Details

analyze3.0ms (0.1%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
0%	0%	100%	0%	0%	0%	0%	2
33.3%	25%	50%	0%	0%	25%	0%	3
66.7%	50%	25%	0%	0%	25%	0%	4
83.3%	62.5%	12.5%	0%	0%	25%	0%	5
91.7%	68.7%	6.2%	0%	0%	25%	0%	6
95.8%	71.8%	3.1%	0%	0%	25%	0%	7
97.9%	73.4%	1.6%	0%	0%	25%	0%	8
99%	74.2%	0.8%	0%	0%	25%	0%	9
99.5%	74.6%	0.4%	0%	0%	25%	0%	10
99.7%	74.8%	0.2%	0%	0%	25%	0%	11
99.9%	74.9%	0.1%	0%	0%	25%	0%	12

Compiler

Compiled 10 to 8 computations (20% saved)

sample698.0ms (23.8%)

Results

686.0ms	8254×	body	256	valid
1.0ms	2×	body	2048	valid
0.0ms	1×	body	256	invalid

Bogosity

preprocess14.0ms (0.5%)

Algorithm

2×	egg-herbie

Rules

4×	`+-commutative`
2×	`1-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	13	23
0	1	1

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0

Outputs
0

Call 2

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

Outputs
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))

Compiler

Compiled 10 to 8 computations (20% saved)

simplify11.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative`
2×	`1-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	13	23

Stop Event

1×

saturated

Counts

1 → 1

Calls

Call 1

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

Outputs
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))

eval0.0ms (0%)

Compiler: Compiled 9 to 7 computations (22.2% saved)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Accurracy

99.8%

Counts

2 → 1

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.8%	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))

Compiler

Compiled 9 to 7 computations (22.2% saved)

localize10.0ms (0.3%)

Local Accuracy

Found 3 expressions with local accuracy:

New	Accuracy	Program
✓	100.0%	(sqrt.f64 (+.f64 x 1))
✓	100.0%	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
✓	99.8%	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))

Compiler

Compiled 24 to 18 computations (25% saved)

series4.0ms (0.1%)

Counts

3 → 12

Calls

9 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
1.0ms	x	@	-inf	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
0.0ms	x	@	0	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
0.0ms	x	@	inf	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
0.0ms	x	@	-inf	(+.f64 1 (sqrt.f64 (+.f64 x 1)))

rewrite76.0ms (2.6%)

Algorithm

1×	batch-egg-rewrite

Rules

882×	`log-prod`
848×	`prod-diff`
678×	`prod-exp`
596×	`fma-def`
560×	`pow-prod-down`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	51
1	195	51
2	2725	51

Stop Event

1×	node limit

Counts

3 → 133

Calls

Call 1

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

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

simplify70.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

1736×	`fma-def`
892×	`unswap-sqr`
876×	`distribute-lft-in`
852×	`distribute-rgt-in`
426×	`exp-prod`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	316	3885
1	715	3601
2	2364	3515

Stop Event

1×	node limit

Counts

145 → 191

Calls

Call 1

Inputs
(*.f64 1/2 x)
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (.f64 1/2 x))
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) (*.f64 1/16 (pow.f64 x 3))))
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) (+.f64 (.f64 -5/128 (pow.f64 x 4)) (.f64 1/16 (pow.f64 x 3)))))
2
(+.f64 (*.f64 1/2 x) 2)
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) 2))
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) (+.f64 2 (*.f64 1/16 (pow.f64 x 3)))))
1
(+.f64 (*.f64 1/2 x) 1)
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) 1))
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) (+.f64 1 (*.f64 1/16 (pow.f64 x 3)))))
(+.f64 0 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))
(-.f64 (exp.f64 (log1p.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))))) 1)
(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
(*.f64 1 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
(*.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 1)
(*.f64 (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))) (cbrt.f64 (pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 2)))
(*.f64 (cbrt.f64 (pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 2)) (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))
(.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))
(*.f64 (sqrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))
(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))
(*.f64 (neg.f64 x) (/.f64 1 (+.f64 (neg.f64 (sqrt.f64 (+.f64 x 1))) -1)))
(*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) x)
(*.f64 (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) -2) (/.f64 x (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))
(*.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) -1/2) (/.f64 x (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) 1) (/.f64 (cbrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 2))) (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4))) (/.f64 (cbrt.f64 x) (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4))))
(*.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
(*.f64 (/.f64 (sqrt.f64 x) (cbrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 2))) (/.f64 (sqrt.f64 x) (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))
(*.f64 (/.f64 x (+.f64 1 (pow.f64 (+.f64 x 1) 3/2))) (-.f64 (+.f64 1 (+.f64 x 1)) (sqrt.f64 (+.f64 x 1))))
(*.f64 (/.f64 x (neg.f64 x)) (-.f64 1 (sqrt.f64 (+.f64 x 1))))
(pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 1)
(pow.f64 (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))) 3)
(pow.f64 (pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 2) 1/2)
(pow.f64 (pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 3) 1/3)
(pow.f64 (sqrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))) 2)
(pow.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x) -1)
(pow.f64 (/.f64 (pow.f64 x 3) (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 3)) 1/3)
(pow.f64 (/.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x) 1) -1)
(neg.f64 (/.f64 x (+.f64 (neg.f64 (sqrt.f64 (+.f64 x 1))) -1)))
(sqrt.f64 (pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 2))
(log.f64 (exp.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))
(cbrt.f64 (pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 3))
(cbrt.f64 (/.f64 (pow.f64 x 3) (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 3)))
(expm1.f64 (log1p.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))
(exp.f64 (-.f64 (log.f64 x) (log1p.f64 (sqrt.f64 (+.f64 x 1)))))
(exp.f64 (*.f64 (-.f64 (log.f64 x) (log1p.f64 (sqrt.f64 (+.f64 x 1)))) 1))
(exp.f64 (.f64 (.f64 (-.f64 (log.f64 x) (log1p.f64 (sqrt.f64 (+.f64 x 1)))) 1) 1))
(exp.f64 (.f64 (.f64 1/3 (-.f64 (log.f64 x) (log1p.f64 (sqrt.f64 (+.f64 x 1))))) 3))
(exp.f64 (.f64 (.f64 3 (-.f64 (log.f64 x) (log1p.f64 (sqrt.f64 (+.f64 x 1))))) 1/3))
(exp.f64 (.f64 (.f64 1/2 (-.f64 (log.f64 x) (log1p.f64 (sqrt.f64 (+.f64 x 1))))) 2))
(exp.f64 (*.f64 (-.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1))) (log.f64 x)) -1))
(exp.f64 (+.f64 (*.f64 (log.f64 x) 1) (neg.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1))))))
(exp.f64 (+.f64 (neg.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1)))) (*.f64 (log.f64 x) 1)))
(log1p.f64 (expm1.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))
(-.f64 (exp.f64 (log1p.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))) 1)
(-.f64 (/.f64 1 (-.f64 1 (sqrt.f64 (+.f64 x 1)))) (/.f64 (+.f64 x 1) (-.f64 1 (sqrt.f64 (+.f64 x 1)))))
(*.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))
(*.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 1)
(*.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) (cbrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 2)))
(*.f64 (cbrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 2)) (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
(*.f64 (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4)) (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4)))
(*.f64 (neg.f64 x) (/.f64 1 (-.f64 1 (sqrt.f64 (+.f64 x 1)))))
(*.f64 (+.f64 1 (pow.f64 (+.f64 x 1) 3/2)) (/.f64 1 (-.f64 (+.f64 1 (+.f64 x 1)) (sqrt.f64 (+.f64 x 1)))))
(/.f64 x (expm1.f64 (*.f64 1/2 (log1p.f64 x))))
(/.f64 1 (/.f64 (-.f64 (+.f64 1 (+.f64 x 1)) (sqrt.f64 (+.f64 x 1))) (+.f64 1 (pow.f64 (+.f64 x 1) 3/2))))
(/.f64 1 (/.f64 (-.f64 1 (sqrt.f64 (+.f64 x 1))) (neg.f64 x)))
(/.f64 (neg.f64 x) (-.f64 1 (sqrt.f64 (+.f64 x 1))))
(/.f64 (+.f64 1 (pow.f64 (+.f64 x 1) 3/2)) (-.f64 (+.f64 1 (+.f64 x 1)) (sqrt.f64 (+.f64 x 1))))
(/.f64 (+.f64 1 (pow.f64 (+.f64 x 1) 3/2)) (+.f64 (+.f64 x 1) (-.f64 1 (sqrt.f64 (+.f64 x 1)))))
(/.f64 (neg.f64 (+.f64 1 (pow.f64 (+.f64 x 1) 3/2))) (neg.f64 (-.f64 (+.f64 1 (+.f64 x 1)) (sqrt.f64 (+.f64 x 1)))))
(/.f64 (neg.f64 (neg.f64 x)) (neg.f64 (-.f64 1 (sqrt.f64 (+.f64 x 1)))))
(pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 1)
(pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 3)
(pow.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 2) 1/2)
(pow.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 3) 1/3)
(pow.f64 (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4)) 2)
(pow.f64 (/.f64 (-.f64 (+.f64 1 (+.f64 x 1)) (sqrt.f64 (+.f64 x 1))) (+.f64 1 (pow.f64 (+.f64 x 1) 3/2))) -1)
(pow.f64 (/.f64 (-.f64 1 (sqrt.f64 (+.f64 x 1))) (neg.f64 x)) -1)
(sqrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 2))
(log.f64 (exp.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
(log.f64 (+.f64 1 (expm1.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))
(cbrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 3))
(expm1.f64 (log1p.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
(exp.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1))))
(exp.f64 (*.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1))) 1))
(exp.f64 (.f64 (.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1))) 1) 1))
(exp.f64 (.f64 (.f64 1/3 (log1p.f64 (sqrt.f64 (+.f64 x 1)))) 3))
(exp.f64 (.f64 (.f64 3 (log1p.f64 (sqrt.f64 (+.f64 x 1)))) 1/3))
(exp.f64 (.f64 (.f64 1/2 (log1p.f64 (sqrt.f64 (+.f64 x 1)))) 2))
(log1p.f64 (expm1.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
(fma.f64 1 (sqrt.f64 (+.f64 x 1)) 1)
(fma.f64 (sqrt.f64 (+.f64 x 1)) 1 1)
(fma.f64 (cbrt.f64 (+.f64 x 1)) (pow.f64 (+.f64 x 1) 1/6) 1)
(fma.f64 (pow.f64 (+.f64 x 1) 1/6) (cbrt.f64 (+.f64 x 1)) 1)
(fma.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4) 1)
(+.f64 0 (sqrt.f64 (+.f64 x 1)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (+.f64 x 1)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (+.f64 x 1))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (+.f64 x 1))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (+.f64 x 1))))))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 1)
(*.f64 1 (sqrt.f64 (+.f64 x 1)))
(*.f64 (sqrt.f64 (+.f64 x 1)) 1)
(*.f64 (cbrt.f64 (+.f64 x 1)) (pow.f64 (+.f64 x 1) 1/6))
(*.f64 (pow.f64 (+.f64 x 1) 1/6) (cbrt.f64 (+.f64 x 1)))
(*.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4))
(/.f64 (hypot.f64 1 (pow.f64 x 3/2)) (hypot.f64 x (sqrt.f64 (-.f64 1 x))))
(/.f64 (sqrt.f64 (fma.f64 x x -1)) (sqrt.f64 (+.f64 x -1)))
(pow.f64 (+.f64 x 1) 1/2)
(pow.f64 (sqrt.f64 (+.f64 x 1)) 1)
(pow.f64 (cbrt.f64 (+.f64 x 1)) 3/2)
(pow.f64 (pow.f64 (+.f64 x 1) 1/6) 3)
(pow.f64 (pow.f64 (+.f64 x 1) 2) 1/4)
(pow.f64 (pow.f64 (+.f64 x 1) 3) 1/6)
(pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2)
(pow.f64 (pow.f64 (+.f64 x 1) 3/2) 1/3)
(fabs.f64 (sqrt.f64 (+.f64 x 1)))
(log.f64 (exp.f64 (sqrt.f64 (+.f64 x 1))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (+.f64 x 1)))))
(cbrt.f64 (pow.f64 (+.f64 x 1) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1))))
(expm1.f64 (*.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1))) 1))
(hypot.f64 1 (sqrt.f64 x))
(exp.f64 (*.f64 1/2 (log1p.f64 x)))
(exp.f64 (*.f64 (log1p.f64 x) 1/2))
(exp.f64 (.f64 (.f64 1/2 (log1p.f64 x)) 1))
(exp.f64 (.f64 (.f64 (log1p.f64 x) 1) 1/2))
(exp.f64 (.f64 (.f64 (log1p.f64 x) 1/2) 1))
(exp.f64 (.f64 (.f64 (*.f64 1/2 (log1p.f64 x)) 1) 1))
(exp.f64 (.f64 (.f64 1/3 (*.f64 1/2 (log1p.f64 x))) 3))
(exp.f64 (.f64 (.f64 1/4 (log1p.f64 x)) 2))
(exp.f64 (.f64 (.f64 3/2 (log1p.f64 x)) 1/3))
(exp.f64 (.f64 (.f64 (*.f64 1/2 (log1p.f64 x)) 3) 1/3))
(log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 x 1))))
(fma.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))) -1)
(fma.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 1 -1)
(fma.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) (cbrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 2)) -1)
(fma.f64 (cbrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 2)) (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) -1)
(fma.f64 (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4)) (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4)) -1)
(fma.f64 (neg.f64 x) (/.f64 1 (-.f64 1 (sqrt.f64 (+.f64 x 1)))) -1)
(fma.f64 (+.f64 1 (pow.f64 (+.f64 x 1) 3/2)) (/.f64 1 (-.f64 (+.f64 1 (+.f64 x 1)) (sqrt.f64 (+.f64 x 1)))) -1)

