Details

analyze98.0ms (3.2%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
0%	0%	100%	0%	0%	0%	0%	2
0%	0%	100%	0%	0%	0%	0%	3
16.7%	12.5%	62.5%	0%	0%	25%	0%	4
30%	18.7%	43.7%	0%	0%	37.5%	0%	5
38.9%	21.9%	34.4%	0%	0%	43.7%	0%	6
44.1%	23.4%	29.7%	0%	0%	46.9%	0%	7
47%	24.2%	27.3%	0%	0%	48.4%	0%	8
48.5%	24.6%	26.2%	0%	0%	49.2%	0%	9
49.2%	24.8%	25.6%	0%	0%	49.6%	0%	10
49.6%	24.9%	25.3%	0%	0%	49.8%	0%	11
49.8%	24.9%	25.1%	0%	0%	49.9%	0%	12

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample1.9s (63%)

Results

981.0ms	8256×	body	256	valid
807.0ms	7253×	body	256	infinite
110.0ms	1095×	body	256	invalid

Bogosity

preprocess124.0ms (4%)

Algorithm

2×	egg-herbie

Rules

1316×	`fma-neg`
1074×	`+-commutative`
1010×	`*-commutative`
776×	`distribute-neg-in`
746×	`associate-+r+`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	23
1	21	23
2	25	23
3	40	23
4	84	23
5	177	23
6	348	23
7	794	23
8	3311	23
9	4904	23
10	6285	23
11	7231	23
12	7581	23
13	7779	23
14	7887	23
0	1	1

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0

Outputs
0

Call 2

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

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

Compiler

Compiled 11 to 8 computations (27.3% saved)

simplify177.0ms (5.8%)

Algorithm

1×	egg-herbie

Rules

1316×	`fma-neg`
1074×	`+-commutative`
1010×	`*-commutative`
776×	`distribute-neg-in`
746×	`associate-+r+`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	23
1	21	23
2	25	23
3	40	23
4	84	23
5	177	23
6	348	23
7	794	23
8	3311	23
9	4904	23
10	6285	23
11	7231	23
12	7581	23
13	7779	23
14	7887	23

Stop Event

1×	node limit

Counts

1 → 2

Calls

Call 1

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

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

eval1.0ms (0%)

Compiler: Compiled 18 to 12 computations (33.3% 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

30.5b

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	30.5b	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))

Compiler

Compiled 10 to 7 computations (30% saved)

localize12.0ms (0.4%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	28.3b	(sqrt.f64 (-.f64 (*.f64 x x) 1))

Compiler

Compiled 34 to 17 computations (50% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite136.0ms (4.4%)

Algorithm

1×	batch-egg-rewrite

Rules

1530×	`add-sqr-sqrt`
1508×	`*-un-lft-identity`
1408×	`add-cube-cbrt`
1398×	`add-cbrt-cube`
1392×	`add-exp-log`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	167	13
2	2062	13

Stop Event

1×	node limit

Counts

1 → 26

Calls

Call 1

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

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

Outputs

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

simplify65.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

1370×	`associate-/l*`
1048×	`fma-def`
934×	`associate-/r*`
760×	`associate-+r+`
734×	`associate-+l+`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	116	1130
1	266	1000
2	715	878
3	2127	842
4	7095	842

Stop Event

1×	node limit

Counts

38 → 77

Calls

Call 1

Inputs
(sqrt.f64 -1)
(+.f64 (sqrt.f64 -1) (*.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3))) (+.f64 (sqrt.f64 -1) (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1)))))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3))) (+.f64 (sqrt.f64 -1) (+.f64 (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))) (*.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 (sqrt.f64 -1) 5))))))
x
(-.f64 x (*.f64 1/2 (/.f64 1 x)))
(-.f64 x (+.f64 (.f64 1/2 (/.f64 1 x)) (.f64 1/8 (/.f64 1 (pow.f64 x 3)))))
(-.f64 x (+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 5))) (*.f64 1/8 (/.f64 1 (pow.f64 x 3))))))
(*.f64 -1 x)
(+.f64 (.f64 -1 x) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (*.f64 -1 x)))
(+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 5))) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (.f64 -1 x))))
(-.f64 (+.f64 1 (sqrt.f64 (fma.f64 x x -1))) 1)
(*.f64 1 (sqrt.f64 (fma.f64 x x -1)))
(*.f64 (sqrt.f64 (fma.f64 x x -1)) 1)
(*.f64 (pow.f64 (fma.f64 x x -1) 1/4) (pow.f64 (fma.f64 x x -1) 1/4))
(*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x x -1))) (cbrt.f64 (fma.f64 x x -1)))
(*.f64 (cbrt.f64 (fma.f64 x x -1)) (cbrt.f64 (sqrt.f64 (fma.f64 x x -1))))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 x x -1)) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 x x -1))))
(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 x -1)))
(*.f64 (pow.f64 1 1/2) (sqrt.f64 (fma.f64 x x -1)))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (fma.f64 x x -1)) 2) 1/2) (pow.f64 (cbrt.f64 (fma.f64 x x -1)) 1/2))
(*.f64 (pow.f64 (+.f64 x 1) 1/2) (pow.f64 (+.f64 x -1) 1/2))
(/.f64 (sqrt.f64 (+.f64 (pow.f64 x 6) -1)) (sqrt.f64 (+.f64 (pow.f64 x 4) (fma.f64 x x 1))))
(/.f64 (sqrt.f64 (+.f64 (pow.f64 x 4) -1)) (sqrt.f64 (fma.f64 x x 1)))
(pow.f64 (fma.f64 x x -1) 1/2)
(pow.f64 (sqrt.f64 (fma.f64 x x -1)) 1)
(pow.f64 (pow.f64 (fma.f64 x x -1) 1/4) 2)
(pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x x -1))) 3)
(pow.f64 (pow.f64 (fma.f64 x x -1) 3/2) 1/3)
(fabs.f64 (sqrt.f64 (fma.f64 x x -1)))
(log.f64 (exp.f64 (sqrt.f64 (fma.f64 x x -1))))
(cbrt.f64 (pow.f64 (fma.f64 x x -1) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (fma.f64 x x -1))))
(exp.f64 (log.f64 (sqrt.f64 (fma.f64 x x -1))))
(exp.f64 (*.f64 (log.f64 (fma.f64 x x -1)) 1/2))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (fma.f64 x x -1))) 1))
(log1p.f64 (expm1.f64 (sqrt.f64 (fma.f64 x x -1))))

