Details

analyze0.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

Compiler

Compiled 13 to 12 computations (7.7% saved)

sample1.7s (24.1%)

Results

781.0ms	2050×	body	1024	valid
610.0ms	4956×	body	256	valid
223.0ms	1039×	body	512	valid
88.0ms	211×	body	2048	valid

preprocess79.0ms (1.1%)

Algorithm

2×	egg-herbie

Rules

868×	`unswap-sqr_binary64`
382×	`associate-l_binary64`
378×	`fma-def_binary64`
314×	`associate-/l/_binary64`
290×	`fma-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	30
1	29	30
2	41	30
3	58	30
4	103	30
5	226	30
6	599	30
7	1901	30
8	4969	30
9	6394	30
0	2	2

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0
1

Outputs
0
1

Call 2

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

Outputs
(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)
(+.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x))) -1)
(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 y)))) 1)
(+.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) y))) -1)

Compiler

Compiled 14 to 13 computations (7.1% saved)

simplify59.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

981×	`times-frac_binary64`
942×	`fma-neg_binary64`
434×	`unswap-sqr_binary64`
363×	`associate-*l/_binary64`
344×	`associate-/l*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	15
1	19	15
2	25	15
3	34	15
4	59	15
5	124	15
6	325	15
7	1000	15
8	2582	15
9	4196	15
10	7165	15

Stop Event

1×	node limit

Counts

1 → 2

Calls

Call 1

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

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

eval1.0ms (0%)

Compiler: Compiled 22 to 20 computations (9.1% saved)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

29.1b

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	29.1b	(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)

Compiler

Compiled 12 to 11 computations (8.3% saved)

localize19.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (exp.f64 (*.f64 -2 x)))
✓	0.0b	(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))
✓	1.9b	(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)

Compiler

Compiled 37 to 31 computations (16.2% saved)

series5.0ms (0.1%)

Counts

3 → 20

Calls

9 calls:

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

rewrite82.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

426×	`log-prod_binary64`
329×	`exp-prod_binary64`
259×	`prod-diff_binary64`
252×	`pow2_binary64`
245×	`pow-prod-down_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	36
1	217	36
2	2720	36

Stop Event

1×	node limit

Counts

3 → 146

Calls

Call 1

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

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

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

simplify57.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

972×	`fma-def_binary64`
612×	`associate-*l/_binary64`
548×	`associate-*r/_binary64`
491×	`associate-/l/_binary64`
451×	`unswap-sqr_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	41	243
1	112	239
2	261	237
3	737	231
4	1648	228
5	2839	228
6	4167	228

Stop Event

1×	node limit

Counts

166 → 168

Calls

Call 1

Inputs
x
(+.f64 (*.f64 -1/3 (pow.f64 x 3)) x)
(+.f64 (.f64 -1/3 (pow.f64 x 3)) (+.f64 (.f64 2/15 (pow.f64 x 5)) x))
(+.f64 (.f64 -17/315 (pow.f64 x 7)) (+.f64 (.f64 -1/3 (pow.f64 x 3)) (+.f64 (*.f64 2/15 (pow.f64 x 5)) x)))
(-.f64 (.f64 2 (/.f64 1 (+.f64 1 (exp.f64 (.f64 -2 x))))) 1)
(-.f64 (.f64 2 (/.f64 1 (+.f64 1 (exp.f64 (.f64 -2 x))))) 1)
(-.f64 (.f64 2 (/.f64 1 (+.f64 1 (exp.f64 (.f64 -2 x))))) 1)
(-.f64 (.f64 2 (/.f64 1 (+.f64 1 (exp.f64 (.f64 -2 x))))) 1)
(-.f64 (.f64 2 (/.f64 1 (+.f64 1 (exp.f64 (.f64 -2 x))))) 1)
(-.f64 (.f64 2 (/.f64 1 (+.f64 1 (exp.f64 (.f64 -2 x))))) 1)
(-.f64 (.f64 2 (/.f64 1 (+.f64 1 (exp.f64 (.f64 -2 x))))) 1)
(-.f64 (.f64 2 (/.f64 1 (+.f64 1 (exp.f64 (.f64 -2 x))))) 1)
1
(+.f64 1 x)
(+.f64 1 (+.f64 (*.f64 -1/3 (pow.f64 x 3)) x))
(+.f64 1 (+.f64 (.f64 -1/3 (pow.f64 x 3)) (+.f64 x (.f64 2/15 (pow.f64 x 5)))))
2
(+.f64 2 (*.f64 -2 x))
(+.f64 (.f64 2 (pow.f64 x 2)) (+.f64 2 (.f64 -2 x)))
(+.f64 (.f64 2 (pow.f64 x 2)) (+.f64 2 (+.f64 (.f64 -2 x) (*.f64 -4/3 (pow.f64 x 3)))))

Outputs
x
(+.f64 (*.f64 -1/3 (pow.f64 x 3)) x)
(fma.f64 -1/3 (pow.f64 x 3) x)
(+.f64 (.f64 -1/3 (pow.f64 x 3)) (+.f64 (.f64 2/15 (pow.f64 x 5)) x))
(fma.f64 -1/3 (pow.f64 x 3) (fma.f64 2/15 (pow.f64 x 5) x))
(+.f64 (.f64 -17/315 (pow.f64 x 7)) (+.f64 (.f64 -1/3 (pow.f64 x 3)) (+.f64 (*.f64 2/15 (pow.f64 x 5)) x)))
(fma.f64 -17/315 (pow.f64 x 7) (fma.f64 -1/3 (pow.f64 x 3) (fma.f64 2/15 (pow.f64 x 5) x)))
(fma.f64 -1/3 (pow.f64 x 3) (fma.f64 -17/315 (pow.f64 x 7) (fma.f64 2/15 (pow.f64 x 5) x)))
(fma.f64 -1/3 (pow.f64 x 3) (fma.f64 2/15 (pow.f64 x 5) (fma.f64 -17/315 (pow.f64 x 7) x)))
(-.f64 (.f64 2 (/.f64 1 (+.f64 1 (exp.f64 (.f64 -2 x))))) 1)
(+.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2)))) -1)
(+.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x))) -1)
(+.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2))) -1)
(-.f64 (.f64 2 (/.f64 1 (+.f64 1 (exp.f64 (.f64 -2 x))))) 1)
(+.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2)))) -1)
(+.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x))) -1)
(+.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2))) -1)
(-.f64 (.f64 2 (/.f64 1 (+.f64 1 (exp.f64 (.f64 -2 x))))) 1)
(+.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2)))) -1)
(+.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x))) -1)
(+.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2))) -1)
(-.f64 (.f64 2 (/.f64 1 (+.f64 1 (exp.f64 (.f64 -2 x))))) 1)
(+.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2)))) -1)
(+.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x))) -1)
(+.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2))) -1)
(-.f64 (.f64 2 (/.f64 1 (+.f64 1 (exp.f64 (.f64 -2 x))))) 1)
(+.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2)))) -1)
(+.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x))) -1)
(+.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2))) -1)
(-.f64 (.f64 2 (/.f64 1 (+.f64 1 (exp.f64 (.f64 -2 x))))) 1)
(+.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2)))) -1)
(+.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x))) -1)
(+.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2))) -1)
(-.f64 (.f64 2 (/.f64 1 (+.f64 1 (exp.f64 (.f64 -2 x))))) 1)
(+.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2)))) -1)
(+.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x))) -1)
(+.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2))) -1)
(-.f64 (.f64 2 (/.f64 1 (+.f64 1 (exp.f64 (.f64 -2 x))))) 1)
(+.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2)))) -1)
(+.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x))) -1)
(+.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2))) -1)
1
(+.f64 1 x)
(+.f64 x 1)
(+.f64 1 (+.f64 (*.f64 -1/3 (pow.f64 x 3)) x))
(+.f64 (fma.f64 -1/3 (pow.f64 x 3) x) 1)
(+.f64 x (fma.f64 -1/3 (pow.f64 x 3) 1))
(+.f64 1 (+.f64 (.f64 -1/3 (pow.f64 x 3)) (+.f64 x (.f64 2/15 (pow.f64 x 5)))))
(+.f64 (fma.f64 -1/3 (pow.f64 x 3) (fma.f64 2/15 (pow.f64 x 5) x)) 1)
(+.f64 (fma.f64 -1/3 (pow.f64 x 3) x) (fma.f64 2/15 (pow.f64 x 5) 1))
(+.f64 x (fma.f64 -1/3 (pow.f64 x 3) (fma.f64 2/15 (pow.f64 x 5) 1)))
2
(+.f64 2 (*.f64 -2 x))
(+.f64 2 (*.f64 x -2))
(fma.f64 x -2 2)
(+.f64 (.f64 2 (pow.f64 x 2)) (+.f64 2 (.f64 -2 x)))
(fma.f64 2 (.f64 x x) (+.f64 2 (.f64 x -2)))
(fma.f64 2 (*.f64 x x) (fma.f64 x -2 2))
(fma.f64 x -2 (*.f64 2 (fma.f64 x x 1)))
(fma.f64 x (fma.f64 x 2 -2) 2)
(+.f64 (.f64 2 (pow.f64 x 2)) (+.f64 2 (+.f64 (.f64 -2 x) (*.f64 -4/3 (pow.f64 x 3)))))
(fma.f64 2 (.f64 x x) (+.f64 2 (fma.f64 -2 x (.f64 (pow.f64 x 3) -4/3))))
(+.f64 (fma.f64 x -2 (.f64 (pow.f64 x 3) -4/3)) (fma.f64 2 (.f64 x x) 2))
(fma.f64 x (*.f64 x 2) (fma.f64 (pow.f64 x 3) -4/3 (fma.f64 x -2 2)))
(fma.f64 (pow.f64 x 3) -4/3 (fma.f64 x (fma.f64 x 2 -2) 2))
(fma.f64 x (fma.f64 x (fma.f64 x -4/3 2) -2) 2)

eval69.0ms (1%)

Compiler: Compiled 2693 to 2214 computations (17.8% saved)

prune28.0ms (0.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	161	7	168
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	161	8	169

Error

0.0b

Counts

169 → 8

Alt Table

Click to see full alt table

Status	Error	Program
▶	29.1b	(-.f64 (-.f64 (+.f64 1 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2)))) 1) 1)
▶	46.4b	(-.f64 (/.f64 2 (+.f64 2 (*.f64 -2 x))) 1)
▶	32.2b	(+.f64 (*.f64 -1/3 (pow.f64 x 3)) x)
	29.1b	(expm1.f64 (-.f64 (log1p.f64 1) (log1p.f64 (pow.f64 (exp.f64 x) -2))))
✓	29.1b	(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)
	30.7b	x
▶	59.7b	(-.f64 (+.f64 x 1) 1)
▶	61.3b	(-.f64 1 1)

Compiler

Compiled 133 to 119 computations (10.5% saved)

localize24.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (exp.f64 x) -2)
✓	0.0b	(/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2)))
✓	0.0b	(-.f64 (+.f64 1 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2)))) 1)
✓	1.9b	(-.f64 (-.f64 (+.f64 1 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2)))) 1) 1)

Compiler

Compiled 62 to 48 computations (22.6% saved)

series9.0ms (0.1%)

Counts

4 → 48

Calls

12 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	(-.f64 (-.f64 (+.f64 1 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2)))) 1) 1)
2.0ms	x	@	-inf	(-.f64 (-.f64 (+.f64 1 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2)))) 1) 1)
1.0ms	x	@	-inf	(-.f64 (+.f64 1 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2)))) 1)
1.0ms	x	@	0	(-.f64 (-.f64 (+.f64 1 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2)))) 1) 1)
1.0ms	x	@	inf	(/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2)))

rewrite112.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

637×	`prod-diff_binary64`
519×	`fma-def_binary64`
498×	`log-prod_binary64`
318×	`fma-neg_binary64`
209×	`expm1-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	60
1	281	45
2	3982	45

Stop Event

1×	node limit

Counts

4 → 251

Calls

Call 1

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

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

simplify76.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

782×	`fma-neg_binary64`
505×	`unswap-sqr_binary64`
456×	`fma-def_binary64`
322×	`distribute-rgt-neg-in_binary64`
294×	`*-commutative_binary64`

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	49	613
1	122	609
2	270	575
3	736	505
4	1689	505
5	2520	505
6	5043	504

Stop Event

1×	node limit

Counts

299 → 207

Calls

Call 1

Inputs
x
(+.f64 (*.f64 -1/3 (pow.f64 x 3)) x)
(+.f64 (.f64 -1/3 (pow.f64 x 3)) (+.f64 (.f64 2/15 (pow.f64 x 5)) x))
(+.f64 (.f64 -17/315 (pow.f64 x 7)) (+.f64 (.f64 -1/3 (pow.f64 x 3)) (+.f64 (*.f64 2/15 (pow.f64 x 5)) x)))
(-.f64 (*.f64 2 (/.f64 1 (+.f64 (/.f64 1 (pow.f64 (exp.f64 x) 2)) 1))) 1)
(-.f64 (*.f64 2 (/.f64 1 (+.f64 (/.f64 1 (pow.f64 (exp.f64 x) 2)) 1))) 1)
(-.f64 (*.f64 2 (/.f64 1 (+.f64 (/.f64 1 (pow.f64 (exp.f64 x) 2)) 1))) 1)
(-.f64 (*.f64 2 (/.f64 1 (+.f64 (/.f64 1 (pow.f64 (exp.f64 x) 2)) 1))) 1)
(-.f64 (*.f64 2 (/.f64 1 (+.f64 1 (/.f64 1 (pow.f64 (exp.f64 x) 2))))) 1)
(-.f64 (*.f64 2 (/.f64 1 (+.f64 1 (/.f64 1 (pow.f64 (exp.f64 x) 2))))) 1)
(-.f64 (*.f64 2 (/.f64 1 (+.f64 1 (/.f64 1 (pow.f64 (exp.f64 x) 2))))) 1)
(-.f64 (*.f64 2 (/.f64 1 (+.f64 1 (/.f64 1 (pow.f64 (exp.f64 x) 2))))) 1)
1
(+.f64 1 x)
(+.f64 1 (+.f64 (*.f64 -1/3 (pow.f64 x 3)) x))
(+.f64 1 (+.f64 (.f64 -1/3 (pow.f64 x 3)) (+.f64 x (.f64 2/15 (pow.f64 x 5)))))
(/.f64 2 (+.f64 1 (/.f64 1 (pow.f64 (exp.f64 x) 2))))
(/.f64 2 (+.f64 1 (/.f64 1 (pow.f64 (exp.f64 x) 2))))
(/.f64 2 (+.f64 1 (/.f64 1 (pow.f64 (exp.f64 x) 2))))
(/.f64 2 (+.f64 1 (/.f64 1 (pow.f64 (exp.f64 x) 2))))
(/.f64 2 (+.f64 1 (/.f64 1 (pow.f64 (exp.f64 x) 2))))
(/.f64 2 (+.f64 1 (/.f64 1 (pow.f64 (exp.f64 x) 2))))
(/.f64 2 (+.f64 1 (/.f64 1 (pow.f64 (exp.f64 x) 2))))
(/.f64 2 (+.f64 1 (/.f64 1 (pow.f64 (exp.f64 x) 2))))
1
(+.f64 1 x)
(+.f64 1 (+.f64 (*.f64 -1/3 (pow.f64 x 3)) x))
(+.f64 1 (+.f64 (.f64 -1/3 (pow.f64 x 3)) (+.f64 x (.f64 2/15 (pow.f64 x 5)))))
(/.f64 2 (+.f64 (/.f64 1 (pow.f64 (exp.f64 x) 2)) 1))
(/.f64 2 (+.f64 (/.f64 1 (pow.f64 (exp.f64 x) 2)) 1))
(/.f64 2 (+.f64 (/.f64 1 (pow.f64 (exp.f64 x) 2)) 1))
(/.f64 2 (+.f64 (/.f64 1 (pow.f64 (exp.f64 x) 2)) 1))
(/.f64 2 (+.f64 1 (/.f64 1 (pow.f64 (exp.f64 x) 2))))
(/.f64 2 (+.f64 1 (/.f64 1 (pow.f64 (exp.f64 x) 2))))
(/.f64 2 (+.f64 1 (/.f64 1 (pow.f64 (exp.f64 x) 2))))
(/.f64 2 (+.f64 1 (/.f64 1 (pow.f64 (exp.f64 x) 2))))
1
(+.f64 1 (*.f64 -2 x))
(+.f64 (.f64 2 (pow.f64 x 2)) (+.f64 1 (.f64 -2 x)))
(+.f64 (.f64 2 (pow.f64 x 2)) (+.f64 1 (+.f64 (.f64 -2 x) (*.f64 -4/3 (pow.f64 x 3)))))
(/.f64 1 (pow.f64 (exp.f64 x) 2))
(/.f64 1 (pow.f64 (exp.f64 x) 2))
(/.f64 1 (pow.f64 (exp.f64 x) 2))
(/.f64 1 (pow.f64 (exp.f64 x) 2))
(/.f64 1 (pow.f64 (exp.f64 x) 2))
(/.f64 1 (pow.f64 (exp.f64 x) 2))
(/.f64 1 (pow.f64 (exp.f64 x) 2))
(/.f64 1 (pow.f64 (exp.f64 x) 2))

