 -1 x)
(neg.f32 x)
(+.f32 (.f32 -1 x) (.f32 1/2 (/.f32 1 x)))
(+.f32 (*.f32 1/2 (/.f32 1 x)) (neg.f32 x))
(+.f32 (.f32 1/2 (/.f32 1 x)) (+.f32 (.f32 1/8 (/.f32 1 (pow.f32 x 3))) (*.f32 -1 x)))
(+.f32 (.f32 1/2 (/.f32 1 x)) (+.f32 (.f32 1/8 (/.f32 1 (pow.f32 x 3))) (neg.f32 x)))
(+.f32 (.f32 1/2 (/.f32 1 x)) (+.f32 (.f32 1/16 (/.f32 1 (pow.f32 x 5))) (+.f32 (.f32 1/8 (/.f32 1 (pow.f32 x 3))) (.f32 -1 x))))
(+.f32 (.f32 1/2 (/.f32 1 x)) (+.f32 (.f32 1/8 (/.f32 1 (pow.f32 x 3))) (+.f32 (neg.f32 x) (*.f32 1/16 (/.f32 1 (pow.f32 x 5))))))
(+.f32 (.f32 1/2 (/.f32 1 x)) (+.f32 (.f32 1/8 (/.f32 1 (pow.f32 x 3))) (+.f32 (*.f32 1/16 (/.f32 1 (pow.f32 x 5))) (neg.f32 x))))
(+.f32 (.f32 1/2 (/.f32 1 x)) (+.f32 (.f32 1/16 (/.f32 1 (pow.f32 x 5))) (+.f32 (*.f32 1/8 (/.f32 1 (pow.f32 x 3))) (neg.f32 x))))
(sqrt.f32 -1)
(+.f32 (sqrt.f32 -1) x)
(+.f32 (sqrt.f32 -1) (+.f32 (*.f32 1/2 (/.f32 (pow.f32 x 2) (sqrt.f32 -1))) x))
(+.f32 (sqrt.f32 -1) (+.f32 x (*.f32 1/2 (/.f32 (pow.f32 x 2) (sqrt.f32 -1)))))
(+.f32 (*.f32 1/2 (/.f32 (pow.f32 x 2) (sqrt.f32 -1))) (+.f32 (sqrt.f32 -1) x))
(+.f32 (.f32 -1/8 (/.f32 (pow.f32 x 4) (pow.f32 (sqrt.f32 -1) 3))) (+.f32 (sqrt.f32 -1) (+.f32 (.f32 1/2 (/.f32 (pow.f32 x 2) (sqrt.f32 -1))) x)))
(+.f32 (sqrt.f32 -1) (+.f32 (+.f32 x (.f32 1/2 (/.f32 (pow.f32 x 2) (sqrt.f32 -1)))) (.f32 -1/8 (/.f32 (pow.f32 x 4) (sqrt.f32 -1)))))
(+.f32 (sqrt.f32 -1) (+.f32 (.f32 -1/8 (/.f32 (pow.f32 x 4) (sqrt.f32 -1))) (+.f32 x (.f32 1/2 (/.f32 (pow.f32 x 2) (sqrt.f32 -1))))))
(+.f32 (sqrt.f32 -1) (+.f32 (.f32 1/2 (/.f32 (pow.f32 x 2) (sqrt.f32 -1))) (+.f32 x (.f32 -1/8 (/.f32 (pow.f32 x 4) (sqrt.f32 -1))))))
(*.f32 2 x)
(*.f32 x 2)
(+.f32 x x)
(-.f32 (.f32 2 x) (.f32 1/2 (/.f32 1 x)))
(-.f32 (.f32 x 2) (.f32 1/2 (/.f32 1 x)))
(-.f32 (+.f32 x x) (*.f32 1/2 (/.f32 1 x)))
(-.f32 (.f32 2 x) (+.f32 (.f32 1/2 (/.f32 1 x)) (*.f32 1/8 (/.f32 1 (pow.f32 x 3)))))
(-.f32 (.f32 x 2) (+.f32 (.f32 1/2 (/.f32 1 x)) (*.f32 1/8 (/.f32 1 (pow.f32 x 3)))))
(-.f32 (+.f32 x x) (+.f32 (.f32 1/2 (/.f32 1 x)) (.f32 1/8 (/.f32 1 (pow.f32 x 3)))))
(-.f32 (.f32 2 x) (+.f32 (.f32 1/2 (/.f32 1 x)) (+.f32 (.f32 1/16 (/.f32 1 (pow.f32 x 5))) (.f32 1/8 (/.f32 1 (pow.f32 x 3))))))
(-.f32 (.f32 x 2) (+.f32 (.f32 1/2 (/.f32 1 x)) (+.f32 (.f32 1/8 (/.f32 1 (pow.f32 x 3))) (.f32 1/16 (/.f32 1 (pow.f32 x 5))))))
(-.f32 (+.f32 x x) (+.f32 (.f32 1/2 (/.f32 1 x)) (+.f32 (.f32 1/8 (/.f32 1 (pow.f32 x 3))) (*.f32 1/16 (/.f32 1 (pow.f32 x 5))))))
(/.f32 1/2 x)
(+.f32 (.f32 1/8 (/.f32 1 (pow.f32 x 3))) (.f32 1/2 (/.f32 1 x)))
(+.f32 (.f32 1/2 (/.f32 1 x)) (.f32 1/8 (/.f32 1 (pow.f32 x 3))))
(+.f32 (.f32 1/16 (/.f32 1 (pow.f32 x 5))) (+.f32 (.f32 1/8 (/.f32 1 (pow.f32 x 3))) (*.f32 1/2 (/.f32 1 x))))
(+.f32 (.f32 1/2 (/.f32 1 x)) (+.f32 (.f32 1/8 (/.f32 1 (pow.f32 x 3))) (*.f32 1/16 (/.f32 1 (pow.f32 x 5)))))
(+.f32 (.f32 1/16 (/.f32 1 (pow.f32 x 5))) (+.f32 (.f32 1/8 (/.f32 1 (pow.f32 x 3))) (+.f32 (.f32 1/2 (/.f32 1 x)) (.f32 5/128 (/.f32 1 (pow.f32 x 7))))))
(+.f32 (.f32 1/8 (/.f32 1 (pow.f32 x 3))) (+.f32 (+.f32 (.f32 1/2 (/.f32 1 x)) (.f32 5/128 (/.f32 1 (pow.f32 x 7)))) (.f32 1/16 (/.f32 1 (pow.f32 x 5)))))