Outputs
(sqrt.f64 -1)
(+.f64 (sqrt.f64 -1) (*.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))))
(+.f64 (sqrt.f64 -1) (.f64 1/2 (/.f64 (.f64 x x) (sqrt.f64 -1))))
(fma.f64 1/2 (/.f64 x (/.f64 (sqrt.f64 -1) x)) (sqrt.f64 -1))
(fma.f64 1/2 (*.f64 (/.f64 x (sqrt.f64 -1)) x) (sqrt.f64 -1))
(fma.f64 1/2 (*.f64 x (/.f64 x (sqrt.f64 -1))) (sqrt.f64 -1))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3))) (+.f64 (sqrt.f64 -1) (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1)))))
(fma.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3)) (+.f64 (sqrt.f64 -1) (.f64 1/2 (/.f64 (.f64 x x) (sqrt.f64 -1)))))
(+.f64 (fma.f64 1/2 (/.f64 x (/.f64 (sqrt.f64 -1) x)) (sqrt.f64 -1)) (*.f64 1/8 (/.f64 (pow.f64 x 4) (sqrt.f64 -1))))
(fma.f64 1/2 (*.f64 (/.f64 x (sqrt.f64 -1)) x) (fma.f64 1/8 (/.f64 (pow.f64 x 4) (sqrt.f64 -1)) (sqrt.f64 -1)))
(+.f64 (sqrt.f64 -1) (.f64 (.f64 x (/.f64 x (sqrt.f64 -1))) (+.f64 1/2 (/.f64 (*.f64 x x) 8))))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3))) (+.f64 (sqrt.f64 -1) (+.f64 (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))) (*.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 (sqrt.f64 -1) 5))))))
(fma.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3)) (+.f64 (sqrt.f64 -1) (fma.f64 1/2 (/.f64 (.f64 x x) (sqrt.f64 -1)) (.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 (sqrt.f64 -1) 5))))))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 x 4) (sqrt.f64 -1))) (+.f64 (sqrt.f64 -1) (fma.f64 1/2 (/.f64 x (/.f64 (sqrt.f64 -1) x)) (.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 (sqrt.f64 -1) 5))))))
(fma.f64 1/8 (/.f64 (pow.f64 x 4) (sqrt.f64 -1)) (fma.f64 1/2 (*.f64 (/.f64 x (sqrt.f64 -1)) x) (fma.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 (sqrt.f64 -1) 5)) (sqrt.f64 -1))))
(+.f64 (sqrt.f64 -1) (fma.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 (sqrt.f64 -1) 5)) (.f64 (.f64 x (/.f64 x (sqrt.f64 -1))) (+.f64 1/2 (/.f64 (*.f64 x x) 8)))))
x
(-.f64 x (*.f64 1/2 (/.f64 1 x)))
(-.f64 x (/.f64 1/2 x))
(+.f64 x (/.f64 -1/2 x))
(-.f64 x (+.f64 (.f64 1/2 (/.f64 1 x)) (.f64 1/8 (/.f64 1 (pow.f64 x 3)))))
(-.f64 x (+.f64 (/.f64 1/2 x) (/.f64 1/8 (pow.f64 x 3))))
(+.f64 x (-.f64 (/.f64 -1/2 x) (/.f64 1/8 (pow.f64 x 3))))
(-.f64 (+.f64 x (/.f64 -1/2 x)) (/.f64 1/8 (pow.f64 x 3)))
(-.f64 (/.f64 -1/2 x) (-.f64 (/.f64 1/8 (pow.f64 x 3)) x))
(-.f64 x (+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 5))) (*.f64 1/8 (/.f64 1 (pow.f64 x 3))))))
(-.f64 x (+.f64 (/.f64 1/2 x) (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/16 (pow.f64 x 5)))))
(+.f64 x (-.f64 (-.f64 (/.f64 -1/2 x) (/.f64 1/8 (pow.f64 x 3))) (/.f64 1/16 (pow.f64 x 5))))
(+.f64 x (-.f64 (+.f64 (/.f64 -1/2 x) (/.f64 -1/8 (pow.f64 x 3))) (/.f64 1/16 (pow.f64 x 5))))
(*.f64 -1 x)
(neg.f64 x)
(+.f64 (.f64 -1 x) (.f64 1/2 (/.f64 1 x)))
(fma.f64 -1 x (/.f64 1/2 x))
(-.f64 (/.f64 1/2 x) x)
(+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (*.f64 -1 x)))
(+.f64 (/.f64 1/2 x) (+.f64 (/.f64 1/8 (pow.f64 x 3)) (neg.f64 x)))
(+.f64 (/.f64 1/2 x) (-.f64 (/.f64 1/8 (pow.f64 x 3)) x))
(+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 5))) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (.f64 -1 x))))
(+.f64 (/.f64 1/2 x) (+.f64 (/.f64 1/16 (pow.f64 x 5)) (+.f64 (/.f64 1/8 (pow.f64 x 3)) (neg.f64 x))))
(+.f64 (/.f64 1/2 x) (+.f64 (/.f64 1/16 (pow.f64 x 5)) (-.f64 (/.f64 1/8 (pow.f64 x 3)) x)))
(+.f64 (/.f64 1/2 x) (+.f64 (/.f64 1/8 (pow.f64 x 3)) (-.f64 (/.f64 1/16 (pow.f64 x 5)) x)))
(-.f64 (+.f64 1 (sqrt.f64 (fma.f64 x x -1))) 1)
(+.f64 1 (-.f64 (sqrt.f64 (fma.f64 x x -1)) 1))
(+.f64 (sqrt.f64 (fma.f64 x x -1)) 0)
(sqrt.f64 (fma.f64 x x -1))
(*.f64 1 (sqrt.f64 (fma.f64 x x -1)))
(+.f64 1 (-.f64 (sqrt.f64 (fma.f64 x x -1)) 1))
(+.f64 (sqrt.f64 (fma.f64 x x -1)) 0)
(sqrt.f64 (fma.f64 x x -1))
(*.f64 (sqrt.f64 (fma.f64 x x -1)) 1)
(+.f64 1 (-.f64 (sqrt.f64 (fma.f64 x x -1)) 1))
(+.f64 (sqrt.f64 (fma.f64 x x -1)) 0)
(sqrt.f64 (fma.f64 x x -1))
(*.f64 (pow.f64 (fma.f64 x x -1) 1/4) (pow.f64 (fma.f64 x x -1) 1/4))
(+.f64 1 (-.f64 (sqrt.f64 (fma.f64 x x -1)) 1))
(+.f64 (sqrt.f64 (fma.f64 x x -1)) 0)
(sqrt.f64 (fma.f64 x x -1))
(*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x x -1))) (cbrt.f64 (fma.f64 x x -1)))
(*.f64 (cbrt.f64 (fma.f64 x x -1)) (cbrt.f64 (sqrt.f64 (fma.f64 x x -1))))
(*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x x -1))) (cbrt.f64 (fma.f64 x x -1)))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 x x -1)) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 x x -1))))
(*.f64 (fabs.f64 (cbrt.f64 (fma.f64 x x -1))) (sqrt.f64 (cbrt.f64 (fma.f64 x x -1))))
(*.f64 (cbrt.f64 (fma.f64 x x -1)) (sqrt.f64 (cbrt.f64 (fma.f64 x x -1))))
(pow.f64 (cbrt.f64 (fma.f64 x x -1)) 3/2)
(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 x -1)))
(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 -1 x)))
(*.f64 (pow.f64 1 1/2) (sqrt.f64 (fma.f64 x x -1)))
(+.f64 1 (-.f64 (sqrt.f64 (fma.f64 x x -1)) 1))
(+.f64 (sqrt.f64 (fma.f64 x x -1)) 0)
(sqrt.f64 (fma.f64 x x -1))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (fma.f64 x x -1)) 2) 1/2) (pow.f64 (cbrt.f64 (fma.f64 x x -1)) 1/2))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 x x -1)) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 x x -1))))
(*.f64 (fabs.f64 (cbrt.f64 (fma.f64 x x -1))) (sqrt.f64 (cbrt.f64 (fma.f64 x x -1))))
(*.f64 (cbrt.f64 (fma.f64 x x -1)) (sqrt.f64 (cbrt.f64 (fma.f64 x x -1))))
(pow.f64 (cbrt.f64 (fma.f64 x x -1)) 3/2)
(*.f64 (pow.f64 (+.f64 x 1) 1/2) (pow.f64 (+.f64 x -1) 1/2))
(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 -1 x)))
(/.f64 (sqrt.f64 (+.f64 (pow.f64 x 6) -1)) (sqrt.f64 (+.f64 (pow.f64 x 4) (fma.f64 x x 1))))
(/.f64 (sqrt.f64 (+.f64 -1 (pow.f64 x 6))) (sqrt.f64 (+.f64 (pow.f64 x 4) (fma.f64 x x 1))))
(/.f64 (sqrt.f64 (+.f64 (pow.f64 x 4) -1)) (sqrt.f64 (fma.f64 x x 1)))
(/.f64 (sqrt.f64 (+.f64 -1 (pow.f64 x 4))) (sqrt.f64 (fma.f64 x x 1)))
(/.f64 (sqrt.f64 (+.f64 -1 (pow.f64 x 4))) (hypot.f64 1 x))
(pow.f64 (fma.f64 x x -1) 1/2)
(+.f64 1 (-.f64 (sqrt.f64 (fma.f64 x x -1)) 1))
(+.f64 (sqrt.f64 (fma.f64 x x -1)) 0)
(sqrt.f64 (fma.f64 x x -1))
(pow.f64 (sqrt.f64 (fma.f64 x x -1)) 1)
(+.f64 1 (-.f64 (sqrt.f64 (fma.f64 x x -1)) 1))
(+.f64 (sqrt.f64 (fma.f64 x x -1)) 0)
(sqrt.f64 (fma.f64 x x -1))
(pow.f64 (pow.f64 (fma.f64 x x -1) 1/4) 2)
(+.f64 1 (-.f64 (sqrt.f64 (fma.f64 x x -1)) 1))
(+.f64 (sqrt.f64 (fma.f64 x x -1)) 0)
(sqrt.f64 (fma.f64 x x -1))
(pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x x -1))) 3)
(+.f64 1 (-.f64 (sqrt.f64 (fma.f64 x x -1)) 1))
(+.f64 (sqrt.f64 (fma.f64 x x -1)) 0)
(sqrt.f64 (fma.f64 x x -1))
(pow.f64 (pow.f64 (fma.f64 x x -1) 3/2) 1/3)
(cbrt.f64 (pow.f64 (fma.f64 x x -1) 3/2))
(fabs.f64 (sqrt.f64 (fma.f64 x x -1)))
(+.f64 1 (-.f64 (sqrt.f64 (fma.f64 x x -1)) 1))
(+.f64 (sqrt.f64 (fma.f64 x x -1)) 0)
(sqrt.f64 (fma.f64 x x -1))
(log.f64 (exp.f64 (sqrt.f64 (fma.f64 x x -1))))
(+.f64 1 (-.f64 (sqrt.f64 (fma.f64 x x -1)) 1))
(+.f64 (sqrt.f64 (fma.f64 x x -1)) 0)
(sqrt.f64 (fma.f64 x x -1))
(cbrt.f64 (pow.f64 (fma.f64 x x -1) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (fma.f64 x x -1))))
(+.f64 1 (-.f64 (sqrt.f64 (fma.f64 x x -1)) 1))
(+.f64 (sqrt.f64 (fma.f64 x x -1)) 0)
(sqrt.f64 (fma.f64 x x -1))
(exp.f64 (log.f64 (sqrt.f64 (fma.f64 x x -1))))
(+.f64 1 (-.f64 (sqrt.f64 (fma.f64 x x -1)) 1))
(+.f64 (sqrt.f64 (fma.f64 x x -1)) 0)
(sqrt.f64 (fma.f64 x x -1))
(exp.f64 (*.f64 (log.f64 (fma.f64 x x -1)) 1/2))
(+.f64 1 (-.f64 (sqrt.f64 (fma.f64 x x -1)) 1))
(+.f64 (sqrt.f64 (fma.f64 x x -1)) 0)
(sqrt.f64 (fma.f64 x x -1))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (fma.f64 x x -1))) 1))
(+.f64 1 (-.f64 (sqrt.f64 (fma.f64 x x -1)) 1))
(+.f64 (sqrt.f64 (fma.f64 x x -1)) 0)
(sqrt.f64 (fma.f64 x x -1))
(log1p.f64 (expm1.f64 (sqrt.f64 (fma.f64 x x -1))))
(+.f64 1 (-.f64 (sqrt.f64 (fma.f64 x x -1)) 1))
(+.f64 (sqrt.f64 (fma.f64 x x -1)) 0)
(sqrt.f64 (fma.f64 x x -1))