Outputs
x
(+.f64 (*.f64 -1/3 (pow.f64 x 3)) x)
(fma.f64 -1/3 (pow.f64 x 3) x)
(+.f64 (.f64 -1/3 (pow.f64 x 3)) (+.f64 (.f64 2/15 (pow.f64 x 5)) x))
(fma.f64 -1/3 (pow.f64 x 3) (fma.f64 2/15 (pow.f64 x 5) x))
(+.f64 (.f64 -17/315 (pow.f64 x 7)) (+.f64 (.f64 -1/3 (pow.f64 x 3)) (+.f64 (*.f64 2/15 (pow.f64 x 5)) x)))
(fma.f64 -17/315 (pow.f64 x 7) (fma.f64 -1/3 (pow.f64 x 3) (fma.f64 2/15 (pow.f64 x 5) x)))
(fma.f64 -1/3 (pow.f64 x 3) (fma.f64 -17/315 (pow.f64 x 7) (fma.f64 2/15 (pow.f64 x 5) x)))
(fma.f64 -1/3 (pow.f64 x 3) (fma.f64 2/15 (pow.f64 x 5) (fma.f64 -17/315 (pow.f64 x 7) x)))
(-.f64 (*.f64 2 (/.f64 1 (+.f64 (/.f64 1 (pow.f64 (exp.f64 x) 2)) 1))) 1)
(+.f64 (/.f64 2 (+.f64 1 (/.f64 1 (pow.f64 (exp.f64 x) 2)))) -1)
(+.f64 (/.f64 2 (+.f64 1 (exp.f64 (neg.f64 (+.f64 x x))))) -1)
(+.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2)))) -1)
(+.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2))) -1)
(-.f64 (*.f64 2 (/.f64 1 (+.f64 (/.f64 1 (pow.f64 (exp.f64 x) 2)) 1))) 1)
(+.f64 (/.f64 2 (+.f64 1 (/.f64 1 (pow.f64 (exp.f64 x) 2)))) -1)
(+.f64 (/.f64 2 (+.f64 1 (exp.f64 (neg.f64 (+.f64 x x))))) -1)
(+.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2)))) -1)
(+.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2))) -1)
(-.f64 (*.f64 2 (/.f64 1 (+.f64 (/.f64 1 (pow.f64 (exp.f64 x) 2)) 1))) 1)
(+.f64 (/.f64 2 (+.f64 1 (/.f64 1 (pow.f64 (exp.f64 x) 2)))) -1)
(+.f64 (/.f64 2 (+.f64 1 (exp.f64 (neg.f64 (+.f64 x x))))) -1)
(+.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2)))) -1)
(+.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2))) -1)
(-.f64 (*.f64 2 (/.f64 1 (+.f64 (/.f64 1 (pow.f64 (exp.f64 x) 2)) 1))) 1)
(+.f64 (/.f64 2 (+.f64 1 (/.f64 1 (pow.f64 (exp.f64 x) 2)))) -1)
(+.f64 (/.f64 2 (+.f64 1 (exp.f64 (neg.f64 (+.f64 x x))))) -1)
(+.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2)))) -1)
(+.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2))) -1)
(-.f64 (*.f64 2 (/.f64 1 (+.f64 1 (/.f64 1 (pow.f64 (exp.f64 x) 2))))) 1)
(+.f64 (/.f64 2 (+.f64 1 (/.f64 1 (pow.f64 (exp.f64 x) 2)))) -1)
(+.f64 (/.f64 2 (+.f64 1 (exp.f64 (neg.f64 (+.f64 x x))))) -1)
(+.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2)))) -1)
(+.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2))) -1)
(-.f64 (*.f64 2 (/.f64 1 (+.f64 1 (/.f64 1 (pow.f64 (exp.f64 x) 2))))) 1)
(+.f64 (/.f64 2 (+.f64 1 (/.f64 1 (pow.f64 (exp.f64 x) 2)))) -1)
(+.f64 (/.f64 2 (+.f64 1 (exp.f64 (neg.f64 (+.f64 x x))))) -1)
(+.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2)))) -1)
(+.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2))) -1)
(-.f64 (*.f64 2 (/.f64 1 (+.f64 1 (/.f64 1 (pow.f64 (exp.f64 x) 2))))) 1)
(+.f64 (/.f64 2 (+.f64 1 (/.f64 1 (pow.f64 (exp.f64 x) 2)))) -1)
(+.f64 (/.f64 2 (+.f64 1 (exp.f64 (neg.f64 (+.f64 x x))))) -1)
(+.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2)))) -1)
(+.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2))) -1)
(-.f64 (*.f64 2 (/.f64 1 (+.f64 1 (/.f64 1 (pow.f64 (exp.f64 x) 2))))) 1)
(+.f64 (/.f64 2 (+.f64 1 (/.f64 1 (pow.f64 (exp.f64 x) 2)))) -1)
(+.f64 (/.f64 2 (+.f64 1 (exp.f64 (neg.f64 (+.f64 x x))))) -1)
(+.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2)))) -1)
(+.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2))) -1)
1
(+.f64 1 x)
(+.f64 x 1)
(+.f64 1 (+.f64 (*.f64 -1/3 (pow.f64 x 3)) x))
(+.f64 (fma.f64 -1/3 (pow.f64 x 3) x) 1)
(fma.f64 -1/3 (pow.f64 x 3) (+.f64 x 1))
(+.f64 1 (+.f64 (.f64 -1/3 (pow.f64 x 3)) (+.f64 x (.f64 2/15 (pow.f64 x 5)))))
(+.f64 (fma.f64 -1/3 (pow.f64 x 3) (fma.f64 2/15 (pow.f64 x 5) x)) 1)
(+.f64 (fma.f64 -1/3 (pow.f64 x 3) x) (fma.f64 2/15 (pow.f64 x 5) 1))
(+.f64 x (fma.f64 -1/3 (pow.f64 x 3) (fma.f64 2/15 (pow.f64 x 5) 1)))
(/.f64 2 (+.f64 1 (/.f64 1 (pow.f64 (exp.f64 x) 2))))
(/.f64 2 (+.f64 1 (exp.f64 (neg.f64 (+.f64 x x)))))
(/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2))))
(/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2)))
(/.f64 2 (+.f64 1 (/.f64 1 (pow.f64 (exp.f64 x) 2))))
(/.f64 2 (+.f64 1 (exp.f64 (neg.f64 (+.f64 x x)))))
(/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2))))
(/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2)))
(/.f64 2 (+.f64 1 (/.f64 1 (pow.f64 (exp.f64 x) 2))))
(/.f64 2 (+.f64 1 (exp.f64 (neg.f64 (+.f64 x x)))))
(/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2))))
(/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2)))
(/.f64 2 (+.f64 1 (/.f64 1 (pow.f64 (exp.f64 x) 2))))
(/.f64 2 (+.f64 1 (exp.f64 (neg.f64 (+.f64 x x)))))
(/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2))))
(/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2)))
(/.f64 2 (+.f64 1 (/.f64 1 (pow.f64 (exp.f64 x) 2))))
(/.f64 2 (+.f64 1 (exp.f64 (neg.f64 (+.f64 x x)))))
(/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2))))
(/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2)))
(/.f64 2 (+.f64 1 (/.f64 1 (pow.f64 (exp.f64 x) 2))))
(/.f64 2 (+.f64 1 (exp.f64 (neg.f64 (+.f64 x x)))))
(/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2))))
(/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2)))
(/.f64 2 (+.f64 1 (/.f64 1 (pow.f64 (exp.f64 x) 2))))
(/.f64 2 (+.f64 1 (exp.f64 (neg.f64 (+.f64 x x)))))
(/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2))))
(/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2)))
(/.f64 2 (+.f64 1 (/.f64 1 (pow.f64 (exp.f64 x) 2))))
(/.f64 2 (+.f64 1 (exp.f64 (neg.f64 (+.f64 x x)))))
(/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2))))
(/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2)))
1
(+.f64 1 x)
(+.f64 x 1)
(+.f64 1 (+.f64 (*.f64 -1/3 (pow.f64 x 3)) x))
(+.f64 (fma.f64 -1/3 (pow.f64 x 3) x) 1)
(fma.f64 -1/3 (pow.f64 x 3) (+.f64 x 1))
(+.f64 1 (+.f64 (.f64 -1/3 (pow.f64 x 3)) (+.f64 x (.f64 2/15 (pow.f64 x 5)))))
(+.f64 (fma.f64 -1/3 (pow.f64 x 3) (fma.f64 2/15 (pow.f64 x 5) x)) 1)
(+.f64 (fma.f64 -1/3 (pow.f64 x 3) x) (fma.f64 2/15 (pow.f64 x 5) 1))
(+.f64 x (fma.f64 -1/3 (pow.f64 x 3) (fma.f64 2/15 (pow.f64 x 5) 1)))
(/.f64 2 (+.f64 (/.f64 1 (pow.f64 (exp.f64 x) 2)) 1))
(/.f64 2 (+.f64 1 (/.f64 1 (pow.f64 (exp.f64 x) 2))))
(/.f64 2 (+.f64 1 (exp.f64 (neg.f64 (+.f64 x x)))))
(/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2))))
(/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2)))
(/.f64 2 (+.f64 (/.f64 1 (pow.f64 (exp.f64 x) 2)) 1))
(/.f64 2 (+.f64 1 (/.f64 1 (pow.f64 (exp.f64 x) 2))))
(/.f64 2 (+.f64 1 (exp.f64 (neg.f64 (+.f64 x x)))))
(/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2))))
(/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2)))
(/.f64 2 (+.f64 (/.f64 1 (pow.f64 (exp.f64 x) 2)) 1))
(/.f64 2 (+.f64 1 (/.f64 1 (pow.f64 (exp.f64 x) 2))))
(/.f64 2 (+.f64 1 (exp.f64 (neg.f64 (+.f64 x x)))))
(/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2))))
(/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2)))
(/.f64 2 (+.f64 (/.f64 1 (pow.f64 (exp.f64 x) 2)) 1))
(/.f64 2 (+.f64 1 (/.f64 1 (pow.f64 (exp.f64 x) 2))))
(/.f64 2 (+.f64 1 (exp.f64 (neg.f64 (+.f64 x x)))))
(/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2))))
(/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2)))
(/.f64 2 (+.f64 1 (/.f64 1 (pow.f64 (exp.f64 x) 2))))
(/.f64 2 (+.f64 1 (exp.f64 (neg.f64 (+.f64 x x)))))
(/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2))))
(/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2)))
(/.f64 2 (+.f64 1 (/.f64 1 (pow.f64 (exp.f64 x) 2))))
(/.f64 2 (+.f64 1 (exp.f64 (neg.f64 (+.f64 x x)))))
(/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2))))
(/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2)))
(/.f64 2 (+.f64 1 (/.f64 1 (pow.f64 (exp.f64 x) 2))))
(/.f64 2 (+.f64 1 (exp.f64 (neg.f64 (+.f64 x x)))))
(/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2))))
(/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2)))
(/.f64 2 (+.f64 1 (/.f64 1 (pow.f64 (exp.f64 x) 2))))
(/.f64 2 (+.f64 1 (exp.f64 (neg.f64 (+.f64 x x)))))
(/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2))))
(/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2)))
1
(+.f64 1 (*.f64 -2 x))
(+.f64 1 (*.f64 x -2))
(fma.f64 x -2 1)
(+.f64 (.f64 2 (pow.f64 x 2)) (+.f64 1 (.f64 -2 x)))
(fma.f64 2 (.f64 x x) (+.f64 1 (.f64 x -2)))
(fma.f64 2 (*.f64 x x) (fma.f64 x -2 1))
(fma.f64 x -2 (fma.f64 x (+.f64 x x) 1))
(fma.f64 x (fma.f64 x 2 -2) 1)
(+.f64 (.f64 2 (pow.f64 x 2)) (+.f64 1 (+.f64 (.f64 -2 x) (*.f64 -4/3 (pow.f64 x 3)))))
(fma.f64 2 (.f64 x x) (+.f64 1 (fma.f64 -2 x (.f64 (pow.f64 x 3) -4/3))))
(+.f64 (fma.f64 (pow.f64 x 3) -4/3 (.f64 x -2)) (fma.f64 2 (.f64 x x) 1))
(fma.f64 x (+.f64 x x) (fma.f64 (pow.f64 x 3) -4/3 (fma.f64 x -2 1)))
(fma.f64 x (fma.f64 x 2 -2) (fma.f64 (pow.f64 x 3) -4/3 1))
(fma.f64 (pow.f64 x 3) -4/3 (fma.f64 x (fma.f64 x 2 -2) 1))
(fma.f64 (*.f64 x x) (fma.f64 x -4/3 2) (fma.f64 x -2 1))
(+.f64 1 (*.f64 x (fma.f64 x (fma.f64 x -4/3 2) -2)))
(/.f64 1 (pow.f64 (exp.f64 x) 2))
(exp.f64 (neg.f64 (+.f64 x x)))
(exp.f64 (*.f64 x -2))
(pow.f64 (exp.f64 x) -2)
(/.f64 1 (pow.f64 (exp.f64 x) 2))
(exp.f64 (neg.f64 (+.f64 x x)))
(exp.f64 (*.f64 x -2))
(pow.f64 (exp.f64 x) -2)
(/.f64 1 (pow.f64 (exp.f64 x) 2))
(exp.f64 (neg.f64 (+.f64 x x)))
(exp.f64 (*.f64 x -2))
(pow.f64 (exp.f64 x) -2)
(/.f64 1 (pow.f64 (exp.f64 x) 2))
(exp.f64 (neg.f64 (+.f64 x x)))
(exp.f64 (*.f64 x -2))
(pow.f64 (exp.f64 x) -2)
(/.f64 1 (pow.f64 (exp.f64 x) 2))
(exp.f64 (neg.f64 (+.f64 x x)))
(exp.f64 (*.f64 x -2))
(pow.f64 (exp.f64 x) -2)
(/.f64 1 (pow.f64 (exp.f64 x) 2))
(exp.f64 (neg.f64 (+.f64 x x)))
(exp.f64 (*.f64 x -2))
(pow.f64 (exp.f64 x) -2)
(/.f64 1 (pow.f64 (exp.f64 x) 2))
(exp.f64 (neg.f64 (+.f64 x x)))
(exp.f64 (*.f64 x -2))
(pow.f64 (exp.f64 x) -2)
(/.f64 1 (pow.f64 (exp.f64 x) 2))
(exp.f64 (neg.f64 (+.f64 x x)))
(exp.f64 (*.f64 x -2))
(pow.f64 (exp.f64 x) -2)

localize3.0ms (0%)