(+.f32 (.f32 1/8 (/.f32 1 (pow.f32 x 3))) (+.f32 (.f32 1/16 (/.f32 1 (pow.f32 x 5))) (+.f32 (.f32 1/2 (/.f32 1 x)) (.f32 5/128 (/.f32 1 (pow.f32 x 7))))))
(+.f32 (.f32 1/2 (/.f32 1 x)) (+.f32 (.f32 1/16 (/.f32 1 (pow.f32 x 5))) (+.f32 (.f32 1/8 (/.f32 1 (pow.f32 x 3))) (.f32 5/128 (/.f32 1 (pow.f32 x 7))))))
-1
(-.f32 (pow.f32 x 2) 1)
(+.f32 (pow.f32 x 2) -1)
(+.f32 -1 (pow.f32 x 2))
(-.f32 (pow.f32 x 2) 1)
(+.f32 (pow.f32 x 2) -1)
(+.f32 -1 (pow.f32 x 2))
(-.f32 (pow.f32 x 2) 1)
(+.f32 (pow.f32 x 2) -1)
(+.f32 -1 (pow.f32 x 2))
(pow.f32 x 2)
(-.f32 (pow.f32 x 2) 1)
(+.f32 (pow.f32 x 2) -1)
(+.f32 -1 (pow.f32 x 2))
(-.f32 (pow.f32 x 2) 1)
(+.f32 (pow.f32 x 2) -1)
(+.f32 -1 (pow.f32 x 2))
(-.f32 (pow.f32 x 2) 1)
(+.f32 (pow.f32 x 2) -1)
(+.f32 -1 (pow.f32 x 2))
(pow.f32 x 2)
(-.f32 (pow.f32 x 2) 1)
(+.f32 (pow.f32 x 2) -1)
(+.f32 -1 (pow.f32 x 2))
(-.f32 (pow.f32 x 2) 1)
(+.f32 (pow.f32 x 2) -1)
(+.f32 -1 (pow.f32 x 2))
(-.f32 (pow.f32 x 2) 1)
(+.f32 (pow.f32 x 2) -1)
(+.f32 -1 (pow.f32 x 2))
(log.f32 (sqrt.f32 -1))
(+.f32 (/.f32 x (sqrt.f32 -1)) (log.f32 (sqrt.f32 -1)))
(+.f32 (log.f32 (sqrt.f32 -1)) (/.f32 x (sqrt.f32 -1)))
(+.f32 (*.f32 -1/6 (/.f32 (pow.f32 x 3) (pow.f32 (sqrt.f32 -1) 3))) (+.f32 (/.f32 x (sqrt.f32 -1)) (log.f32 (sqrt.f32 -1))))
(+.f32 (+.f32 (log.f32 (sqrt.f32 -1)) (/.f32 x (sqrt.f32 -1))) (*.f32 -1/6 (/.f32 (pow.f32 x 3) (sqrt.f32 -1))))
(+.f32 (log.f32 (sqrt.f32 -1)) (+.f32 (*.f32 -1/6 (/.f32 (pow.f32 x 3) (sqrt.f32 -1))) (/.f32 x (sqrt.f32 -1))))
(+.f32 (log.f32 (sqrt.f32 -1)) (+.f32 (/.f32 x (sqrt.f32 -1)) (*.f32 -1/6 (/.f32 (pow.f32 x 3) (sqrt.f32 -1)))))
(+.f32 (.f32 3/40 (/.f32 (pow.f32 x 5) (pow.f32 (sqrt.f32 -1) 5))) (+.f32 (.f32 -1/6 (/.f32 (pow.f32 x 3) (pow.f32 (sqrt.f32 -1) 3))) (+.f32 (/.f32 x (sqrt.f32 -1)) (log.f32 (sqrt.f32 -1)))))
(+.f32 (.f32 -1/6 (/.f32 (pow.f32 x 3) (sqrt.f32 -1))) (+.f32 (+.f32 (log.f32 (sqrt.f32 -1)) (/.f32 x (sqrt.f32 -1))) (.f32 3/40 (/.f32 (pow.f32 x 5) (sqrt.f32 -1)))))
(+.f32 (log.f32 (sqrt.f32 -1)) (+.f32 (+.f32 (/.f32 x (sqrt.f32 -1)) (.f32 -1/6 (/.f32 (pow.f32 x 3) (sqrt.f32 -1)))) (.f32 3/40 (/.f32 (pow.f32 x 5) (sqrt.f32 -1)))))
(+.f32 (log.f32 2) (*.f32 -1 (log.f32 (/.f32 1 x))))
(+.f32 (log.f32 2) (neg.f32 (log.f32 (/.f32 1 x))))
(-.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 1 x))) (log.f32 2)) (.f32 1/4 (/.f32 1 (pow.f32 x 2))))
(-.f32 (+.f32 (log.f32 2) (.f32 -1 (log.f32 (/.f32 1 x)))) (.f32 1/4 (/.f32 1 (pow.f32 x 2))))
(-.f32 (+.f32 (log.f32 2) (neg.f32 (log.f32 (/.f32 1 x)))) (*.f32 1/4 (/.f32 1 (pow.f32 x 2))))
(-.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 1 x))) (log.f32 2)) (+.f32 (.f32 3/32 (/.f32 1 (pow.f32 x 4))) (*.f32 1/4 (/.f32 1 (pow.f32 x 2)))))
(-.f32 (+.f32 (log.f32 2) (.f32 -1 (log.f32 (/.f32 1 x)))) (+.f32 (.f32 1/4 (/.f32 1 (pow.f32 x 2))) (*.f32 3/32 (/.f32 1 (pow.f32 x 4)))))
(+.f32 (neg.f32 (log.f32 (/.f32 1 x))) (-.f32 (log.f32 2) (+.f32 (.f32 1/4 (/.f32 1 (pow.f32 x 2))) (.f32 3/32 (/.f32 1 (pow.f32 x 4))))))
(+.f32 (log.f32 2) (-.f32 (neg.f32 (log.f32 (/.f32 1 x))) (+.f32 (.f32 1/4 (/.f32 1 (pow.f32 x 2))) (.f32 3/32 (/.f32 1 (pow.f32 x 4))))))