eval59.0ms (1.9%)

Compiler: Compiled 1169 to 879 computations (24.8% saved)

prune11.0ms (0.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	75	2	77
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	75	3	78

Error

Counts

78 → 3

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.1b	(log.f64 (+.f64 x (-.f64 x (/.f64 1/2 x))))
✓	30.5b	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
▶	0.4b	(log.f64 (+.f64 x x))

Compiler

Compiled 24 to 16 computations (33.3% saved)

localize4.0ms (0.1%)

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

localize13.0ms (0.4%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 26 to 16 computations (38.5% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite94.0ms (3.1%)

Algorithm

1×	batch-egg-rewrite

Rules

1594×	`associate-*r/`
956×	`associate-*l/`
818×	`*-commutative`
718×	`distribute-lft-in`
702×	`distribute-rgt-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	19
1	170	19
2	2496	19

Stop Event

1×	node limit

Counts

1 → 91

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 x (-.f64 (/.f64 1/2 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 x x) (/.f64 1/2 x))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 x)) (-.f64 1 (+.f64 x (/.f64 -1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 x)) (+.f64 1 (-.f64 (/.f64 1/2 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 x (+.f64 x (/.f64 -1/2 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 x (/.f64 -1/2 x)))) (-.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 x (/.f64 (+.f64 x (/.f64 1/2 x)) x)) (-.f64 (/.f64 (/.f64 1/4 (.f64 x x)) (+.f64 x (/.f64 1/2 x))) x))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 x 3) (fma.f64 x x (.f64 (/.f64 1/2 x) (+.f64 x (/.f64 1/2 x))))) (-.f64 (/.f64 1/8 (.f64 (fma.f64 x x (.f64 (/.f64 1/2 x) (+.f64 x (/.f64 1/2 x)))) (pow.f64 x 3))) x))))) (#(struct:change 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Outputs

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

simplify80.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

1584×	`associate-*r/`
1262×	`associate-*l/`
1240×	`associate-+l+`
1172×	`associate-+r+`
594×	`+-commutative`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	274	5595
1	834	4875
2	3843	4827