Outputs
(*.f64 1/2 x)
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (.f64 1/2 x))
(fma.f64 -1/8 (.f64 x x) (.f64 1/2 x))
(.f64 x (+.f64 1/2 (.f64 x -1/8)))
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) (*.f64 1/16 (pow.f64 x 3))))
(fma.f64 -1/8 (.f64 x x) (fma.f64 1/2 x (.f64 1/16 (pow.f64 x 3))))
(fma.f64 -1/8 (.f64 x x) (fma.f64 1/16 (pow.f64 x 3) (.f64 1/2 x)))
(fma.f64 1/2 x (.f64 (.f64 x x) (+.f64 -1/8 (*.f64 x 1/16))))
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) (+.f64 (.f64 -5/128 (pow.f64 x 4)) (.f64 1/16 (pow.f64 x 3)))))
(fma.f64 -1/8 (.f64 x x) (fma.f64 1/2 x (fma.f64 -5/128 (pow.f64 x 4) (.f64 1/16 (pow.f64 x 3)))))
(fma.f64 -1/8 (.f64 x x) (fma.f64 1/2 x (fma.f64 1/16 (pow.f64 x 3) (.f64 -5/128 (pow.f64 x 4)))))
(fma.f64 x (.f64 x -1/8) (fma.f64 1/16 (pow.f64 x 3) (fma.f64 1/2 x (.f64 -5/128 (pow.f64 x 4)))))
2
(+.f64 (*.f64 1/2 x) 2)
(fma.f64 1/2 x 2)
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) 2))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 1/2 x 2))
(fma.f64 1/2 x (fma.f64 x (*.f64 x -1/8) 2))
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) (+.f64 2 (*.f64 1/16 (pow.f64 x 3)))))
(fma.f64 -1/8 (.f64 x x) (+.f64 (fma.f64 1/2 x 2) (.f64 1/16 (pow.f64 x 3))))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 1/2 x (fma.f64 1/16 (pow.f64 x 3) 2)))
(fma.f64 x (*.f64 x -1/8) (fma.f64 1/16 (pow.f64 x 3) (fma.f64 1/2 x 2)))
1
(+.f64 (*.f64 1/2 x) 1)
(fma.f64 1/2 x 1)
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) 1))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 1/2 x 1))
(fma.f64 x (*.f64 x -1/8) (fma.f64 1/2 x 1))
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) (+.f64 1 (*.f64 1/16 (pow.f64 x 3)))))
(fma.f64 -1/8 (.f64 x x) (+.f64 (fma.f64 1/2 x 1) (.f64 1/16 (pow.f64 x 3))))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 1/2 x (fma.f64 1/16 (pow.f64 x 3) 1)))
(fma.f64 x (*.f64 x -1/8) (fma.f64 1/16 (pow.f64 x 3) (fma.f64 1/2 x 1)))
(+.f64 0 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))
(*.f64 3 (log.f64 (cbrt.f64 (exp.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))
(*.f64 2 (log.f64 (sqrt.f64 (exp.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))
(-.f64 (exp.f64 (log1p.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))))) 1)
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
(*.f64 1 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
(*.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 1)
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
(*.f64 (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))) (cbrt.f64 (pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 2)))
(*.f64 (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))) (cbrt.f64 (pow.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x) -2)))
(*.f64 (cbrt.f64 (pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 2)) (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))
(*.f64 (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))) (cbrt.f64 (pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 2)))
(*.f64 (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))) (cbrt.f64 (pow.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x) -2)))
(.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
(*.f64 (sqrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
(*.f64 (neg.f64 x) (/.f64 1 (+.f64 (neg.f64 (sqrt.f64 (+.f64 x 1))) -1)))
(/.f64 (neg.f64 x) (-.f64 -1 (sqrt.f64 (+.f64 x 1))))
(*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) x)
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
(*.f64 (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) -2) (/.f64 x (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))
(*.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) -1/2) (/.f64 x (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) 1) (/.f64 (cbrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 2))) (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))
(*.f64 (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))) (/.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 2))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4))) (/.f64 (cbrt.f64 x) (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4))))
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
(*.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
(*.f64 (/.f64 (sqrt.f64 x) (cbrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 2))) (/.f64 (sqrt.f64 x) (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))
(/.f64 (/.f64 x (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))) (cbrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 2)))
(*.f64 (/.f64 x (+.f64 1 (pow.f64 (+.f64 x 1) 3/2))) (-.f64 (+.f64 1 (+.f64 x 1)) (sqrt.f64 (+.f64 x 1))))
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(+.f64 -1 (/.f64 (neg.f64 x) (-.f64 1 (sqrt.f64 (+.f64 x 1)))))
(+.f64 -1 (/.f64 x (+.f64 (sqrt.f64 (+.f64 x 1)) -1)))
(fma.f64 (+.f64 1 (pow.f64 (+.f64 x 1) 3/2)) (/.f64 1 (-.f64 (+.f64 1 (+.f64 x 1)) (sqrt.f64 (+.f64 x 1)))) -1)
(fma.f64 (+.f64 1 (pow.f64 (+.f64 x 1) 3/2)) (/.f64 1 (+.f64 1 (-.f64 (+.f64 x 1) (sqrt.f64 (+.f64 x 1))))) -1)
(+.f64 -1 (/.f64 (+.f64 1 (pow.f64 (+.f64 x 1) 3/2)) (+.f64 x (-.f64 2 (sqrt.f64 (+.f64 x 1))))))

eval57.0ms (1.9%)

Compiler: Compiled 2569 to 1999 computations (22.2% saved)

prune240.0ms (8.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	186	5	191
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	186	6	192

Accurracy

100.0%

Counts

192 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	72.2%	(fma.f64 -1/8 (.f64 x x) (.f64 1/2 x))
▶	97.9%	(/.f64 x (/.f64 x (expm1.f64 (*.f64 1/2 (log1p.f64 x)))))
▶	74.1%	(/.f64 x (+.f64 (*.f64 1/2 x) 2))
✓	99.8%	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
▶	73.4%	(/.f64 x 2)
▶	33.3%	(+.f64 (sqrt.f64 (+.f64 x 1)) -1)

Compiler

Compiled 85 to 63 computations (25.9% saved)

localize13.0ms (0.5%)

Local Accuracy

Found 3 expressions with local accuracy:

New	Accuracy	Program
✓	99.8%	(/.f64 x (/.f64 x (expm1.f64 (*.f64 1/2 (log1p.f64 x)))))
✓	99.8%	(/.f64 x (expm1.f64 (*.f64 1/2 (log1p.f64 x))))
✓	97.9%	(expm1.f64 (*.f64 1/2 (log1p.f64 x)))

Compiler

Compiled 30 to 17 computations (43.3% saved)

series6.0ms (0.2%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	(/.f64 x (expm1.f64 (*.f64 1/2 (log1p.f64 x))))
1.0ms	x	@	inf	(/.f64 x (expm1.f64 (*.f64 1/2 (log1p.f64 x))))
1.0ms	x	@	-inf	(expm1.f64 (*.f64 1/2 (log1p.f64 x)))
1.0ms	x	@	inf	(expm1.f64 (*.f64 1/2 (log1p.f64 x)))
0.0ms	x	@	0	(expm1.f64 (*.f64 1/2 (log1p.f64 x)))

rewrite344.0ms (11.8%)

Algorithm

1×	batch-egg-rewrite

Rules

1928×	`pow1`
1786×	`add-exp-log`
1786×	`log1p-expm1-u`
1784×	`expm1-log1p-u`
206×	`add-sqr-sqrt`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	51
1	207	51
2	2738	51

Stop Event

1×	node limit

Counts

3 → 121

Calls

Call 1

Inputs
(expm1.f64 (*.f64 1/2 (log1p.f64 x)))
(/.f64 x (expm1.f64 (*.f64 1/2 (log1p.f64 x))))
(/.f64 x (/.f64 x (expm1.f64 (*.f64 1/2 (log1p.f64 x)))))

Outputs
(+.f64 (pow.f64 (+.f64 x 1) 1/2) -1)
(-.f64 (pow.f64 (+.f64 x 1) 1/2) 1)
(.f64 x (/.f64 (expm1.f64 (.f64 1/2 (log1p.f64 x))) x))
(.f64 (expm1.f64 (.f64 1/2 (log1p.f64 x))) 1)
(.f64 1 (expm1.f64 (.f64 1/2 (log1p.f64 x))))
(.f64 (cbrt.f64 (expm1.f64 (.f64 1/2 (log1p.f64 x)))) (pow.f64 (cbrt.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x)))) 2))
(.f64 (pow.f64 (cbrt.f64 (expm1.f64 (.f64 1/2 (log1p.f64 x)))) 2) (cbrt.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x)))))
(.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (/.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x))) x)))
(.f64 (sqrt.f64 (expm1.f64 (.f64 1/2 (log1p.f64 x)))) (sqrt.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x)))))
(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (/.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x))) x)))
(.f64 (neg.f64 x) (/.f64 1 (/.f64 (neg.f64 x) (expm1.f64 (.f64 1/2 (log1p.f64 x))))))
(.f64 (/.f64 (expm1.f64 (.f64 1/2 (log1p.f64 x))) x) x)
(.f64 (/.f64 1 x) (/.f64 x (/.f64 1 (expm1.f64 (.f64 1/2 (log1p.f64 x))))))
(.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) 1) (/.f64 (cbrt.f64 x) (/.f64 x (expm1.f64 (.f64 1/2 (log1p.f64 x))))))
(.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (/.f64 x (expm1.f64 (.f64 1/2 (log1p.f64 x))))))
(.f64 (/.f64 x 1) (/.f64 (expm1.f64 (.f64 1/2 (log1p.f64 x))) x))
(.f64 (/.f64 1 (pow.f64 (cbrt.f64 (/.f64 x (expm1.f64 (.f64 1/2 (log1p.f64 x))))) 2)) (/.f64 x (cbrt.f64 (/.f64 x (expm1.f64 (*.f64 1/2 (log1p.f64 x)))))))
(.f64 (/.f64 1 (sqrt.f64 (/.f64 x (expm1.f64 (.f64 1/2 (log1p.f64 x)))))) (/.f64 x (sqrt.f64 (/.f64 x (expm1.f64 (*.f64 1/2 (log1p.f64 x)))))))
(.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) x) (/.f64 (cbrt.f64 x) (/.f64 1 (expm1.f64 (.f64 1/2 (log1p.f64 x))))))
(.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 (/.f64 x (expm1.f64 (.f64 1/2 (log1p.f64 x))))) 2)) (cbrt.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x)))))
(.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (sqrt.f64 (/.f64 x (expm1.f64 (.f64 1/2 (log1p.f64 x)))))) (/.f64 (cbrt.f64 x) (sqrt.f64 (/.f64 x (expm1.f64 (*.f64 1/2 (log1p.f64 x)))))))
(.f64 (/.f64 (sqrt.f64 x) x) (/.f64 (sqrt.f64 x) (/.f64 1 (expm1.f64 (.f64 1/2 (log1p.f64 x))))))
(.f64 (/.f64 (sqrt.f64 x) (pow.f64 (cbrt.f64 (/.f64 x (expm1.f64 (.f64 1/2 (log1p.f64 x))))) 2)) (/.f64 (sqrt.f64 x) (cbrt.f64 (/.f64 x (expm1.f64 (*.f64 1/2 (log1p.f64 x)))))))
(.f64 (/.f64 x (neg.f64 x)) (neg.f64 (expm1.f64 (.f64 1/2 (log1p.f64 x)))))
(/.f64 x (/.f64 x (expm1.f64 (*.f64 1/2 (log1p.f64 x)))))
(/.f64 1 (/.f64 1 (expm1.f64 (*.f64 1/2 (log1p.f64 x)))))
(/.f64 1 (/.f64 (/.f64 1 (expm1.f64 (*.f64 1/2 (log1p.f64 x)))) 1))
(/.f64 (pow.f64 (cbrt.f64 x) 2) (/.f64 (/.f64 x (expm1.f64 (*.f64 1/2 (log1p.f64 x)))) (cbrt.f64 x)))
(/.f64 (sqrt.f64 x) (/.f64 (/.f64 x (expm1.f64 (*.f64 1/2 (log1p.f64 x)))) (sqrt.f64 x)))
(/.f64 (neg.f64 x) (/.f64 (neg.f64 x) (expm1.f64 (*.f64 1/2 (log1p.f64 x)))))
(/.f64 -1 (neg.f64 (/.f64 1 (expm1.f64 (*.f64 1/2 (log1p.f64 x))))))
(/.f64 (neg.f64 (neg.f64 x)) (neg.f64 (/.f64 (neg.f64 x) (expm1.f64 (*.f64 1/2 (log1p.f64 x))))))
(/.f64 (/.f64 x 1) (/.f64 x (expm1.f64 (*.f64 1/2 (log1p.f64 x)))))
(/.f64 (/.f64 x (sqrt.f64 (/.f64 x (expm1.f64 (.f64 1/2 (log1p.f64 x)))))) (sqrt.f64 (/.f64 x (expm1.f64 (.f64 1/2 (log1p.f64 x))))))
(/.f64 (-.f64 (pow.f64 (pow.f64 (+.f64 x 1) 1/2) 3) 1) (+.f64 (.f64 (pow.f64 (+.f64 x 1) 1/2) (pow.f64 (+.f64 x 1) 1/2)) (+.f64 1 (.f64 (pow.f64 (+.f64 x 1) 1/2) 1))))
(/.f64 (-.f64 (*.f64 (pow.f64 (+.f64 x 1) 1/2) (pow.f64 (+.f64 x 1) 1/2)) 1) (+.f64 (pow.f64 (+.f64 x 1) 1/2) 1))
(/.f64 (.f64 x (expm1.f64 (.f64 1/2 (log1p.f64 x)))) x)
(/.f64 (/.f64 x (pow.f64 (cbrt.f64 (/.f64 x (expm1.f64 (.f64 1/2 (log1p.f64 x))))) 2)) (cbrt.f64 (/.f64 x (expm1.f64 (.f64 1/2 (log1p.f64 x))))))
(pow.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x))) 1)
(pow.f64 (cbrt.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x)))) 3)
(pow.f64 (pow.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x))) 3) 1/3)
(pow.f64 (sqrt.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x)))) 2)
(pow.f64 (/.f64 1 (expm1.f64 (*.f64 1/2 (log1p.f64 x)))) -1)
(neg.f64 (/.f64 x (/.f64 (neg.f64 x) (expm1.f64 (*.f64 1/2 (log1p.f64 x))))))
(sqrt.f64 (pow.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x))) 2))
(log.f64 (exp.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x)))))
(cbrt.f64 (pow.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x))) 3))
(cbrt.f64 (/.f64 (pow.f64 x 3) (pow.f64 (/.f64 x (expm1.f64 (*.f64 1/2 (log1p.f64 x)))) 3)))
(exp.f64 (log.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x)))))
(exp.f64 (.f64 (log.f64 (expm1.f64 (.f64 1/2 (log1p.f64 x)))) 1))
(log1p.f64 (expm1.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x)))))
(-.f64 (+.f64 1 (/.f64 x (expm1.f64 (*.f64 1/2 (log1p.f64 x))))) 1)
(.f64 x (/.f64 1 (expm1.f64 (.f64 1/2 (log1p.f64 x)))))
(.f64 (/.f64 x (expm1.f64 (.f64 1/2 (log1p.f64 x)))) 1)
(.f64 1 (/.f64 x (expm1.f64 (.f64 1/2 (log1p.f64 x)))))
(.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (/.f64 1 (expm1.f64 (*.f64 1/2 (log1p.f64 x))))))
(.f64 (cbrt.f64 (/.f64 x (expm1.f64 (.f64 1/2 (log1p.f64 x))))) (pow.f64 (cbrt.f64 (/.f64 x (expm1.f64 (*.f64 1/2 (log1p.f64 x))))) 2))
(.f64 (pow.f64 (cbrt.f64 (/.f64 x (expm1.f64 (.f64 1/2 (log1p.f64 x))))) 2) (cbrt.f64 (/.f64 x (expm1.f64 (*.f64 1/2 (log1p.f64 x))))))
(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (/.f64 1 (expm1.f64 (*.f64 1/2 (log1p.f64 x))))))
(.f64 (sqrt.f64 (/.f64 x (expm1.f64 (.f64 1/2 (log1p.f64 x))))) (sqrt.f64 (/.f64 x (expm1.f64 (*.f64 1/2 (log1p.f64 x))))))
(.f64 (neg.f64 x) (/.f64 1 (neg.f64 (expm1.f64 (.f64 1/2 (log1p.f64 x))))))
(.f64 (/.f64 1 (expm1.f64 (.f64 1/2 (log1p.f64 x)))) x)
(.f64 (/.f64 1 (pow.f64 (cbrt.f64 (expm1.f64 (.f64 1/2 (log1p.f64 x)))) 2)) (/.f64 x (cbrt.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x))))))
(.f64 (/.f64 1 (sqrt.f64 (expm1.f64 (.f64 1/2 (log1p.f64 x))))) (/.f64 x (sqrt.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x))))))
(.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) 1) (/.f64 (cbrt.f64 x) (expm1.f64 (.f64 1/2 (log1p.f64 x)))))
(.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 (expm1.f64 (.f64 1/2 (log1p.f64 x)))) 2)) (cbrt.f64 (/.f64 x (expm1.f64 (*.f64 1/2 (log1p.f64 x))))))
(.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (sqrt.f64 (expm1.f64 (.f64 1/2 (log1p.f64 x))))) (/.f64 (cbrt.f64 x) (sqrt.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x))))))
(.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (expm1.f64 (.f64 1/2 (log1p.f64 x)))))
(.f64 (/.f64 (sqrt.f64 x) (pow.f64 (cbrt.f64 (expm1.f64 (.f64 1/2 (log1p.f64 x)))) 2)) (/.f64 (sqrt.f64 x) (cbrt.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x))))))
(pow.f64 (/.f64 x (expm1.f64 (*.f64 1/2 (log1p.f64 x)))) 1)
(pow.f64 (cbrt.f64 (/.f64 x (expm1.f64 (*.f64 1/2 (log1p.f64 x))))) 3)
(pow.f64 (pow.f64 (/.f64 x (expm1.f64 (*.f64 1/2 (log1p.f64 x)))) 3) 1/3)
(pow.f64 (sqrt.f64 (/.f64 x (expm1.f64 (*.f64 1/2 (log1p.f64 x))))) 2)
(pow.f64 (/.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x))) x) -1)
(neg.f64 (/.f64 x (neg.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x))))))
(sqrt.f64 (pow.f64 (/.f64 x (expm1.f64 (*.f64 1/2 (log1p.f64 x)))) 2))
(log.f64 (exp.f64 (/.f64 x (expm1.f64 (*.f64 1/2 (log1p.f64 x))))))
(cbrt.f64 (pow.f64 (/.f64 x (expm1.f64 (*.f64 1/2 (log1p.f64 x)))) 3))
(cbrt.f64 (/.f64 (pow.f64 x 3) (pow.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x))) 3)))
(expm1.f64 (log1p.f64 (/.f64 x (expm1.f64 (*.f64 1/2 (log1p.f64 x))))))
(exp.f64 (log.f64 (/.f64 x (expm1.f64 (*.f64 1/2 (log1p.f64 x))))))
(exp.f64 (.f64 (log.f64 (/.f64 x (expm1.f64 (.f64 1/2 (log1p.f64 x))))) 1))
(log1p.f64 (expm1.f64 (/.f64 x (expm1.f64 (*.f64 1/2 (log1p.f64 x))))))
(+.f64 (pow.f64 (+.f64 x 1) 1/2) -1)
(-.f64 (pow.f64 (+.f64 x 1) 1/2) 1)
(.f64 x (/.f64 (expm1.f64 (.f64 1/2 (log1p.f64 x))) x))
(.f64 (expm1.f64 (.f64 1/2 (log1p.f64 x))) 1)
(.f64 1 (expm1.f64 (.f64 1/2 (log1p.f64 x))))
(.f64 (cbrt.f64 (expm1.f64 (.f64 1/2 (log1p.f64 x)))) (pow.f64 (cbrt.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x)))) 2))
(.f64 (pow.f64 (cbrt.f64 (expm1.f64 (.f64 1/2 (log1p.f64 x)))) 2) (cbrt.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x)))))
(.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (/.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x))) x)))
(.f64 (sqrt.f64 (expm1.f64 (.f64 1/2 (log1p.f64 x)))) (sqrt.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x)))))
(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (/.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x))) x)))
(.f64 (neg.f64 x) (/.f64 1 (/.f64 (neg.f64 x) (expm1.f64 (.f64 1/2 (log1p.f64 x))))))
(.f64 (/.f64 (expm1.f64 (.f64 1/2 (log1p.f64 x))) x) x)
(.f64 (/.f64 1 x) (/.f64 x (/.f64 1 (expm1.f64 (.f64 1/2 (log1p.f64 x))))))
(.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) 1) (/.f64 (cbrt.f64 x) (/.f64 x (expm1.f64 (.f64 1/2 (log1p.f64 x))))))
(.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (/.f64 x (expm1.f64 (.f64 1/2 (log1p.f64 x))))))
(.f64 (/.f64 x 1) (/.f64 (expm1.f64 (.f64 1/2 (log1p.f64 x))) x))
(.f64 (/.f64 1 (pow.f64 (cbrt.f64 (/.f64 x (expm1.f64 (.f64 1/2 (log1p.f64 x))))) 2)) (/.f64 x (cbrt.f64 (/.f64 x (expm1.f64 (*.f64 1/2 (log1p.f64 x)))))))
(.f64 (/.f64 1 (sqrt.f64 (/.f64 x (expm1.f64 (.f64 1/2 (log1p.f64 x)))))) (/.f64 x (sqrt.f64 (/.f64 x (expm1.f64 (*.f64 1/2 (log1p.f64 x)))))))
(.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) x) (/.f64 (cbrt.f64 x) (/.f64 1 (expm1.f64 (.f64 1/2 (log1p.f64 x))))))
(.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 (/.f64 x (expm1.f64 (.f64 1/2 (log1p.f64 x))))) 2)) (cbrt.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x)))))
(.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (sqrt.f64 (/.f64 x (expm1.f64 (.f64 1/2 (log1p.f64 x)))))) (/.f64 (cbrt.f64 x) (sqrt.f64 (/.f64 x (expm1.f64 (*.f64 1/2 (log1p.f64 x)))))))
(.f64 (/.f64 (sqrt.f64 x) x) (/.f64 (sqrt.f64 x) (/.f64 1 (expm1.f64 (.f64 1/2 (log1p.f64 x))))))
(.f64 (/.f64 (sqrt.f64 x) (pow.f64 (cbrt.f64 (/.f64 x (expm1.f64 (.f64 1/2 (log1p.f64 x))))) 2)) (/.f64 (sqrt.f64 x) (cbrt.f64 (/.f64 x (expm1.f64 (*.f64 1/2 (log1p.f64 x)))))))
(.f64 (/.f64 x (neg.f64 x)) (neg.f64 (expm1.f64 (.f64 1/2 (log1p.f64 x)))))
(pow.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x))) 1)
(pow.f64 (cbrt.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x)))) 3)
(pow.f64 (pow.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x))) 3) 1/3)
(pow.f64 (sqrt.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x)))) 2)
(pow.f64 (/.f64 1 (expm1.f64 (*.f64 1/2 (log1p.f64 x)))) -1)
(neg.f64 (/.f64 x (/.f64 (neg.f64 x) (expm1.f64 (*.f64 1/2 (log1p.f64 x))))))
(sqrt.f64 (pow.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x))) 2))
(log.f64 (exp.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x)))))
(cbrt.f64 (pow.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x))) 3))
(cbrt.f64 (/.f64 (pow.f64 x 3) (pow.f64 (/.f64 x (expm1.f64 (*.f64 1/2 (log1p.f64 x)))) 3)))
(expm1.f64 (*.f64 1/2 (log1p.f64 x)))
(exp.f64 (log.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x)))))
(exp.f64 (.f64 (log.f64 (expm1.f64 (.f64 1/2 (log1p.f64 x)))) 1))
(log1p.f64 (expm1.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x)))))