(-.f32 (+.f32 (log.f32 2) (neg.f32 (log.f32 (/.f32 1 x)))) (+.f32 (.f32 1/4 (/.f32 1 (pow.f32 x 2))) (.f32 3/32 (/.f32 1 (pow.f32 x 4)))))
(-.f32 (+.f32 (.f32 -1 (log.f32 (/.f32 1 x))) (log.f32 2)) (+.f32 (.f32 3/32 (/.f32 1 (pow.f32 x 4))) (+.f32 (.f32 5/96 (/.f32 1 (pow.f32 x 6))) (.f32 1/4 (/.f32 1 (pow.f32 x 2))))))
(-.f32 (+.f32 (log.f32 2) (.f32 -1 (log.f32 (/.f32 1 x)))) (+.f32 (.f32 3/32 (/.f32 1 (pow.f32 x 4))) (+.f32 (.f32 1/4 (/.f32 1 (pow.f32 x 2))) (.f32 5/96 (/.f32 1 (pow.f32 x 6))))))
(-.f32 (+.f32 (log.f32 2) (neg.f32 (log.f32 (/.f32 1 x)))) (+.f32 (.f32 1/4 (/.f32 1 (pow.f32 x 2))) (+.f32 (.f32 5/96 (/.f32 1 (pow.f32 x 6))) (*.f32 3/32 (/.f32 1 (pow.f32 x 4))))))
(+.f32 (log.f32 2) (-.f32 (neg.f32 (log.f32 (/.f32 1 x))) (+.f32 (.f32 3/32 (/.f32 1 (pow.f32 x 4))) (+.f32 (.f32 1/4 (/.f32 1 (pow.f32 x 2))) (*.f32 5/96 (/.f32 1 (pow.f32 x 6)))))))
(-.f32 (+.f32 (log.f32 2) (neg.f32 (log.f32 (/.f32 1 x)))) (+.f32 (.f32 3/32 (/.f32 1 (pow.f32 x 4))) (+.f32 (.f32 1/4 (/.f32 1 (pow.f32 x 2))) (*.f32 5/96 (/.f32 1 (pow.f32 x 6))))))
(+.f32 (log.f32 2) (-.f32 (neg.f32 (log.f32 (/.f32 1 x))) (+.f32 (.f32 1/4 (/.f32 1 (pow.f32 x 2))) (+.f32 (.f32 3/32 (/.f32 1 (pow.f32 x 4))) (*.f32 5/96 (/.f32 1 (pow.f32 x 6)))))))
(+.f32 (log.f32 -1/2) (log.f32 (/.f32 -1 x)))
(+.f32 (log.f32 (/.f32 -1 x)) (+.f32 (log.f32 -1/2) (*.f32 1/4 (/.f32 1 (pow.f32 x 2)))))
(+.f32 (log.f32 -1/2) (+.f32 (*.f32 1/4 (/.f32 1 (pow.f32 x 2))) (log.f32 (/.f32 -1 x))))
(+.f32 (*.f32 1/4 (/.f32 1 (pow.f32 x 2))) (+.f32 (log.f32 -1/2) (log.f32 (/.f32 -1 x))))
(+.f32 (log.f32 (/.f32 -1 x)) (+.f32 (log.f32 -1/2) (+.f32 (.f32 3/32 (/.f32 1 (pow.f32 x 4))) (.f32 1/4 (/.f32 1 (pow.f32 x 2))))))
(+.f32 (log.f32 -1/2) (+.f32 (+.f32 (.f32 1/4 (/.f32 1 (pow.f32 x 2))) (.f32 3/32 (/.f32 1 (pow.f32 x 4)))) (log.f32 (/.f32 -1 x))))
(+.f32 (.f32 3/32 (/.f32 1 (pow.f32 x 4))) (+.f32 (.f32 1/4 (/.f32 1 (pow.f32 x 2))) (+.f32 (log.f32 -1/2) (log.f32 (/.f32 -1 x)))))
(+.f32 (.f32 1/4 (/.f32 1 (pow.f32 x 2))) (+.f32 (+.f32 (log.f32 -1/2) (log.f32 (/.f32 -1 x))) (.f32 3/32 (/.f32 1 (pow.f32 x 4)))))
(+.f32 (+.f32 (.f32 1/4 (/.f32 1 (pow.f32 x 2))) (.f32 3/32 (/.f32 1 (pow.f32 x 4)))) (+.f32 (log.f32 -1/2) (log.f32 (/.f32 -1 x))))
(+.f32 (log.f32 (/.f32 -1 x)) (+.f32 (log.f32 -1/2) (+.f32 (.f32 3/32 (/.f32 1 (pow.f32 x 4))) (+.f32 (.f32 5/96 (/.f32 1 (pow.f32 x 6))) (*.f32 1/4 (/.f32 1 (pow.f32 x 2)))))))
(+.f32 (log.f32 (/.f32 -1 x)) (+.f32 (+.f32 (.f32 3/32 (/.f32 1 (pow.f32 x 4))) (+.f32 (.f32 1/4 (/.f32 1 (pow.f32 x 2))) (*.f32 5/96 (/.f32 1 (pow.f32 x 6))))) (log.f32 -1/2)))
(+.f32 (+.f32 (.f32 1/4 (/.f32 1 (pow.f32 x 2))) (+.f32 (.f32 5/96 (/.f32 1 (pow.f32 x 6))) (*.f32 3/32 (/.f32 1 (pow.f32 x 4))))) (+.f32 (log.f32 -1/2) (log.f32 (/.f32 -1 x))))
(+.f32 (.f32 3/32 (/.f32 1 (pow.f32 x 4))) (+.f32 (log.f32 (/.f32 -1 x)) (+.f32 (.f32 1/4 (/.f32 1 (pow.f32 x 2))) (+.f32 (*.f32 5/96 (/.f32 1 (pow.f32 x 6))) (log.f32 -1/2)))))
(+.f32 (.f32 1/4 (/.f32 1 (pow.f32 x 2))) (+.f32 (+.f32 (.f32 3/32 (/.f32 1 (pow.f32 x 4))) (+.f32 (log.f32 -1/2) (log.f32 (/.f32 -1 x)))) (*.f32 5/96 (/.f32 1 (pow.f32 x 6)))))