Stop Event

1×	node limit

Counts

103 → 157

Calls

Call 1

Inputs
(/.f64 -1/2 x)
(-.f64 (.f64 2 x) (.f64 1/2 (/.f64 1 x)))
(-.f64 (.f64 2 x) (.f64 1/2 (/.f64 1 x)))
(-.f64 (.f64 2 x) (.f64 1/2 (/.f64 1 x)))
(*.f64 2 x)
(-.f64 (.f64 2 x) (.f64 1/2 (/.f64 1 x)))
(-.f64 (.f64 2 x) (.f64 1/2 (/.f64 1 x)))
(-.f64 (.f64 2 x) (.f64 1/2 (/.f64 1 x)))
(*.f64 2 x)
(-.f64 (.f64 2 x) (.f64 1/2 (/.f64 1 x)))
(-.f64 (.f64 2 x) (.f64 1/2 (/.f64 1 x)))
(-.f64 (.f64 2 x) (.f64 1/2 (/.f64 1 x)))
(-.f64 x (-.f64 (/.f64 1/2 x) x))
(-.f64 (+.f64 x x) (/.f64 1/2 x))
(-.f64 (exp.f64 (log1p.f64 x)) (-.f64 1 (+.f64 x (/.f64 -1/2 x))))
(-.f64 (exp.f64 (log1p.f64 x)) (+.f64 1 (-.f64 (/.f64 1/2 x) x)))
(-.f64 (exp.f64 (log1p.f64 (+.f64 x (+.f64 x (/.f64 -1/2 x))))) 1)
(-.f64 (exp.f64 (log1p.f64 (+.f64 x (/.f64 -1/2 x)))) (-.f64 1 x))
(-.f64 (/.f64 x (/.f64 (+.f64 x (/.f64 1/2 x)) x)) (-.f64 (/.f64 (/.f64 1/4 (*.f64 x x)) (+.f64 x (/.f64 1/2 x))) x))
(-.f64 (/.f64 (pow.f64 x 3) (fma.f64 x x (.f64 (/.f64 1/2 x) (+.f64 x (/.f64 1/2 x))))) (-.f64 (/.f64 1/8 (.f64 (fma.f64 x x (*.f64 (/.f64 1/2 x) (+.f64 x (/.f64 1/2 x)))) (pow.f64 x 3))) x))
(-.f64 (/.f64 x (/.f64 (+.f64 (/.f64 1/2 x) (-.f64 x x)) x)) (/.f64 (pow.f64 (+.f64 x (/.f64 -1/2 x)) 2) (+.f64 (/.f64 1/2 x) (-.f64 x x))))
(-.f64 (+.f64 x (exp.f64 (log1p.f64 (+.f64 x (/.f64 -1/2 x))))) 1)
(-.f64 (+.f64 x (/.f64 x (/.f64 (+.f64 x (/.f64 1/2 x)) x))) (/.f64 (/.f64 1/4 (*.f64 x x)) (+.f64 x (/.f64 1/2 x))))
(-.f64 (+.f64 x (/.f64 (pow.f64 x 3) (fma.f64 x x (.f64 (/.f64 1/2 x) (+.f64 x (/.f64 1/2 x)))))) (/.f64 1/8 (.f64 (fma.f64 x x (*.f64 (/.f64 1/2 x) (+.f64 x (/.f64 1/2 x)))) (pow.f64 x 3))))
(-.f64 (+.f64 (+.f64 x (/.f64 -1/2 x)) (exp.f64 (log1p.f64 x))) 1)
(-.f64 (+.f64 (+.f64 x x) 0) (/.f64 1/2 x))
(*.f64 (+.f64 x (+.f64 x (/.f64 -1/2 x))) 1)
(*.f64 1 (+.f64 x (+.f64 x (/.f64 -1/2 x))))
(*.f64 (sqrt.f64 (+.f64 x (+.f64 x (/.f64 -1/2 x)))) (sqrt.f64 (+.f64 x (+.f64 x (/.f64 -1/2 x)))))
(*.f64 (cbrt.f64 (+.f64 x (+.f64 x (/.f64 -1/2 x)))) (pow.f64 (cbrt.f64 (+.f64 x (+.f64 x (/.f64 -1/2 x)))) 2))
(*.f64 (pow.f64 (cbrt.f64 (+.f64 x (+.f64 x (/.f64 -1/2 x)))) 2) (cbrt.f64 (+.f64 x (+.f64 x (/.f64 -1/2 x)))))
(.f64 (-.f64 (.f64 x x) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 2)) (/.f64 1 (+.f64 (/.f64 1/2 x) (-.f64 x x))))
(.f64 (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 3)) (/.f64 1 (fma.f64 x x (.f64 (+.f64 x (/.f64 -1/2 x)) (+.f64 (/.f64 -1/2 x) (-.f64 x x))))))
(.f64 (/.f64 1 (+.f64 (/.f64 1/2 x) (-.f64 x x))) (-.f64 (.f64 x x) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 2)))
(.f64 (/.f64 1 (fma.f64 x x (.f64 (+.f64 x (/.f64 -1/2 x)) (+.f64 (/.f64 -1/2 x) (-.f64 x x))))) (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 3)))
(.f64 (/.f64 (-.f64 (.f64 x x) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 2)) (-.f64 (*.f64 x x) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 2))) (+.f64 x (+.f64 x (/.f64 -1/2 x))))
(.f64 (/.f64 (-.f64 (.f64 x x) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 2)) (-.f64 (pow.f64 x 3) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 3))) (+.f64 (.f64 x x) (.f64 (+.f64 x (/.f64 -1/2 x)) (+.f64 x (+.f64 x (/.f64 -1/2 x))))))
(.f64 (/.f64 (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 3)) (-.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 (+.f64 x (/.f64 -1/2 x)) (+.f64 (/.f64 -1/2 x) (-.f64 x x))) (.f64 (+.f64 x (/.f64 -1/2 x)) (+.f64 (/.f64 -1/2 x) (-.f64 x x)))))) (-.f64 (.f64 x x) (*.f64 (+.f64 x (/.f64 -1/2 x)) (+.f64 (/.f64 -1/2 x) (-.f64 x x)))))
(.f64 (/.f64 (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 3)) (+.f64 (pow.f64 (.f64 x x) 3) (pow.f64 (.f64 (+.f64 x (/.f64 -1/2 x)) (+.f64 (/.f64 -1/2 x) (-.f64 x x))) 3))) (+.f64 (.f64 (.f64 x x) (.f64 x x)) (-.f64 (.f64 (.f64 (+.f64 x (/.f64 -1/2 x)) (+.f64 (/.f64 -1/2 x) (-.f64 x x))) (.f64 (+.f64 x (/.f64 -1/2 x)) (+.f64 (/.f64 -1/2 x) (-.f64 x x)))) (.f64 (.f64 x x) (.f64 (+.f64 x (/.f64 -1/2 x)) (+.f64 (/.f64 -1/2 x) (-.f64 x x)))))))
(/.f64 (+.f64 x (+.f64 x (/.f64 -1/2 x))) (/.f64 (+.f64 (/.f64 1/2 x) (-.f64 x x)) (+.f64 (/.f64 1/2 x) (-.f64 x x))))
(/.f64 1 (/.f64 1 (+.f64 x (+.f64 x (/.f64 -1/2 x)))))
(/.f64 (-.f64 (*.f64 x x) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 2)) (+.f64 (/.f64 1/2 x) (-.f64 x x)))
(/.f64 (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 3)) (fma.f64 x x (*.f64 (+.f64 x (/.f64 -1/2 x)) (+.f64 (/.f64 -1/2 x) (-.f64 x x)))))
(/.f64 (fma.f64 x x (.f64 (+.f64 x (/.f64 -1/2 x)) (+.f64 (/.f64 -1/2 x) (-.f64 x x)))) (/.f64 (fma.f64 x x (.f64 (+.f64 x (/.f64 -1/2 x)) (+.f64 (/.f64 -1/2 x) (-.f64 x x)))) (+.f64 x (+.f64 x (/.f64 -1/2 x)))))
(/.f64 (sqrt.f64 (-.f64 (.f64 x x) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 2))) (/.f64 (+.f64 (/.f64 1/2 x) (-.f64 x x)) (sqrt.f64 (-.f64 (.f64 x x) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 2)))))
(/.f64 (sqrt.f64 (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 3))) (/.f64 (fma.f64 x x (*.f64 (+.f64 x (/.f64 -1/2 x)) (+.f64 (/.f64 -1/2 x) (-.f64 x x)))) (sqrt.f64 (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 3)))))
(/.f64 (.f64 (cbrt.f64 (-.f64 (.f64 x x) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 2))) (cbrt.f64 (-.f64 (.f64 x x) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 2)))) (/.f64 (+.f64 (/.f64 1/2 x) (-.f64 x x)) (cbrt.f64 (-.f64 (.f64 x x) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 2)))))
(/.f64 (.f64 (cbrt.f64 (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 3))) (cbrt.f64 (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 3)))) (/.f64 (fma.f64 x x (.f64 (+.f64 x (/.f64 -1/2 x)) (+.f64 (/.f64 -1/2 x) (-.f64 x x)))) (cbrt.f64 (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 3)))))
(/.f64 (-.f64 (.f64 (pow.f64 x 3) (pow.f64 x 3)) (.f64 (pow.f64 (+.f64 x (/.f64 -1/2 x)) 3) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 3))) (.f64 (fma.f64 x x (.f64 (+.f64 x (/.f64 -1/2 x)) (+.f64 (/.f64 -1/2 x) (-.f64 x x)))) (-.f64 (pow.f64 x 3) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 3))))
(/.f64 (-.f64 (pow.f64 (+.f64 x (/.f64 -1/2 x)) 2) (*.f64 x x)) (+.f64 (/.f64 -1/2 x) (-.f64 x x)))
(/.f64 (-.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (pow.f64 (+.f64 x (/.f64 -1/2 x)) 2) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 2))) (.f64 (+.f64 (/.f64 1/2 x) (-.f64 x x)) (+.f64 (pow.f64 (+.f64 x (/.f64 -1/2 x)) 2) (.f64 x x))))
(/.f64 (-.f64 (.f64 (+.f64 x x) (+.f64 x x)) (/.f64 1/4 (.f64 x x))) (+.f64 (/.f64 1/2 x) (+.f64 x x)))
(/.f64 (+.f64 (pow.f64 (pow.f64 x 3) 3) (pow.f64 (pow.f64 (+.f64 x (/.f64 -1/2 x)) 3) 3)) (.f64 (fma.f64 x x (.f64 (+.f64 x (/.f64 -1/2 x)) (+.f64 (/.f64 -1/2 x) (-.f64 x x)))) (+.f64 (.f64 (pow.f64 x 3) (pow.f64 x 3)) (-.f64 (.f64 (pow.f64 (+.f64 x (/.f64 -1/2 x)) 3) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 3)) (*.f64 (pow.f64 x 3) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 3))))))
(/.f64 (-.f64 (pow.f64 (.f64 x x) 3) (pow.f64 (pow.f64 (+.f64 x (/.f64 -1/2 x)) 2) 3)) (.f64 (+.f64 (/.f64 1/2 x) (-.f64 x x)) (+.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 (.f64 (pow.f64 (+.f64 x (/.f64 -1/2 x)) 2) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 2)) (.f64 (pow.f64 (+.f64 x (/.f64 -1/2 x)) 2) (.f64 x x))))))
(/.f64 (-.f64 (pow.f64 (+.f64 x x) 3) (/.f64 1/8 (pow.f64 x 3))) (+.f64 (.f64 (+.f64 x x) (+.f64 x x)) (+.f64 (/.f64 1/4 (.f64 x x)) (*.f64 (/.f64 1/2 x) (+.f64 x x)))))