Compiler: Compiled 6 to 6 computations (0% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.0b	(-.f64 (+.f64 x 1) 1)

Compiler

Compiled 12 to 9 computations (25% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite49.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

533×	`pow1_binary64`
502×	`add-log-exp_binary64`
502×	`log1p-expm1-u_binary64`
502×	`expm1-log1p-u_binary64`
494×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	5	4
1	116	1
2	1623	1

Stop Event

1×	node limit

Counts

1 → 41

Calls

Call 1

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

Outputs

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

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1	12

Stop Event

1×

saturated

Counts

53 → 42

Calls

Call 1

Inputs
x
x
x
x
x
x
x
x
x
x
x
x

Outputs
x
x
x
x
x
x
x
x
x
x
x
x

localize13.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 2 (+.f64 2 (*.f64 -2 x)))
✓	1.9b	(-.f64 (/.f64 2 (+.f64 2 (*.f64 -2 x))) 1)

Compiler

Compiled 30 to 25 computations (16.7% saved)

series3.0ms (0%)

Counts

2 → 24

Calls

6 calls:

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

rewrite71.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

590×	`unpow-prod-down_binary64`
401×	`log-prod_binary64`
306×	`exp-prod_binary64`
301×	`prod-diff_binary64`
238×	`pow2_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	202	19
2	2555	19

Stop Event

1×	node limit

Counts

2 → 124

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 2 (fma.f64 -2 x 2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (+.f64 (/.f64 2 (fma.f64 -2 x 2)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (/.f64 2 (fma.f64 -2 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (+.f64 (/.f64 2 (fma.f64 -2 x 2)) -1))) 2)) (log.f64 (cbrt.f64 (exp.f64 (+.f64 (/.f64 2 (fma.f64 -2 x 2)) -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (+.f64 (/.f64 2 (fma.f64 -2 x 2)) -1)))) (log.f64 (sqrt.f64 (exp.f64 (+.f64 (/.f64 2 (fma.f64 -2 x 2)) -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 (/.f64 2 (fma.f64 -2 x 2)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (/.f64 2 (fma.f64 -2 x 2)) -1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 (/.f64 2 (fma.f64 -2 x 2)) -1)) (cbrt.f64 (pow.f64 (+.f64 (/.f64 2 (fma.f64 -2 x 2)) -1) 2)))))) (#(struct:change 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((x log.f64 (exp.f64 (+.f64 (/.f64 2 (fma.f64 -2 x 2)) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 (/.f64 2 (fma.f64 -2 x 2)) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 (/.f64 2 (fma.f64 -2 x 2)) -1) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log.f64 (/.f64 2 (fma.f64 -2 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (*.f64 (log.f64 (/.f64 2 (fma.f64 -2 x 2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 (/.f64 2 (fma.f64 -2 x 2)) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 (/.f64 2 (fma.f64 -2 x 2)) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (+.f64 (/.f64 2 (fma.f64 -2 x 2)) -1)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (+.f64 (/.f64 2 (fma.f64 -2 x 2)) -1) 3)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (+.f64 (/.f64 2 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((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 2 (fma.f64 -2 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 2 (fma.f64 -2 x 2)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 2 (fma.f64 -2 x 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 2 (fma.f64 -2 x 2))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 2 (fma.f64 -2 x 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (/.f64 2 (fma.f64 -2 x 2)) 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (/.f64 1 (fma.f64 -2 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -2 (/.f64 1 (neg.f64 (fma.f64 -2 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -2 (pow.f64 (/.f64 1 (neg.f64 (fma.f64 -2 x 2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 2 (fma.f64 -2 x 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 2 (fma.f64 -2 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 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(fma.f64 -2 x 2)))) 2) 3) (cbrt.f64 (/.f64 2 (fma.f64 -2 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 2) 2) (/.f64 1 (fma.f64 -2 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 8 1/3) (/.f64 1 (fma.f64 -2 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (*.f64 4 (pow.f64 (fma.f64 -2 x 2) -2)) 2) 1/3) (cbrt.f64 (/.f64 1 (fma.f64 -2 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (*.f64 (/.f64 2 (fma.f64 -2 x 2)) (cbrt.f64 (/.f64 2 (fma.f64 -2 x 2)))) 2) 1/3) (cbrt.f64 (cbrt.f64 (/.f64 2 (fma.f64 -2 x 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (/.f64 2 (fma.f64 -2 x 2)) 5/2) 1/3) (cbrt.f64 (sqrt.f64 (/.f64 2 (fma.f64 -2 x 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 (fma.f64 -2 x 2) 1/2)) 2) -1) (cbrt.f64 (/.f64 2 (fma.f64 -2 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 2 (fma.f64 -2 x 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (log.f64 (/.f64 2 (fma.f64 -2 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 4 (pow.f64 (fma.f64 -2 x 2) -2)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 2 (fma.f64 -2 x 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 2 (fma.f64 -2 x 2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 8 (pow.f64 (fma.f64 -2 x 2) -3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (fma.f64 -2 x 2) 1/2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1 (+.f64 (/.f64 2 (fma.f64 -2 x 2)) -1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (*.f64 (fma.f64 -2 x 2) 1/2) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (/.f64 2 (fma.f64 -2 x 2)))) 2)) (cbrt.f64 (log.f64 (/.f64 2 (fma.f64 -2 x 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (/.f64 2 (fma.f64 -2 x 2))))) (sqrt.f64 (log.f64 (/.f64 2 (fma.f64 -2 x 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 4 (pow.f64 (fma.f64 -2 x 2) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 2 (fma.f64 -2 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 2 (fma.f64 -2 x 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 8 (pow.f64 (fma.f64 -2 x 2) -3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 2 (fma.f64 -2 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 2 (fma.f64 -2 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 2 (fma.f64 -2 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 2 (fma.f64 -2 x 2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (/.f64 2 (fma.f64 -2 x 2)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 2 (fma.f64 -2 x 2)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 8 (pow.f64 (fma.f64 -2 x 2) -3))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (fma.f64 -2 x 2) 1/2)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (/.f64 2 (fma.f64 -2 x 2))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (/.f64 2 (fma.f64 -2 x 2))) 3) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 (/.f64 2 (fma.f64 -2 x 2)) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (/.f64 2 (fma.f64 -2 x 2)) 1) 1 -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 (/.f64 2 (fma.f64 -2 x 2)) 1)) 2) (cbrt.f64 (+.f64 (/.f64 2 (fma.f64 -2 x 2)) 1)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 (/.f64 2 (fma.f64 -2 x 2)) 1)) (sqrt.f64 (+.f64 (/.f64 2 (fma.f64 -2 x 2)) 1)) -1)))))

simplify51.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

774×	`fma-neg_binary64`
535×	`associate-l_binary64`
445×	`fma-def_binary64`
443×	`associate-r_binary64`
425×	`associate-/r*_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	38	333
1	112	299
2	345	290
3	1021	289
4	2833	289

Stop Event

1×	node limit

Counts

148 → 152

Calls

Call 1

Inputs
x
(+.f64 (pow.f64 x 2) x)
(+.f64 (pow.f64 x 2) (+.f64 (pow.f64 x 3) x))
(+.f64 (pow.f64 x 2) (+.f64 (pow.f64 x 4) (+.f64 (pow.f64 x 3) x)))
-1
(neg.f64 (+.f64 1 (/.f64 1 x)))
(neg.f64 (+.f64 1 (+.f64 (/.f64 1 (pow.f64 x 2)) (/.f64 1 x))))
(neg.f64 (+.f64 1 (+.f64 (/.f64 1 (pow.f64 x 2)) (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 3))))))
-1
(neg.f64 (+.f64 1 (/.f64 1 x)))
(neg.f64 (+.f64 1 (+.f64 (/.f64 1 (pow.f64 x 2)) (/.f64 1 x))))
(neg.f64 (+.f64 1 (+.f64 (/.f64 1 (pow.f64 x 2)) (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 3))))))
1
(+.f64 1 x)
(+.f64 1 (+.f64 (pow.f64 x 2) x))
(+.f64 1 (+.f64 (pow.f64 x 2) (+.f64 (pow.f64 x 3) x)))
(/.f64 -1 x)
(neg.f64 (+.f64 (/.f64 1 (pow.f64 x 2)) (/.f64 1 x)))
(neg.f64 (+.f64 (/.f64 1 (pow.f64 x 2)) (+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 1 x))))
(neg.f64 (+.f64 (/.f64 1 (pow.f64 x 4)) (+.f64 (/.f64 1 (pow.f64 x 2)) (+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 1 x)))))
(/.f64 -1 x)
(neg.f64 (+.f64 (/.f64 1 (pow.f64 x 2)) (/.f64 1 x)))
(neg.f64 (+.f64 (/.f64 1 (pow.f64 x 2)) (+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 1 x))))
(neg.f64 (+.f64 (/.f64 1 (pow.f64 x 4)) (+.f64 (/.f64 1 (pow.f64 x 2)) (+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 1 x)))))

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

localize20.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (*.f64 -1/3 (pow.f64 x 3)) x)
✓	0.1b	(*.f64 -1/3 (pow.f64 x 3))

Compiler

Compiled 20 to 15 computations (25% saved)

series6.0ms (0.1%)

Counts

2 → 3

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(*.f64 -1/3 (pow.f64 x 3))
1.0ms	x	@	-inf	(*.f64 -1/3 (pow.f64 x 3))
1.0ms	x	@	inf	(*.f64 -1/3 (pow.f64 x 3))
1.0ms	x	@	inf	(+.f64 (*.f64 -1/3 (pow.f64 x 3)) x)
1.0ms	x	@	-inf	(+.f64 (*.f64 -1/3 (pow.f64 x 3)) x)

rewrite95.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

744×	`pow1_binary64`
701×	`add-log-exp_binary64`
701×	`log1p-expm1-u_binary64`
701×	`expm1-log1p-u_binary64`
687×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	15
1	159	15
2	1912	15

Stop Event

1×	node limit

Counts

2 → 46

Calls

Call 1

Inputs
(*.f64 -1/3 (pow.f64 x 3))
(+.f64 (*.f64 -1/3 (pow.f64 x 3)) x)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 -1/3 (pow.f64 x 3))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 -1/3 (pow.f64 x 3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (cbrt.f64 -1/3)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 -1/3) (pow.f64 x 3/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (pow.f64 x 3) 3) -1/27) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 x 6) 1/9))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 -1/3) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (pow.f64 x 3) 3) -1/27))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 -1/3 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 -1/3 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 -1/3 (pow.f64 x 3))))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (fma.f64 -1/3 (pow.f64 x 3) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (*.f64 (pow.f64 x 6) 1/9) (-.f64 (*.f64 -1/3 (pow.f64 x 3)) x)) (/.f64 (*.f64 x x) (-.f64 (*.f64 -1/3 (pow.f64 x 3)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 -1/3 (pow.f64 x 3) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 -1/3 (pow.f64 x 3) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 -1/3 (pow.f64 x 3) x)) (pow.f64 (cbrt.f64 (fma.f64 -1/3 (pow.f64 x 3) x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 -1/3 (pow.f64 x 3) x)) 2) (cbrt.f64 (fma.f64 -1/3 (pow.f64 x 3) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 -1/3 (pow.f64 x 3) x)) (sqrt.f64 (fma.f64 -1/3 (pow.f64 x 3) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 x 3) (*.f64 (pow.f64 (pow.f64 x 3) 3) -1/27)) (/.f64 1 (+.f64 (*.f64 (pow.f64 x 6) 1/9) (*.f64 x (-.f64 x (*.f64 -1/3 (pow.f64 x 3)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 (pow.f64 x 6) 1/9) (*.f64 x x)) (/.f64 1 (-.f64 (*.f64 -1/3 (pow.f64 x 3)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (*.f64 (pow.f64 x 6) 1/9) (*.f64 x (-.f64 x (*.f64 -1/3 (pow.f64 x 3))))) (+.f64 (pow.f64 x 3) (*.f64 (pow.f64 (pow.f64 x 3) 3) -1/27))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (*.f64 -1/3 (pow.f64 x 3)) x) (-.f64 (*.f64 (pow.f64 x 6) 1/9) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 3) (*.f64 (pow.f64 (pow.f64 x 3) 3) -1/27)) (+.f64 (*.f64 (pow.f64 x 6) 1/9) (*.f64 x (-.f64 x (*.f64 -1/3 (pow.f64 x 3))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 3) (*.f64 (pow.f64 (pow.f64 x 3) 3) -1/27)) (+.f64 (*.f64 x x) (-.f64 (*.f64 (pow.f64 x 6) 1/9) (*.f64 -1/3 (*.f64 (pow.f64 x 3) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (pow.f64 x 6) 1/9) (*.f64 x x)) (-.f64 (*.f64 -1/3 (pow.f64 x 3)) x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 x 3) (*.f64 (pow.f64 (pow.f64 x 3) 3) -1/27))) (neg.f64 (+.f64 (*.f64 (pow.f64 x 6) 1/9) (*.f64 x (-.f64 x (*.f64 -1/3 (pow.f64 x 3)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (*.f64 (pow.f64 x 6) 1/9) (*.f64 x x))) (neg.f64 (-.f64 (*.f64 -1/3 (pow.f64 x 3)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 x x) (*.f64 (pow.f64 x 6) 1/9)) (-.f64 x (*.f64 -1/3 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 -1/3 (pow.f64 x 3) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 -1/3 (pow.f64 x 3) x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 -1/3 (pow.f64 x 3) x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 -1/3 (pow.f64 x 3) x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 -1/3 (pow.f64 x 3) x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 -1/3 (pow.f64 x 3) x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 -1/3 (pow.f64 x 3) x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 -1/3 (pow.f64 x 3) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 -1/3 (pow.f64 x 3) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 -1/3 (pow.f64 x 3) x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1/3 (pow.f64 x 3) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 3) -1/3 x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 x (*.f64 -1/3 (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 -1/3 (pow.f64 x 3)) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (*.f64 x (cbrt.f64 -1/3)) 2) (*.f64 x (cbrt.f64 -1/3)) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 x) (*.f64 -1/3 (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (sqrt.f64 -1/3) (pow.f64 x 3/2)) (*.f64 (sqrt.f64 -1/3) (pow.f64 x 3/2)) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (sqrt.f64 x) (*.f64 -1/3 (pow.f64 x 3)))))))

simplify172.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

1274×	`sqr-pow_binary64`
666×	`pow-sqr_binary64`
529×	`cube-prod_binary64`
471×	`fabs-mul_binary64`
438×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	15
1	15	15
2	32	15
3	56	15
4	114	15
5	326	15
6	1180	15
7	1869	15
8	1956	15
9	2089	15
10	2247	15
11	2486	15
12	2808	15
13	3231	15
14	3733	15
15	4335	15
16	5057	15
17	5378	15
18	5664	15
19	5886	15
20	6064	15
21	6144	15
22	7084	15