(+.f32 (sqrt.f32 (+.f32 (*.f32 x x) -1)) 0)
(sqrt.f32 (+.f32 -1 (*.f32 x x)))
(+.f32 0 (sqrt.f32 (+.f32 (*.f32 x x) -1)))
(sqrt.f32 (+.f32 -1 (*.f32 x x)))
(-.f32 (sqrt.f32 (+.f32 (*.f32 x x) -1)) 0)
(sqrt.f32 (+.f32 -1 (*.f32 x x)))
(.f32 1 (sqrt.f32 (+.f32 (.f32 x x) -1)))
(sqrt.f32 (+.f32 -1 (*.f32 x x)))
(.f32 (sqrt.f32 (+.f32 (.f32 x x) -1)) 1)
(sqrt.f32 (+.f32 -1 (*.f32 x x)))
(.f32 2 (/.f32 (sqrt.f32 (+.f32 (.f32 x x) -1)) 2))
(sqrt.f32 (+.f32 -1 (*.f32 x x)))
(.f32 2 (.f32 (/.f32 (sqrt.f32 (+.f32 (*.f32 x x) -1)) 2) 1))
(sqrt.f32 (+.f32 -1 (*.f32 x x)))
(.f32 (.f32 (sqrt.f32 (+.f32 (*.f32 x x) -1)) 2) 1/2)
(sqrt.f32 (+.f32 -1 (*.f32 x x)))
(.f32 1/2 (.f32 (sqrt.f32 (+.f32 (*.f32 x x) -1)) 2))
(sqrt.f32 (+.f32 -1 (*.f32 x x)))
(.f32 (/.f32 (sqrt.f32 (+.f32 (.f32 x x) -1)) 2) 2)
(sqrt.f32 (+.f32 -1 (*.f32 x x)))
(/.f32 (sqrt.f32 (+.f32 (*.f32 x x) -1)) 1)
(sqrt.f32 (+.f32 -1 (*.f32 x x)))
(/.f32 (.f32 (sqrt.f32 (+.f32 (.f32 x x) -1)) 2) 2)
(sqrt.f32 (+.f32 -1 (*.f32 x x)))
(/.f32 (.f32 (sqrt.f32 (+.f32 (.f32 x x) -1)) 4) 4)
(sqrt.f32 (+.f32 -1 (*.f32 x x)))
(/.f32 (.f32 2 (.f32 (sqrt.f32 (+.f32 (*.f32 x x) -1)) 4)) 8)
(sqrt.f32 (+.f32 -1 (*.f32 x x)))
(/.f32 (+.f32 (.f32 2 (.f32 (sqrt.f32 (+.f32 (.f32 x x) -1)) 4)) (.f32 2 (.f32 (sqrt.f32 (+.f32 (.f32 x x) -1)) 4))) 16)
(sqrt.f32 (+.f32 -1 (*.f32 x x)))
(pow.f32 (sqrt.f32 (+.f32 (*.f32 x x) -1)) 1)
(sqrt.f32 (+.f32 -1 (*.f32 x x)))
(-.f32 (+.f32 x (sqrt.f32 (+.f32 (*.f32 x x) -1))) 0)
(+.f32 x (sqrt.f32 (+.f32 -1 (*.f32 x x))))
(.f32 1 (+.f32 x (sqrt.f32 (+.f32 (.f32 x x) -1))))
(+.f32 x (sqrt.f32 (+.f32 -1 (*.f32 x x))))
(.f32 (+.f32 x (sqrt.f32 (+.f32 (.f32 x x) -1))) 1)
(+.f32 x (sqrt.f32 (+.f32 -1 (*.f32 x x))))
(.f32 2 (/.f32 (+.f32 x (sqrt.f32 (+.f32 (.f32 x x) -1))) 2))
(+.f32 x (sqrt.f32 (+.f32 -1 (*.f32 x x))))
(.f32 2 (.f32 (/.f32 (+.f32 x (sqrt.f32 (+.f32 (*.f32 x x) -1))) 2) 1))
(+.f32 x (sqrt.f32 (+.f32 -1 (*.f32 x x))))
(.f32 (.f32 (+.f32 x (sqrt.f32 (+.f32 (*.f32 x x) -1))) 2) 1/2)
(+.f32 x (sqrt.f32 (+.f32 -1 (*.f32 x x))))
(.f32 1/2 (.f32 (+.f32 x (sqrt.f32 (+.f32 (*.f32 x x) -1))) 2))
(+.f32 x (sqrt.f32 (+.f32 -1 (*.f32 x x))))
(.f32 (/.f32 (+.f32 x (sqrt.f32 (+.f32 (.f32 x x) -1))) 2) 2)
(+.f32 x (sqrt.f32 (+.f32 -1 (*.f32 x x))))
(/.f32 (+.f32 x (sqrt.f32 (+.f32 (*.f32 x x) -1))) 1)
(+.f32 x (sqrt.f32 (+.f32 -1 (*.f32 x x))))
(/.f32 (.f32 (+.f32 x (sqrt.f32 (+.f32 (.f32 x x) -1))) 2) 2)
(+.f32 x (sqrt.f32 (+.f32 -1 (*.f32 x x))))
(/.f32 (.f32 (+.f32 x (sqrt.f32 (+.f32 (.f32 x x) -1))) 4) 4)
(+.f32 x (sqrt.f32 (+.f32 -1 (*.f32 x x))))
(/.f32 (.f32 2 (.f32 (+.f32 x (sqrt.f32 (+.f32 (*.f32 x x) -1))) 4)) 8)
(+.f32 x (sqrt.f32 (+.f32 -1 (*.f32 x x))))
(/.f32 (+.f32 (.f32 2 (.f32 (+.f32 x (sqrt.f32 (+.f32 (.f32 x x) -1))) 4)) (.f32 2 (.f32 (+.f32 x (sqrt.f32 (+.f32 (.f32 x x) -1))) 4))) 16)
(+.f32 x (sqrt.f32 (+.f32 -1 (*.f32 x x))))
(pow.f32 (+.f32 x (sqrt.f32 (+.f32 (*.f32 x x) -1))) 1)
(+.f32 x (sqrt.f32 (+.f32 -1 (*.f32 x x))))
(+.f32 (*.f32 x x) -1)
(+.f32 -1 (*.f32 x x))
(+.f32 (+.f32 (*.f32 x x) -1) 0)
(+.f32 -1 (*.f32 x x))