(/.f64 (neg.f64 (-.f64 (*.f64 x x) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 2))) (neg.f64 (+.f64 (/.f64 1/2 x) (-.f64 x x))))
(/.f64 (neg.f64 (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 3))) (neg.f64 (fma.f64 x x (*.f64 (+.f64 x (/.f64 -1/2 x)) (+.f64 (/.f64 -1/2 x) (-.f64 x x))))))
(/.f64 (.f64 1 (-.f64 (pow.f64 (+.f64 x (/.f64 -1/2 x)) 2) (.f64 x x))) (+.f64 (/.f64 -1/2 x) (-.f64 x x)))
(/.f64 (.f64 1 (-.f64 (.f64 (+.f64 x x) (+.f64 x x)) (/.f64 1/4 (*.f64 x x)))) (+.f64 (/.f64 1/2 x) (+.f64 x x)))
(/.f64 (.f64 1 (-.f64 (pow.f64 (+.f64 x x) 3) (/.f64 1/8 (pow.f64 x 3)))) (+.f64 (.f64 (+.f64 x x) (+.f64 x x)) (+.f64 (/.f64 1/4 (.f64 x x)) (.f64 (/.f64 1/2 x) (+.f64 x x)))))
(/.f64 (.f64 1 (neg.f64 (-.f64 (.f64 x x) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 2)))) (neg.f64 (+.f64 (/.f64 1/2 x) (-.f64 x x))))
(/.f64 (.f64 1 (neg.f64 (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 3)))) (neg.f64 (fma.f64 x x (.f64 (+.f64 x (/.f64 -1/2 x)) (+.f64 (/.f64 -1/2 x) (-.f64 x x))))))
(/.f64 (.f64 (sqrt.f64 (+.f64 x (+.f64 x (/.f64 -1/2 x)))) (sqrt.f64 (-.f64 (.f64 x x) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 2)))) (sqrt.f64 (+.f64 (/.f64 1/2 x) (-.f64 x x))))
(/.f64 (.f64 (sqrt.f64 (+.f64 x (+.f64 x (/.f64 -1/2 x)))) (sqrt.f64 (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 3)))) (sqrt.f64 (fma.f64 x x (.f64 (+.f64 x (/.f64 -1/2 x)) (+.f64 (/.f64 -1/2 x) (-.f64 x x))))))
(/.f64 (.f64 (pow.f64 (cbrt.f64 (+.f64 x (+.f64 x (/.f64 -1/2 x)))) 2) (cbrt.f64 (-.f64 (.f64 x x) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 2)))) (cbrt.f64 (+.f64 (/.f64 1/2 x) (-.f64 x x))))
(/.f64 (.f64 (pow.f64 (cbrt.f64 (+.f64 x (+.f64 x (/.f64 -1/2 x)))) 2) (cbrt.f64 (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 3)))) (cbrt.f64 (fma.f64 x x (.f64 (+.f64 x (/.f64 -1/2 x)) (+.f64 (/.f64 -1/2 x) (-.f64 x x))))))
(/.f64 (.f64 (-.f64 (pow.f64 (+.f64 x (/.f64 -1/2 x)) 2) (.f64 x x)) 1) (+.f64 (/.f64 -1/2 x) (-.f64 x x)))
(/.f64 (.f64 (-.f64 (.f64 (+.f64 x x) (+.f64 x x)) (/.f64 1/4 (*.f64 x x))) 1) (+.f64 (/.f64 1/2 x) (+.f64 x x)))
(/.f64 (.f64 (-.f64 (pow.f64 (+.f64 x x) 3) (/.f64 1/8 (pow.f64 x 3))) 1) (+.f64 (.f64 (+.f64 x x) (+.f64 x x)) (+.f64 (/.f64 1/4 (.f64 x x)) (.f64 (/.f64 1/2 x) (+.f64 x x)))))
(/.f64 (.f64 (neg.f64 (-.f64 (.f64 x x) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 2))) 1) (neg.f64 (+.f64 (/.f64 1/2 x) (-.f64 x x))))
(/.f64 (.f64 (neg.f64 (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 3))) 1) (neg.f64 (fma.f64 x x (.f64 (+.f64 x (/.f64 -1/2 x)) (+.f64 (/.f64 -1/2 x) (-.f64 x x))))))
(/.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x x) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 2))) (sqrt.f64 (+.f64 x (+.f64 x (/.f64 -1/2 x))))) (sqrt.f64 (+.f64 (/.f64 1/2 x) (-.f64 x x))))
(/.f64 (.f64 (sqrt.f64 (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 3))) (sqrt.f64 (+.f64 x (+.f64 x (/.f64 -1/2 x))))) (sqrt.f64 (fma.f64 x x (.f64 (+.f64 x (/.f64 -1/2 x)) (+.f64 (/.f64 -1/2 x) (-.f64 x x))))))
(/.f64 (.f64 (cbrt.f64 (-.f64 (.f64 x x) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 2))) (pow.f64 (cbrt.f64 (+.f64 x (+.f64 x (/.f64 -1/2 x)))) 2)) (cbrt.f64 (+.f64 (/.f64 1/2 x) (-.f64 x x))))
(/.f64 (.f64 (cbrt.f64 (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 3))) (pow.f64 (cbrt.f64 (+.f64 x (+.f64 x (/.f64 -1/2 x)))) 2)) (cbrt.f64 (fma.f64 x x (.f64 (+.f64 x (/.f64 -1/2 x)) (+.f64 (/.f64 -1/2 x) (-.f64 x x))))))
(/.f64 (.f64 (-.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (pow.f64 (+.f64 x (/.f64 -1/2 x)) 2) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 2))) (/.f64 1 (+.f64 (/.f64 1/2 x) (-.f64 x x)))) (+.f64 (pow.f64 (+.f64 x (/.f64 -1/2 x)) 2) (.f64 x x)))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 x x) 3) (pow.f64 (pow.f64 (+.f64 x (/.f64 -1/2 x)) 2) 3)) (/.f64 1 (+.f64 (/.f64 1/2 x) (-.f64 x x)))) (+.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 (.f64 (pow.f64 (+.f64 x (/.f64 -1/2 x)) 2) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 2)) (.f64 (pow.f64 (+.f64 x (/.f64 -1/2 x)) 2) (.f64 x x)))))
(/.f64 (.f64 (-.f64 (.f64 (pow.f64 x 3) (pow.f64 x 3)) (.f64 (pow.f64 (+.f64 x (/.f64 -1/2 x)) 3) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 3))) (/.f64 1 (fma.f64 x x (.f64 (+.f64 x (/.f64 -1/2 x)) (+.f64 (/.f64 -1/2 x) (-.f64 x x)))))) (-.f64 (pow.f64 x 3) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 3)))
(/.f64 (.f64 (+.f64 (pow.f64 (pow.f64 x 3) 3) (pow.f64 (pow.f64 (+.f64 x (/.f64 -1/2 x)) 3) 3)) (/.f64 1 (fma.f64 x x (.f64 (+.f64 x (/.f64 -1/2 x)) (+.f64 (/.f64 -1/2 x) (-.f64 x x)))))) (+.f64 (.f64 (pow.f64 x 3) (pow.f64 x 3)) (-.f64 (.f64 (pow.f64 (+.f64 x (/.f64 -1/2 x)) 3) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 3)) (*.f64 (pow.f64 x 3) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 3)))))
(/.f64 (/.f64 (-.f64 (*.f64 x x) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 2)) 1) (+.f64 (/.f64 1/2 x) (-.f64 x x)))
(/.f64 (/.f64 (-.f64 (*.f64 x x) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 2)) (sqrt.f64 (+.f64 (/.f64 1/2 x) (-.f64 x x)))) (sqrt.f64 (+.f64 (/.f64 1/2 x) (-.f64 x x))))
(/.f64 (/.f64 (-.f64 (.f64 x x) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 2)) (.f64 (cbrt.f64 (+.f64 (/.f64 1/2 x) (-.f64 x x))) (cbrt.f64 (+.f64 (/.f64 1/2 x) (-.f64 x x))))) (cbrt.f64 (+.f64 (/.f64 1/2 x) (-.f64 x x))))
(/.f64 (/.f64 (-.f64 (*.f64 x x) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 2)) (+.f64 (sqrt.f64 (+.f64 x (/.f64 -1/2 x))) (sqrt.f64 x))) (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x (/.f64 -1/2 x)))))
(/.f64 (/.f64 (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 3)) 1) (fma.f64 x x (*.f64 (+.f64 x (/.f64 -1/2 x)) (+.f64 (/.f64 -1/2 x) (-.f64 x x)))))
(/.f64 (/.f64 (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 3)) (sqrt.f64 (fma.f64 x x (.f64 (+.f64 x (/.f64 -1/2 x)) (+.f64 (/.f64 -1/2 x) (-.f64 x x)))))) (sqrt.f64 (fma.f64 x x (.f64 (+.f64 x (/.f64 -1/2 x)) (+.f64 (/.f64 -1/2 x) (-.f64 x x))))))
(/.f64 (/.f64 (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 3)) (.f64 (cbrt.f64 (fma.f64 x x (.f64 (+.f64 x (/.f64 -1/2 x)) (+.f64 (/.f64 -1/2 x) (-.f64 x x))))) (cbrt.f64 (fma.f64 x x (.f64 (+.f64 x (/.f64 -1/2 x)) (+.f64 (/.f64 -1/2 x) (-.f64 x x))))))) (cbrt.f64 (fma.f64 x x (.f64 (+.f64 x (/.f64 -1/2 x)) (+.f64 (/.f64 -1/2 x) (-.f64 x x))))))
(pow.f64 (+.f64 x (+.f64 x (/.f64 -1/2 x))) 1)
(pow.f64 (sqrt.f64 (+.f64 x (+.f64 x (/.f64 -1/2 x)))) 2)
(pow.f64 (cbrt.f64 (+.f64 x (+.f64 x (/.f64 -1/2 x)))) 3)
(pow.f64 (pow.f64 (+.f64 x (+.f64 x (/.f64 -1/2 x))) 3) 1/3)
(sqrt.f64 (pow.f64 (+.f64 x (+.f64 x (/.f64 -1/2 x))) 2))
(log.f64 (exp.f64 (+.f64 x (+.f64 x (/.f64 -1/2 x)))))
(log.f64 (+.f64 1 (expm1.f64 (+.f64 x (+.f64 x (/.f64 -1/2 x))))))
(cbrt.f64 (pow.f64 (+.f64 x (+.f64 x (/.f64 -1/2 x))) 3))
(expm1.f64 (log1p.f64 (+.f64 x (+.f64 x (/.f64 -1/2 x)))))
(exp.f64 (log.f64 (+.f64 x (+.f64 x (/.f64 -1/2 x)))))
(log1p.f64 (expm1.f64 (+.f64 x (+.f64 x (/.f64 -1/2 x)))))
(fma.f64 1 x (+.f64 x (/.f64 -1/2 x)))
(fma.f64 1 (+.f64 x (/.f64 -1/2 x)) x)
(fma.f64 (sqrt.f64 (+.f64 x (/.f64 -1/2 x))) (sqrt.f64 (+.f64 x (/.f64 -1/2 x))) x)
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (+.f64 x (/.f64 -1/2 x)))
(fma.f64 (pow.f64 (cbrt.f64 (+.f64 x (/.f64 -1/2 x))) 2) (cbrt.f64 (+.f64 x (/.f64 -1/2 x))) x)
(fma.f64 (cbrt.f64 (*.f64 x x)) (cbrt.f64 x) (+.f64 x (/.f64 -1/2 x)))