simplify105.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

564×	`log-prod`
488×	`distribute-lft-neg-in`
458×	`cancel-sign-sub-inv`
454×	`distribute-rgt-neg-in`
434×	`exp-prod`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	313	7089
1	851	5733
2	3485	4367

Stop Event

1×	node limit

Counts

157 → 171

Calls

Call 1

Inputs
(*.f64 1/2 x)
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (.f64 1/2 x))
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) (*.f64 1/16 (pow.f64 x 3))))
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) (+.f64 (.f64 -5/128 (pow.f64 x 4)) (.f64 1/16 (pow.f64 x 3)))))
(-.f64 (pow.f64 (/.f64 1 x) -1/2) 1)
(-.f64 (+.f64 (pow.f64 (/.f64 1 x) -1/2) (*.f64 1/2 (sqrt.f64 (/.f64 1 x)))) 1)
(-.f64 (+.f64 (pow.f64 (/.f64 1 x) -1/2) (+.f64 (.f64 -1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (.f64 1/2 (sqrt.f64 (/.f64 1 x))))) 1)
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(pow.f64 (/.f64 x (expm1.f64 (*.f64 1/2 (log1p.f64 x)))) 1)
(pow.f64 (cbrt.f64 (/.f64 x (expm1.f64 (*.f64 1/2 (log1p.f64 x))))) 3)
(pow.f64 (pow.f64 (/.f64 x (expm1.f64 (*.f64 1/2 (log1p.f64 x)))) 3) 1/3)
(pow.f64 (sqrt.f64 (/.f64 x (expm1.f64 (*.f64 1/2 (log1p.f64 x))))) 2)
(pow.f64 (/.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x))) x) -1)
(neg.f64 (/.f64 x (neg.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x))))))
(sqrt.f64 (pow.f64 (/.f64 x (expm1.f64 (*.f64 1/2 (log1p.f64 x)))) 2))
(log.f64 (exp.f64 (/.f64 x (expm1.f64 (*.f64 1/2 (log1p.f64 x))))))
(cbrt.f64 (pow.f64 (/.f64 x (expm1.f64 (*.f64 1/2 (log1p.f64 x)))) 3))
(cbrt.f64 (/.f64 (pow.f64 x 3) (pow.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x))) 3)))
(expm1.f64 (log1p.f64 (/.f64 x (expm1.f64 (*.f64 1/2 (log1p.f64 x))))))
(exp.f64 (log.f64 (/.f64 x (expm1.f64 (*.f64 1/2 (log1p.f64 x))))))
(exp.f64 (.f64 (log.f64 (/.f64 x (expm1.f64 (.f64 1/2 (log1p.f64 x))))) 1))
(log1p.f64 (expm1.f64 (/.f64 x (expm1.f64 (*.f64 1/2 (log1p.f64 x))))))
(+.f64 (pow.f64 (+.f64 x 1) 1/2) -1)
(-.f64 (pow.f64 (+.f64 x 1) 1/2) 1)
(.f64 x (/.f64 (expm1.f64 (.f64 1/2 (log1p.f64 x))) x))
(.f64 (expm1.f64 (.f64 1/2 (log1p.f64 x))) 1)
(.f64 1 (expm1.f64 (.f64 1/2 (log1p.f64 x))))
(.f64 (cbrt.f64 (expm1.f64 (.f64 1/2 (log1p.f64 x)))) (pow.f64 (cbrt.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x)))) 2))
(.f64 (pow.f64 (cbrt.f64 (expm1.f64 (.f64 1/2 (log1p.f64 x)))) 2) (cbrt.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x)))))
(.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (/.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x))) x)))
(.f64 (sqrt.f64 (expm1.f64 (.f64 1/2 (log1p.f64 x)))) (sqrt.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x)))))
(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (/.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x))) x)))
(.f64 (neg.f64 x) (/.f64 1 (/.f64 (neg.f64 x) (expm1.f64 (.f64 1/2 (log1p.f64 x))))))
(.f64 (/.f64 (expm1.f64 (.f64 1/2 (log1p.f64 x))) x) x)
(.f64 (/.f64 1 x) (/.f64 x (/.f64 1 (expm1.f64 (.f64 1/2 (log1p.f64 x))))))
(.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) 1) (/.f64 (cbrt.f64 x) (/.f64 x (expm1.f64 (.f64 1/2 (log1p.f64 x))))))
(.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (/.f64 x (expm1.f64 (.f64 1/2 (log1p.f64 x))))))
(.f64 (/.f64 x 1) (/.f64 (expm1.f64 (.f64 1/2 (log1p.f64 x))) x))
(.f64 (/.f64 1 (pow.f64 (cbrt.f64 (/.f64 x (expm1.f64 (.f64 1/2 (log1p.f64 x))))) 2)) (/.f64 x (cbrt.f64 (/.f64 x (expm1.f64 (*.f64 1/2 (log1p.f64 x)))))))
(.f64 (/.f64 1 (sqrt.f64 (/.f64 x (expm1.f64 (.f64 1/2 (log1p.f64 x)))))) (/.f64 x (sqrt.f64 (/.f64 x (expm1.f64 (*.f64 1/2 (log1p.f64 x)))))))
(.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) x) (/.f64 (cbrt.f64 x) (/.f64 1 (expm1.f64 (.f64 1/2 (log1p.f64 x))))))
(.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 (/.f64 x (expm1.f64 (.f64 1/2 (log1p.f64 x))))) 2)) (cbrt.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x)))))
(.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (sqrt.f64 (/.f64 x (expm1.f64 (.f64 1/2 (log1p.f64 x)))))) (/.f64 (cbrt.f64 x) (sqrt.f64 (/.f64 x (expm1.f64 (*.f64 1/2 (log1p.f64 x)))))))
(.f64 (/.f64 (sqrt.f64 x) x) (/.f64 (sqrt.f64 x) (/.f64 1 (expm1.f64 (.f64 1/2 (log1p.f64 x))))))
(.f64 (/.f64 (sqrt.f64 x) (pow.f64 (cbrt.f64 (/.f64 x (expm1.f64 (.f64 1/2 (log1p.f64 x))))) 2)) (/.f64 (sqrt.f64 x) (cbrt.f64 (/.f64 x (expm1.f64 (*.f64 1/2 (log1p.f64 x)))))))
(.f64 (/.f64 x (neg.f64 x)) (neg.f64 (expm1.f64 (.f64 1/2 (log1p.f64 x)))))
(pow.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x))) 1)
(pow.f64 (cbrt.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x)))) 3)
(pow.f64 (pow.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x))) 3) 1/3)
(pow.f64 (sqrt.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x)))) 2)
(pow.f64 (/.f64 1 (expm1.f64 (*.f64 1/2 (log1p.f64 x)))) -1)
(neg.f64 (/.f64 x (/.f64 (neg.f64 x) (expm1.f64 (*.f64 1/2 (log1p.f64 x))))))
(sqrt.f64 (pow.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x))) 2))
(log.f64 (exp.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x)))))
(cbrt.f64 (pow.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x))) 3))
(cbrt.f64 (/.f64 (pow.f64 x 3) (pow.f64 (/.f64 x (expm1.f64 (*.f64 1/2 (log1p.f64 x)))) 3)))
(expm1.f64 (*.f64 1/2 (log1p.f64 x)))
(exp.f64 (log.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x)))))
(exp.f64 (.f64 (log.f64 (expm1.f64 (.f64 1/2 (log1p.f64 x)))) 1))
(log1p.f64 (expm1.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x)))))