(+.f32 0 (+.f32 (*.f32 x x) -1))
(+.f32 -1 (*.f32 x x))
(+.f32 -1 (*.f32 x x))
(+.f32 -2 (-.f32 1 (*.f32 x (neg.f32 x))))
(+.f32 -2 (-.f32 (*.f32 x x) -1))
(.f32 1 (+.f32 (.f32 x x) -1))
(+.f32 -1 (*.f32 x x))
(.f32 (+.f32 (.f32 x x) -1) 1)
(+.f32 -1 (*.f32 x x))
(.f32 2 (/.f32 (+.f32 (.f32 x x) -1) 2))
(+.f32 -1 (*.f32 x x))
(.f32 2 (.f32 (/.f32 (+.f32 (*.f32 x x) -1) 2) 1))
(+.f32 -1 (*.f32 x x))
(.f32 (.f32 (+.f32 (*.f32 x x) -1) 2) 1/2)
(+.f32 -1 (*.f32 x x))
(.f32 1/2 (.f32 (+.f32 (*.f32 x x) -1) 2))
(+.f32 -1 (*.f32 x x))
(.f32 (/.f32 (+.f32 (.f32 x x) -1) 2) 2)
(+.f32 -1 (*.f32 x x))
(/.f32 (+.f32 (*.f32 x x) -1) 1)
(+.f32 -1 (*.f32 x x))
(/.f32 (.f32 (+.f32 (.f32 x x) -1) 2) 2)
(+.f32 -1 (*.f32 x x))
(/.f32 (.f32 (+.f32 (.f32 x x) -1) 4) 4)
(+.f32 -1 (*.f32 x x))
(/.f32 (.f32 2 (.f32 (+.f32 (*.f32 x x) -1) 4)) 8)
(+.f32 -1 (*.f32 x x))
(/.f32 (+.f32 (.f32 2 (.f32 (+.f32 (.f32 x x) -1) 4)) (.f32 2 (.f32 (+.f32 (.f32 x x) -1) 4))) 16)
(+.f32 -1 (*.f32 x x))
(pow.f32 (+.f32 (*.f32 x x) -1) 1)
(+.f32 -1 (*.f32 x x))
(+.f32 (log.f32 (+.f32 x (sqrt.f32 (+.f32 (*.f32 x x) -1)))) 0)
(log.f32 (+.f32 x (sqrt.f32 (+.f32 -1 (*.f32 x x)))))
(+.f32 0 (log.f32 (+.f32 x (sqrt.f32 (+.f32 (*.f32 x x) -1)))))
(log.f32 (+.f32 x (sqrt.f32 (+.f32 -1 (*.f32 x x)))))
(-.f32 (log.f32 (+.f32 x (sqrt.f32 (+.f32 (*.f32 x x) -1)))) 0)
(log.f32 (+.f32 x (sqrt.f32 (+.f32 -1 (*.f32 x x)))))
(.f32 1 (log.f32 (+.f32 x (sqrt.f32 (+.f32 (.f32 x x) -1)))))
(log.f32 (+.f32 x (sqrt.f32 (+.f32 -1 (*.f32 x x)))))
(.f32 (log.f32 (+.f32 x (sqrt.f32 (+.f32 (.f32 x x) -1)))) 1)
(log.f32 (+.f32 x (sqrt.f32 (+.f32 -1 (*.f32 x x)))))
(.f32 2 (/.f32 (log.f32 (+.f32 x (sqrt.f32 (+.f32 (.f32 x x) -1)))) 2))
(log.f32 (+.f32 x (sqrt.f32 (+.f32 -1 (*.f32 x x)))))
(.f32 2 (.f32 (/.f32 (log.f32 (+.f32 x (sqrt.f32 (+.f32 (*.f32 x x) -1)))) 2) 1))
(log.f32 (+.f32 x (sqrt.f32 (+.f32 -1 (*.f32 x x)))))
(.f32 (.f32 (log.f32 (+.f32 x (sqrt.f32 (+.f32 (*.f32 x x) -1)))) 2) 1/2)
(log.f32 (+.f32 x (sqrt.f32 (+.f32 -1 (*.f32 x x)))))
(.f32 1/2 (.f32 (log.f32 (+.f32 x (sqrt.f32 (+.f32 (*.f32 x x) -1)))) 2))
(log.f32 (+.f32 x (sqrt.f32 (+.f32 -1 (*.f32 x x)))))
(.f32 (/.f32 (log.f32 (+.f32 x (sqrt.f32 (+.f32 (.f32 x x) -1)))) 2) 2)
(log.f32 (+.f32 x (sqrt.f32 (+.f32 -1 (*.f32 x x)))))
(/.f32 (log.f32 (+.f32 x (sqrt.f32 (+.f32 (*.f32 x x) -1)))) 1)
(log.f32 (+.f32 x (sqrt.f32 (+.f32 -1 (*.f32 x x)))))
(/.f32 (.f32 (log.f32 (+.f32 x (sqrt.f32 (+.f32 (.f32 x x) -1)))) 2) 2)
(log.f32 (+.f32 x (sqrt.f32 (+.f32 -1 (*.f32 x x)))))
(/.f32 (.f32 (log.f32 (+.f32 x (sqrt.f32 (+.f32 (.f32 x x) -1)))) 4) 4)
(log.f32 (+.f32 x (sqrt.f32 (+.f32 -1 (*.f32 x x)))))
(/.f32 (.f32 2 (.f32 (log.f32 (+.f32 x (sqrt.f32 (+.f32 (*.f32 x x) -1)))) 4)) 8)
(log.f32 (+.f32 x (sqrt.f32 (+.f32 -1 (*.f32 x x)))))
(/.f32 (+.f32 (.f32 2 (.f32 (log.f32 (+.f32 x (sqrt.f32 (+.f32 (.f32 x x) -1)))) 4)) (.f32 2 (.f32 (log.f32 (+.f32 x (sqrt.f32 (+.f32 (.f32 x x) -1)))) 4))) 16)
(log.f32 (+.f32 x (sqrt.f32 (+.f32 -1 (*.f32 x x)))))
(pow.f32 (log.f32 (+.f32 x (sqrt.f32 (+.f32 (*.f32 x x) -1)))) 1)
(log.f32 (+.f32 x (sqrt.f32 (+.f32 -1 (*.f32 x x)))))