Outputs
(/.f64 -1/2 x)
(-.f64 (.f64 2 x) (.f64 1/2 (/.f64 1 x)))
(+.f64 x (-.f64 x (/.f64 1/2 x)))
(fma.f64 x 2 (/.f64 -1/2 x))
(-.f64 (.f64 2 x) (.f64 1/2 (/.f64 1 x)))
(+.f64 x (-.f64 x (/.f64 1/2 x)))
(fma.f64 x 2 (/.f64 -1/2 x))
(-.f64 (.f64 2 x) (.f64 1/2 (/.f64 1 x)))
(+.f64 x (-.f64 x (/.f64 1/2 x)))
(fma.f64 x 2 (/.f64 -1/2 x))
(*.f64 2 x)
(+.f64 x x)
(-.f64 (.f64 2 x) (.f64 1/2 (/.f64 1 x)))
(+.f64 x (-.f64 x (/.f64 1/2 x)))
(fma.f64 x 2 (/.f64 -1/2 x))
(-.f64 (.f64 2 x) (.f64 1/2 (/.f64 1 x)))
(+.f64 x (-.f64 x (/.f64 1/2 x)))
(fma.f64 x 2 (/.f64 -1/2 x))
(-.f64 (.f64 2 x) (.f64 1/2 (/.f64 1 x)))
(+.f64 x (-.f64 x (/.f64 1/2 x)))
(fma.f64 x 2 (/.f64 -1/2 x))
(*.f64 2 x)
(+.f64 x x)
(-.f64 (.f64 2 x) (.f64 1/2 (/.f64 1 x)))
(+.f64 x (-.f64 x (/.f64 1/2 x)))
(fma.f64 x 2 (/.f64 -1/2 x))
(-.f64 (.f64 2 x) (.f64 1/2 (/.f64 1 x)))
(+.f64 x (-.f64 x (/.f64 1/2 x)))
(fma.f64 x 2 (/.f64 -1/2 x))
(-.f64 (.f64 2 x) (.f64 1/2 (/.f64 1 x)))
(+.f64 x (-.f64 x (/.f64 1/2 x)))
(fma.f64 x 2 (/.f64 -1/2 x))
(-.f64 x (-.f64 (/.f64 1/2 x) x))
(+.f64 x (-.f64 x (/.f64 1/2 x)))
(fma.f64 x 2 (/.f64 -1/2 x))
(-.f64 (+.f64 x x) (/.f64 1/2 x))
(+.f64 x (-.f64 x (/.f64 1/2 x)))
(fma.f64 x 2 (/.f64 -1/2 x))
(-.f64 (exp.f64 (log1p.f64 x)) (-.f64 1 (+.f64 x (/.f64 -1/2 x))))
(+.f64 (-.f64 (exp.f64 (log1p.f64 x)) 1) (+.f64 x (/.f64 -1/2 x)))
(+.f64 (+.f64 x (/.f64 -1/2 x)) (expm1.f64 (log1p.f64 x)))
(-.f64 (exp.f64 (log1p.f64 x)) (+.f64 1 (-.f64 (/.f64 1/2 x) x)))
(+.f64 (-.f64 (exp.f64 (log1p.f64 x)) 1) (+.f64 x (/.f64 -1/2 x)))
(+.f64 (+.f64 x (/.f64 -1/2 x)) (expm1.f64 (log1p.f64 x)))
(-.f64 (exp.f64 (log1p.f64 (+.f64 x (+.f64 x (/.f64 -1/2 x))))) 1)
(+.f64 x (-.f64 x (/.f64 1/2 x)))
(fma.f64 x 2 (/.f64 -1/2 x))
(-.f64 (exp.f64 (log1p.f64 (+.f64 x (/.f64 -1/2 x)))) (-.f64 1 x))
(+.f64 x (expm1.f64 (log1p.f64 (+.f64 x (/.f64 -1/2 x)))))
(-.f64 (/.f64 x (/.f64 (+.f64 x (/.f64 1/2 x)) x)) (-.f64 (/.f64 (/.f64 1/4 (*.f64 x x)) (+.f64 x (/.f64 1/2 x))) x))
(+.f64 (-.f64 (.f64 (/.f64 x (+.f64 x (/.f64 1/2 x))) x) (/.f64 1/4 (.f64 (+.f64 x (/.f64 1/2 x)) (*.f64 x x)))) x)
(+.f64 x (fma.f64 (/.f64 x (+.f64 x (/.f64 1/2 x))) x (/.f64 -1/4 (.f64 (+.f64 x (/.f64 1/2 x)) (.f64 x x)))))
(+.f64 (fma.f64 (/.f64 x (+.f64 x (/.f64 1/2 x))) x x) (/.f64 (/.f64 -1/4 (*.f64 x x)) (+.f64 x (/.f64 1/2 x))))
(-.f64 (/.f64 (pow.f64 x 3) (fma.f64 x x (.f64 (/.f64 1/2 x) (+.f64 x (/.f64 1/2 x))))) (-.f64 (/.f64 1/8 (.f64 (fma.f64 x x (*.f64 (/.f64 1/2 x) (+.f64 x (/.f64 1/2 x)))) (pow.f64 x 3))) x))
(+.f64 (-.f64 (/.f64 (pow.f64 x 3) (fma.f64 x x (.f64 (/.f64 1/2 x) (+.f64 x (/.f64 1/2 x))))) (/.f64 (/.f64 1/8 (fma.f64 x x (.f64 (/.f64 1/2 x) (+.f64 x (/.f64 1/2 x))))) (pow.f64 x 3))) x)
(+.f64 x (-.f64 (/.f64 (pow.f64 x 3) (fma.f64 x x (.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/2 x)))) (/.f64 (/.f64 1/8 (pow.f64 x 3)) (fma.f64 x x (.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/2 x))))))
(+.f64 (+.f64 x (/.f64 (pow.f64 x 3) (fma.f64 x x (.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/2 x))))) (/.f64 (/.f64 -1/8 (pow.f64 x 3)) (fma.f64 x x (.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/2 x)))))
(-.f64 (/.f64 x (/.f64 (+.f64 (/.f64 1/2 x) (-.f64 x x)) x)) (/.f64 (pow.f64 (+.f64 x (/.f64 -1/2 x)) 2) (+.f64 (/.f64 1/2 x) (-.f64 x x))))
(+.f64 x (-.f64 x (/.f64 1/2 x)))
(fma.f64 x 2 (/.f64 -1/2 x))
(-.f64 (+.f64 x (exp.f64 (log1p.f64 (+.f64 x (/.f64 -1/2 x))))) 1)
(-.f64 (exp.f64 (log1p.f64 (+.f64 x (/.f64 -1/2 x)))) (-.f64 1 x))
(+.f64 x (expm1.f64 (log1p.f64 (+.f64 x (/.f64 -1/2 x)))))
(-.f64 (+.f64 x (/.f64 x (/.f64 (+.f64 x (/.f64 1/2 x)) x))) (/.f64 (/.f64 1/4 (*.f64 x x)) (+.f64 x (/.f64 1/2 x))))
(+.f64 (-.f64 (.f64 (/.f64 x (+.f64 x (/.f64 1/2 x))) x) (/.f64 1/4 (.f64 (+.f64 x (/.f64 1/2 x)) (*.f64 x x)))) x)
(+.f64 x (fma.f64 (/.f64 x (+.f64 x (/.f64 1/2 x))) x (/.f64 -1/4 (.f64 (+.f64 x (/.f64 1/2 x)) (.f64 x x)))))
(+.f64 (fma.f64 (/.f64 x (+.f64 x (/.f64 1/2 x))) x x) (/.f64 (/.f64 -1/4 (*.f64 x x)) (+.f64 x (/.f64 1/2 x))))
(-.f64 (+.f64 x (/.f64 (pow.f64 x 3) (fma.f64 x x (.f64 (/.f64 1/2 x) (+.f64 x (/.f64 1/2 x)))))) (/.f64 1/8 (.f64 (fma.f64 x x (*.f64 (/.f64 1/2 x) (+.f64 x (/.f64 1/2 x)))) (pow.f64 x 3))))
(+.f64 (-.f64 (/.f64 (pow.f64 x 3) (fma.f64 x x (.f64 (/.f64 1/2 x) (+.f64 x (/.f64 1/2 x))))) (/.f64 (/.f64 1/8 (fma.f64 x x (.f64 (/.f64 1/2 x) (+.f64 x (/.f64 1/2 x))))) (pow.f64 x 3))) x)
(+.f64 x (-.f64 (/.f64 (pow.f64 x 3) (fma.f64 x x (.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/2 x)))) (/.f64 (/.f64 1/8 (pow.f64 x 3)) (fma.f64 x x (.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/2 x))))))
(+.f64 (+.f64 x (/.f64 (pow.f64 x 3) (fma.f64 x x (.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/2 x))))) (/.f64 (/.f64 -1/8 (pow.f64 x 3)) (fma.f64 x x (.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/2 x)))))
(-.f64 (+.f64 (+.f64 x (/.f64 -1/2 x)) (exp.f64 (log1p.f64 x))) 1)
(+.f64 (-.f64 (exp.f64 (log1p.f64 x)) 1) (+.f64 x (/.f64 -1/2 x)))
(+.f64 (+.f64 x (/.f64 -1/2 x)) (expm1.f64 (log1p.f64 x)))
(-.f64 (+.f64 (+.f64 x x) 0) (/.f64 1/2 x))
(+.f64 x (-.f64 x (/.f64 1/2 x)))
(fma.f64 x 2 (/.f64 -1/2 x))
(*.f64 (+.f64 x (+.f64 x (/.f64 -1/2 x))) 1)
(+.f64 x (-.f64 x (/.f64 1/2 x)))
(fma.f64 x 2 (/.f64 -1/2 x))
(*.f64 1 (+.f64 x (+.f64 x (/.f64 -1/2 x))))
(+.f64 x (-.f64 x (/.f64 1/2 x)))
(fma.f64 x 2 (/.f64 -1/2 x))
(*.f64 (sqrt.f64 (+.f64 x (+.f64 x (/.f64 -1/2 x)))) (sqrt.f64 (+.f64 x (+.f64 x (/.f64 -1/2 x)))))