Outputs
(*.f64 1/2 x)
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (.f64 1/2 x))
(fma.f64 -1/8 (.f64 x x) (.f64 1/2 x))
(fma.f64 1/2 x (.f64 -1/8 (.f64 x x)))
(fma.f64 1/2 x (.f64 (.f64 -1/8 x) x))
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) (*.f64 1/16 (pow.f64 x 3))))
(fma.f64 -1/8 (.f64 x x) (fma.f64 1/2 x (.f64 1/16 (pow.f64 x 3))))
(fma.f64 -1/8 (.f64 x x) (fma.f64 1/16 (pow.f64 x 3) (.f64 1/2 x)))
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) (+.f64 (.f64 -5/128 (pow.f64 x 4)) (.f64 1/16 (pow.f64 x 3)))))
(fma.f64 -1/8 (.f64 x x) (fma.f64 1/2 x (fma.f64 -5/128 (pow.f64 x 4) (.f64 1/16 (pow.f64 x 3)))))
(fma.f64 -1/8 (.f64 x x) (fma.f64 1/2 x (fma.f64 1/16 (pow.f64 x 3) (.f64 -5/128 (pow.f64 x 4)))))
(-.f64 (pow.f64 (/.f64 1 x) -1/2) 1)
(+.f64 (pow.f64 (/.f64 1 x) -1/2) -1)
(-.f64 (+.f64 (pow.f64 (/.f64 1 x) -1/2) (*.f64 1/2 (sqrt.f64 (/.f64 1 x)))) 1)
(+.f64 (+.f64 (pow.f64 (/.f64 1 x) -1/2) (*.f64 1/2 (sqrt.f64 (/.f64 1 x)))) -1)
(+.f64 (pow.f64 (/.f64 1 x) -1/2) (fma.f64 1/2 (sqrt.f64 (/.f64 1 x)) -1))
(-.f64 (+.f64 (pow.f64 (/.f64 1 x) -1/2) (+.f64 (.f64 -1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (.f64 1/2 (sqrt.f64 (/.f64 1 x))))) 1)
(+.f64 (+.f64 (pow.f64 (/.f64 1 x) -1/2) (fma.f64 -1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 1/2 (sqrt.f64 (/.f64 1 x))))) -1)
(+.f64 (pow.f64 (/.f64 1 x) -1/2) (+.f64 (*.f64 -1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (fma.f64 1/2 (sqrt.f64 (/.f64 1 x)) -1)))
(+.f64 (fma.f64 -1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 1/2 (sqrt.f64 (/.f64 1 x)))) (+.f64 (pow.f64 (/.f64 1 x) -1/2) -1))
(-.f64 (+.f64 (.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (pow.f64 (/.f64 1 x) -1/2) (+.f64 (.f64 -1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 1/2 (sqrt.f64 (/.f64 1 x)))))) 1)
(+.f64 (fma.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (+.f64 (pow.f64 (/.f64 1 x) -1/2) (fma.f64 -1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 1/2 (sqrt.f64 (/.f64 1 x)))))) -1)
(+.f64 (+.f64 (fma.f64 1/2 (sqrt.f64 (/.f64 1 x)) (*.f64 -1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (fma.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (pow.f64 (/.f64 1 x) -1/2))) -1)
(+.f64 (+.f64 (pow.f64 (/.f64 1 x) -1/2) (fma.f64 -1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 1/2 (sqrt.f64 (/.f64 1 x))))) (fma.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) -1))
(-.f64 (exp.f64 (.f64 1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 1)
(expm1.f64 (*.f64 1/2 (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))))
(expm1.f64 (*.f64 1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))
(+.f64 -1 (sqrt.f64 x))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (exp.f64 (.f64 1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)) (exp.f64 (.f64 1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))) 1)
(+.f64 (.f64 1/2 (/.f64 (pow.f64 (exp.f64 1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) x)) (expm1.f64 (.f64 1/2 (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)))))
(fma.f64 1/2 (/.f64 (pow.f64 (exp.f64 1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x) (expm1.f64 (*.f64 1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))))
(+.f64 -1 (fma.f64 1/2 (/.f64 (sqrt.f64 x) x) (sqrt.f64 x)))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (exp.f64 (.f64 1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)) (+.f64 (exp.f64 (.f64 1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (.f64 -1/8 (/.f64 (exp.f64 (.f64 1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))))) 1)
(+.f64 (+.f64 (fma.f64 1/2 (/.f64 (pow.f64 (exp.f64 1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) x) (pow.f64 (exp.f64 1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)))) (.f64 -1/8 (/.f64 (pow.f64 (exp.f64 1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (.f64 x x)))) -1)
(fma.f64 1/2 (/.f64 (pow.f64 (exp.f64 1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 (exp.f64 1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (.f64 x x))) (expm1.f64 (*.f64 1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))))
(fma.f64 1/2 (/.f64 (sqrt.f64 x) x) (+.f64 (fma.f64 -1/8 (/.f64 (sqrt.f64 x) (*.f64 x x)) (sqrt.f64 x)) -1))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (exp.f64 (.f64 1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)) (+.f64 (.f64 1/16 (/.f64 (exp.f64 (.f64 1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3))) (+.f64 (exp.f64 (.f64 1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (.f64 -1/8 (/.f64 (exp.f64 (.f64 1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2)))))) 1)
(+.f64 (fma.f64 1/2 (/.f64 (pow.f64 (exp.f64 1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) x) (fma.f64 1/16 (/.f64 (pow.f64 (exp.f64 1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (pow.f64 x 3)) (+.f64 (pow.f64 (exp.f64 1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (.f64 -1/8 (/.f64 (pow.f64 (exp.f64 1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (.f64 x x)))))) -1)
(+.f64 -1 (fma.f64 1/2 (/.f64 (pow.f64 (exp.f64 1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x) (fma.f64 1/16 (/.f64 (pow.f64 (exp.f64 1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (pow.f64 x 3)) (fma.f64 -1/8 (/.f64 (pow.f64 (exp.f64 1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (*.f64 x x)) (pow.f64 (exp.f64 1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))))))
(+.f64 -1 (fma.f64 1/2 (/.f64 (sqrt.f64 x) x) (fma.f64 1/16 (/.f64 (sqrt.f64 x) (pow.f64 x 3)) (fma.f64 -1/8 (/.f64 (sqrt.f64 x) (*.f64 x x)) (sqrt.f64 x)))))
2
(+.f64 (*.f64 1/2 x) 2)
(fma.f64 1/2 x 2)
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) 2))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 1/2 x 2))
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) (+.f64 2 (*.f64 1/16 (pow.f64 x 3)))))
(fma.f64 -1/8 (.f64 x x) (+.f64 (fma.f64 1/2 x 2) (.f64 1/16 (pow.f64 x 3))))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 1/2 x (fma.f64 1/16 (pow.f64 x 3) 2)))
(/.f64 x (-.f64 (pow.f64 (/.f64 1 x) -1/2) 1))
(/.f64 x (+.f64 (pow.f64 (/.f64 1 x) -1/2) -1))
(+.f64 (.f64 -1/2 (.f64 (/.f64 1 (pow.f64 (-.f64 (pow.f64 (/.f64 1 x) -1/2) 1) 2)) (sqrt.f64 x))) (/.f64 x (-.f64 (pow.f64 (/.f64 1 x) -1/2) 1)))
(fma.f64 -1/2 (*.f64 (/.f64 1 (pow.f64 (+.f64 (pow.f64 (/.f64 1 x) -1/2) -1) 2)) (sqrt.f64 x)) (/.f64 x (+.f64 (pow.f64 (/.f64 1 x) -1/2) -1)))
(fma.f64 -1/2 (/.f64 (sqrt.f64 x) (pow.f64 (+.f64 (pow.f64 (/.f64 1 x) -1/2) -1) 2)) (/.f64 x (+.f64 (pow.f64 (/.f64 1 x) -1/2) -1)))
(-.f64 (+.f64 (.f64 1/4 (/.f64 1 (pow.f64 (-.f64 (pow.f64 (/.f64 1 x) -1/2) 1) 3))) (+.f64 (.f64 -1/2 (.f64 (/.f64 1 (pow.f64 (-.f64 (pow.f64 (/.f64 1 x) -1/2) 1) 2)) (sqrt.f64 x))) (/.f64 x (-.f64 (pow.f64 (/.f64 1 x) -1/2) 1)))) (.f64 -1/8 (*.f64 (/.f64 1 (pow.f64 (-.f64 (pow.f64 (/.f64 1 x) -1/2) 1) 2)) (sqrt.f64 (/.f64 1 x)))))
(+.f64 (/.f64 1/4 (pow.f64 (+.f64 (pow.f64 (/.f64 1 x) -1/2) -1) 3)) (-.f64 (fma.f64 -1/2 (.f64 (/.f64 1 (pow.f64 (+.f64 (pow.f64 (/.f64 1 x) -1/2) -1) 2)) (sqrt.f64 x)) (/.f64 x (+.f64 (pow.f64 (/.f64 1 x) -1/2) -1))) (.f64 -1/8 (/.f64 (*.f64 1 (sqrt.f64 (/.f64 1 x))) (pow.f64 (+.f64 (pow.f64 (/.f64 1 x) -1/2) -1) 2)))))
(+.f64 (fma.f64 -1/2 (/.f64 (sqrt.f64 x) (pow.f64 (+.f64 (pow.f64 (/.f64 1 x) -1/2) -1) 2)) (/.f64 x (+.f64 (pow.f64 (/.f64 1 x) -1/2) -1))) (+.f64 (/.f64 1/4 (pow.f64 (+.f64 (pow.f64 (/.f64 1 x) -1/2) -1) 3)) (/.f64 (*.f64 1/8 (sqrt.f64 (/.f64 1 x))) (pow.f64 (+.f64 (pow.f64 (/.f64 1 x) -1/2) -1) 2))))
(+.f64 (fma.f64 -1/2 (/.f64 (sqrt.f64 x) (pow.f64 (+.f64 (pow.f64 (/.f64 1 x) -1/2) -1) 2)) (/.f64 x (+.f64 (pow.f64 (/.f64 1 x) -1/2) -1))) (+.f64 (/.f64 1/4 (pow.f64 (+.f64 (pow.f64 (/.f64 1 x) -1/2) -1) 3)) (*.f64 (/.f64 (sqrt.f64 (/.f64 1 x)) (pow.f64 (+.f64 (pow.f64 (/.f64 1 x) -1/2) -1) 2)) 1/8)))
(-.f64 (+.f64 (.f64 -1/2 (.f64 (/.f64 1 (pow.f64 (-.f64 (pow.f64 (/.f64 1 x) -1/2) 1) 2)) (sqrt.f64 x))) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 1/16 (/.f64 x (pow.f64 (-.f64 (pow.f64 (/.f64 1 x) -1/2) 1) 3))) (+.f64 (.f64 1/2 (.f64 (/.f64 (-.f64 (.f64 1/4 (/.f64 x (pow.f64 (-.f64 (pow.f64 (/.f64 1 x) -1/2) 1) 3))) (.f64 -1/8 (.f64 (/.f64 1 (pow.f64 (-.f64 (pow.f64 (/.f64 1 x) -1/2) 1) 2)) (sqrt.f64 x)))) (-.f64 (pow.f64 (/.f64 1 x) -1/2) 1)) (sqrt.f64 x))) (.f64 1/16 (.f64 (/.f64 1 (pow.f64 (-.f64 (pow.f64 (/.f64 1 x) -1/2) 1) 2)) (sqrt.f64 x))))) (pow.f64 x 2))) (+.f64 (.f64 1/4 (/.f64 1 (pow.f64 (-.f64 (pow.f64 (/.f64 1 x) -1/2) 1) 3))) (/.f64 x (-.f64 (pow.f64 (/.f64 1 x) -1/2) 1))))) (.f64 -1/8 (.f64 (/.f64 1 (pow.f64 (-.f64 (pow.f64 (/.f64 1 x) -1/2) 1) 2)) (sqrt.f64 (/.f64 1 x)))))
(+.f64 (fma.f64 -1/2 (.f64 (/.f64 1 (pow.f64 (+.f64 (pow.f64 (/.f64 1 x) -1/2) -1) 2)) (sqrt.f64 x)) (fma.f64 -1 (/.f64 (fma.f64 1/16 (/.f64 x (pow.f64 (+.f64 (pow.f64 (/.f64 1 x) -1/2) -1) 3)) (fma.f64 1/2 (.f64 (sqrt.f64 x) (/.f64 (-.f64 (.f64 1/4 (/.f64 x (pow.f64 (+.f64 (pow.f64 (/.f64 1 x) -1/2) -1) 3))) (.f64 -1/8 (.f64 (/.f64 1 (pow.f64 (+.f64 (pow.f64 (/.f64 1 x) -1/2) -1) 2)) (sqrt.f64 x)))) (+.f64 (pow.f64 (/.f64 1 x) -1/2) -1))) (.f64 1/16 (.f64 (/.f64 1 (pow.f64 (+.f64 (pow.f64 (/.f64 1 x) -1/2) -1) 2)) (sqrt.f64 x))))) (.f64 x x)) (+.f64 (/.f64 x (+.f64 (pow.f64 (/.f64 1 x) -1/2) -1)) (/.f64 1/4 (pow.f64 (+.f64 (pow.f64 (/.f64 1 x) -1/2) -1) 3))))) (.f64 1/8 (/.f64 (.f64 1 (sqrt.f64 (/.f64 1 x))) (pow.f64 (+.f64 (pow.f64 (/.f64 1 x) -1/2) -1) 2))))
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(expm1.f64 (*.f64 1/2 (log1p.f64 x)))
(pow.f64 (/.f64 1 (expm1.f64 (*.f64 1/2 (log1p.f64 x)))) -1)
(.f64 x (/.f64 (expm1.f64 (.f64 1/2 (log1p.f64 x))) x))
(expm1.f64 (*.f64 1/2 (log1p.f64 x)))
(neg.f64 (/.f64 x (/.f64 (neg.f64 x) (expm1.f64 (*.f64 1/2 (log1p.f64 x))))))
(.f64 x (/.f64 (expm1.f64 (.f64 1/2 (log1p.f64 x))) x))
(expm1.f64 (*.f64 1/2 (log1p.f64 x)))
(sqrt.f64 (pow.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x))) 2))
(.f64 x (/.f64 (expm1.f64 (.f64 1/2 (log1p.f64 x))) x))
(expm1.f64 (*.f64 1/2 (log1p.f64 x)))
(log.f64 (exp.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x)))))
(.f64 x (/.f64 (expm1.f64 (.f64 1/2 (log1p.f64 x))) x))
(expm1.f64 (*.f64 1/2 (log1p.f64 x)))
(cbrt.f64 (pow.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x))) 3))
(.f64 x (/.f64 (expm1.f64 (.f64 1/2 (log1p.f64 x))) x))
(expm1.f64 (*.f64 1/2 (log1p.f64 x)))
(cbrt.f64 (/.f64 (pow.f64 x 3) (pow.f64 (/.f64 x (expm1.f64 (*.f64 1/2 (log1p.f64 x)))) 3)))
(.f64 x (/.f64 (expm1.f64 (.f64 1/2 (log1p.f64 x))) x))
(expm1.f64 (*.f64 1/2 (log1p.f64 x)))
(expm1.f64 (*.f64 1/2 (log1p.f64 x)))
(.f64 x (/.f64 (expm1.f64 (.f64 1/2 (log1p.f64 x))) x))
(exp.f64 (log.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x)))))
(.f64 x (/.f64 (expm1.f64 (.f64 1/2 (log1p.f64 x))) x))
(expm1.f64 (*.f64 1/2 (log1p.f64 x)))
(exp.f64 (.f64 (log.f64 (expm1.f64 (.f64 1/2 (log1p.f64 x)))) 1))
(.f64 x (/.f64 (expm1.f64 (.f64 1/2 (log1p.f64 x))) x))
(expm1.f64 (*.f64 1/2 (log1p.f64 x)))
(log1p.f64 (expm1.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x)))))
(.f64 x (/.f64 (expm1.f64 (.f64 1/2 (log1p.f64 x))) x))
(expm1.f64 (*.f64 1/2 (log1p.f64 x)))

localize2.0ms (0.1%)

Compiler: Compiled 6 to 4 computations (33.3% saved)

localize7.0ms (0.3%)

Local Accuracy

Found 1 expressions with local accuracy:

New	Accuracy	Program
✓	100.0%	(/.f64 x (+.f64 (*.f64 1/2 x) 2))

Compiler

Compiled 19 to 14 computations (26.3% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite100.0ms (3.4%)

Algorithm

1×	batch-egg-rewrite

Rules

1876×	`pow1`
1752×	`add-exp-log`
1750×	`log1p-expm1-u`
1750×	`expm1-log1p-u`
1722×	`add-log-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	180	15
2	2330	15

Stop Event

1×	node limit

Counts

1 → 33

Calls

Call 1

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

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

simplify69.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

1850×	`fma-def`
778×	`log-prod`
724×	`log-div`
438×	`associate-/l*`
412×	`associate-*r/`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	130	1251
1	325	1071
2	1013	887
3	4298	873