eval56.0ms (1.1%)

Compiler: Compiled 2853 to 2269 computations (20.5% saved)

prune106.0ms (2.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	166	2	168
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	166	3	169

Error

0.0b

Counts

169 → 3

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.4b	(log.f32 (-.f32 (+.f32 x x) (*.f32 1/2 (/.f32 1 x))))
✓	16.6b	(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) 1))))
▶	0.8b	(log.f32 (+.f32 x x))

Compiler

Compiled 26 to 18 computations (30.8% saved)

localize11.0ms (0.2%)

Compiler: Compiled 9 to 3 computations (66.7% saved)

localize551.0ms (11.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(/.f32 1 x)

Compiler

Compiled 34 to 21 computations (38.2% saved)

series1.0ms (0%)

Counts

1 → 0

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	x	@	-inf	(/.f32 1 x)
0.0ms	x	@	0	(/.f32 1 x)
0.0ms	x	@	inf	(/.f32 1 x)

rewrite737.0ms (15.1%)

Algorithm

1×	batch-egg-rewrite

Rules

1570×	`rational.json-simplify-35`
1234×	`rational.json-simplify-2`
1148×	`rational.json-1`
1148×	`rational.json-2`
1148×	`rational.json-4`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	45	7
2	120	7
3	235	7
4	477	7
5	1262	7
6	4088	7

Stop Event

1×	node limit

Counts

1 → 51

Calls

Call 1

Inputs
(/.f32 1 x)

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 1 x) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 0 (/.f32 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 -1 (-.f32 1 (/.f32 -1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 1/2 x) (/.f32 1/2 x))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (/.f32 1 x) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 0 (/.f32 -1 x))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 1 (/.f32 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 x (/.f32 1 (.f32 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 x (.f32 1/2 (/.f32 2 (.f32 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 x (.f32 1/4 (.f32 2 (/.f32 2 (.f32 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 1 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 2 (/.f32 1/2 x))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (+.f32 x x) (/.f32 (/.f32 1/2 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (+.f32 x x) (.f32 1/2 (/.f32 1 (.f32 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (+.f32 x x) (.f32 1/4 (/.f32 2 (.f32 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 4 (/.f32 1/4 x))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 4 (.f32 1/2 (/.f32 1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 4 (.f32 (/.f32 1 x) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 4 (.f32 (/.f32 1 (.f32 x x)) (.f32 x 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 2 x) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (.f32 x 4) (.f32 1/4 (/.f32 1 (.f32 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (.f32 x 4) (.f32 (/.f32 2 (.f32 x x)) 1/8))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (.f32 x 4) (.f32 1/2 (/.f32 (/.f32 1/2 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 -1 (.f32 (neg.f32 x) (/.f32 1 (.f32 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (neg.f32 x) (.f32 -1 (/.f32 1 (.f32 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (.f32 x 8) (.f32 (/.f32 1 (.f32 x x)) 1/8))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 4 x) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 1/2 (/.f32 2 x))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (.f32 x 1/2) (/.f32 2 (.f32 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 1/4 (/.f32 4 x))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 1 (.f32 x x)) x)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 2 (.f32 x x)) (.f32 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 1/2 x) 2)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 1/4 x) 4)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 -1 x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 (/.f32 1/2 x) x) (+.f32 x x))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (.f32 1/2 (/.f32 2 (.f32 x x))) x)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (.f32 1/2 (/.f32 1 (.f32 x x))) (+.f32 x x))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (.f32 1/4 (/.f32 1 (.f32 x x))) (.f32 x 4))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (.f32 1/4 (/.f32 2 (.f32 x x))) (+.f32 x x))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (.f32 (/.f32 2 (.f32 x x)) 1/8) (.f32 x 4))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (.f32 1/2 (/.f32 1/2 x)) 4)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (.f32 1/2 (/.f32 (/.f32 1/2 x) x)) (.f32 x 4))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (.f32 1/4 (.f32 2 (/.f32 2 (.f32 x x)))) x)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (.f32 (/.f32 1 x) 1/4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (.f32 (/.f32 1 (.f32 x x)) (.f32 x 1/4)) 4)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (.f32 (neg.f32 x) (/.f32 1 (.f32 x x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (.f32 -1 (/.f32 1 (.f32 x x))) (neg.f32 x))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (.f32 (/.f32 1 (.f32 x x)) 1/8) (*.f32 x 8))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (/.f32 1 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f32 (/.f32 -1 x))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 1 x) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 0 (/.f32 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 -1 (-.f32 1 (/.f32 -1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 1/2 x) (/.f32 1/2 x))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (/.f32 1 x) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 0 (/.f32 -1 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 1 (/.f32 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 x (/.f32 1 (*.f32 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 x (*.f32 1/2 (/.f32 2 (*.f32 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 x (*.f32 1/4 (*.f32 2 (/.f32 2 (*.f32 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 1 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 2 (/.f32 1/2 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (+.f32 x x) (/.f32 (/.f32 1/2 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (+.f32 x x) (*.f32 1/2 (/.f32 1 (*.f32 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (+.f32 x x) (*.f32 1/4 (/.f32 2 (*.f32 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 4 (/.f32 1/4 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 4 (*.f32 1/2 (/.f32 1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 4 (*.f32 (/.f32 1 x) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 4 (*.f32 (/.f32 1 (*.f32 x x)) (*.f32 x 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 2 x) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (*.f32 x 4) (*.f32 1/4 (/.f32 1 (*.f32 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (*.f32 x 4) (*.f32 (/.f32 2 (*.f32 x x)) 1/8))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (*.f32 x 4) (*.f32 1/2 (/.f32 (/.f32 1/2 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 -1 (*.f32 (neg.f32 x) (/.f32 1 (*.f32 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (neg.f32 x) (*.f32 -1 (/.f32 1 (*.f32 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (*.f32 x 8) (*.f32 (/.f32 1 (*.f32 x x)) 1/8))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 4 x) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 1/2 (/.f32 2 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (*.f32 x 1/2) (/.f32 2 (*.f32 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 1/4 (/.f32 4 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 1 (*.f32 x x)) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 2 (*.f32 x x)) (*.f32 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 1/2 x) 2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 1/4 x) 4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 -1 x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (/.f32 1/2 x) x) (+.f32 x x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (*.f32 1/2 (/.f32 2 (*.f32 x x))) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (*.f32 1/2 (/.f32 1 (*.f32 x x))) (+.f32 x x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (*.f32 1/4 (/.f32 1 (*.f32 x x))) (*.f32 x 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (*.f32 1/4 (/.f32 2 (*.f32 x x))) (+.f32 x x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (*.f32 (/.f32 2 (*.f32 x x)) 1/8) (*.f32 x 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (*.f32 1/2 (/.f32 1/2 x)) 4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (*.f32 1/2 (/.f32 (/.f32 1/2 x) x)) (*.f32 x 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (*.f32 1/4 (*.f32 2 (/.f32 2 (*.f32 x x)))) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (*.f32 (/.f32 1 x) 1/4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (*.f32 (/.f32 1 (*.f32 x x)) (*.f32 x 1/4)) 4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (*.f32 (neg.f32 x) (/.f32 1 (*.f32 x x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (*.f32 -1 (/.f32 1 (*.f32 x x))) (neg.f32 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (*.f32 (/.f32 1 (*.f32 x x)) 1/8) (*.f32 x 8))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (/.f32 1 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f32 (/.f32 -1 x))))))

simplify148.0ms (3%)