Stop Event

1×	node limit

Counts

49 → 48

Calls

Call 1

Inputs
x
(*.f64 -1/3 (pow.f64 x 3))
(*.f64 -1/3 (pow.f64 x 3))

Outputs
x
(*.f64 -1/3 (pow.f64 x 3))
(*.f64 -1/3 (pow.f64 x 3))

eval277.0ms (3.9%)

Compiler: Compiled 7343 to 6129 computations (16.5% saved)

prune70.0ms (1%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	441	8	449
Fresh	2	0	2
Picked	0	1	1
Done	3	2	5
Total	446	11	457

Error

0.0b

Counts

457 → 11

Alt Table

Click to see full alt table

Status	Error	Program
▶	29.1b	(-.f64 (-.f64 (+.f64 1 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2))))) 1) 1)
✓	29.1b	(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)
	30.7b	x
▶	59.8b	(+.f64 1 (+.f64 x -1))
✓	32.2b	(+.f64 (*.f64 -1/3 (pow.f64 x 3)) x)
	47.4b	-1
▶	31.4b	(/.f64 1 (/.f64 (+.f64 x 2) (*.f64 (+.f64 x 2) x)))
▶	45.7b	(/.f64 (-.f64 (*.f64 x x) 0) (-.f64 x 0))
	29.6b	(-.f64 (/.f64 (/.f64 2 (hypot.f64 1 (exp.f64 (neg.f64 x)))) (hypot.f64 1 (exp.f64 (neg.f64 x)))) 1)
▶	31.3b	(.f64 (.f64 (+.f64 x 2) x) (/.f64 1 (+.f64 x 2)))
✓	59.7b	(-.f64 (+.f64 x 1) 1)

Compiler

Compiled 188 to 153 computations (18.6% saved)

localize26.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (exp.f64 (*.f64 x -2)))
✓	0.0b	(/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2))))
✓	0.0b	(-.f64 (+.f64 1 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2))))) 1)
✓	1.9b	(-.f64 (-.f64 (+.f64 1 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2))))) 1) 1)

Compiler

Compiled 63 to 55 computations (12.7% saved)

series4.0ms (0.1%)

Counts

4 → 48

Calls

12 calls:

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

rewrite107.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

593×	`prod-diff_binary64`
522×	`fma-def_binary64`
506×	`log-prod_binary64`
309×	`fma-neg_binary64`
209×	`expm1-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	63
1	278	48
2	3951	48

Stop Event

1×	node limit

Counts

4 → 258

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (+.f64 (expm1.f64 (-.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 -2) x)))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (-.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 1 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x)))) -2)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (expm1.f64 (-.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 -2) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (expm1.f64 (-.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 -2) x)))))) (cbrt.f64 (exp.f64 (expm1.f64 (-.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 -2) x)))))))) (log.f64 (cbrt.f64 (exp.f64 (expm1.f64 (-.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 -2) x))))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (expm1.f64 (-.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 -2) x))))))) (log.f64 (sqrt.f64 (exp.f64 (expm1.f64 (-.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 -2) x))))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (expm1.f64 (-.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 -2) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (expm1.f64 (-.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 -2) x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (expm1.f64 (-.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 -2) x))))) (pow.f64 (cbrt.f64 (expm1.f64 (-.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 -2) x))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (expm1.f64 (-.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 -2) x))))) 2) (cbrt.f64 (expm1.f64 (-.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 -2) x))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (expm1.f64 (-.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 -2) x))))) (sqrt.f64 (expm1.f64 (-.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 -2) x))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 (/.f64 8 (pow.f64 (+.f64 1 (pow.f64 (exp.f64 -2) x)) 3)) -1) (/.f64 1 (+.f64 (+.f64 1 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x)))) (/.f64 4 (pow.f64 (+.f64 1 (pow.f64 (exp.f64 -2) x)) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 (/.f64 4 (pow.f64 (+.f64 1 (pow.f64 (exp.f64 -2) x)) 2)) -1) (/.f64 1 (+.f64 1 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 (/.f64 (sqrt.f64 2) (hypot.f64 1 (pow.f64 (exp.f64 x) -1))) 1) (-.f64 (/.f64 (sqrt.f64 2) (hypot.f64 1 (pow.f64 (exp.f64 x) -1))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (+.f64 1 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x)))) (/.f64 4 (pow.f64 (+.f64 1 (pow.f64 (exp.f64 -2) x)) 2))) (+.f64 (/.f64 8 (pow.f64 (+.f64 1 (pow.f64 (exp.f64 -2) x)) 3)) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x)))) (+.f64 (/.f64 4 (pow.f64 (+.f64 1 (pow.f64 (exp.f64 -2) x)) 2)) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (/.f64 8 (pow.f64 (+.f64 1 (pow.f64 (exp.f64 -2) x)) 3)) -1) (+.f64 (+.f64 1 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x)))) (/.f64 4 (pow.f64 (+.f64 1 (pow.f64 (exp.f64 -2) x)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (/.f64 8 (pow.f64 (+.f64 1 (pow.f64 (exp.f64 -2) x)) 3)) -1) (+.f64 (/.f64 4 (pow.f64 (+.f64 1 (pow.f64 (exp.f64 -2) x)) 2)) (-.f64 1 (.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x))) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (/.f64 4 (pow.f64 (+.f64 1 (pow.f64 (exp.f64 -2) x)) 2)) -1) (+.f64 1 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (/.f64 8 (pow.f64 (+.f64 1 (pow.f64 (exp.f64 -2) x)) 3)) -1)) (neg.f64 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(+.f64 1 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x))))) (pow.f64 (cbrt.f64 (+.f64 1 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x))))) 2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 1 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x))))) 2) (cbrt.f64 (+.f64 1 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x))))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 1 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x))))) 2) (.f64 (cbrt.f64 (+.f64 1 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x))))) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (expm1.f64 (-.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 -2) x))))) (sqrt.f64 (expm1.f64 (-.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 -2) x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (sqrt.f64 2) (hypot.f64 1 (pow.f64 (exp.f64 x) -1))) (/.f64 (sqrt.f64 2) (hypot.f64 1 (pow.f64 (exp.f64 x) -1))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (sqrt.f64 2) (hypot.f64 1 (pow.f64 (exp.f64 x) -1))) (.f64 (/.f64 (sqrt.f64 2) (hypot.f64 1 (pow.f64 (exp.f64 x) -1))) 1) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 1 (/.f64 (sqrt.f64 2) (hypot.f64 1 (pow.f64 (exp.f64 x) -1)))) (hypot.f64 1 (/.f64 (sqrt.f64 2) (hypot.f64 1 (pow.f64 (exp.f64 x) -1)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 1 (/.f64 (sqrt.f64 2) (hypot.f64 1 (pow.f64 (exp.f64 x) -1)))) (.f64 (hypot.f64 1 (/.f64 (sqrt.f64 2) (hypot.f64 1 (pow.f64 (exp.f64 x) -1)))) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (expm1.f64 (.f64 3 (log1p.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x)))))) (/.f64 1 (+.f64 (pow.f64 (+.f64 1 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x)))) 2) (+.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x))) 2))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (/.f64 8 (pow.f64 (+.f64 1 (pow.f64 (exp.f64 -2) x)) 3)) -1) (/.f64 1 (+.f64 (+.f64 1 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x)))) (/.f64 4 (pow.f64 (+.f64 1 (pow.f64 (exp.f64 -2) x)) 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 1 (/.f64 8 (pow.f64 (+.f64 1 (pow.f64 (exp.f64 -2) x)) 3))) (/.f64 1 (fma.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x))) (expm1.f64 (-.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 -2) x)))) 1)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (exp.f64 (neg.f64 (log1p.f64 (pow.f64 (exp.f64 -2) x)))) 2 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (expm1.f64 (.f64 2 (log1p.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x)))))) (/.f64 1 (+.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x))) 2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (/.f64 4 (pow.f64 (+.f64 1 (pow.f64 (exp.f64 -2) x)) 2)) -1) (/.f64 1 (+.f64 1 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 1 (/.f64 4 (pow.f64 (+.f64 1 (pow.f64 (exp.f64 -2) x)) 2))) (/.f64 1 (-.f64 1 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x))))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (hypot.f64 1 (/.f64 (sqrt.f64 2) (hypot.f64 1 (pow.f64 (exp.f64 x) -1)))) 1) (expm1.f64 (.f64 1/2 (log1p.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x)))))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (/.f64 (sqrt.f64 2) (hypot.f64 1 (pow.f64 (exp.f64 x) -1))) 1) (-.f64 (/.f64 (sqrt.f64 2) (hypot.f64 1 (pow.f64 (exp.f64 x) -1))) 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -6))) (fma.f64 (pow.f64 (exp.f64 -2) x) (expm1.f64 (*.f64 x -2)) 1) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 2 (-.f64 1 (pow.f64 (exp.f64 x) -4))) (-.f64 1 (pow.f64 (exp.f64 -2) x)) 0)))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 1 (pow.f64 (exp.f64 -2) x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1 (-.f64 1 (pow.f64 (exp.f64 -2) x))) (/.f64 (pow.f64 (exp.f64 x) -4) (-.f64 1 (pow.f64 (exp.f64 -2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (+.f64 1 (pow.f64 (exp.f64 -2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 1 (pow.f64 (exp.f64 -2) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (+.f64 1 (pow.f64 (exp.f64 -2) x))) (cbrt.f64 (pow.f64 (+.f64 1 (pow.f64 (exp.f64 -2) x)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (+.f64 1 (pow.f64 (exp.f64 -2) x)) 2)) (cbrt.f64 (+.f64 1 (pow.f64 (exp.f64 -2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (hypot.f64 1 (pow.f64 (exp.f64 x) -1)) (hypot.f64 1 (pow.f64 (exp.f64 x) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 1 (pow.f64 (exp.f64 x) -6)) (/.f64 1 (fma.f64 (pow.f64 (exp.f64 -2) x) (expm1.f64 (.f64 x -2)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 1 (pow.f64 (exp.f64 x) -4)) (/.f64 1 (-.f64 1 (pow.f64 (exp.f64 -2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 (pow.f64 (exp.f64 -2) x) (expm1.f64 (.f64 x -2)) 1) (+.f64 1 (pow.f64 (exp.f64 x) -6))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 1 (pow.f64 (exp.f64 -2) x)) (-.f64 1 (pow.f64 (exp.f64 x) -4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (exp.f64 x) -6)) (fma.f64 (pow.f64 (exp.f64 -2) x) (expm1.f64 (.f64 x -2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (exp.f64 x) -6)) (+.f64 (pow.f64 (exp.f64 x) -4) (-.f64 1 (pow.f64 (exp.f64 -2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (exp.f64 x) -4)) (-.f64 1 (pow.f64 (exp.f64 -2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 1 (pow.f64 (exp.f64 x) -6))) (neg.f64 (fma.f64 (pow.f64 (exp.f64 -2) x) (expm1.f64 (.f64 x -2)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1 (pow.f64 (exp.f64 x) -4))) (neg.f64 (-.f64 1 (pow.f64 (exp.f64 -2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (expm1.f64 (.f64 -4 x)) (expm1.f64 (.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1 (pow.f64 (exp.f64 -2) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 (pow.f64 (exp.f64 -2) x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 1 (pow.f64 (exp.f64 -2) x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 1 (pow.f64 (exp.f64 x) -1)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 1 (pow.f64 (exp.f64 -2) x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 1 (pow.f64 (exp.f64 -2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 1 (pow.f64 (exp.f64 -2) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 1 (pow.f64 (exp.f64 -2) x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 1 (pow.f64 (exp.f64 -2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 1 (pow.f64 (exp.f64 -2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log1p.f64 (pow.f64 (exp.f64 -2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log1p.f64 (pow.f64 (exp.f64 -2) x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (pow.f64 (exp.f64 -2) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (exp.f64 -2) x) 1 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 (exp.f64 -2) x)) (cbrt.f64 (pow.f64 (exp.f64 x) -4)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 (exp.f64 x) -4)) (cbrt.f64 (pow.f64 (exp.f64 -2) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (exp.f64 x) -1) (pow.f64 (exp.f64 x) -1) 1)))))

simplify66.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

972×	`fma-def_binary64`
611×	`associate-*l/_binary64`
550×	`associate-*r/_binary64`
488×	`associate-/l/_binary64`
451×	`unswap-sqr_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	42	541
1	112	537
2	261	535
3	728	529
4	1639	526
5	2831	526
6	4160	526

Stop Event

1×	node limit

Counts

306 → 213

Calls

Call 1

Inputs
x
(+.f64 (*.f64 -1/3 (pow.f64 x 3)) x)
(+.f64 (.f64 -1/3 (pow.f64 x 3)) (+.f64 (.f64 2/15 (pow.f64 x 5)) x))
(+.f64 (.f64 -17/315 (pow.f64 x 7)) (+.f64 (.f64 -1/3 (pow.f64 x 3)) (+.f64 (*.f64 2/15 (pow.f64 x 5)) x)))
(-.f64 (.f64 2 (/.f64 1 (+.f64 1 (exp.f64 (.f64 -2 x))))) 1)
(-.f64 (.f64 2 (/.f64 1 (+.f64 1 (exp.f64 (.f64 -2 x))))) 1)
(-.f64 (.f64 2 (/.f64 1 (+.f64 1 (exp.f64 (.f64 -2 x))))) 1)
(-.f64 (.f64 2 (/.f64 1 (+.f64 1 (exp.f64 (.f64 -2 x))))) 1)
(-.f64 (.f64 2 (/.f64 1 (+.f64 1 (exp.f64 (.f64 -2 x))))) 1)
(-.f64 (.f64 2 (/.f64 1 (+.f64 1 (exp.f64 (.f64 -2 x))))) 1)
(-.f64 (.f64 2 (/.f64 1 (+.f64 1 (exp.f64 (.f64 -2 x))))) 1)
(-.f64 (.f64 2 (/.f64 1 (+.f64 1 (exp.f64 (.f64 -2 x))))) 1)
1
(+.f64 1 x)
(+.f64 1 (+.f64 (*.f64 -1/3 (pow.f64 x 3)) x))
(+.f64 1 (+.f64 (.f64 -1/3 (pow.f64 x 3)) (+.f64 x (.f64 2/15 (pow.f64 x 5)))))
(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))
(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))
(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))
(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))
(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))
(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))
(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))
(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))
1
(+.f64 1 x)
(+.f64 1 (+.f64 (*.f64 -1/3 (pow.f64 x 3)) x))
(+.f64 1 (+.f64 (.f64 -1/3 (pow.f64 x 3)) (+.f64 x (.f64 2/15 (pow.f64 x 5)))))
(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))
(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))
(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))
(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))
(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))
(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))
(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))
(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))
2
(+.f64 2 (*.f64 -2 x))
(+.f64 (.f64 2 (pow.f64 x 2)) (+.f64 2 (.f64 -2 x)))
(+.f64 (.f64 2 (pow.f64 x 2)) (+.f64 2 (+.f64 (.f64 -2 x) (*.f64 -4/3 (pow.f64 x 3)))))
(+.f64 1 (exp.f64 (*.f64 -2 x)))
(+.f64 1 (exp.f64 (*.f64 -2 x)))
(+.f64 1 (exp.f64 (*.f64 -2 x)))
(+.f64 1 (exp.f64 (*.f64 -2 x)))
(+.f64 1 (exp.f64 (*.f64 -2 x)))
(+.f64 1 (exp.f64 (*.f64 -2 x)))
(+.f64 1 (exp.f64 (*.f64 -2 x)))
(+.f64 1 (exp.f64 (*.f64 -2 x)))