(+.f64 x (-.f64 x (/.f64 1/2 x)))
(fma.f64 x 2 (/.f64 -1/2 x))
(*.f64 (cbrt.f64 (+.f64 x (+.f64 x (/.f64 -1/2 x)))) (pow.f64 (cbrt.f64 (+.f64 x (+.f64 x (/.f64 -1/2 x)))) 2))
(+.f64 x (-.f64 x (/.f64 1/2 x)))
(fma.f64 x 2 (/.f64 -1/2 x))
(*.f64 (pow.f64 (cbrt.f64 (+.f64 x (+.f64 x (/.f64 -1/2 x)))) 2) (cbrt.f64 (+.f64 x (+.f64 x (/.f64 -1/2 x)))))
(+.f64 x (-.f64 x (/.f64 1/2 x)))
(fma.f64 x 2 (/.f64 -1/2 x))
(.f64 (-.f64 (.f64 x x) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 2)) (/.f64 1 (+.f64 (/.f64 1/2 x) (-.f64 x x))))
(+.f64 x (-.f64 x (/.f64 1/2 x)))
(fma.f64 x 2 (/.f64 -1/2 x))
(.f64 (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 3)) (/.f64 1 (fma.f64 x x (.f64 (+.f64 x (/.f64 -1/2 x)) (+.f64 (/.f64 -1/2 x) (-.f64 x x))))))
(/.f64 (.f64 (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 3)) 1) (fma.f64 x x (.f64 (+.f64 x (/.f64 -1/2 x)) (+.f64 (/.f64 -1/2 x) 0))))
(/.f64 (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 3)) (fma.f64 x x (*.f64 (+.f64 x (/.f64 -1/2 x)) (/.f64 -1/2 x))))
(.f64 (/.f64 1 (+.f64 (/.f64 1/2 x) (-.f64 x x))) (-.f64 (.f64 x x) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 2)))
(+.f64 x (-.f64 x (/.f64 1/2 x)))
(fma.f64 x 2 (/.f64 -1/2 x))
(.f64 (/.f64 1 (fma.f64 x x (.f64 (+.f64 x (/.f64 -1/2 x)) (+.f64 (/.f64 -1/2 x) (-.f64 x x))))) (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 3)))
(/.f64 (.f64 (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 3)) 1) (fma.f64 x x (.f64 (+.f64 x (/.f64 -1/2 x)) (+.f64 (/.f64 -1/2 x) 0))))
(/.f64 (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 3)) (fma.f64 x x (*.f64 (+.f64 x (/.f64 -1/2 x)) (/.f64 -1/2 x))))
(.f64 (/.f64 (-.f64 (.f64 x x) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 2)) (-.f64 (*.f64 x x) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 2))) (+.f64 x (+.f64 x (/.f64 -1/2 x))))
(+.f64 x (-.f64 x (/.f64 1/2 x)))
(fma.f64 x 2 (/.f64 -1/2 x))
(.f64 (/.f64 (-.f64 (.f64 x x) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 2)) (-.f64 (pow.f64 x 3) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 3))) (+.f64 (.f64 x x) (.f64 (+.f64 x (/.f64 -1/2 x)) (+.f64 x (+.f64 x (/.f64 -1/2 x))))))
(/.f64 (.f64 (-.f64 (.f64 x x) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 2)) (fma.f64 x x (*.f64 (+.f64 x (/.f64 -1/2 x)) (+.f64 x (+.f64 x (/.f64 -1/2 x)))))) (-.f64 (pow.f64 x 3) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 3)))
(/.f64 (-.f64 (.f64 x x) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 2)) (/.f64 (-.f64 (pow.f64 x 3) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 3)) (fma.f64 x x (.f64 (+.f64 x (/.f64 -1/2 x)) (fma.f64 x 2 (/.f64 -1/2 x))))))
(/.f64 (.f64 (fma.f64 x 2 (/.f64 -1/2 x)) (/.f64 1/2 x)) (/.f64 (-.f64 (pow.f64 x 3) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 3)) (fma.f64 x x (.f64 (+.f64 x (/.f64 -1/2 x)) (fma.f64 x 2 (/.f64 -1/2 x))))))
(.f64 (/.f64 (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 3)) (-.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 (+.f64 x (/.f64 -1/2 x)) (+.f64 (/.f64 -1/2 x) (-.f64 x x))) (.f64 (+.f64 x (/.f64 -1/2 x)) (+.f64 (/.f64 -1/2 x) (-.f64 x x)))))) (-.f64 (.f64 x x) (*.f64 (+.f64 x (/.f64 -1/2 x)) (+.f64 (/.f64 -1/2 x) (-.f64 x x)))))
(.f64 (/.f64 (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 3)) (-.f64 (.f64 x (pow.f64 x 3)) (.f64 (pow.f64 (+.f64 x (/.f64 -1/2 x)) 2) (.f64 (+.f64 (/.f64 -1/2 x) 0) (+.f64 (/.f64 -1/2 x) 0))))) (-.f64 (.f64 x x) (.f64 (+.f64 x (/.f64 -1/2 x)) (+.f64 (/.f64 -1/2 x) 0))))
(.f64 (/.f64 (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 3)) (-.f64 (pow.f64 x 4) (.f64 (pow.f64 (+.f64 x (/.f64 -1/2 x)) 2) (.f64 (/.f64 -1/2 x) (/.f64 -1/2 x))))) (-.f64 (.f64 x x) (*.f64 (+.f64 x (/.f64 -1/2 x)) (/.f64 -1/2 x))))
(.f64 (/.f64 (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 3)) (-.f64 (pow.f64 x 4) (.f64 (pow.f64 (+.f64 x (/.f64 -1/2 x)) 2) (.f64 (/.f64 -1/2 x) (/.f64 -1/2 x))))) (fma.f64 x x (.f64 (-.f64 (/.f64 1/2 x) x) (/.f64 -1/2 x))))
(.f64 (/.f64 (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 3)) (+.f64 (pow.f64 (.f64 x x) 3) (pow.f64 (.f64 (+.f64 x (/.f64 -1/2 x)) (+.f64 (/.f64 -1/2 x) (-.f64 x x))) 3))) (+.f64 (.f64 (.f64 x x) (.f64 x x)) (-.f64 (.f64 (.f64 (+.f64 x (/.f64 -1/2 x)) (+.f64 (/.f64 -1/2 x) (-.f64 x x))) (.f64 (+.f64 x (/.f64 -1/2 x)) (+.f64 (/.f64 -1/2 x) (-.f64 x x)))) (.f64 (.f64 x x) (.f64 (+.f64 x (/.f64 -1/2 x)) (+.f64 (/.f64 -1/2 x) (-.f64 x x)))))))
(/.f64 (.f64 (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 3)) (+.f64 (.f64 x (pow.f64 x 3)) (.f64 (.f64 (+.f64 x (/.f64 -1/2 x)) (+.f64 (/.f64 -1/2 x) 0)) (-.f64 (.f64 (+.f64 x (/.f64 -1/2 x)) (+.f64 (/.f64 -1/2 x) 0)) (.f64 x x))))) (+.f64 (pow.f64 (*.f64 (+.f64 x (/.f64 -1/2 x)) (+.f64 (/.f64 -1/2 x) 0)) 3) (pow.f64 x 6)))
(.f64 (/.f64 (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 3)) (+.f64 (pow.f64 (.f64 (+.f64 x (/.f64 -1/2 x)) (/.f64 -1/2 x)) 3) (pow.f64 x 6))) (fma.f64 (.f64 (+.f64 x (/.f64 -1/2 x)) (/.f64 -1/2 x)) (fma.f64 (+.f64 x (/.f64 -1/2 x)) (/.f64 -1/2 x) (.f64 x (neg.f64 x))) (pow.f64 x 4)))
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(fma.f64 (pow.f64 (cbrt.f64 (+.f64 x (/.f64 -1/2 x))) 2) (cbrt.f64 (+.f64 x (/.f64 -1/2 x))) x)
(+.f64 x (-.f64 x (/.f64 1/2 x)))
(fma.f64 x 2 (/.f64 -1/2 x))
(fma.f64 (cbrt.f64 (*.f64 x x)) (cbrt.f64 x) (+.f64 x (/.f64 -1/2 x)))