Algorithm

1×	egg-herbie

Rules

1200×	`rational.json-simplify-53`
806×	`rational.json-simplify-19`
756×	`rational.json-simplify-2`
652×	`rational.json-simplify-51`
564×	`rational.json-simplify-41`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	95	417
1	173	417
2	359	417
3	923	417
4	3049	417
5	6271	417

Stop Event

1×	node limit

Counts

51 → 52

Calls

Call 1

Inputs
(+.f32 (/.f32 1 x) 0)
(+.f32 0 (/.f32 1 x))
(+.f32 -1 (-.f32 1 (/.f32 -1 x)))
(+.f32 (/.f32 1/2 x) (/.f32 1/2 x))
(-.f32 (/.f32 1 x) 0)
(-.f32 0 (/.f32 -1 x))
(*.f32 1 (/.f32 1 x))
(.f32 x (/.f32 1 (.f32 x x)))
(.f32 x (.f32 1/2 (/.f32 2 (*.f32 x x))))
(.f32 x (.f32 1/4 (.f32 2 (/.f32 2 (.f32 x x)))))
(*.f32 (/.f32 1 x) 1)
(*.f32 2 (/.f32 1/2 x))
(*.f32 (+.f32 x x) (/.f32 (/.f32 1/2 x) x))
(.f32 (+.f32 x x) (.f32 1/2 (/.f32 1 (*.f32 x x))))
(.f32 (+.f32 x x) (.f32 1/4 (/.f32 2 (*.f32 x x))))
(*.f32 4 (/.f32 1/4 x))
(.f32 4 (.f32 1/2 (/.f32 1/2 x)))
(.f32 4 (.f32 (/.f32 1 x) 1/4))
(.f32 4 (.f32 (/.f32 1 (.f32 x x)) (.f32 x 1/4)))
(*.f32 (/.f32 2 x) 1/2)
(.f32 (.f32 x 4) (.f32 1/4 (/.f32 1 (.f32 x x))))
(.f32 (.f32 x 4) (.f32 (/.f32 2 (.f32 x x)) 1/8))
(.f32 (.f32 x 4) (*.f32 1/2 (/.f32 (/.f32 1/2 x) x)))
(.f32 -1 (.f32 (neg.f32 x) (/.f32 1 (*.f32 x x))))
(.f32 (neg.f32 x) (.f32 -1 (/.f32 1 (*.f32 x x))))
(.f32 (.f32 x 8) (.f32 (/.f32 1 (.f32 x x)) 1/8))
(*.f32 (/.f32 4 x) 1/4)
(*.f32 1/2 (/.f32 2 x))
(.f32 (.f32 x 1/2) (/.f32 2 (*.f32 x x)))
(*.f32 1/4 (/.f32 4 x))
(.f32 (/.f32 1 (.f32 x x)) x)
(.f32 (/.f32 2 (.f32 x x)) (*.f32 x 1/2))
(*.f32 (/.f32 1/2 x) 2)
(*.f32 (/.f32 1/4 x) 4)
(*.f32 (/.f32 -1 x) -1)
(*.f32 (/.f32 (/.f32 1/2 x) x) (+.f32 x x))
(.f32 (.f32 1/2 (/.f32 2 (*.f32 x x))) x)
(.f32 (.f32 1/2 (/.f32 1 (*.f32 x x))) (+.f32 x x))
(.f32 (.f32 1/4 (/.f32 1 (.f32 x x))) (.f32 x 4))
(.f32 (.f32 1/4 (/.f32 2 (*.f32 x x))) (+.f32 x x))
(.f32 (.f32 (/.f32 2 (.f32 x x)) 1/8) (.f32 x 4))
(.f32 (.f32 1/2 (/.f32 1/2 x)) 4)
(.f32 (.f32 1/2 (/.f32 (/.f32 1/2 x) x)) (*.f32 x 4))
(.f32 (.f32 1/4 (.f32 2 (/.f32 2 (.f32 x x)))) x)
(.f32 (.f32 (/.f32 1 x) 1/4) 4)
(.f32 (.f32 (/.f32 1 (.f32 x x)) (.f32 x 1/4)) 4)
(.f32 (.f32 (neg.f32 x) (/.f32 1 (*.f32 x x))) -1)
(.f32 (.f32 -1 (/.f32 1 (*.f32 x x))) (neg.f32 x))
(.f32 (.f32 (/.f32 1 (.f32 x x)) 1/8) (.f32 x 8))
(pow.f32 (/.f32 1 x) 1)
(neg.f32 (/.f32 -1 x))