Outputs
x
(+.f64 (*.f64 -1/3 (pow.f64 x 3)) x)
(fma.f64 -1/3 (pow.f64 x 3) x)
(+.f64 (.f64 -1/3 (pow.f64 x 3)) (+.f64 (.f64 2/15 (pow.f64 x 5)) x))
(fma.f64 -1/3 (pow.f64 x 3) (fma.f64 2/15 (pow.f64 x 5) x))
(+.f64 (.f64 -17/315 (pow.f64 x 7)) (+.f64 (.f64 -1/3 (pow.f64 x 3)) (+.f64 (*.f64 2/15 (pow.f64 x 5)) x)))
(fma.f64 -17/315 (pow.f64 x 7) (fma.f64 -1/3 (pow.f64 x 3) (fma.f64 2/15 (pow.f64 x 5) x)))
(fma.f64 -1/3 (pow.f64 x 3) (fma.f64 2/15 (pow.f64 x 5) (fma.f64 -17/315 (pow.f64 x 7) x)))
(fma.f64 -1/3 (pow.f64 x 3) (fma.f64 -17/315 (pow.f64 x 7) (fma.f64 2/15 (pow.f64 x 5) x)))
(-.f64 (.f64 2 (/.f64 1 (+.f64 1 (exp.f64 (.f64 -2 x))))) 1)
(+.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2)))) -1)
(+.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x))) -1)
(-.f64 (.f64 2 (/.f64 1 (+.f64 1 (exp.f64 (.f64 -2 x))))) 1)
(+.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2)))) -1)
(+.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x))) -1)
(-.f64 (.f64 2 (/.f64 1 (+.f64 1 (exp.f64 (.f64 -2 x))))) 1)
(+.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2)))) -1)
(+.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x))) -1)
(-.f64 (.f64 2 (/.f64 1 (+.f64 1 (exp.f64 (.f64 -2 x))))) 1)
(+.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2)))) -1)
(+.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x))) -1)
(-.f64 (.f64 2 (/.f64 1 (+.f64 1 (exp.f64 (.f64 -2 x))))) 1)
(+.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2)))) -1)
(+.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x))) -1)
(-.f64 (.f64 2 (/.f64 1 (+.f64 1 (exp.f64 (.f64 -2 x))))) 1)
(+.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2)))) -1)
(+.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x))) -1)
(-.f64 (.f64 2 (/.f64 1 (+.f64 1 (exp.f64 (.f64 -2 x))))) 1)
(+.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2)))) -1)
(+.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x))) -1)
(-.f64 (.f64 2 (/.f64 1 (+.f64 1 (exp.f64 (.f64 -2 x))))) 1)
(+.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2)))) -1)
(+.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x))) -1)
1
(+.f64 1 x)
(+.f64 x 1)
(+.f64 1 (+.f64 (*.f64 -1/3 (pow.f64 x 3)) x))
(+.f64 (fma.f64 -1/3 (pow.f64 x 3) x) 1)
(+.f64 x (fma.f64 -1/3 (pow.f64 x 3) 1))
(+.f64 1 (+.f64 (.f64 -1/3 (pow.f64 x 3)) (+.f64 x (.f64 2/15 (pow.f64 x 5)))))
(+.f64 (fma.f64 -1/3 (pow.f64 x 3) (fma.f64 2/15 (pow.f64 x 5) x)) 1)
(+.f64 (fma.f64 -1/3 (pow.f64 x 3) x) (fma.f64 2/15 (pow.f64 x 5) 1))
(+.f64 x (fma.f64 -1/3 (pow.f64 x 3) (fma.f64 2/15 (pow.f64 x 5) 1)))
(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))
(/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2))))
(/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x)))
(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))
(/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2))))
(/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x)))
(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))
(/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2))))
(/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x)))
(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))
(/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2))))
(/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x)))
(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))
(/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2))))
(/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x)))
(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))
(/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2))))
(/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x)))
(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))
(/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2))))
(/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x)))
(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))
(/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2))))
(/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x)))
1
(+.f64 1 x)
(+.f64 x 1)
(+.f64 1 (+.f64 (*.f64 -1/3 (pow.f64 x 3)) x))
(+.f64 (fma.f64 -1/3 (pow.f64 x 3) x) 1)
(+.f64 x (fma.f64 -1/3 (pow.f64 x 3) 1))
(+.f64 1 (+.f64 (.f64 -1/3 (pow.f64 x 3)) (+.f64 x (.f64 2/15 (pow.f64 x 5)))))
(+.f64 (fma.f64 -1/3 (pow.f64 x 3) (fma.f64 2/15 (pow.f64 x 5) x)) 1)
(+.f64 (fma.f64 -1/3 (pow.f64 x 3) x) (fma.f64 2/15 (pow.f64 x 5) 1))
(+.f64 x (fma.f64 -1/3 (pow.f64 x 3) (fma.f64 2/15 (pow.f64 x 5) 1)))
(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))
(/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2))))
(/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x)))
(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))
(/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2))))
(/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x)))
(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))
(/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2))))
(/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x)))
(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))
(/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2))))
(/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x)))
(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))
(/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2))))
(/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x)))
(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))
(/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2))))
(/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x)))
(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))
(/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2))))
(/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x)))
(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))
(/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2))))
(/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x)))
2
(+.f64 2 (*.f64 -2 x))
(+.f64 2 (*.f64 x -2))
(fma.f64 x -2 2)
(+.f64 (.f64 2 (pow.f64 x 2)) (+.f64 2 (.f64 -2 x)))
(fma.f64 2 (.f64 x x) (+.f64 2 (.f64 x -2)))
(fma.f64 2 (*.f64 x x) (fma.f64 x -2 2))
(fma.f64 x -2 (fma.f64 2 (*.f64 x x) 2))
(fma.f64 x (fma.f64 x 2 -2) 2)
(+.f64 (.f64 2 (pow.f64 x 2)) (+.f64 2 (+.f64 (.f64 -2 x) (*.f64 -4/3 (pow.f64 x 3)))))
(fma.f64 2 (.f64 x x) (+.f64 2 (fma.f64 -2 x (.f64 (pow.f64 x 3) -4/3))))
(+.f64 (fma.f64 (pow.f64 x 3) -4/3 (.f64 x -2)) (fma.f64 2 (.f64 x x) 2))
(fma.f64 (fma.f64 x x 1) 2 (fma.f64 (pow.f64 x 3) -4/3 (*.f64 x -2)))
(fma.f64 x (*.f64 x (fma.f64 x -4/3 2)) (fma.f64 x -2 2))
(fma.f64 x (fma.f64 x (fma.f64 x -4/3 2) -2) 2)
(+.f64 1 (exp.f64 (*.f64 -2 x)))
(+.f64 1 (exp.f64 (*.f64 x -2)))
(+.f64 1 (pow.f64 (exp.f64 -2) x))
(+.f64 1 (exp.f64 (*.f64 -2 x)))
(+.f64 1 (exp.f64 (*.f64 x -2)))
(+.f64 1 (pow.f64 (exp.f64 -2) x))
(+.f64 1 (exp.f64 (*.f64 -2 x)))
(+.f64 1 (exp.f64 (*.f64 x -2)))
(+.f64 1 (pow.f64 (exp.f64 -2) x))
(+.f64 1 (exp.f64 (*.f64 -2 x)))
(+.f64 1 (exp.f64 (*.f64 x -2)))
(+.f64 1 (pow.f64 (exp.f64 -2) x))
(+.f64 1 (exp.f64 (*.f64 -2 x)))
(+.f64 1 (exp.f64 (*.f64 x -2)))
(+.f64 1 (pow.f64 (exp.f64 -2) x))
(+.f64 1 (exp.f64 (*.f64 -2 x)))
(+.f64 1 (exp.f64 (*.f64 x -2)))
(+.f64 1 (pow.f64 (exp.f64 -2) x))
(+.f64 1 (exp.f64 (*.f64 -2 x)))
(+.f64 1 (exp.f64 (*.f64 x -2)))
(+.f64 1 (pow.f64 (exp.f64 -2) x))
(+.f64 1 (exp.f64 (*.f64 -2 x)))
(+.f64 1 (exp.f64 (*.f64 x -2)))
(+.f64 1 (pow.f64 (exp.f64 -2) x))

localize7.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.0b	(+.f64 1 (+.f64 x -1))

Compiler

Compiled 13 to 10 computations (23.1% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite50.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

691×	`pow1_binary64`
647×	`add-log-exp_binary64`
645×	`log1p-expm1-u_binary64`
645×	`expm1-log1p-u_binary64`
637×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	129	4
2	1704	4

Stop Event

1×	node limit

Counts

1 → 32

Calls

Call 1

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

Outputs

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

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1	12

Stop Event

1×

saturated

Counts

44 → 33

Calls

Call 1

Inputs
x
x
x
x
x
x
x
x
x
x
x
x

Outputs
x
x
x
x
x
x
x
x
x
x
x
x

localize10.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	29.0b	(/.f64 (-.f64 (*.f64 x x) 0) (-.f64 x 0))

Compiler

Compiled 24 to 13 computations (45.8% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite42.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

452×	`pow1_binary64`
439×	`add-sqr-sqrt_binary64`
434×	`add-log-exp_binary64`
433×	`log1p-expm1-u_binary64`
433×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	1
1	175	1
2	1854	1

Stop Event

1×	node limit

Counts

1 → 46

Calls

Call 1

Inputs
(/.f64 (-.f64 (*.f64 x x) 0) (-.f64 x 0))

Outputs

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

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1	12

Stop Event

1×

saturated

Counts

58 → 47

Calls

Call 1

Inputs
x
x
x
x
x
x
x
x
x
x
x
x

Outputs
x
x
x
x
x
x
x
x
x
x
x
x

localize13.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (+.f64 x 2) x)
✓	0.0b	(/.f64 1 (+.f64 x 2))
✓	14.7b	(.f64 (.f64 (+.f64 x 2) x) (/.f64 1 (+.f64 x 2)))

Compiler

Compiled 29 to 21 computations (27.6% saved)

series4.0ms (0%)

Counts

3 → 36

Calls

9 calls:

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

rewrite65.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

880×	`pow1_binary64`
823×	`add-log-exp_binary64`
822×	`log1p-expm1-u_binary64`
822×	`expm1-log1p-u_binary64`
808×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	27
1	175	27
2	2275	27

Stop Event

1×	node limit

Counts

3 → 69

Calls

Call 1

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

Outputs

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

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

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

simplify59.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

790×	`distribute-neg-frac_binary64`
787×	`fma-def_binary64`
714×	`associate-r_binary64`
415×	`times-frac_binary64`
285×	`associate-/l/_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	35	279
1	97	264
2	244	264
3	668	258
4	1987	255
5	6993	255

Stop Event

1×	node limit

Counts

105 → 90

Calls

Call 1

Inputs
x
x
x
x
x
x
x
x
x
x
x
x
1/2
(+.f64 1/2 (*.f64 -1/4 x))
(+.f64 (.f64 1/8 (pow.f64 x 2)) (+.f64 1/2 (.f64 -1/4 x)))
(+.f64 (.f64 1/8 (pow.f64 x 2)) (+.f64 (.f64 -1/16 (pow.f64 x 3)) (+.f64 1/2 (*.f64 -1/4 x))))
(/.f64 1 x)
(-.f64 (/.f64 1 x) (*.f64 2 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (.f64 4 (/.f64 1 (pow.f64 x 3))) (/.f64 1 x)) (.f64 2 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (.f64 4 (/.f64 1 (pow.f64 x 3))) (/.f64 1 x)) (+.f64 (.f64 8 (/.f64 1 (pow.f64 x 4))) (*.f64 2 (/.f64 1 (pow.f64 x 2)))))
(/.f64 1 x)
(-.f64 (/.f64 1 x) (*.f64 2 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (.f64 4 (/.f64 1 (pow.f64 x 3))) (/.f64 1 x)) (.f64 2 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (.f64 4 (/.f64 1 (pow.f64 x 3))) (/.f64 1 x)) (+.f64 (.f64 8 (/.f64 1 (pow.f64 x 4))) (*.f64 2 (/.f64 1 (pow.f64 x 2)))))
(*.f64 2 x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))