Stop Event

1×	node limit

Counts

45 → 74

Calls

Call 1

Inputs
(*.f64 1/2 x)
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (.f64 1/2 x))
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (+.f64 (.f64 1/32 (pow.f64 x 3)) (*.f64 1/2 x)))
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (+.f64 (.f64 1/32 (pow.f64 x 3)) (+.f64 (.f64 1/2 x) (.f64 -1/128 (pow.f64 x 4)))))
2
(-.f64 2 (*.f64 8 (/.f64 1 x)))
(-.f64 (+.f64 2 (.f64 32 (/.f64 1 (pow.f64 x 2)))) (.f64 8 (/.f64 1 x)))
(-.f64 (+.f64 2 (.f64 32 (/.f64 1 (pow.f64 x 2)))) (+.f64 (.f64 8 (/.f64 1 x)) (*.f64 128 (/.f64 1 (pow.f64 x 3)))))
2
(-.f64 2 (*.f64 8 (/.f64 1 x)))
(-.f64 (+.f64 2 (.f64 32 (/.f64 1 (pow.f64 x 2)))) (.f64 8 (/.f64 1 x)))
(-.f64 (+.f64 2 (.f64 32 (/.f64 1 (pow.f64 x 2)))) (+.f64 (.f64 8 (/.f64 1 x)) (*.f64 128 (/.f64 1 (pow.f64 x 3)))))
(-.f64 (+.f64 1 (/.f64 x (fma.f64 x 1/2 2))) 1)
(*.f64 x (/.f64 1 (fma.f64 x 1/2 2)))
(*.f64 (/.f64 x (fma.f64 x 1/2 2)) 1)
(*.f64 1 (/.f64 x (fma.f64 x 1/2 2)))
(*.f64 (cbrt.f64 (/.f64 x (fma.f64 x 1/2 2))) (pow.f64 (cbrt.f64 (/.f64 x (fma.f64 x 1/2 2))) 2))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 x (fma.f64 x 1/2 2))) 2) (cbrt.f64 (/.f64 x (fma.f64 x 1/2 2))))
(.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (/.f64 1 (fma.f64 x 1/2 2))))
(*.f64 (sqrt.f64 (/.f64 x (fma.f64 x 1/2 2))) (sqrt.f64 (/.f64 x (fma.f64 x 1/2 2))))
(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (/.f64 1 (fma.f64 x 1/2 2))))
(*.f64 (neg.f64 x) (/.f64 1 (neg.f64 (fma.f64 x 1/2 2))))
(*.f64 (/.f64 1 (fma.f64 x 1/2 2)) x)
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (fma.f64 x 1/2 2)) 2)) (/.f64 x (cbrt.f64 (fma.f64 x 1/2 2))))
(*.f64 (/.f64 1 (sqrt.f64 (fma.f64 x 1/2 2))) (/.f64 x (sqrt.f64 (fma.f64 x 1/2 2))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) 1) (/.f64 (cbrt.f64 x) (fma.f64 x 1/2 2)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 (fma.f64 x 1/2 2)) 2)) (cbrt.f64 (/.f64 x (fma.f64 x 1/2 2))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (sqrt.f64 (fma.f64 x 1/2 2))) (/.f64 (cbrt.f64 x) (sqrt.f64 (fma.f64 x 1/2 2))))
(*.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (fma.f64 x 1/2 2)))
(*.f64 (/.f64 (sqrt.f64 x) (pow.f64 (cbrt.f64 (fma.f64 x 1/2 2)) 2)) (/.f64 (sqrt.f64 x) (cbrt.f64 (fma.f64 x 1/2 2))))
(.f64 (/.f64 x (+.f64 (.f64 (pow.f64 x 3) 1/8) 8)) (+.f64 (.f64 (.f64 x x) 1/4) (-.f64 4 x)))
(.f64 (/.f64 x (+.f64 (.f64 (*.f64 x x) 1/4) -4)) (fma.f64 x 1/2 -2))
(pow.f64 (/.f64 x (fma.f64 x 1/2 2)) 1)
(pow.f64 (cbrt.f64 (/.f64 x (fma.f64 x 1/2 2))) 3)
(pow.f64 (pow.f64 (/.f64 x (fma.f64 x 1/2 2)) 3) 1/3)
(pow.f64 (sqrt.f64 (/.f64 x (fma.f64 x 1/2 2))) 2)
(pow.f64 (/.f64 (fma.f64 x 1/2 2) x) -1)
(neg.f64 (/.f64 x (neg.f64 (fma.f64 x 1/2 2))))
(sqrt.f64 (pow.f64 (/.f64 x (fma.f64 x 1/2 2)) 2))
(log.f64 (exp.f64 (/.f64 x (fma.f64 x 1/2 2))))
(cbrt.f64 (pow.f64 (/.f64 x (fma.f64 x 1/2 2)) 3))
(cbrt.f64 (/.f64 (pow.f64 x 3) (pow.f64 (fma.f64 x 1/2 2) 3)))
(expm1.f64 (log1p.f64 (/.f64 x (fma.f64 x 1/2 2))))
(exp.f64 (log.f64 (/.f64 x (fma.f64 x 1/2 2))))
(log1p.f64 (expm1.f64 (/.f64 x (fma.f64 x 1/2 2))))

Outputs
(*.f64 1/2 x)
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (.f64 1/2 x))
(fma.f64 -1/8 (.f64 x x) (.f64 1/2 x))
(fma.f64 1/2 x (.f64 -1/8 (.f64 x x)))
(.f64 x (+.f64 (.f64 x -1/8) 1/2))
(*.f64 x (fma.f64 x -1/8 1/2))
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (+.f64 (.f64 1/32 (pow.f64 x 3)) (*.f64 1/2 x)))
(fma.f64 -1/8 (.f64 x x) (fma.f64 1/32 (pow.f64 x 3) (.f64 1/2 x)))
(fma.f64 -1/8 (.f64 x x) (fma.f64 1/2 x (.f64 1/32 (pow.f64 x 3))))
(fma.f64 1/2 x (.f64 (.f64 x x) (+.f64 -1/8 (*.f64 x 1/32))))
(fma.f64 (.f64 x x) (fma.f64 x 1/32 -1/8) (.f64 1/2 x))
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (+.f64 (.f64 1/32 (pow.f64 x 3)) (+.f64 (.f64 1/2 x) (.f64 -1/128 (pow.f64 x 4)))))
(fma.f64 -1/8 (.f64 x x) (fma.f64 1/32 (pow.f64 x 3) (fma.f64 1/2 x (.f64 -1/128 (pow.f64 x 4)))))
(fma.f64 x (.f64 x -1/8) (fma.f64 1/32 (pow.f64 x 3) (fma.f64 1/2 x (.f64 -1/128 (pow.f64 x 4)))))
(fma.f64 1/2 x (fma.f64 -1/128 (pow.f64 x 4) (.f64 (.f64 x x) (fma.f64 x 1/32 -1/8))))
2
(-.f64 2 (*.f64 8 (/.f64 1 x)))
(-.f64 2 (/.f64 8 x))
(+.f64 2 (/.f64 -8 x))
(-.f64 (+.f64 2 (.f64 32 (/.f64 1 (pow.f64 x 2)))) (.f64 8 (/.f64 1 x)))
(+.f64 2 (-.f64 (/.f64 32 (*.f64 x x)) (/.f64 8 x)))
(+.f64 (/.f64 32 (*.f64 x x)) (+.f64 2 (/.f64 -8 x)))
(+.f64 2 (+.f64 (/.f64 32 (*.f64 x x)) (/.f64 -8 x)))
(-.f64 (+.f64 2 (.f64 32 (/.f64 1 (pow.f64 x 2)))) (+.f64 (.f64 8 (/.f64 1 x)) (*.f64 128 (/.f64 1 (pow.f64 x 3)))))
(+.f64 2 (-.f64 (/.f64 32 (*.f64 x x)) (+.f64 (/.f64 8 x) (/.f64 128 (pow.f64 x 3)))))
(+.f64 (/.f64 32 (*.f64 x x)) (-.f64 2 (+.f64 (/.f64 8 x) (/.f64 128 (pow.f64 x 3)))))
(+.f64 2 (+.f64 (/.f64 32 (*.f64 x x)) (+.f64 (/.f64 -8 x) (/.f64 -128 (pow.f64 x 3)))))
(+.f64 2 (+.f64 (+.f64 (/.f64 32 (*.f64 x x)) (/.f64 -8 x)) (/.f64 -128 (pow.f64 x 3))))
2
(-.f64 2 (*.f64 8 (/.f64 1 x)))
(-.f64 2 (/.f64 8 x))
(+.f64 2 (/.f64 -8 x))
(-.f64 (+.f64 2 (.f64 32 (/.f64 1 (pow.f64 x 2)))) (.f64 8 (/.f64 1 x)))
(+.f64 2 (-.f64 (/.f64 32 (*.f64 x x)) (/.f64 8 x)))
(+.f64 (/.f64 32 (*.f64 x x)) (+.f64 2 (/.f64 -8 x)))
(+.f64 2 (+.f64 (/.f64 32 (*.f64 x x)) (/.f64 -8 x)))
(-.f64 (+.f64 2 (.f64 32 (/.f64 1 (pow.f64 x 2)))) (+.f64 (.f64 8 (/.f64 1 x)) (*.f64 128 (/.f64 1 (pow.f64 x 3)))))
(+.f64 2 (-.f64 (/.f64 32 (*.f64 x x)) (+.f64 (/.f64 8 x) (/.f64 128 (pow.f64 x 3)))))
(+.f64 (/.f64 32 (*.f64 x x)) (-.f64 2 (+.f64 (/.f64 8 x) (/.f64 128 (pow.f64 x 3)))))
(+.f64 2 (+.f64 (/.f64 32 (*.f64 x x)) (+.f64 (/.f64 -8 x) (/.f64 -128 (pow.f64 x 3)))))
(+.f64 2 (+.f64 (+.f64 (/.f64 32 (*.f64 x x)) (/.f64 -8 x)) (/.f64 -128 (pow.f64 x 3))))
(-.f64 (+.f64 1 (/.f64 x (fma.f64 x 1/2 2))) 1)
(+.f64 1 (-.f64 (/.f64 x (fma.f64 x 1/2 2)) 1))
(+.f64 (/.f64 x (fma.f64 1/2 x 2)) 0)
(/.f64 x (fma.f64 1/2 x 2))
(*.f64 x (/.f64 1 (fma.f64 x 1/2 2)))
(+.f64 1 (-.f64 (/.f64 x (fma.f64 x 1/2 2)) 1))
(+.f64 (/.f64 x (fma.f64 1/2 x 2)) 0)
(/.f64 x (fma.f64 1/2 x 2))
(*.f64 (/.f64 x (fma.f64 x 1/2 2)) 1)
(+.f64 1 (-.f64 (/.f64 x (fma.f64 x 1/2 2)) 1))
(+.f64 (/.f64 x (fma.f64 1/2 x 2)) 0)
(/.f64 x (fma.f64 1/2 x 2))
(*.f64 1 (/.f64 x (fma.f64 x 1/2 2)))
(+.f64 1 (-.f64 (/.f64 x (fma.f64 x 1/2 2)) 1))
(+.f64 (/.f64 x (fma.f64 1/2 x 2)) 0)
(/.f64 x (fma.f64 1/2 x 2))
(*.f64 (cbrt.f64 (/.f64 x (fma.f64 x 1/2 2))) (pow.f64 (cbrt.f64 (/.f64 x (fma.f64 x 1/2 2))) 2))
(+.f64 1 (-.f64 (/.f64 x (fma.f64 x 1/2 2)) 1))
(+.f64 (/.f64 x (fma.f64 1/2 x 2)) 0)
(/.f64 x (fma.f64 1/2 x 2))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 x (fma.f64 x 1/2 2))) 2) (cbrt.f64 (/.f64 x (fma.f64 x 1/2 2))))
(+.f64 1 (-.f64 (/.f64 x (fma.f64 x 1/2 2)) 1))
(+.f64 (/.f64 x (fma.f64 1/2 x 2)) 0)
(/.f64 x (fma.f64 1/2 x 2))
(.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (/.f64 1 (fma.f64 x 1/2 2))))
(+.f64 1 (-.f64 (/.f64 x (fma.f64 x 1/2 2)) 1))
(+.f64 (/.f64 x (fma.f64 1/2 x 2)) 0)
(/.f64 x (fma.f64 1/2 x 2))
(*.f64 (sqrt.f64 (/.f64 x (fma.f64 x 1/2 2))) (sqrt.f64 (/.f64 x (fma.f64 x 1/2 2))))
(+.f64 1 (-.f64 (/.f64 x (fma.f64 x 1/2 2)) 1))
(+.f64 (/.f64 x (fma.f64 1/2 x 2)) 0)
(/.f64 x (fma.f64 1/2 x 2))
(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (/.f64 1 (fma.f64 x 1/2 2))))
(+.f64 1 (-.f64 (/.f64 x (fma.f64 x 1/2 2)) 1))
(+.f64 (/.f64 x (fma.f64 1/2 x 2)) 0)
(/.f64 x (fma.f64 1/2 x 2))
(*.f64 (neg.f64 x) (/.f64 1 (neg.f64 (fma.f64 x 1/2 2))))
(+.f64 1 (-.f64 (/.f64 x (fma.f64 x 1/2 2)) 1))
(+.f64 (/.f64 x (fma.f64 1/2 x 2)) 0)
(/.f64 x (fma.f64 1/2 x 2))
(*.f64 (/.f64 1 (fma.f64 x 1/2 2)) x)
(+.f64 1 (-.f64 (/.f64 x (fma.f64 x 1/2 2)) 1))
(+.f64 (/.f64 x (fma.f64 1/2 x 2)) 0)
(/.f64 x (fma.f64 1/2 x 2))
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (fma.f64 x 1/2 2)) 2)) (/.f64 x (cbrt.f64 (fma.f64 x 1/2 2))))
(+.f64 1 (-.f64 (/.f64 x (fma.f64 x 1/2 2)) 1))
(+.f64 (/.f64 x (fma.f64 1/2 x 2)) 0)
(/.f64 x (fma.f64 1/2 x 2))
(*.f64 (/.f64 1 (sqrt.f64 (fma.f64 x 1/2 2))) (/.f64 x (sqrt.f64 (fma.f64 x 1/2 2))))
(+.f64 1 (-.f64 (/.f64 x (fma.f64 x 1/2 2)) 1))
(+.f64 (/.f64 x (fma.f64 1/2 x 2)) 0)
(/.f64 x (fma.f64 1/2 x 2))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) 1) (/.f64 (cbrt.f64 x) (fma.f64 x 1/2 2)))
(+.f64 1 (-.f64 (/.f64 x (fma.f64 x 1/2 2)) 1))
(+.f64 (/.f64 x (fma.f64 1/2 x 2)) 0)
(/.f64 x (fma.f64 1/2 x 2))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 (fma.f64 x 1/2 2)) 2)) (cbrt.f64 (/.f64 x (fma.f64 x 1/2 2))))
(*.f64 (cbrt.f64 (/.f64 x (fma.f64 x 1/2 2))) (/.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 (fma.f64 x 1/2 2)) 2)))
(*.f64 (cbrt.f64 (/.f64 x (fma.f64 1/2 x 2))) (/.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 (fma.f64 1/2 x 2)) 2)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (sqrt.f64 (fma.f64 x 1/2 2))) (/.f64 (cbrt.f64 x) (sqrt.f64 (fma.f64 x 1/2 2))))
(+.f64 1 (-.f64 (/.f64 x (fma.f64 x 1/2 2)) 1))
(+.f64 (/.f64 x (fma.f64 1/2 x 2)) 0)
(/.f64 x (fma.f64 1/2 x 2))
(*.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (fma.f64 x 1/2 2)))
(+.f64 1 (-.f64 (/.f64 x (fma.f64 x 1/2 2)) 1))
(+.f64 (/.f64 x (fma.f64 1/2 x 2)) 0)
(/.f64 x (fma.f64 1/2 x 2))
(*.f64 (/.f64 (sqrt.f64 x) (pow.f64 (cbrt.f64 (fma.f64 x 1/2 2)) 2)) (/.f64 (sqrt.f64 x) (cbrt.f64 (fma.f64 x 1/2 2))))
(+.f64 1 (-.f64 (/.f64 x (fma.f64 x 1/2 2)) 1))
(+.f64 (/.f64 x (fma.f64 1/2 x 2)) 0)
(/.f64 x (fma.f64 1/2 x 2))
(.f64 (/.f64 x (+.f64 (.f64 (pow.f64 x 3) 1/8) 8)) (+.f64 (.f64 (.f64 x x) 1/4) (-.f64 4 x)))
(.f64 (/.f64 x (fma.f64 (pow.f64 x 3) 1/8 8)) (fma.f64 (.f64 x x) 1/4 (-.f64 4 x)))
(.f64 (/.f64 x (fma.f64 (pow.f64 x 3) 1/8 8)) (-.f64 (fma.f64 x (.f64 x 1/4) 4) x))
(/.f64 (.f64 x (fma.f64 (.f64 x x) 1/4 (-.f64 4 x))) (fma.f64 (pow.f64 x 3) 1/8 8))
(/.f64 x (/.f64 (fma.f64 (pow.f64 x 3) 1/8 8) (-.f64 (fma.f64 x (*.f64 x 1/4) 4) x)))
(.f64 (/.f64 x (+.f64 (.f64 (*.f64 x x) 1/4) -4)) (fma.f64 x 1/2 -2))
(/.f64 (.f64 x (fma.f64 x 1/2 -2)) (fma.f64 (.f64 x x) 1/4 -4))
(.f64 (/.f64 x (fma.f64 x (.f64 x 1/4) -4)) (fma.f64 1/2 x -2))
(/.f64 (.f64 x (fma.f64 1/2 x -2)) (fma.f64 (.f64 x x) 1/4 -4))
(/.f64 (fma.f64 1/2 x -2) (/.f64 (fma.f64 x (*.f64 x 1/4) -4) x))
(pow.f64 (/.f64 x (fma.f64 x 1/2 2)) 1)
(+.f64 1 (-.f64 (/.f64 x (fma.f64 x 1/2 2)) 1))
(+.f64 (/.f64 x (fma.f64 1/2 x 2)) 0)
(/.f64 x (fma.f64 1/2 x 2))
(pow.f64 (cbrt.f64 (/.f64 x (fma.f64 x 1/2 2))) 3)
(+.f64 1 (-.f64 (/.f64 x (fma.f64 x 1/2 2)) 1))
(+.f64 (/.f64 x (fma.f64 1/2 x 2)) 0)
(/.f64 x (fma.f64 1/2 x 2))
(pow.f64 (pow.f64 (/.f64 x (fma.f64 x 1/2 2)) 3) 1/3)
(+.f64 1 (-.f64 (/.f64 x (fma.f64 x 1/2 2)) 1))
(+.f64 (/.f64 x (fma.f64 1/2 x 2)) 0)
(/.f64 x (fma.f64 1/2 x 2))
(pow.f64 (sqrt.f64 (/.f64 x (fma.f64 x 1/2 2))) 2)
(+.f64 1 (-.f64 (/.f64 x (fma.f64 x 1/2 2)) 1))
(+.f64 (/.f64 x (fma.f64 1/2 x 2)) 0)
(/.f64 x (fma.f64 1/2 x 2))
(pow.f64 (/.f64 (fma.f64 x 1/2 2) x) -1)
(+.f64 1 (-.f64 (/.f64 x (fma.f64 x 1/2 2)) 1))
(+.f64 (/.f64 x (fma.f64 1/2 x 2)) 0)
(/.f64 x (fma.f64 1/2 x 2))
(neg.f64 (/.f64 x (neg.f64 (fma.f64 x 1/2 2))))
(+.f64 1 (-.f64 (/.f64 x (fma.f64 x 1/2 2)) 1))
(+.f64 (/.f64 x (fma.f64 1/2 x 2)) 0)
(/.f64 x (fma.f64 1/2 x 2))
(sqrt.f64 (pow.f64 (/.f64 x (fma.f64 x 1/2 2)) 2))
(+.f64 1 (-.f64 (/.f64 x (fma.f64 x 1/2 2)) 1))
(+.f64 (/.f64 x (fma.f64 1/2 x 2)) 0)
(/.f64 x (fma.f64 1/2 x 2))
(log.f64 (exp.f64 (/.f64 x (fma.f64 x 1/2 2))))
(+.f64 1 (-.f64 (/.f64 x (fma.f64 x 1/2 2)) 1))
(+.f64 (/.f64 x (fma.f64 1/2 x 2)) 0)
(/.f64 x (fma.f64 1/2 x 2))
(cbrt.f64 (pow.f64 (/.f64 x (fma.f64 x 1/2 2)) 3))
(+.f64 1 (-.f64 (/.f64 x (fma.f64 x 1/2 2)) 1))
(+.f64 (/.f64 x (fma.f64 1/2 x 2)) 0)
(/.f64 x (fma.f64 1/2 x 2))
(cbrt.f64 (/.f64 (pow.f64 x 3) (pow.f64 (fma.f64 x 1/2 2) 3)))
(+.f64 1 (-.f64 (/.f64 x (fma.f64 x 1/2 2)) 1))
(+.f64 (/.f64 x (fma.f64 1/2 x 2)) 0)
(/.f64 x (fma.f64 1/2 x 2))
(expm1.f64 (log1p.f64 (/.f64 x (fma.f64 x 1/2 2))))
(+.f64 1 (-.f64 (/.f64 x (fma.f64 x 1/2 2)) 1))
(+.f64 (/.f64 x (fma.f64 1/2 x 2)) 0)
(/.f64 x (fma.f64 1/2 x 2))
(exp.f64 (log.f64 (/.f64 x (fma.f64 x 1/2 2))))
(+.f64 1 (-.f64 (/.f64 x (fma.f64 x 1/2 2)) 1))
(+.f64 (/.f64 x (fma.f64 1/2 x 2)) 0)
(/.f64 x (fma.f64 1/2 x 2))
(log1p.f64 (expm1.f64 (/.f64 x (fma.f64 x 1/2 2))))
(+.f64 1 (-.f64 (/.f64 x (fma.f64 x 1/2 2)) 1))
(+.f64 (/.f64 x (fma.f64 1/2 x 2)) 0)
(/.f64 x (fma.f64 1/2 x 2))