Outputs
(+.f32 (/.f32 1 x) 0)
(/.f32 1 x)
(+.f32 0 (/.f32 1 x))
(/.f32 1 x)
(+.f32 -1 (-.f32 1 (/.f32 -1 x)))
(/.f32 1 x)
(+.f32 (/.f32 1/2 x) (/.f32 1/2 x))
(/.f32 1 x)
(-.f32 (/.f32 1 x) 0)
(/.f32 1 x)
(-.f32 0 (/.f32 -1 x))
(/.f32 1 x)
(*.f32 1 (/.f32 1 x))
(/.f32 1 x)
(.f32 x (/.f32 1 (.f32 x x)))
(/.f32 1 x)
(.f32 x (.f32 1/2 (/.f32 2 (*.f32 x x))))
(/.f32 1 x)
(.f32 x (.f32 1/4 (.f32 2 (/.f32 2 (.f32 x x)))))
(/.f32 1 x)
(*.f32 (/.f32 1 x) 1)
(/.f32 1 x)
(*.f32 2 (/.f32 1/2 x))
(*.f32 (/.f32 1/2 x) 2)
(*.f32 (+.f32 x x) (/.f32 (/.f32 1/2 x) x))
(/.f32 1 x)
(.f32 (+.f32 x x) (.f32 1/2 (/.f32 1 (*.f32 x x))))
(/.f32 1 x)
(.f32 (+.f32 x x) (.f32 1/4 (/.f32 2 (*.f32 x x))))
(/.f32 1 x)
(*.f32 4 (/.f32 1/4 x))
(.f32 4 (.f32 1/2 (/.f32 1/2 x)))
(*.f32 (/.f32 1/2 x) 2)
(.f32 4 (.f32 (/.f32 1 x) 1/4))
(/.f32 1 x)
(.f32 4 (.f32 (/.f32 1 (.f32 x x)) (.f32 x 1/4)))
(/.f32 1 x)
(*.f32 (/.f32 2 x) 1/2)
(*.f32 1/2 (/.f32 2 x))
(.f32 (.f32 x 4) (.f32 1/4 (/.f32 1 (.f32 x x))))
(/.f32 1 x)
(.f32 (.f32 x 4) (.f32 (/.f32 2 (.f32 x x)) 1/8))
(/.f32 1 x)
(.f32 (.f32 x 4) (*.f32 1/2 (/.f32 (/.f32 1/2 x) x)))
(/.f32 1 x)
(.f32 -1 (.f32 (neg.f32 x) (/.f32 1 (*.f32 x x))))
(/.f32 1 x)
(.f32 (neg.f32 x) (.f32 -1 (/.f32 1 (*.f32 x x))))
(/.f32 1 x)
(.f32 (.f32 x 8) (.f32 (/.f32 1 (.f32 x x)) 1/8))
(/.f32 1 x)
(*.f32 (/.f32 4 x) 1/4)
(*.f32 1/4 (/.f32 4 x))
(*.f32 1/2 (/.f32 2 x))
(.f32 (.f32 x 1/2) (/.f32 2 (*.f32 x x)))
(/.f32 1 x)
(*.f32 1/4 (/.f32 4 x))
(.f32 (/.f32 1 (.f32 x x)) x)
(/.f32 1 x)
(.f32 (/.f32 2 (.f32 x x)) (*.f32 x 1/2))
(/.f32 1 x)
(*.f32 (/.f32 1/2 x) 2)
(*.f32 (/.f32 1/4 x) 4)
(*.f32 4 (/.f32 1/4 x))
(*.f32 (/.f32 -1 x) -1)
(/.f32 1 x)
(*.f32 (/.f32 (/.f32 1/2 x) x) (+.f32 x x))
(/.f32 1 x)
(.f32 (.f32 1/2 (/.f32 2 (*.f32 x x))) x)
(/.f32 1 x)
(.f32 (.f32 1/2 (/.f32 1 (*.f32 x x))) (+.f32 x x))
(/.f32 1 x)
(.f32 (.f32 1/4 (/.f32 1 (.f32 x x))) (.f32 x 4))
(/.f32 1 x)
(.f32 (.f32 1/4 (/.f32 2 (*.f32 x x))) (+.f32 x x))
(/.f32 1 x)
(.f32 (.f32 (/.f32 2 (.f32 x x)) 1/8) (.f32 x 4))
(/.f32 1 x)
(.f32 (.f32 1/2 (/.f32 1/2 x)) 4)
(*.f32 (/.f32 1/2 x) 2)
(.f32 (.f32 1/2 (/.f32 (/.f32 1/2 x) x)) (*.f32 x 4))
(/.f32 1 x)
(.f32 (.f32 1/4 (.f32 2 (/.f32 2 (.f32 x x)))) x)
(/.f32 1 x)
(.f32 (.f32 (/.f32 1 x) 1/4) 4)
(/.f32 1 x)
(.f32 (.f32 (/.f32 1 (.f32 x x)) (.f32 x 1/4)) 4)
(/.f32 1 x)
(.f32 (.f32 (neg.f32 x) (/.f32 1 (*.f32 x x))) -1)
(/.f32 1 x)
(.f32 (.f32 -1 (/.f32 1 (*.f32 x x))) (neg.f32 x))
(/.f32 1 x)
(.f32 (.f32 (/.f32 1 (.f32 x x)) 1/8) (.f32 x 8))
(/.f32 1 x)
(pow.f32 (/.f32 1 x) 1)
(/.f32 1 x)
(neg.f32 (/.f32 -1 x))
(/.f32 1 x)

eval12.0ms (0.2%)

Compiler: Compiled 778 to 476 computations (38.8% saved)

prune85.0ms (1.7%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	52	0	52
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	52	3	55

Error

0.0b

Counts

55 → 3

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.4b	(log.f32 (-.f32 (+.f32 x x) (*.f32 1/2 (/.f32 1 x))))
✓	16.6b	(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) 1))))
✓	0.8b	(log.f32 (+.f32 x x))

Compiler

Compiled 26 to 18 computations (30.8% saved)

regimes10.0ms (0.2%)

Accuracy

Total -17.1b remaining (-4672.1%)

Threshold costs -17.1b (-4672.1%)

Counts

3 → 1

Calls

Call 1

Inputs
(log.f32 (+.f32 x x))
(log.f32 (-.f32 (+.f32 x x) (*.f32 1/2 (/.f32 1 x))))
(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) 1))))

Outputs
(log.f32 (-.f32 (+.f32 x x) (*.f32 1/2 (/.f32 1 x))))

Calls

3 calls:

3.0ms	x
3.0ms	(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) 1))))
3.0ms	(+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) 1)))

Results

Error	Segments	Branch
0.4b	1	`x`
0.4b	1	`(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) 1))))`
0.4b	1	`(+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) 1)))`

Compiler

Compiled 45 to 29 computations (35.6% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	40

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(log.f32 (-.f32 (+.f32 x x) (*.f32 1/2 (/.f32 1 x))))
(log.f32 (+.f32 x x))

Outputs
(log.f32 (-.f32 (+.f32 x x) (*.f32 1/2 (/.f32 1 x))))
(log.f32 (+.f32 x x))

Compiler

Compiled 16 to 11 computations (31.3% saved)

soundness189.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

1032×	`rational.json-simplify-2`
858×	`rational.json-simplify-35`
846×	`rational.json-simplify-41`
748×	`rational.json-simplify-59`
692×	`rational.json-simplify-51`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	213	2980
1	435	2972
2	825	2972
3	1958	2972
4	4098	2972
5	6287	2968

Stop Event

1×	node limit

Compiler

Compiled 59 to 47 computations (20.3% saved)

end55.0ms (1.1%)

Compiler: Compiled 15 to 9 computations (40% saved)

Details

analyze0.0ms (0%)

sample2.5s (50.4%)

preprocess11.0ms (0.2%)

simplify141.0ms (2.9%)

eval1.0ms (0%)

prune1.0ms (0%)

localize30.0ms (0.6%)

series4.0ms (0.1%)

rewrite75.0ms (1.5%)

simplify203.0ms (4.1%)

eval56.0ms (1.1%)

prune106.0ms (2.2%)

localize11.0ms (0.2%)

localize551.0ms (11.3%)

series1.0ms (0%)

rewrite737.0ms (15.1%)

simplify148.0ms (3%)

eval12.0ms (0.2%)

prune85.0ms (1.7%)

regimes10.0ms (0.2%)

simplify2.0ms (0%)

soundness189.0ms (3.9%)

end55.0ms (1.1%)

Profiling