Outputs
x
x
x
x
x
x
x
x
x
x
x
x
1/2
(+.f64 1/2 (*.f64 -1/4 x))
(+.f64 1/2 (*.f64 x -1/4))
(fma.f64 x -1/4 1/2)
(+.f64 (.f64 1/8 (pow.f64 x 2)) (+.f64 1/2 (.f64 -1/4 x)))
(fma.f64 1/8 (.f64 x x) (+.f64 1/2 (.f64 x -1/4)))
(fma.f64 1/8 (*.f64 x x) (fma.f64 x -1/4 1/2))
(fma.f64 x -1/4 (fma.f64 x (*.f64 x 1/8) 1/2))
(fma.f64 x (fma.f64 x 1/8 -1/4) 1/2)
(+.f64 (.f64 1/8 (pow.f64 x 2)) (+.f64 (.f64 -1/16 (pow.f64 x 3)) (+.f64 1/2 (*.f64 -1/4 x))))
(fma.f64 1/8 (.f64 x x) (fma.f64 -1/16 (pow.f64 x 3) (+.f64 1/2 (.f64 x -1/4))))
(fma.f64 1/8 (*.f64 x x) (fma.f64 -1/16 (pow.f64 x 3) (fma.f64 x -1/4 1/2)))
(fma.f64 x (*.f64 x 1/8) (fma.f64 -1/16 (pow.f64 x 3) (fma.f64 x -1/4 1/2)))
(fma.f64 x (*.f64 x (fma.f64 x -1/16 1/8)) (fma.f64 x -1/4 1/2))
(fma.f64 x (fma.f64 x (fma.f64 x -1/16 1/8) -1/4) 1/2)
(/.f64 1 x)
(-.f64 (/.f64 1 x) (*.f64 2 (/.f64 1 (pow.f64 x 2))))
(-.f64 (/.f64 1 x) (/.f64 2 (*.f64 x x)))
(-.f64 (/.f64 1 x) (/.f64 (/.f64 2 x) x))
(+.f64 (/.f64 1 x) (/.f64 -2 (*.f64 x x)))
(+.f64 (/.f64 1 x) (/.f64 (/.f64 -2 x) x))
(-.f64 (+.f64 (.f64 4 (/.f64 1 (pow.f64 x 3))) (/.f64 1 x)) (.f64 2 (/.f64 1 (pow.f64 x 2))))
(+.f64 (/.f64 4 (pow.f64 x 3)) (-.f64 (/.f64 1 x) (/.f64 2 (*.f64 x x))))
(+.f64 (/.f64 1 x) (+.f64 (/.f64 4 (pow.f64 x 3)) (/.f64 -2 (*.f64 x x))))
(+.f64 (/.f64 1 x) (+.f64 (/.f64 4 (pow.f64 x 3)) (/.f64 (/.f64 -2 x) x)))
(+.f64 (/.f64 1 x) (*.f64 (/.f64 (/.f64 1 x) x) (-.f64 (/.f64 4 x) 2)))
(+.f64 (/.f64 1 x) (*.f64 (/.f64 (/.f64 1 x) x) (+.f64 (/.f64 4 x) -2)))
(-.f64 (+.f64 (.f64 4 (/.f64 1 (pow.f64 x 3))) (/.f64 1 x)) (+.f64 (.f64 8 (/.f64 1 (pow.f64 x 4))) (*.f64 2 (/.f64 1 (pow.f64 x 2)))))
(-.f64 (+.f64 (/.f64 1 x) (/.f64 4 (pow.f64 x 3))) (+.f64 (/.f64 2 (*.f64 x x)) (/.f64 8 (pow.f64 x 4))))
(-.f64 (+.f64 (/.f64 1 x) (/.f64 4 (pow.f64 x 3))) (+.f64 (/.f64 (/.f64 2 x) x) (/.f64 8 (pow.f64 x 4))))
(+.f64 (/.f64 1 x) (+.f64 (/.f64 4 (pow.f64 x 3)) (+.f64 (/.f64 -2 (*.f64 x x)) (/.f64 -8 (pow.f64 x 4)))))
(+.f64 (/.f64 1 x) (+.f64 (/.f64 4 (pow.f64 x 3)) (+.f64 (/.f64 (/.f64 -2 x) x) (/.f64 -8 (pow.f64 x 4)))))
(+.f64 (+.f64 (/.f64 1 x) (/.f64 (/.f64 -2 x) x)) (*.f64 (/.f64 1 (pow.f64 x 3)) (+.f64 4 (/.f64 -8 x))))
(/.f64 1 x)
(-.f64 (/.f64 1 x) (*.f64 2 (/.f64 1 (pow.f64 x 2))))
(-.f64 (/.f64 1 x) (/.f64 2 (*.f64 x x)))
(-.f64 (/.f64 1 x) (/.f64 (/.f64 2 x) x))
(+.f64 (/.f64 1 x) (/.f64 -2 (*.f64 x x)))
(+.f64 (/.f64 1 x) (/.f64 (/.f64 -2 x) x))
(-.f64 (+.f64 (.f64 4 (/.f64 1 (pow.f64 x 3))) (/.f64 1 x)) (.f64 2 (/.f64 1 (pow.f64 x 2))))
(+.f64 (/.f64 4 (pow.f64 x 3)) (-.f64 (/.f64 1 x) (/.f64 2 (*.f64 x x))))
(+.f64 (/.f64 1 x) (+.f64 (/.f64 4 (pow.f64 x 3)) (/.f64 -2 (*.f64 x x))))
(+.f64 (/.f64 1 x) (+.f64 (/.f64 4 (pow.f64 x 3)) (/.f64 (/.f64 -2 x) x)))
(+.f64 (/.f64 1 x) (*.f64 (/.f64 (/.f64 1 x) x) (-.f64 (/.f64 4 x) 2)))
(+.f64 (/.f64 1 x) (*.f64 (/.f64 (/.f64 1 x) x) (+.f64 (/.f64 4 x) -2)))
(-.f64 (+.f64 (.f64 4 (/.f64 1 (pow.f64 x 3))) (/.f64 1 x)) (+.f64 (.f64 8 (/.f64 1 (pow.f64 x 4))) (*.f64 2 (/.f64 1 (pow.f64 x 2)))))
(-.f64 (+.f64 (/.f64 1 x) (/.f64 4 (pow.f64 x 3))) (+.f64 (/.f64 2 (*.f64 x x)) (/.f64 8 (pow.f64 x 4))))
(-.f64 (+.f64 (/.f64 1 x) (/.f64 4 (pow.f64 x 3))) (+.f64 (/.f64 (/.f64 2 x) x) (/.f64 8 (pow.f64 x 4))))
(+.f64 (/.f64 1 x) (+.f64 (/.f64 4 (pow.f64 x 3)) (+.f64 (/.f64 -2 (*.f64 x x)) (/.f64 -8 (pow.f64 x 4)))))
(+.f64 (/.f64 1 x) (+.f64 (/.f64 4 (pow.f64 x 3)) (+.f64 (/.f64 (/.f64 -2 x) x) (/.f64 -8 (pow.f64 x 4)))))
(+.f64 (+.f64 (/.f64 1 x) (/.f64 (/.f64 -2 x) x)) (*.f64 (/.f64 1 (pow.f64 x 3)) (+.f64 4 (/.f64 -8 x))))
(*.f64 2 x)
(*.f64 x 2)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 x 2))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 x 2))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 x 2))

localize14.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(*.f64 (+.f64 x 2) x)
✓	0.2b	(/.f64 1 (/.f64 (+.f64 x 2) (*.f64 (+.f64 x 2) x)))
✓	14.6b	(/.f64 (+.f64 x 2) (*.f64 (+.f64 x 2) x))

Compiler

Compiled 33 to 23 computations (30.3% saved)

series2.0ms (0%)

Counts

2 → 24

Calls

6 calls:

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

rewrite66.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

882×	`pow1_binary64`
830×	`add-log-exp_binary64`
829×	`log1p-expm1-u_binary64`
829×	`expm1-log1p-u_binary64`
814×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	29
1	180	5
2	2566	5

Stop Event

1×	node limit

Counts

2 → 81

Calls

Call 1

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

Outputs

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

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

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	60
1	6	60

Stop Event

1×

saturated

Counts

105 → 83

Calls

Call 1

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

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

eval189.0ms (2.6%)

Compiler: Compiled 7560 to 6252 computations (17.3% saved)

prune86.0ms (1.2%)

Pruning

15 alts after pruning (10 fresh and 5 done)

	Pruned	Kept	Total
New	482	9	491
Fresh	2	1	3
Picked	1	0	1
Done	2	5	7
Total	487	15	502

Error

0.0b

Counts

502 → 15

Alt Table

Click to see full alt table

Status	Error	Program
✓	29.1b	(-.f64 (-.f64 (+.f64 1 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2))))) 1) 1)
✓	29.1b	(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)
	29.4b	(/.f64 1 (/.f64 (+.f64 x 2) (*.f64 x 2)))
▶	29.1b	(-.f64 (*.f64 (exp.f64 (neg.f64 (log1p.f64 (pow.f64 (exp.f64 -2) x)))) 2) 1)
	45.7b	(.f64 (/.f64 1 x) (.f64 x x))
✓	59.8b	(+.f64 1 (+.f64 x -1))
▶	32.3b	(.f64 (.f64 (+.f64 x 2) x) (+.f64 1/2 (*.f64 -1/4 x)))
✓	32.2b	(+.f64 (*.f64 -1/3 (pow.f64 x 3)) x)
▶	29.4b	(.f64 (.f64 x 2) (/.f64 1 (+.f64 x 2)))
	30.7b	x
▶	30.8b	(.f64 x (.f64 x (/.f64 1 x)))
	45.7b	(neg.f64 (/.f64 (*.f64 x x) (neg.f64 x)))
	47.4b	-1
✓	59.7b	(-.f64 (+.f64 x 1) 1)
▶	30.8b	(/.f64 1 (/.f64 1 x))

Compiler

Compiled 221 to 178 computations (19.5% saved)

localize35.0ms (0.5%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f64 (pow.f64 (exp.f64 -2) x))
✓	0.0b	(pow.f64 (exp.f64 -2) x)
✓	1.9b	(-.f64 (*.f64 (exp.f64 (neg.f64 (log1p.f64 (pow.f64 (exp.f64 -2) x)))) 2) 1)

Compiler

Compiled 50 to 43 computations (14% saved)

series54.0ms (0.8%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
28.0ms	x	@	inf	(-.f64 (*.f64 (exp.f64 (neg.f64 (log1p.f64 (pow.f64 (exp.f64 -2) x)))) 2) 1)
23.0ms	x	@	-inf	(-.f64 (*.f64 (exp.f64 (neg.f64 (log1p.f64 (pow.f64 (exp.f64 -2) x)))) 2) 1)
2.0ms	x	@	0	(-.f64 (*.f64 (exp.f64 (neg.f64 (log1p.f64 (pow.f64 (exp.f64 -2) x)))) 2) 1)
0.0ms	x	@	0	(log1p.f64 (pow.f64 (exp.f64 -2) x))
0.0ms	x	@	0	(pow.f64 (exp.f64 -2) x)

rewrite85.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

967×	`pow1_binary64`
897×	`add-log-exp_binary64`
894×	`expm1-log1p-u_binary64`
893×	`log1p-expm1-u_binary64`
117×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	30
1	243	27
2	2815	27

Stop Event

1×	node limit

Counts

3 → 80

Calls

Call 1

Inputs
(-.f64 (*.f64 (exp.f64 (neg.f64 (log1p.f64 (pow.f64 (exp.f64 -2) x)))) 2) 1)
(pow.f64 (exp.f64 -2) x)
(log1p.f64 (pow.f64 (exp.f64 -2) x))

Outputs

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

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

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

simplify60.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

531×	`associate-l_binary64`
420×	`associate-r_binary64`
279×	`fma-def_binary64`
277×	`associate-+l+_binary64`
276×	`distribute-rgt-out_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	61	468
1	168	356
2	506	338
3	1413	338
4	5081	338

Stop Event

1×	node limit

Counts

116 → 107

Calls

Call 1

Inputs
(-.f64 (*.f64 2 (exp.f64 (neg.f64 (log.f64 2)))) 1)
(-.f64 (+.f64 (.f64 2 (.f64 (exp.f64 (neg.f64 (log.f64 2))) x)) (*.f64 2 (exp.f64 (neg.f64 (log.f64 2))))) 1)
(-.f64 (+.f64 (.f64 2 (.f64 (exp.f64 (neg.f64 (log.f64 2))) x)) (+.f64 (.f64 -2/3 (.f64 (exp.f64 (neg.f64 (log.f64 2))) (pow.f64 x 3))) (*.f64 2 (exp.f64 (neg.f64 (log.f64 2)))))) 1)
(-.f64 (+.f64 (.f64 2 (.f64 (exp.f64 (neg.f64 (log.f64 2))) x)) (+.f64 (.f64 -2/3 (.f64 (exp.f64 (neg.f64 (log.f64 2))) (pow.f64 x 3))) (+.f64 (.f64 4/15 (.f64 (exp.f64 (neg.f64 (log.f64 2))) (pow.f64 x 5))) (*.f64 2 (exp.f64 (neg.f64 (log.f64 2))))))) 1)
(-.f64 (.f64 2 (exp.f64 (neg.f64 (log.f64 (+.f64 1 (exp.f64 (.f64 -2 x))))))) 1)
(-.f64 (.f64 2 (exp.f64 (neg.f64 (log.f64 (+.f64 1 (exp.f64 (.f64 -2 x))))))) 1)
(-.f64 (.f64 2 (exp.f64 (neg.f64 (log.f64 (+.f64 1 (exp.f64 (.f64 -2 x))))))) 1)
(-.f64 (.f64 2 (exp.f64 (neg.f64 (log.f64 (+.f64 1 (exp.f64 (.f64 -2 x))))))) 1)
(-.f64 (.f64 2 (exp.f64 (neg.f64 (log.f64 (+.f64 1 (exp.f64 (.f64 -2 x))))))) 1)
(-.f64 (.f64 2 (exp.f64 (neg.f64 (log.f64 (+.f64 1 (exp.f64 (.f64 -2 x))))))) 1)
(-.f64 (.f64 2 (exp.f64 (neg.f64 (log.f64 (+.f64 1 (exp.f64 (.f64 -2 x))))))) 1)
(-.f64 (.f64 2 (exp.f64 (neg.f64 (log.f64 (+.f64 1 (exp.f64 (.f64 -2 x))))))) 1)
1
(+.f64 1 (*.f64 -2 x))
(+.f64 (.f64 2 (pow.f64 x 2)) (+.f64 1 (.f64 -2 x)))
(+.f64 (.f64 2 (pow.f64 x 2)) (+.f64 1 (+.f64 (.f64 -2 x) (*.f64 -4/3 (pow.f64 x 3)))))
(exp.f64 (*.f64 -2 x))
(exp.f64 (*.f64 -2 x))
(exp.f64 (*.f64 -2 x))
(exp.f64 (*.f64 -2 x))
(exp.f64 (*.f64 -2 x))
(exp.f64 (*.f64 -2 x))
(exp.f64 (*.f64 -2 x))
(exp.f64 (*.f64 -2 x))
(log.f64 2)
(+.f64 (log.f64 2) (*.f64 -1 x))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (+.f64 (log.f64 2) (.f64 -1 x)))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (+.f64 (log.f64 2) (+.f64 (.f64 -1 x) (*.f64 -1/12 (pow.f64 x 4)))))
(log.f64 (+.f64 1 (exp.f64 (*.f64 -2 x))))
(log.f64 (+.f64 1 (exp.f64 (*.f64 -2 x))))
(log.f64 (+.f64 1 (exp.f64 (*.f64 -2 x))))
(log.f64 (+.f64 1 (exp.f64 (*.f64 -2 x))))
(log.f64 (+.f64 1 (exp.f64 (*.f64 -2 x))))
(log.f64 (+.f64 1 (exp.f64 (*.f64 -2 x))))
(log.f64 (+.f64 1 (exp.f64 (*.f64 -2 x))))
(log.f64 (+.f64 1 (exp.f64 (*.f64 -2 x))))