localize7.0ms (0.2%)

Local Accuracy

Found 2 expressions with local accuracy:

New	Accuracy	Program
	100.0%	(sqrt.f64 (+.f64 x 1))
✓	94.1%	(+.f64 (sqrt.f64 (+.f64 x 1)) -1)

Compiler

Compiled 17 to 13 computations (23.5% saved)

series1.0ms (0%)

Counts

1 → 4

Calls

3 calls:

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

rewrite64.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

1798×	`pow1`
1664×	`add-exp-log`
1664×	`log1p-expm1-u`
1664×	`expm1-log1p-u`
1636×	`add-log-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	189	17
2	2335	17

Stop Event

1×	node limit

Counts

1 → 31

Calls

Call 1

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

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

simplify53.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

1268×	`distribute-lft-in`
1222×	`distribute-rgt-in`
828×	`times-frac`
612×	`div-sub`
608×	`associate-r`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	98	1363
1	237	1159
2	741	1041
3	3560	837

Stop Event

1×	node limit

Counts

35 → 53

Calls

Call 1

Inputs
(*.f64 1/2 x)
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (.f64 1/2 x))
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) (*.f64 1/16 (pow.f64 x 3))))
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) (+.f64 (.f64 -5/128 (pow.f64 x 4)) (.f64 1/16 (pow.f64 x 3)))))
(-.f64 (+.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) -1)) 1)
(-.f64 (/.f64 (+.f64 x 1) (+.f64 (sqrt.f64 (+.f64 x 1)) 1)) (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) 1)))
(*.f64 x (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) 1)))
(*.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) -1))
(*.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) -1) 1)
(*.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) -1)) (pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) -1)) 2))
(*.f64 (pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) -1)) 2) (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) -1)))
(*.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) -1)) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) -1)))
(.f64 (+.f64 -1 (pow.f64 (+.f64 x 1) 3/2)) (/.f64 1 (+.f64 (+.f64 x 1) (-.f64 1 (.f64 (sqrt.f64 (+.f64 x 1)) -1)))))
(*.f64 (+.f64 (pow.f64 (+.f64 x 1) 1/4) 1) (-.f64 (pow.f64 (+.f64 x 1) 1/4) 1))
(/.f64 x (+.f64 (sqrt.f64 (+.f64 x 1)) 1))
(/.f64 1 (/.f64 (+.f64 (+.f64 x 1) (-.f64 1 (*.f64 (sqrt.f64 (+.f64 x 1)) -1))) (+.f64 -1 (pow.f64 (+.f64 x 1) 3/2))))
(/.f64 1 (/.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) 1) x))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 x 1) 3/2)) (+.f64 (+.f64 x 1) (-.f64 1 (*.f64 (sqrt.f64 (+.f64 x 1)) -1))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 x 1) 3/2)) (+.f64 1 (-.f64 (+.f64 x 1) (*.f64 (sqrt.f64 (+.f64 x 1)) -1))))
(/.f64 (neg.f64 (+.f64 -1 (pow.f64 (+.f64 x 1) 3/2))) (neg.f64 (+.f64 (+.f64 x 1) (-.f64 1 (*.f64 (sqrt.f64 (+.f64 x 1)) -1)))))
(/.f64 (-.f64 1 (+.f64 x 1)) (-.f64 -1 (sqrt.f64 (+.f64 x 1))))
(/.f64 (neg.f64 x) (neg.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) 1)))
(pow.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) -1) 1)
(pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) -1)) 3)
(pow.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) -1) 3) 1/3)
(pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) -1)) 2)
(sqrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) -1) 2))
(log.f64 (exp.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) -1)))
(cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) -1) 3))
(expm1.f64 (log1p.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) -1)))
(exp.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) -1)))
(log1p.f64 (expm1.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) -1)))
(fma.f64 1 (sqrt.f64 (+.f64 x 1)) -1)
(fma.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1))) -1)
(fma.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4) -1)

Outputs
(*.f64 1/2 x)
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (.f64 1/2 x))
(fma.f64 -1/8 (.f64 x x) (.f64 1/2 x))
(fma.f64 1/2 x (.f64 x (.f64 x -1/8)))
(.f64 x (+.f64 1/2 (.f64 x -1/8)))
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) (*.f64 1/16 (pow.f64 x 3))))
(fma.f64 -1/8 (.f64 x x) (fma.f64 1/2 x (.f64 1/16 (pow.f64 x 3))))
(fma.f64 1/2 x (.f64 (.f64 x x) (+.f64 -1/8 (*.f64 x 1/16))))
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) (+.f64 (.f64 -5/128 (pow.f64 x 4)) (.f64 1/16 (pow.f64 x 3)))))
(fma.f64 -1/8 (.f64 x x) (fma.f64 1/2 x (fma.f64 -5/128 (pow.f64 x 4) (.f64 1/16 (pow.f64 x 3)))))
(fma.f64 -1/8 (.f64 x x) (fma.f64 1/2 x (fma.f64 1/16 (pow.f64 x 3) (.f64 -5/128 (pow.f64 x 4)))))
(fma.f64 1/2 x (fma.f64 x (.f64 x -1/8) (fma.f64 1/16 (pow.f64 x 3) (.f64 -5/128 (pow.f64 x 4)))))
(-.f64 (+.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) -1)) 1)
(+.f64 1 (-.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) -1) 1))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) -2))
(+.f64 (sqrt.f64 (+.f64 x 1)) -1)
(-.f64 (/.f64 (+.f64 x 1) (+.f64 (sqrt.f64 (+.f64 x 1)) 1)) (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) 1)))
(-.f64 (/.f64 (+.f64 x 1) (+.f64 1 (sqrt.f64 (+.f64 x 1)))) (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
(+.f64 (/.f64 (+.f64 x 1) (+.f64 1 (sqrt.f64 (+.f64 x 1)))) (/.f64 -1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
(+.f64 (/.f64 (+.f64 x 1) (+.f64 1 (sqrt.f64 (+.f64 x 1)))) (/.f64 1 (-.f64 -1 (sqrt.f64 (+.f64 x 1)))))
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
(*.f64 x (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) 1)))
(-.f64 (/.f64 (+.f64 x 1) (+.f64 1 (sqrt.f64 (+.f64 x 1)))) (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
(+.f64 (/.f64 (+.f64 x 1) (+.f64 1 (sqrt.f64 (+.f64 x 1)))) (/.f64 -1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
(+.f64 (/.f64 (+.f64 x 1) (+.f64 1 (sqrt.f64 (+.f64 x 1)))) (/.f64 1 (-.f64 -1 (sqrt.f64 (+.f64 x 1)))))
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
(*.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) -1))
(+.f64 1 (-.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) -1) 1))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) -2))
(+.f64 (sqrt.f64 (+.f64 x 1)) -1)
(*.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) -1) 1)
(+.f64 1 (-.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) -1) 1))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) -2))
(+.f64 (sqrt.f64 (+.f64 x 1)) -1)
(*.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) -1)) (pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) -1)) 2))
(+.f64 1 (-.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) -1) 1))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) -2))
(+.f64 (sqrt.f64 (+.f64 x 1)) -1)
(*.f64 (pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) -1)) 2) (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) -1)))
(+.f64 1 (-.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) -1) 1))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) -2))
(+.f64 (sqrt.f64 (+.f64 x 1)) -1)
(*.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) -1)) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) -1)))
(+.f64 1 (-.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) -1) 1))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) -2))
(+.f64 (sqrt.f64 (+.f64 x 1)) -1)
(.f64 (+.f64 -1 (pow.f64 (+.f64 x 1) 3/2)) (/.f64 1 (+.f64 (+.f64 x 1) (-.f64 1 (.f64 (sqrt.f64 (+.f64 x 1)) -1)))))
(.f64 (+.f64 -1 (pow.f64 (+.f64 x 1) 3/2)) (/.f64 1 (-.f64 (+.f64 (+.f64 x 1) 1) (.f64 (sqrt.f64 (+.f64 x 1)) -1))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 x 1) 3/2)) (+.f64 x (+.f64 2 (sqrt.f64 (+.f64 x 1)))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 x 1) 3/2)) (+.f64 2 (+.f64 x (sqrt.f64 (+.f64 x 1)))))
(*.f64 (+.f64 (pow.f64 (+.f64 x 1) 1/4) 1) (-.f64 (pow.f64 (+.f64 x 1) 1/4) 1))
(+.f64 1 (-.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) -1) 1))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) -2))
(+.f64 (sqrt.f64 (+.f64 x 1)) -1)
(/.f64 x (+.f64 (sqrt.f64 (+.f64 x 1)) 1))
(-.f64 (/.f64 (+.f64 x 1) (+.f64 1 (sqrt.f64 (+.f64 x 1)))) (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
(+.f64 (/.f64 (+.f64 x 1) (+.f64 1 (sqrt.f64 (+.f64 x 1)))) (/.f64 -1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
(+.f64 (/.f64 (+.f64 x 1) (+.f64 1 (sqrt.f64 (+.f64 x 1)))) (/.f64 1 (-.f64 -1 (sqrt.f64 (+.f64 x 1)))))
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
(/.f64 1 (/.f64 (+.f64 (+.f64 x 1) (-.f64 1 (*.f64 (sqrt.f64 (+.f64 x 1)) -1))) (+.f64 -1 (pow.f64 (+.f64 x 1) 3/2))))
(.f64 (+.f64 -1 (pow.f64 (+.f64 x 1) 3/2)) (/.f64 1 (-.f64 (+.f64 (+.f64 x 1) 1) (.f64 (sqrt.f64 (+.f64 x 1)) -1))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 x 1) 3/2)) (+.f64 x (+.f64 2 (sqrt.f64 (+.f64 x 1)))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 x 1) 3/2)) (+.f64 2 (+.f64 x (sqrt.f64 (+.f64 x 1)))))
(/.f64 1 (/.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) 1) x))
(-.f64 (/.f64 (+.f64 x 1) (+.f64 1 (sqrt.f64 (+.f64 x 1)))) (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
(+.f64 (/.f64 (+.f64 x 1) (+.f64 1 (sqrt.f64 (+.f64 x 1)))) (/.f64 -1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
(+.f64 (/.f64 (+.f64 x 1) (+.f64 1 (sqrt.f64 (+.f64 x 1)))) (/.f64 1 (-.f64 -1 (sqrt.f64 (+.f64 x 1)))))
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 x 1) 3/2)) (+.f64 (+.f64 x 1) (-.f64 1 (*.f64 (sqrt.f64 (+.f64 x 1)) -1))))
(.f64 (+.f64 -1 (pow.f64 (+.f64 x 1) 3/2)) (/.f64 1 (-.f64 (+.f64 (+.f64 x 1) 1) (.f64 (sqrt.f64 (+.f64 x 1)) -1))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 x 1) 3/2)) (+.f64 x (+.f64 2 (sqrt.f64 (+.f64 x 1)))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 x 1) 3/2)) (+.f64 2 (+.f64 x (sqrt.f64 (+.f64 x 1)))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 x 1) 3/2)) (+.f64 1 (-.f64 (+.f64 x 1) (*.f64 (sqrt.f64 (+.f64 x 1)) -1))))
(.f64 (+.f64 -1 (pow.f64 (+.f64 x 1) 3/2)) (/.f64 1 (-.f64 (+.f64 (+.f64 x 1) 1) (.f64 (sqrt.f64 (+.f64 x 1)) -1))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 x 1) 3/2)) (+.f64 x (+.f64 2 (sqrt.f64 (+.f64 x 1)))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 x 1) 3/2)) (+.f64 2 (+.f64 x (sqrt.f64 (+.f64 x 1)))))
(/.f64 (neg.f64 (+.f64 -1 (pow.f64 (+.f64 x 1) 3/2))) (neg.f64 (+.f64 (+.f64 x 1) (-.f64 1 (*.f64 (sqrt.f64 (+.f64 x 1)) -1)))))
(.f64 (+.f64 -1 (pow.f64 (+.f64 x 1) 3/2)) (/.f64 1 (-.f64 (+.f64 (+.f64 x 1) 1) (.f64 (sqrt.f64 (+.f64 x 1)) -1))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 x 1) 3/2)) (+.f64 x (+.f64 2 (sqrt.f64 (+.f64 x 1)))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 x 1) 3/2)) (+.f64 2 (+.f64 x (sqrt.f64 (+.f64 x 1)))))
(/.f64 (-.f64 1 (+.f64 x 1)) (-.f64 -1 (sqrt.f64 (+.f64 x 1))))
(-.f64 (/.f64 (+.f64 x 1) (+.f64 1 (sqrt.f64 (+.f64 x 1)))) (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
(+.f64 (/.f64 (+.f64 x 1) (+.f64 1 (sqrt.f64 (+.f64 x 1)))) (/.f64 -1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
(+.f64 (/.f64 (+.f64 x 1) (+.f64 1 (sqrt.f64 (+.f64 x 1)))) (/.f64 1 (-.f64 -1 (sqrt.f64 (+.f64 x 1)))))
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
(/.f64 (neg.f64 x) (neg.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) 1)))
(-.f64 (/.f64 (+.f64 x 1) (+.f64 1 (sqrt.f64 (+.f64 x 1)))) (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
(+.f64 (/.f64 (+.f64 x 1) (+.f64 1 (sqrt.f64 (+.f64 x 1)))) (/.f64 -1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
(+.f64 (/.f64 (+.f64 x 1) (+.f64 1 (sqrt.f64 (+.f64 x 1)))) (/.f64 1 (-.f64 -1 (sqrt.f64 (+.f64 x 1)))))
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
(pow.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) -1) 1)
(+.f64 1 (-.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) -1) 1))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) -2))
(+.f64 (sqrt.f64 (+.f64 x 1)) -1)
(pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) -1)) 3)
(+.f64 1 (-.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) -1) 1))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) -2))
(+.f64 (sqrt.f64 (+.f64 x 1)) -1)
(pow.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) -1) 3) 1/3)
(+.f64 1 (-.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) -1) 1))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) -2))
(+.f64 (sqrt.f64 (+.f64 x 1)) -1)
(pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) -1)) 2)
(+.f64 1 (-.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) -1) 1))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) -2))
(+.f64 (sqrt.f64 (+.f64 x 1)) -1)
(sqrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) -1) 2))
(+.f64 1 (-.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) -1) 1))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) -2))
(+.f64 (sqrt.f64 (+.f64 x 1)) -1)
(log.f64 (exp.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) -1)))
(+.f64 1 (-.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) -1) 1))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) -2))
(+.f64 (sqrt.f64 (+.f64 x 1)) -1)
(cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) -1) 3))
(+.f64 1 (-.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) -1) 1))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) -2))
(+.f64 (sqrt.f64 (+.f64 x 1)) -1)
(expm1.f64 (log1p.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) -1)))
(+.f64 1 (-.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) -1) 1))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) -2))
(+.f64 (sqrt.f64 (+.f64 x 1)) -1)
(exp.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) -1)))
(+.f64 1 (-.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) -1) 1))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) -2))
(+.f64 (sqrt.f64 (+.f64 x 1)) -1)
(log1p.f64 (expm1.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) -1)))
(+.f64 1 (-.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) -1) 1))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) -2))
(+.f64 (sqrt.f64 (+.f64 x 1)) -1)
(fma.f64 1 (sqrt.f64 (+.f64 x 1)) -1)
(+.f64 1 (-.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) -1) 1))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) -2))
(+.f64 (sqrt.f64 (+.f64 x 1)) -1)
(fma.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1))) -1)
(fma.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4) -1)
(+.f64 1 (-.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) -1) 1))
(+.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) -2))
(+.f64 (sqrt.f64 (+.f64 x 1)) -1)