eval100.0ms (3.3%)

Compiler: Compiled 4691 to 3042 computations (35.2% saved)

prune32.0ms (1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	157	0	157
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	157	3	160

Error

Counts

160 → 3

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.1b	(log.f64 (+.f64 x (-.f64 x (/.f64 1/2 x))))
✓	30.5b	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
✓	0.4b	(log.f64 (+.f64 x x))

Compiler

Compiled 24 to 16 computations (33.3% saved)

regimes15.0ms (0.5%)

Accuracy

Total -30.7b remaining (-23177.1%)

Threshold costs -30.7b (-23177.1%)

Counts

3 → 1

Calls

Call 1

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

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

Calls

3 calls:

8.0ms	x
3.0ms	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
3.0ms	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))

Results

Error	Segments	Branch
0.1b	1	`x`
0.1b	1	`(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))`
0.1b	1	`(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))`

Compiler

Compiled 43 to 28 computations (34.9% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative`
4×	`sub-neg`
2×	`neg-mul-1`
2×	`distribute-neg-frac`
2×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	34
1	14	34
2	22	34
3	24	34
4	25	34

Stop Event

1×	done
1×	saturated

Calls

Call 1

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

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

Compiler

Compiled 14 to 9 computations (35.7% saved)

soundness87.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

1370×	`associate-/l*`
1048×	`fma-def`
934×	`associate-/r*`
760×	`associate-+r+`
734×	`associate-+l+`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	116	1130
1	266	1000
2	715	878
3	2127	842
4	7095	842

Stop Event

1×	node limit

Compiler

Compiled 29 to 20 computations (31% saved)

end17.0ms (0.6%)

Compiler: Compiled 13 to 8 computations (38.5% saved)

Details

analyze98.0ms (3.2%)

sample1.9s (63%)

preprocess124.0ms (4%)

simplify177.0ms (5.8%)

eval1.0ms (0%)

prune1.0ms (0%)

localize12.0ms (0.4%)

series1.0ms (0%)

rewrite136.0ms (4.4%)

simplify65.0ms (2.1%)

eval59.0ms (1.9%)

prune11.0ms (0.4%)

localize4.0ms (0.1%)

localize13.0ms (0.4%)

series1.0ms (0%)

rewrite94.0ms (3.1%)

simplify80.0ms (2.6%)

eval100.0ms (3.3%)

prune32.0ms (1%)

regimes15.0ms (0.5%)

simplify4.0ms (0.1%)

soundness87.0ms (2.9%)

end17.0ms (0.6%)

Profiling