Outputs
(-.f64 (*.f64 2 (exp.f64 (neg.f64 (log.f64 2)))) 1)
(fma.f64 2 (exp.f64 (neg.f64 (log.f64 2))) -1)
0
(-.f64 (+.f64 (.f64 2 (.f64 (exp.f64 (neg.f64 (log.f64 2))) x)) (*.f64 2 (exp.f64 (neg.f64 (log.f64 2))))) 1)
(+.f64 (.f64 2 (+.f64 (.f64 (exp.f64 (neg.f64 (log.f64 2))) x) (exp.f64 (neg.f64 (log.f64 2))))) -1)
(fma.f64 1 x 0)
x
(-.f64 (+.f64 (.f64 2 (.f64 (exp.f64 (neg.f64 (log.f64 2))) x)) (+.f64 (.f64 -2/3 (.f64 (exp.f64 (neg.f64 (log.f64 2))) (pow.f64 x 3))) (*.f64 2 (exp.f64 (neg.f64 (log.f64 2)))))) 1)
(+.f64 (fma.f64 2 (.f64 (exp.f64 (neg.f64 (log.f64 2))) x) (fma.f64 -2/3 (.f64 (exp.f64 (neg.f64 (log.f64 2))) (pow.f64 x 3)) (*.f64 2 (exp.f64 (neg.f64 (log.f64 2)))))) -1)
(fma.f64 1 x (+.f64 (*.f64 (pow.f64 x 3) -1/3) 0))
(fma.f64 (pow.f64 x 3) -1/3 x)
(-.f64 (+.f64 (.f64 2 (.f64 (exp.f64 (neg.f64 (log.f64 2))) x)) (+.f64 (.f64 -2/3 (.f64 (exp.f64 (neg.f64 (log.f64 2))) (pow.f64 x 3))) (+.f64 (.f64 4/15 (.f64 (exp.f64 (neg.f64 (log.f64 2))) (pow.f64 x 5))) (*.f64 2 (exp.f64 (neg.f64 (log.f64 2))))))) 1)
(+.f64 (fma.f64 2 (.f64 (exp.f64 (neg.f64 (log.f64 2))) x) (fma.f64 -2/3 (.f64 (exp.f64 (neg.f64 (log.f64 2))) (pow.f64 x 3)) (fma.f64 4/15 (.f64 (exp.f64 (neg.f64 (log.f64 2))) (pow.f64 x 5)) (.f64 2 (exp.f64 (neg.f64 (log.f64 2))))))) -1)
(fma.f64 1 x (+.f64 (fma.f64 -1/3 (pow.f64 x 3) (*.f64 (pow.f64 x 5) 2/15)) 0))
(+.f64 x (fma.f64 (pow.f64 x 3) -1/3 (*.f64 (pow.f64 x 5) 2/15)))
(+.f64 x (fma.f64 (pow.f64 x 5) 2/15 (*.f64 (pow.f64 x 3) -1/3)))
(-.f64 (.f64 2 (exp.f64 (neg.f64 (log.f64 (+.f64 1 (exp.f64 (.f64 -2 x))))))) 1)
(fma.f64 2 (exp.f64 (neg.f64 (log1p.f64 (pow.f64 (exp.f64 -2) x)))) -1)
(+.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x))) -1)
(+.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2)))) -1)
(-.f64 (.f64 2 (exp.f64 (neg.f64 (log.f64 (+.f64 1 (exp.f64 (.f64 -2 x))))))) 1)
(fma.f64 2 (exp.f64 (neg.f64 (log1p.f64 (pow.f64 (exp.f64 -2) x)))) -1)
(+.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x))) -1)
(+.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2)))) -1)
(-.f64 (.f64 2 (exp.f64 (neg.f64 (log.f64 (+.f64 1 (exp.f64 (.f64 -2 x))))))) 1)
(fma.f64 2 (exp.f64 (neg.f64 (log1p.f64 (pow.f64 (exp.f64 -2) x)))) -1)
(+.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x))) -1)
(+.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2)))) -1)
(-.f64 (.f64 2 (exp.f64 (neg.f64 (log.f64 (+.f64 1 (exp.f64 (.f64 -2 x))))))) 1)
(fma.f64 2 (exp.f64 (neg.f64 (log1p.f64 (pow.f64 (exp.f64 -2) x)))) -1)
(+.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x))) -1)
(+.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2)))) -1)
(-.f64 (.f64 2 (exp.f64 (neg.f64 (log.f64 (+.f64 1 (exp.f64 (.f64 -2 x))))))) 1)
(fma.f64 2 (exp.f64 (neg.f64 (log1p.f64 (pow.f64 (exp.f64 -2) x)))) -1)
(+.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x))) -1)
(+.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2)))) -1)
(-.f64 (.f64 2 (exp.f64 (neg.f64 (log.f64 (+.f64 1 (exp.f64 (.f64 -2 x))))))) 1)
(fma.f64 2 (exp.f64 (neg.f64 (log1p.f64 (pow.f64 (exp.f64 -2) x)))) -1)
(+.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x))) -1)
(+.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2)))) -1)
(-.f64 (.f64 2 (exp.f64 (neg.f64 (log.f64 (+.f64 1 (exp.f64 (.f64 -2 x))))))) 1)
(fma.f64 2 (exp.f64 (neg.f64 (log1p.f64 (pow.f64 (exp.f64 -2) x)))) -1)
(+.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x))) -1)
(+.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2)))) -1)
(-.f64 (.f64 2 (exp.f64 (neg.f64 (log.f64 (+.f64 1 (exp.f64 (.f64 -2 x))))))) 1)
(fma.f64 2 (exp.f64 (neg.f64 (log1p.f64 (pow.f64 (exp.f64 -2) x)))) -1)
(+.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x))) -1)
(+.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2)))) -1)
1
(+.f64 1 (*.f64 -2 x))
(+.f64 1 (*.f64 x -2))
(fma.f64 x -2 1)
(+.f64 (.f64 2 (pow.f64 x 2)) (+.f64 1 (.f64 -2 x)))
(fma.f64 2 (.f64 x x) (+.f64 1 (.f64 x -2)))
(fma.f64 2 (*.f64 x x) (fma.f64 x -2 1))
(fma.f64 x -2 (fma.f64 2 (*.f64 x x) 1))
(+.f64 (.f64 2 (pow.f64 x 2)) (+.f64 1 (+.f64 (.f64 -2 x) (*.f64 -4/3 (pow.f64 x 3)))))
(fma.f64 2 (.f64 x x) (+.f64 1 (fma.f64 -2 x (.f64 (pow.f64 x 3) -4/3))))
(+.f64 (fma.f64 2 (.f64 x x) (fma.f64 x -2 1)) (.f64 (pow.f64 x 3) -4/3))
(fma.f64 2 (*.f64 x x) (fma.f64 (pow.f64 x 3) -4/3 (fma.f64 x -2 1)))
(+.f64 1 (.f64 x (+.f64 (.f64 x (+.f64 2 (*.f64 x -4/3))) -2)))
(exp.f64 (*.f64 -2 x))
(pow.f64 (exp.f64 -2) x)
(exp.f64 (*.f64 x -2))
(exp.f64 (*.f64 -2 x))
(pow.f64 (exp.f64 -2) x)
(exp.f64 (*.f64 x -2))
(exp.f64 (*.f64 -2 x))
(pow.f64 (exp.f64 -2) x)
(exp.f64 (*.f64 x -2))
(exp.f64 (*.f64 -2 x))
(pow.f64 (exp.f64 -2) x)
(exp.f64 (*.f64 x -2))
(exp.f64 (*.f64 -2 x))
(pow.f64 (exp.f64 -2) x)
(exp.f64 (*.f64 x -2))
(exp.f64 (*.f64 -2 x))
(pow.f64 (exp.f64 -2) x)
(exp.f64 (*.f64 x -2))
(exp.f64 (*.f64 -2 x))
(pow.f64 (exp.f64 -2) x)
(exp.f64 (*.f64 x -2))
(exp.f64 (*.f64 -2 x))
(pow.f64 (exp.f64 -2) x)
(exp.f64 (*.f64 x -2))
(log.f64 2)
(+.f64 (log.f64 2) (*.f64 -1 x))
(+.f64 (log.f64 2) (neg.f64 x))
(-.f64 (log.f64 2) x)
(+.f64 (.f64 1/2 (pow.f64 x 2)) (+.f64 (log.f64 2) (.f64 -1 x)))
(fma.f64 1/2 (*.f64 x x) (+.f64 (log.f64 2) (neg.f64 x)))
(-.f64 (fma.f64 1/2 (*.f64 x x) (log.f64 2)) x)
(+.f64 (.f64 1/2 (pow.f64 x 2)) (+.f64 (log.f64 2) (+.f64 (.f64 -1 x) (*.f64 -1/12 (pow.f64 x 4)))))
(fma.f64 1/2 (.f64 x x) (+.f64 (log.f64 2) (fma.f64 -1 x (.f64 -1/12 (pow.f64 x 4)))))
(+.f64 (fma.f64 -1/12 (pow.f64 x 4) (neg.f64 x)) (fma.f64 1/2 (*.f64 x x) (log.f64 2)))
(fma.f64 1/2 (*.f64 x x) (-.f64 (fma.f64 -1/12 (pow.f64 x 4) (log.f64 2)) x))
(fma.f64 -1/12 (pow.f64 x 4) (-.f64 (fma.f64 1/2 (*.f64 x x) (log.f64 2)) x))
(log.f64 (+.f64 1 (exp.f64 (*.f64 -2 x))))
(log1p.f64 (pow.f64 (exp.f64 -2) x))
(log1p.f64 (exp.f64 (*.f64 x -2)))
(log.f64 (+.f64 1 (exp.f64 (*.f64 -2 x))))
(log1p.f64 (pow.f64 (exp.f64 -2) x))
(log1p.f64 (exp.f64 (*.f64 x -2)))
(log.f64 (+.f64 1 (exp.f64 (*.f64 -2 x))))
(log1p.f64 (pow.f64 (exp.f64 -2) x))
(log1p.f64 (exp.f64 (*.f64 x -2)))
(log.f64 (+.f64 1 (exp.f64 (*.f64 -2 x))))
(log1p.f64 (pow.f64 (exp.f64 -2) x))
(log1p.f64 (exp.f64 (*.f64 x -2)))
(log.f64 (+.f64 1 (exp.f64 (*.f64 -2 x))))
(log1p.f64 (pow.f64 (exp.f64 -2) x))
(log1p.f64 (exp.f64 (*.f64 x -2)))
(log.f64 (+.f64 1 (exp.f64 (*.f64 -2 x))))
(log1p.f64 (pow.f64 (exp.f64 -2) x))
(log1p.f64 (exp.f64 (*.f64 x -2)))
(log.f64 (+.f64 1 (exp.f64 (*.f64 -2 x))))
(log1p.f64 (pow.f64 (exp.f64 -2) x))
(log1p.f64 (exp.f64 (*.f64 x -2)))
(log.f64 (+.f64 1 (exp.f64 (*.f64 -2 x))))
(log1p.f64 (pow.f64 (exp.f64 -2) x))
(log1p.f64 (exp.f64 (*.f64 x -2)))

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1 (/.f64 1 x))

Compiler

Compiled 12 to 9 computations (25% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite47.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

348×	`pow1_binary64`
336×	`add-sqr-sqrt_binary64`
328×	`*-un-lft-identity_binary64`
323×	`add-log-exp_binary64`
323×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	1
1	105	1
2	997	1

Stop Event

1×	node limit

Counts

1 → 47

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 x)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 x))) (log.f64 (sqrt.f64 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 2) x))) (log.f64 (cbrt.f64 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 x)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 x) (cbrt.f64 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 x x)) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 x x)) (neg.f64 (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (neg.f64 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x 1/4) (sqrt.f64 (pow.f64 x 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (cbrt.f64 (*.f64 x x))) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 x 5/2)) (pow.f64 x 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (*.f64 x (cbrt.f64 x)) 2)) (cbrt.f64 (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 x) 5)) (pow.f64 x 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 x 3/2)) (pow.f64 x 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (*.f64 x (cbrt.f64 x)) 2) 1/3) (cbrt.f64 (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 x 5/2) 1/3) (pow.f64 x 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 x 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (log.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x x) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x -2) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x -3) -1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 x) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (cbrt.f64 x)) -3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 x) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x -1/2) -2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 -1) (neg.f64 (log.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 x)) 2)) (cbrt.f64 (log.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 x))) (sqrt.f64 (log.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 x)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 x 3))))) (#(struct:change #<rule egg-rr> (2) ((x . x)))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 x)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 x)) 2))))))

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1	12

Stop Event

1×

saturated

Counts

59 → 48

Calls

Call 1

Inputs
x
x
x
x
x
x
x
x
x
x
x
x

Outputs
x
x
x
x
x
x
x
x
x
x
x
x

localize9.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 x (/.f64 1 x))

Compiler

Compiled 19 to 12 computations (36.8% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite57.0ms (0.8%)

Algorithm

1×	egg-rewrite-iter-limit
1×	batch-egg-rewrite

Rules

328×	`pow1_binary64`
318×	`add-sqr-sqrt_binary64`
310×	`*-un-lft-identity_binary64`
304×	`add-log-exp_binary64`
304×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	1
1	103	1
2	915	1
0	5	1

Stop Event

1×	iter limit
1×	node limit

Counts

1 → 1

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x . 1)))))

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1	12
1	4	12

Stop Event

1×

saturated

Counts

13 → 1

Calls

Call 1

Inputs
1
1
1
1
1
1
1
1
1
1
1
1

Outputs
1
1
1
1
1
1
1
1
1
1
1
1

localize11.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(/.f64 1 (+.f64 x 2))
✓	0.4b	(.f64 (.f64 x 2) (/.f64 1 (+.f64 x 2)))

Compiler

Compiled 25 to 19 computations (24% saved)

series2.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite58.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

854×	`pow1_binary64`
798×	`add-log-exp_binary64`
797×	`log1p-expm1-u_binary64`
797×	`expm1-log1p-u_binary64`
784×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	174	10
2	2218	10

Stop Event

1×	node limit

Counts

1 → 26

Calls

Call 1

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

Outputs

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

simplify52.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

805×	`unswap-sqr_binary64`
798×	`distribute-neg-frac_binary64`
531×	`associate-/r*_binary64`
368×	`fma-def_binary64`
334×	`times-frac_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	33	144
1	95	144
2	236	144
3	662	138
4	2155	138
5	6078	138

Stop Event

1×	node limit

Counts

38 → 40

Calls

Call 1

Inputs
x
(+.f64 (*.f64 -1/2 (pow.f64 x 2)) x)
(+.f64 (.f64 -1/2 (pow.f64 x 2)) (+.f64 (.f64 1/4 (pow.f64 x 3)) x))
(+.f64 (.f64 -1/2 (pow.f64 x 2)) (+.f64 (.f64 -1/8 (pow.f64 x 4)) (+.f64 (*.f64 1/4 (pow.f64 x 3)) x)))
2
(-.f64 2 (*.f64 4 (/.f64 1 x)))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (pow.f64 x 2))) 2) (.f64 4 (/.f64 1 x)))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (pow.f64 x 2))) 2) (+.f64 (.f64 16 (/.f64 1 (pow.f64 x 3))) (*.f64 4 (/.f64 1 x))))
2
(-.f64 2 (*.f64 4 (/.f64 1 x)))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (pow.f64 x 2))) 2) (.f64 4 (/.f64 1 x)))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (pow.f64 x 2))) 2) (+.f64 (.f64 16 (/.f64 1 (pow.f64 x 3))) (*.f64 4 (/.f64 1 x))))