localize7.0ms (0.2%)

Local Accuracy

Found 1 expressions with local accuracy:

New	Accuracy	Program
✓	99.7%	(fma.f64 -1/8 (.f64 x x) (.f64 1/2 x))

Compiler

Compiled 18 to 10 computations (44.4% saved)

series2.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(fma.f64 -1/8 (.f64 x x) (.f64 1/2 x))
0.0ms	x	@	inf	(fma.f64 -1/8 (.f64 x x) (.f64 1/2 x))
0.0ms	x	@	-inf	(fma.f64 -1/8 (.f64 x x) (.f64 1/2 x))

rewrite98.0ms (3.3%)

Algorithm

1×	batch-egg-rewrite

Rules

1556×	`pow1`
1434×	`add-exp-log`
1434×	`log1p-expm1-u`
1434×	`expm1-log1p-u`
1402×	`add-log-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	21
1	181	21
2	2004	21

Stop Event

1×	node limit

Counts

1 → 21

Calls

Call 1

Inputs
(fma.f64 -1/8 (.f64 x x) (.f64 1/2 x))

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

simplify48.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

1028×	`associate-/l*`
890×	`distribute-rgt-in`
880×	`distribute-lft-in`
656×	`associate-/r*`
562×	`fma-def`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	61	809
1	160	709
2	660	577
3	2596	547

Stop Event

1×	node limit

Counts

33 → 37

Calls

Call 1

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

Outputs
(*.f64 1/2 x)
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (.f64 1/2 x))
(fma.f64 x 1/2 (.f64 -1/8 (.f64 x x)))
(.f64 x (+.f64 1/2 (.f64 x -1/8)))
(*.f64 x (fma.f64 x -1/8 1/2))
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (.f64 1/2 x))
(fma.f64 x 1/2 (.f64 -1/8 (.f64 x x)))
(.f64 x (+.f64 1/2 (.f64 x -1/8)))
(*.f64 x (fma.f64 x -1/8 1/2))
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (.f64 1/2 x))
(fma.f64 x 1/2 (.f64 -1/8 (.f64 x x)))
(.f64 x (+.f64 1/2 (.f64 x -1/8)))
(*.f64 x (fma.f64 x -1/8 1/2))
(*.f64 -1/8 (pow.f64 x 2))
(.f64 -1/8 (.f64 x x))
(.f64 x (.f64 x -1/8))
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (.f64 1/2 x))
(fma.f64 x 1/2 (.f64 -1/8 (.f64 x x)))
(.f64 x (+.f64 1/2 (.f64 x -1/8)))
(*.f64 x (fma.f64 x -1/8 1/2))
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (.f64 1/2 x))
(fma.f64 x 1/2 (.f64 -1/8 (.f64 x x)))
(.f64 x (+.f64 1/2 (.f64 x -1/8)))
(*.f64 x (fma.f64 x -1/8 1/2))
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (.f64 1/2 x))
(fma.f64 x 1/2 (.f64 -1/8 (.f64 x x)))
(.f64 x (+.f64 1/2 (.f64 x -1/8)))
(*.f64 x (fma.f64 x -1/8 1/2))
(*.f64 -1/8 (pow.f64 x 2))
(.f64 -1/8 (.f64 x x))
(.f64 x (.f64 x -1/8))
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (.f64 1/2 x))
(fma.f64 x 1/2 (.f64 -1/8 (.f64 x x)))
(.f64 x (+.f64 1/2 (.f64 x -1/8)))
(*.f64 x (fma.f64 x -1/8 1/2))
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (.f64 1/2 x))
(fma.f64 x 1/2 (.f64 -1/8 (.f64 x x)))
(.f64 x (+.f64 1/2 (.f64 x -1/8)))
(*.f64 x (fma.f64 x -1/8 1/2))
(+.f64 (.f64 -1/8 (pow.f64 x 2)) (.f64 1/2 x))
(fma.f64 x 1/2 (.f64 -1/8 (.f64 x x)))
(.f64 x (+.f64 1/2 (.f64 x -1/8)))
(*.f64 x (fma.f64 x -1/8 1/2))
(+.f64 (.f64 x 1/2) (.f64 -1/8 (*.f64 x x)))
(fma.f64 x 1/2 (.f64 -1/8 (.f64 x x)))
(.f64 x (+.f64 1/2 (.f64 x -1/8)))
(*.f64 x (fma.f64 x -1/8 1/2))
(+.f64 (.f64 -1/8 (.f64 x x)) (*.f64 x 1/2))
(fma.f64 x 1/2 (.f64 -1/8 (.f64 x x)))
(.f64 x (+.f64 1/2 (.f64 x -1/8)))
(*.f64 x (fma.f64 x -1/8 1/2))
(+.f64 (.f64 (.f64 -1/8 (.f64 x x)) 1) (.f64 x 1/2))
(fma.f64 x 1/2 (.f64 -1/8 (.f64 x x)))
(.f64 x (+.f64 1/2 (.f64 x -1/8)))
(*.f64 x (fma.f64 x -1/8 1/2))
(-.f64 (+.f64 1 (fma.f64 -1/8 (.f64 x x) (.f64 x 1/2))) 1)
(fma.f64 x 1/2 (.f64 -1/8 (.f64 x x)))
(.f64 x (+.f64 1/2 (.f64 x -1/8)))
(*.f64 x (fma.f64 x -1/8 1/2))
(.f64 (fma.f64 -1/8 (.f64 x x) (*.f64 x 1/2)) 1)
(fma.f64 x 1/2 (.f64 -1/8 (.f64 x x)))
(.f64 x (+.f64 1/2 (.f64 x -1/8)))
(*.f64 x (fma.f64 x -1/8 1/2))
(.f64 1 (fma.f64 -1/8 (.f64 x x) (*.f64 x 1/2)))
(fma.f64 x 1/2 (.f64 -1/8 (.f64 x x)))
(.f64 x (+.f64 1/2 (.f64 x -1/8)))
(*.f64 x (fma.f64 x -1/8 1/2))
(.f64 (cbrt.f64 (fma.f64 -1/8 (.f64 x x) (.f64 x 1/2))) (pow.f64 (cbrt.f64 (fma.f64 -1/8 (.f64 x x) (*.f64 x 1/2))) 2))
(fma.f64 x 1/2 (.f64 -1/8 (.f64 x x)))
(.f64 x (+.f64 1/2 (.f64 x -1/8)))
(*.f64 x (fma.f64 x -1/8 1/2))
(.f64 (pow.f64 (cbrt.f64 (fma.f64 -1/8 (.f64 x x) (.f64 x 1/2))) 2) (cbrt.f64 (fma.f64 -1/8 (.f64 x x) (*.f64 x 1/2))))
(fma.f64 x 1/2 (.f64 -1/8 (.f64 x x)))
(.f64 x (+.f64 1/2 (.f64 x -1/8)))
(*.f64 x (fma.f64 x -1/8 1/2))
(.f64 (sqrt.f64 (fma.f64 -1/8 (.f64 x x) (.f64 x 1/2))) (sqrt.f64 (fma.f64 -1/8 (.f64 x x) (*.f64 x 1/2))))
(fma.f64 x 1/2 (.f64 -1/8 (.f64 x x)))
(.f64 x (+.f64 1/2 (.f64 x -1/8)))
(*.f64 x (fma.f64 x -1/8 1/2))
(/.f64 (+.f64 (pow.f64 (.f64 -1/8 (.f64 x x)) 3) (pow.f64 (.f64 x 1/2) 3)) (+.f64 (.f64 (.f64 -1/8 (.f64 x x)) (.f64 -1/8 (.f64 x x))) (-.f64 (pow.f64 (.f64 x 1/2) 2) (.f64 (.f64 -1/8 (.f64 x x)) (*.f64 x 1/2)))))
(/.f64 (+.f64 (pow.f64 (.f64 -1/8 (.f64 x x)) 3) (.f64 (pow.f64 x 3) 1/8)) (+.f64 (.f64 1/64 (.f64 (.f64 x x) (.f64 x x))) (-.f64 (pow.f64 (.f64 1/2 x) 2) (.f64 -1/8 (.f64 (.f64 x x) (.f64 1/2 x))))))
(/.f64 (fma.f64 -1/512 (pow.f64 (.f64 x x) 3) (.f64 (pow.f64 x 3) 1/8)) (+.f64 (fma.f64 1/64 (pow.f64 x 4) (.f64 (.f64 x x) 1/4)) (.f64 (.f64 -1/8 (pow.f64 x 3)) -1/2)))
(/.f64 (fma.f64 -1/512 (pow.f64 x 6) (.f64 (pow.f64 x 3) 1/8)) (fma.f64 (.f64 1/2 x) (.f64 x (-.f64 1/2 (.f64 x -1/8))) (*.f64 1/64 (pow.f64 x 4))))
(/.f64 (fma.f64 -1/512 (pow.f64 x 6) (.f64 (pow.f64 x 3) 1/8)) (fma.f64 (.f64 x x) 1/4 (.f64 (.f64 -1/8 (pow.f64 x 3)) (fma.f64 x -1/8 -1/2))))
(/.f64 (-.f64 (.f64 (.f64 -1/8 (.f64 x x)) (.f64 -1/8 (.f64 x x))) (pow.f64 (.f64 x 1/2) 2)) (-.f64 (.f64 -1/8 (.f64 x x)) (*.f64 x 1/2)))
(/.f64 (-.f64 (.f64 1/64 (.f64 (.f64 x x) (.f64 x x))) (pow.f64 (.f64 1/2 x) 2)) (-.f64 (.f64 -1/8 (.f64 x x)) (.f64 1/2 x)))
(/.f64 (fma.f64 1/64 (pow.f64 x 4) (neg.f64 (.f64 (.f64 x x) 1/4))) (.f64 x (-.f64 (.f64 x -1/8) 1/2)))
(/.f64 (fma.f64 1/64 (pow.f64 x 4) (.f64 (.f64 x x) -1/4)) (*.f64 x (fma.f64 x -1/8 -1/2)))
(*.f64 x (/.f64 (fma.f64 x -1/8 1/2) 1))
(pow.f64 (fma.f64 -1/8 (.f64 x x) (.f64 x 1/2)) 1)
(fma.f64 x 1/2 (.f64 -1/8 (.f64 x x)))
(.f64 x (+.f64 1/2 (.f64 x -1/8)))
(*.f64 x (fma.f64 x -1/8 1/2))
(pow.f64 (cbrt.f64 (fma.f64 -1/8 (.f64 x x) (.f64 x 1/2))) 3)
(fma.f64 x 1/2 (.f64 -1/8 (.f64 x x)))
(.f64 x (+.f64 1/2 (.f64 x -1/8)))
(*.f64 x (fma.f64 x -1/8 1/2))
(pow.f64 (pow.f64 (fma.f64 -1/8 (.f64 x x) (.f64 x 1/2)) 3) 1/3)
(fma.f64 x 1/2 (.f64 -1/8 (.f64 x x)))
(.f64 x (+.f64 1/2 (.f64 x -1/8)))
(*.f64 x (fma.f64 x -1/8 1/2))
(pow.f64 (sqrt.f64 (fma.f64 -1/8 (.f64 x x) (.f64 x 1/2))) 2)
(fma.f64 x 1/2 (.f64 -1/8 (.f64 x x)))
(.f64 x (+.f64 1/2 (.f64 x -1/8)))
(*.f64 x (fma.f64 x -1/8 1/2))
(sqrt.f64 (pow.f64 (fma.f64 -1/8 (.f64 x x) (.f64 x 1/2)) 2))
(fma.f64 x 1/2 (.f64 -1/8 (.f64 x x)))
(.f64 x (+.f64 1/2 (.f64 x -1/8)))
(*.f64 x (fma.f64 x -1/8 1/2))
(log.f64 (exp.f64 (fma.f64 -1/8 (.f64 x x) (.f64 x 1/2))))
(fma.f64 x 1/2 (.f64 -1/8 (.f64 x x)))
(.f64 x (+.f64 1/2 (.f64 x -1/8)))
(*.f64 x (fma.f64 x -1/8 1/2))
(cbrt.f64 (pow.f64 (fma.f64 -1/8 (.f64 x x) (.f64 x 1/2)) 3))
(fma.f64 x 1/2 (.f64 -1/8 (.f64 x x)))
(.f64 x (+.f64 1/2 (.f64 x -1/8)))
(*.f64 x (fma.f64 x -1/8 1/2))
(expm1.f64 (log1p.f64 (fma.f64 -1/8 (.f64 x x) (.f64 x 1/2))))
(fma.f64 x 1/2 (.f64 -1/8 (.f64 x x)))
(.f64 x (+.f64 1/2 (.f64 x -1/8)))
(*.f64 x (fma.f64 x -1/8 1/2))
(exp.f64 (log.f64 (fma.f64 -1/8 (.f64 x x) (.f64 x 1/2))))
(fma.f64 x 1/2 (.f64 -1/8 (.f64 x x)))
(.f64 x (+.f64 1/2 (.f64 x -1/8)))
(*.f64 x (fma.f64 x -1/8 1/2))
(log1p.f64 (expm1.f64 (fma.f64 -1/8 (.f64 x x) (.f64 x 1/2))))
(fma.f64 x 1/2 (.f64 -1/8 (.f64 x x)))
(.f64 x (+.f64 1/2 (.f64 x -1/8)))
(*.f64 x (fma.f64 x -1/8 1/2))

eval228.0ms (7.8%)

Compiler: Compiled 7783 to 5916 computations (24% saved)

prune48.0ms (1.6%)

Pruning

7 alts after pruning (2 fresh and 5 done)

	Pruned	Kept	Total
New	396	2	398
Fresh	0	0	0
Picked	1	0	1
Done	0	5	5
Total	397	7	404

Accurracy

100.0%

Counts

404 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	97.9%	(/.f64 x (/.f64 x (expm1.f64 (*.f64 1/2 (log1p.f64 x)))))
✓	74.1%	(/.f64 x (+.f64 (*.f64 1/2 x) 2))
✓	99.8%	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
✓	73.4%	(/.f64 x 2)
▶	72.2%	(+.f64 (.f64 x 1/2) (.f64 -1/8 (*.f64 x x)))
✓	33.3%	(+.f64 (sqrt.f64 (+.f64 x 1)) -1)
	4.7%	2

Compiler

Compiled 50 to 38 computations (24% saved)

localize8.0ms (0.3%)

Local Accuracy

Found 1 expressions with local accuracy:

New	Accuracy	Program
✓	99.7%	(.f64 -1/8 (.f64 x x))

Compiler

Compiled 24 to 13 computations (45.8% saved)

series32.0ms (1.1%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
32.0ms	x	@	inf	(.f64 -1/8 (.f64 x x))
0.0ms	x	@	0	(.f64 -1/8 (.f64 x x))
0.0ms	x	@	-inf	(.f64 -1/8 (.f64 x x))

rewrite47.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

1058×	`pow1`
1028×	`add-sqr-sqrt`
980×	`add-exp-log`
980×	`log1p-expm1-u`
980×	`expm1-log1p-u`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	13
1	122	13
2	1386	13

Stop Event

1×	node limit

Counts

1 → 11

Calls

Call 1

Inputs
(.f64 -1/8 (.f64 x x))

Outputs
(-.f64 (+.f64 1 (.f64 -1/8 (.f64 x x))) 1)
(pow.f64 (.f64 -1/8 (.f64 x x)) 1)
(pow.f64 (cbrt.f64 (.f64 -1/8 (.f64 x x))) 3)
(pow.f64 (pow.f64 (.f64 -1/8 (.f64 x x)) 3) 1/3)
(pow.f64 (*.f64 x (sqrt.f64 -1/8)) 2)
(sqrt.f64 (*.f64 1/64 (pow.f64 x 4)))
(log.f64 (pow.f64 (exp.f64 -1/8) (*.f64 x x)))
(cbrt.f64 (pow.f64 (.f64 -1/8 (.f64 x x)) 3))
(expm1.f64 (log1p.f64 (.f64 -1/8 (.f64 x x))))
(exp.f64 (log.f64 (.f64 -1/8 (.f64 x x))))
(log1p.f64 (expm1.f64 (.f64 -1/8 (.f64 x x))))

simplify82.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

2120×	`log-prod`
1106×	`distribute-rgt-in`
1092×	`distribute-lft-in`
768×	`associate-r`
676×	`associate-l`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	299
1	91	299
2	321	299
3	2105	299
4	6977	299

Stop Event

1×	node limit

Counts

23 → 14

Calls

Call 1

Inputs
(*.f64 -1/8 (pow.f64 x 2))
(*.f64 -1/8 (pow.f64 x 2))
(*.f64 -1/8 (pow.f64 x 2))
(*.f64 -1/8 (pow.f64 x 2))
(*.f64 -1/8 (pow.f64 x 2))
(*.f64 -1/8 (pow.f64 x 2))
(*.f64 -1/8 (pow.f64 x 2))
(*.f64 -1/8 (pow.f64 x 2))
(*.f64 -1/8 (pow.f64 x 2))
(*.f64 -1/8 (pow.f64 x 2))
(*.f64 -1/8 (pow.f64 x 2))
(*.f64 -1/8 (pow.f64 x 2))
(-.f64 (+.f64 1 (.f64 -1/8 (.f64 x x))) 1)
(pow.f64 (.f64 -1/8 (.f64 x x)) 1)
(pow.f64 (cbrt.f64 (.f64 -1/8 (.f64 x x))) 3)
(pow.f64 (pow.f64 (.f64 -1/8 (.f64 x x)) 3) 1/3)
(pow.f64 (*.f64 x (sqrt.f64 -1/8)) 2)
(sqrt.f64 (*.f64 1/64 (pow.f64 x 4)))
(log.f64 (pow.f64 (exp.f64 -1/8) (*.f64 x x)))
(cbrt.f64 (pow.f64 (.f64 -1/8 (.f64 x x)) 3))
(expm1.f64 (log1p.f64 (.f64 -1/8 (.f64 x x))))
(exp.f64 (log.f64 (.f64 -1/8 (.f64 x x))))
(log1p.f64 (expm1.f64 (.f64 -1/8 (.f64 x x))))

Outputs
(*.f64 -1/8 (pow.f64 x 2))
(.f64 -1/8 (.f64 x x))
(.f64 x (.f64 -1/8 x))
(*.f64 -1/8 (pow.f64 x 2))
(.f64 -1/8 (.f64 x x))
(.f64 x (.f64 -1/8 x))
(*.f64 -1/8 (pow.f64 x 2))
(.f64 -1/8 (.f64 x x))
(.f64 x (.f64 -1/8 x))
(*.f64 -1/8 (pow.f64 x 2))
(.f64 -1/8 (.f64 x x))
(.f64 x (.f64 -1/8 x))
(*.f64 -1/8 (pow.f64 x 2))
(.f64 -1/8 (.f64 x x))
(.f64 x (.f64 -1/8 x))
(*.f64 -1/8 (pow.f64 x 2))
(.f64 -1/8 (.f64 x x))
(.f64 x (.f64 -1/8 x))
(*.f64 -1/8 (pow.f64 x 2))
(.f64 -1/8 (.f64 x x))
(.f64 x (.f64 -1/8 x))
(*.f64 -1/8 (pow.f64 x 2))
(.f64 -1/8 (.f64 x x))
(.f64 x (.f64 -1/8 x))
(*.f64 -1/8 (pow.f64 x 2))
(.f64 -1/8 (.f64 x x))
(.f64 x (.f64 -1/8 x))
(*.f64 -1/8 (pow.f64 x 2))
(.f64 -1/8 (.f64 x x))
(.f64 x (.f64 -1/8 x))
(*.f64 -1/8 (pow.f64 x 2))
(.f64 -1/8 (.f64 x x))
(.f64 x (.f64 -1/8 x))
(*.f64 -1/8 (pow.f64 x 2))
(.f64 -1/8 (.f64 x x))
(.f64 x (.f64 -1/8 x))
(-.f64 (+.f64 1 (.f64 -1/8 (.f64 x x))) 1)
(.f64 -1/8 (.f64 x x))
(.f64 x (.f64 -1/8 x))
(pow.f64 (.f64 -1/8 (.f64 x x)) 1)
(.f64 -1/8 (.f64 x x))
(.f64 x (.f64 -1/8 x))
(pow.f64 (cbrt.f64 (.f64 -1/8 (.f64 x x))) 3)
(.f64 -1/8 (.f64 x x))
(.f64 x (.f64 -1/8 x))
(pow.f64 (pow.f64 (.f64 -1/8 (.f64 x x)) 3) 1/3)
(.f64 -1/8 (.f64 x x))
(.f64 x (.f64 -1/8 x))
(pow.f64 (*.f64 x (sqrt.f64 -1/8)) 2)
(.f64 -1/8 (.f64 x x))
(.f64 x (.f64 -1/8 x))
(sqrt.f64 (*.f64 1/64 (pow.f64 x 4)))
(.f64 -1/8 (.f64 x x))
(.f64 x (.f64 -1/8 x))
(log.f64 (pow.f64 (exp.f64 -1/8) (*.f64 x x)))
(.f64 -1/8 (.f64 x x))
(.f64 x (.f64 -1/8 x))
(cbrt.f64 (pow.f64 (.f64 -1/8 (.f64 x x)) 3))
(.f64 -1/8 (.f64 x x))
(.f64 x (.f64 -1/8 x))
(expm1.f64 (log1p.f64 (.f64 -1/8 (.f64 x x))))
(.f64 -1/8 (.f64 x x))
(.f64 x (.f64 -1/8 x))
(exp.f64 (log.f64 (.f64 -1/8 (.f64 x x))))
(.f64 -1/8 (.f64 x x))
(.f64 x (.f64 -1/8 x))
(log1p.f64 (expm1.f64 (.f64 -1/8 (.f64 x x))))
(.f64 -1/8 (.f64 x x))
(.f64 x (.f64 -1/8 x))

eval3.0ms (0.1%)

Compiler: Compiled 153 to 105 computations (31.4% saved)

prune4.0ms (0.1%)

Pruning

7 alts after pruning (1 fresh and 6 done)

	Pruned	Kept	Total
New	14	0	14
Fresh	0	1	1
Picked	0	1	1
Done	0	5	5
Total	14	7	21

Accurracy

100.0%

Counts

21 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	97.9%	(/.f64 x (/.f64 x (expm1.f64 (*.f64 1/2 (log1p.f64 x)))))
✓	74.1%	(/.f64 x (+.f64 (*.f64 1/2 x) 2))
✓	99.8%	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
✓	73.4%	(/.f64 x 2)
✓	72.2%	(+.f64 (.f64 x 1/2) (.f64 -1/8 (*.f64 x x)))
✓	33.3%	(+.f64 (sqrt.f64 (+.f64 x 1)) -1)
	4.7%	2

Compiler

Compiled 50 to 38 computations (24% saved)

eval0.0ms (0%)

Compiler: Compiled 1 to 1 computations (0% saved)

prune3.0ms (0.1%)

Pruning

7 alts after pruning (1 fresh and 6 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	6	6
Total	7	7

Accurracy

100.0%

Counts

7 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	97.9%	(/.f64 x (/.f64 x (expm1.f64 (*.f64 1/2 (log1p.f64 x)))))
✓	74.1%	(/.f64 x (+.f64 (*.f64 1/2 x) 2))
✓	99.8%	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
✓	73.4%	(/.f64 x 2)
✓	72.2%	(+.f64 (.f64 x 1/2) (.f64 -1/8 (*.f64 x x)))
✓	33.3%	(+.f64 (sqrt.f64 (+.f64 x 1)) -1)
	4.7%	2

Compiler

Compiled 50 to 38 computations (24% saved)

regimes12.0ms (0.4%)

Counts

8 → 1

Calls

Call 1

Inputs
2
(/.f64 x 2)
(/.f64 x (+.f64 (*.f64 1/2 x) 2))
(+.f64 (.f64 x 1/2) (.f64 -1/8 (*.f64 x x)))
(+.f64 (sqrt.f64 (+.f64 x 1)) -1)
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
(fma.f64 -1/8 (.f64 x x) (.f64 1/2 x))
(/.f64 x (/.f64 x (expm1.f64 (*.f64 1/2 (log1p.f64 x)))))

Outputs
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))

Calls

2 calls:

6.0ms	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
5.0ms	x

Results

Accuracy	Segments	Branch
99.8%	1	`x`
99.8%	1	`(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))`

Compiler

Compiled 63 to 44 computations (30.2% saved)

regimes14.0ms (0.5%)

Counts

5 → 2

Calls

Call 1

Inputs
2
(/.f64 x 2)
(/.f64 x (+.f64 (*.f64 1/2 x) 2))
(+.f64 (.f64 x 1/2) (.f64 -1/8 (*.f64 x x)))
(+.f64 (sqrt.f64 (+.f64 x 1)) -1)

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

Calls

1 calls:

13.0ms

Results

Accuracy	Segments	Branch
99.1%	2	`x`

Compiler

Compiled 29 to 21 computations (27.6% saved)

bsearch10.0ms (0.3%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
10.0ms	5.926125336270423e-6	4.5489564703313723e-5

Results

9.0ms

96×

body

256

valid

Compiler

Compiled 115 to 94 computations (18.3% saved)

regimes5.0ms (0.2%)

Counts

4 → 1

Calls

Call 1

Inputs
2
(/.f64 x 2)
(/.f64 x (+.f64 (*.f64 1/2 x) 2))
(+.f64 (.f64 x 1/2) (.f64 -1/8 (*.f64 x x)))

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

Calls

1 calls:

4.0ms

Results

Accuracy	Segments	Branch
74.1%	1	`x`

Compiler

Compiled 23 to 16 computations (30.4% saved)

regimes4.0ms (0.1%)

Accuracy

Total -44.0b remaining (-258.1%)

Threshold costs -44b (-258.1%)

Counts

2 → 1

Calls

Call 1

Inputs
2
(/.f64 x 2)

Outputs
(/.f64 x 2)

Calls

1 calls:

4.0ms

Results

Accuracy	Segments	Branch
73.4%	1	`x`

Compiler

Compiled 7 to 5 computations (28.6% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

8×	`+-commutative`
2×	`1-exp`
2×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	95
1	30	95

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
(if (<=.f64 x 1357680363825023/147573952589676412928) (/.f64 x (+.f64 (*.f64 1/2 x) 2)) (+.f64 (sqrt.f64 (+.f64 x 1)) -1))
(/.f64 x (+.f64 (*.f64 1/2 x) 2))
(/.f64 x 2)
2

Outputs
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
(if (<=.f64 x 1357680363825023/147573952589676412928) (/.f64 x (+.f64 (*.f64 1/2 x) 2)) (+.f64 (sqrt.f64 (+.f64 x 1)) -1))
(if (<=.f64 x 1357680363825023/147573952589676412928) (/.f64 x (+.f64 (*.f64 x 1/2) 2)) (+.f64 (sqrt.f64 (+.f64 x 1)) -1))
(/.f64 x (+.f64 (*.f64 1/2 x) 2))
(/.f64 x (+.f64 (*.f64 x 1/2) 2))
(/.f64 x 2)
2

Compiler

Compiled 41 to 32 computations (22% saved)

soundness280.0ms (9.6%)

Rules

1736×	`fma-def`
892×	`unswap-sqr`
882×	`log-prod`
876×	`distribute-lft-in`
852×	`distribute-rgt-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	51
1	195	51
2	2725	51
0	316	3885
1	715	3601
2	2364	3515

Stop Event

1×	node limit
1×	node limit

Compiler

Compiled 227 to 177 computations (22% saved)

end31.0ms (1%)

Compiler: Compiled 37 to 28 computations (24.3% saved)

Details

analyze3.0ms (0.1%)

sample698.0ms (23.8%)

preprocess14.0ms (0.5%)

simplify11.0ms (0.4%)

eval0.0ms (0%)

prune1.0ms (0%)

localize10.0ms (0.3%)

series4.0ms (0.1%)

rewrite76.0ms (2.6%)

simplify70.0ms (2.4%)

eval57.0ms (1.9%)

prune240.0ms (8.2%)

localize13.0ms (0.5%)

series6.0ms (0.2%)

rewrite344.0ms (11.8%)

simplify105.0ms (3.6%)

localize2.0ms (0.1%)

localize7.0ms (0.3%)

series1.0ms (0%)

rewrite100.0ms (3.4%)

simplify69.0ms (2.3%)

localize7.0ms (0.2%)

series1.0ms (0%)

rewrite64.0ms (2.2%)

simplify53.0ms (1.8%)

localize7.0ms (0.2%)

series2.0ms (0.1%)

rewrite98.0ms (3.3%)

simplify48.0ms (1.6%)

eval228.0ms (7.8%)

prune48.0ms (1.6%)

localize8.0ms (0.3%)

series32.0ms (1.1%)

rewrite47.0ms (1.6%)

simplify82.0ms (2.8%)

eval3.0ms (0.1%)

prune4.0ms (0.1%)

eval0.0ms (0%)

prune3.0ms (0.1%)

regimes12.0ms (0.4%)

regimes14.0ms (0.5%)

bsearch10.0ms (0.3%)

regimes5.0ms (0.2%)

regimes4.0ms (0.1%)

simplify6.0ms (0.2%)

soundness280.0ms (9.6%)

end31.0ms (1%)

Profiling