Outputs
x
(+.f64 (*.f64 -1/2 (pow.f64 x 2)) x)
(fma.f64 -1/2 (*.f64 x x) x)
(fma.f64 x (*.f64 x -1/2) x)
(*.f64 x (fma.f64 x -1/2 1))
(+.f64 (.f64 -1/2 (pow.f64 x 2)) (+.f64 (.f64 1/4 (pow.f64 x 3)) x))
(fma.f64 -1/2 (*.f64 x x) (fma.f64 1/4 (pow.f64 x 3) x))
(fma.f64 x (*.f64 x -1/2) (fma.f64 1/4 (pow.f64 x 3) x))
(fma.f64 x (*.f64 x (fma.f64 x 1/4 -1/2)) x)
(+.f64 (.f64 -1/2 (pow.f64 x 2)) (+.f64 (.f64 -1/8 (pow.f64 x 4)) (+.f64 (*.f64 1/4 (pow.f64 x 3)) x)))
(fma.f64 -1/2 (*.f64 x x) (fma.f64 -1/8 (pow.f64 x 4) (fma.f64 1/4 (pow.f64 x 3) x)))
(fma.f64 x (*.f64 x -1/2) (fma.f64 1/4 (pow.f64 x 3) (fma.f64 -1/8 (pow.f64 x 4) x)))
(fma.f64 (*.f64 x x) (fma.f64 x 1/4 -1/2) (fma.f64 -1/8 (pow.f64 x 4) x))
(fma.f64 x (*.f64 x (fma.f64 x 1/4 -1/2)) (fma.f64 -1/8 (pow.f64 x 4) x))
2
(-.f64 2 (*.f64 4 (/.f64 1 x)))
(-.f64 2 (/.f64 4 x))
(+.f64 2 (/.f64 -4 x))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (pow.f64 x 2))) 2) (.f64 4 (/.f64 1 x)))
(+.f64 (/.f64 8 (*.f64 x x)) (-.f64 2 (/.f64 4 x)))
(+.f64 (-.f64 2 (/.f64 4 x)) (/.f64 8 (*.f64 x x)))
(+.f64 2 (+.f64 (/.f64 8 (*.f64 x x)) (/.f64 -4 x)))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (pow.f64 x 2))) 2) (+.f64 (.f64 16 (/.f64 1 (pow.f64 x 3))) (*.f64 4 (/.f64 1 x))))
(+.f64 (/.f64 8 (*.f64 x x)) (-.f64 2 (+.f64 (/.f64 4 x) (/.f64 16 (pow.f64 x 3)))))
(+.f64 2 (-.f64 (/.f64 8 (*.f64 x x)) (+.f64 (/.f64 4 x) (/.f64 16 (pow.f64 x 3)))))
(+.f64 2 (+.f64 (/.f64 8 (*.f64 x x)) (+.f64 (/.f64 -4 x) (/.f64 -16 (pow.f64 x 3)))))
(+.f64 (/.f64 8 (*.f64 x x)) (-.f64 (/.f64 -16 (pow.f64 x 3)) (+.f64 (/.f64 4 x) -2)))
(+.f64 (-.f64 2 (/.f64 4 x)) (*.f64 (/.f64 (/.f64 1 x) x) (-.f64 8 (/.f64 16 x))))
(+.f64 (+.f64 2 (/.f64 -4 x)) (.f64 (/.f64 1 (.f64 x x)) (+.f64 8 (/.f64 -16 x))))
2
(-.f64 2 (*.f64 4 (/.f64 1 x)))
(-.f64 2 (/.f64 4 x))
(+.f64 2 (/.f64 -4 x))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (pow.f64 x 2))) 2) (.f64 4 (/.f64 1 x)))
(+.f64 (/.f64 8 (*.f64 x x)) (-.f64 2 (/.f64 4 x)))
(+.f64 (-.f64 2 (/.f64 4 x)) (/.f64 8 (*.f64 x x)))
(+.f64 2 (+.f64 (/.f64 8 (*.f64 x x)) (/.f64 -4 x)))
(-.f64 (+.f64 (.f64 8 (/.f64 1 (pow.f64 x 2))) 2) (+.f64 (.f64 16 (/.f64 1 (pow.f64 x 3))) (*.f64 4 (/.f64 1 x))))
(+.f64 (/.f64 8 (*.f64 x x)) (-.f64 2 (+.f64 (/.f64 4 x) (/.f64 16 (pow.f64 x 3)))))
(+.f64 2 (-.f64 (/.f64 8 (*.f64 x x)) (+.f64 (/.f64 4 x) (/.f64 16 (pow.f64 x 3)))))
(+.f64 2 (+.f64 (/.f64 8 (*.f64 x x)) (+.f64 (/.f64 -4 x) (/.f64 -16 (pow.f64 x 3)))))
(+.f64 (/.f64 8 (*.f64 x x)) (-.f64 (/.f64 -16 (pow.f64 x 3)) (+.f64 (/.f64 4 x) -2)))
(+.f64 (-.f64 2 (/.f64 4 x)) (*.f64 (/.f64 (/.f64 1 x) x) (-.f64 8 (/.f64 16 x))))
(+.f64 (+.f64 2 (/.f64 -4 x)) (.f64 (/.f64 1 (.f64 x x)) (+.f64 8 (/.f64 -16 x))))

localize14.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(*.f64 (+.f64 x 2) x)
✓	0.1b	(.f64 (.f64 (+.f64 x 2) x) (+.f64 1/2 (*.f64 -1/4 x)))

Compiler

Compiled 33 to 24 computations (27.3% saved)

series2.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(.f64 (.f64 (+.f64 x 2) x) (+.f64 1/2 (*.f64 -1/4 x)))
1.0ms	x	@	0	(.f64 (.f64 (+.f64 x 2) x) (+.f64 1/2 (*.f64 -1/4 x)))
1.0ms	x	@	-inf	(.f64 (.f64 (+.f64 x 2) x) (+.f64 1/2 (*.f64 -1/4 x)))

rewrite66.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

541×	`log-prod_binary64`
493×	`prod-diff_binary64`
382×	`pow-prod-down_binary64`
293×	`pow2_binary64`
275×	`fma-def_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	231	14
2	3094	14

Stop Event

1×	node limit

Counts

1 → 64

Calls

Call 1

Inputs
(.f64 (.f64 (+.f64 x 2) x) (+.f64 1/2 (*.f64 -1/4 x)))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 1/2 x) (+.f64 x 2)) (*.f64 x (*.f64 (+.f64 x 2) (*.f64 x -1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x (*.f64 (+.f64 x 2) (*.f64 x -1/4))) (*.f64 (*.f64 1/2 x) (+.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 x (*.f64 (+.f64 x 2) (fma.f64 x -1/4 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 (*.f64 1/2 x) (+.f64 x 2)) 1) (*.f64 (*.f64 x (*.f64 (+.f64 x 2) (*.f64 x -1/4))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) (*.f64 (+.f64 x 2) (fma.f64 x -1/4 1/2)))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 x) (*.f64 (+.f64 x 2) (fma.f64 x -1/4 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 x) (*.f64 (+.f64 x 2) (fma.f64 x -1/4 1/2))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 x) (*.f64 (+.f64 x 2) (fma.f64 x -1/4 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 x (*.f64 (+.f64 x 2) (fma.f64 x -1/4 1/2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 (*.f64 1/2 x) (+.f64 x 2)) 3) (pow.f64 (*.f64 x (*.f64 (+.f64 x 2) (*.f64 x -1/4))) 3)) (+.f64 (pow.f64 (*.f64 (*.f64 1/2 x) (+.f64 x 2)) 2) (-.f64 (pow.f64 (*.f64 x (*.f64 (+.f64 x 2) (*.f64 x -1/4))) 2) (*.f64 (*.f64 (*.f64 1/2 x) (+.f64 x 2)) (*.f64 x (*.f64 (+.f64 x 2) (*.f64 x -1/4)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (*.f64 (*.f64 1/2 x) (+.f64 x 2)) 2) (pow.f64 (*.f64 x (*.f64 (+.f64 x 2) (*.f64 x -1/4))) 2)) (-.f64 (*.f64 (*.f64 1/2 x) (+.f64 x 2)) (*.f64 x (*.f64 (+.f64 x 2) (*.f64 x -1/4)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 8 (pow.f64 x 3)) (*.f64 x (fma.f64 x -1/4 1/2))) (-.f64 (fma.f64 x x 4) (*.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (fma.f64 x x -4) (*.f64 x (fma.f64 x -1/4 1/2))) (+.f64 x -2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (fma.f64 -1/64 (pow.f64 x 3) 1/8) (*.f64 x (+.f64 x 2))) (fma.f64 (*.f64 x -1/4) (fma.f64 x -1/4 -1/2) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1/4 (*.f64 (*.f64 x x) 1/16)) (*.f64 x (+.f64 x 2))) (+.f64 1/2 (*.f64 1/4 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 x (+.f64 x 2)) (fma.f64 -1/64 (pow.f64 x 3) 1/8)) (fma.f64 (*.f64 x -1/4) (fma.f64 x -1/4 -1/2) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 x (+.f64 x 2)) (-.f64 1/4 (*.f64 (*.f64 x x) 1/16))) (+.f64 1/2 (*.f64 1/4 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (*.f64 (+.f64 x 2) (fma.f64 x -1/4 1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x (*.f64 (+.f64 x 2) (fma.f64 x -1/4 1/2))) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x (*.f64 (+.f64 x 2) (fma.f64 x -1/4 1/2))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x (*.f64 (+.f64 x 2) (fma.f64 x -1/4 1/2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 x (*.f64 (+.f64 x 2) (fma.f64 x -1/4 1/2)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 x (*.f64 (+.f64 x 2) (fma.f64 x -1/4 1/2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 x) (*.f64 (+.f64 x 2) (fma.f64 x -1/4 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 x (*.f64 (+.f64 x 2) (fma.f64 x -1/4 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (*.f64 x (*.f64 (+.f64 x 2) (*.f64 x -1/4)))) (exp.f64 (*.f64 (*.f64 1/2 x) (+.f64 x 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x (*.f64 (+.f64 x 2) (fma.f64 x -1/4 1/2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x (*.f64 (+.f64 x 2) (fma.f64 x -1/4 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x (*.f64 (+.f64 x 2) (fma.f64 x -1/4 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x (*.f64 (+.f64 x 2) (fma.f64 x -1/4 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 x (*.f64 (+.f64 x 2) (fma.f64 x -1/4 1/2)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x (*.f64 (+.f64 x 2) 1/2) (*.f64 x (*.f64 (+.f64 x 2) (*.f64 x -1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x (*.f64 (+.f64 x 2) (*.f64 x -1/4)) (*.f64 (*.f64 1/2 x) (+.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x (*.f64 -1/4 (*.f64 x (+.f64 x 2))) (*.f64 (*.f64 1/2 x) (+.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 x 2) (*.f64 x 1/2) (*.f64 x (*.f64 (+.f64 x 2) (*.f64 x -1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 x 2) (*.f64 x (*.f64 x -1/4)) (*.f64 (*.f64 1/2 x) (+.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x (+.f64 x 2)) 1/2 (*.f64 x (*.f64 (+.f64 x 2) (*.f64 x -1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x (+.f64 x 2)) (*.f64 x -1/4) (*.f64 (*.f64 1/2 x) (+.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/2 (*.f64 x (+.f64 x 2)) (*.f64 x (*.f64 (+.f64 x 2) (*.f64 x -1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1/4 (*.f64 x (*.f64 x (+.f64 x 2))) (*.f64 (*.f64 1/2 x) (+.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x -1/4) (*.f64 x (+.f64 x 2)) (*.f64 (*.f64 1/2 x) (+.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 (*.f64 1/2 x) (+.f64 x 2)) (*.f64 x (*.f64 (+.f64 x 2) (*.f64 x -1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 x (*.f64 (+.f64 x 2) (*.f64 x -1/4))) (*.f64 (*.f64 1/2 x) (+.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 (*.f64 x x) 1/16)) (*.f64 (cbrt.f64 (*.f64 x -1/4)) (*.f64 x (+.f64 x 2))) (*.f64 (*.f64 1/2 x) (+.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 2)) (*.f64 (cbrt.f64 (*.f64 x (+.f64 x 2))) 1/2) (*.f64 x (*.f64 (+.f64 x 2) (*.f64 x -1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 2)) (*.f64 (cbrt.f64 (*.f64 x (+.f64 x 2))) (*.f64 x -1/4)) (*.f64 (*.f64 1/2 x) (+.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 x -1/4)) (*.f64 (sqrt.f64 (*.f64 x -1/4)) (*.f64 x (+.f64 x 2))) (*.f64 (*.f64 1/2 x) (+.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 x (+.f64 x 2))) (*.f64 (sqrt.f64 (*.f64 x (+.f64 x 2))) 1/2) (*.f64 x (*.f64 (+.f64 x 2) (*.f64 x -1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 x (+.f64 x 2))) (*.f64 (sqrt.f64 (*.f64 x (+.f64 x 2))) (*.f64 x -1/4)) (*.f64 (*.f64 1/2 x) (+.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 1/2 x) (+.f64 x 2)) 1 (*.f64 (*.f64 x (*.f64 (+.f64 x 2) (*.f64 x -1/4))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 (*.f64 1/2 x) (+.f64 x 2))) 2) (cbrt.f64 (*.f64 (*.f64 1/2 x) (+.f64 x 2))) (*.f64 x (*.f64 (+.f64 x 2) (*.f64 x -1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 x (*.f64 (+.f64 x 2) (*.f64 x -1/4)))) 2) (cbrt.f64 (*.f64 x (*.f64 (+.f64 x 2) (*.f64 x -1/4)))) (*.f64 (*.f64 1/2 x) (+.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 (*.f64 1/2 x) (+.f64 x 2))) (sqrt.f64 (*.f64 (*.f64 1/2 x) (+.f64 x 2))) (*.f64 x (*.f64 (+.f64 x 2) (*.f64 x -1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 x (*.f64 (+.f64 x 2) (*.f64 x -1/4)))) (sqrt.f64 (*.f64 x (*.f64 (+.f64 x 2) (*.f64 x -1/4)))) (*.f64 (*.f64 1/2 x) (+.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 1/2 x) (+.f64 x 2) (*.f64 x (*.f64 (+.f64 x 2) (*.f64 x -1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 x -1/4) x) (+.f64 x 2) (*.f64 (*.f64 1/2 x) (+.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 x (+.f64 x 2)) x) -1/4 (*.f64 (*.f64 1/2 x) (+.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 1/2 (+.f64 x 2)) x (*.f64 x (*.f64 (+.f64 x 2) (*.f64 x -1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 1/2 (cbrt.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 2))) (cbrt.f64 (*.f64 x (+.f64 x 2))) (*.f64 x (*.f64 (+.f64 x 2) (*.f64 x -1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 1/2 (sqrt.f64 (*.f64 x (+.f64 x 2)))) (sqrt.f64 (*.f64 x (+.f64 x 2))) (*.f64 x (*.f64 (+.f64 x 2) (*.f64 x -1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 x (+.f64 x 2)) -1/4) x (*.f64 (*.f64 1/2 x) (+.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 x (+.f64 x 2)) (cbrt.f64 (*.f64 (*.f64 x x) 1/16))) (cbrt.f64 (*.f64 x -1/4)) (*.f64 (*.f64 1/2 x) (+.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 x (+.f64 x 2)) (sqrt.f64 (*.f64 x -1/4))) (sqrt.f64 (*.f64 x -1/4)) (*.f64 (*.f64 1/2 x) (+.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 x -1/4) (+.f64 x 2)) x (*.f64 (*.f64 1/2 x) (+.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 x -1/4) (cbrt.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 2))) (cbrt.f64 (*.f64 x (+.f64 x 2))) (*.f64 (*.f64 1/2 x) (+.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 x -1/4) (sqrt.f64 (*.f64 x (+.f64 x 2)))) (sqrt.f64 (*.f64 x (+.f64 x 2))) (*.f64 (*.f64 1/2 x) (+.f64 x 2)))))))

simplify169.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

1274×	`sqr-pow_binary64`
666×	`pow-sqr_binary64`
531×	`cube-prod_binary64`
473×	`fabs-mul_binary64`
444×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	87
1	18	87
2	36	87
3	74	87
4	142	87
5	373	87
6	1282	87
7	1990	87
8	2077	87
9	2210	87
10	2368	87
11	2609	87
12	2931	87
13	3354	87
14	3857	87
15	4459	87
16	5179	87
17	5502	87
18	5786	87
19	6008	87
20	6190	87
21	6272	87
22	7212	87

Stop Event

1×	node limit

Counts

76 → 68

Calls

Call 1

Inputs
x
(+.f64 (*.f64 -1/4 (pow.f64 x 3)) x)
(+.f64 (*.f64 -1/4 (pow.f64 x 3)) x)
(+.f64 (*.f64 -1/4 (pow.f64 x 3)) x)
(*.f64 -1/4 (pow.f64 x 3))
(+.f64 (*.f64 -1/4 (pow.f64 x 3)) x)
(+.f64 (*.f64 -1/4 (pow.f64 x 3)) x)
(+.f64 (*.f64 -1/4 (pow.f64 x 3)) x)
(*.f64 -1/4 (pow.f64 x 3))
(+.f64 (*.f64 -1/4 (pow.f64 x 3)) x)
(+.f64 (*.f64 -1/4 (pow.f64 x 3)) x)
(+.f64 (*.f64 -1/4 (pow.f64 x 3)) x)

Outputs
x
(+.f64 (*.f64 -1/4 (pow.f64 x 3)) x)
(fma.f64 -1/4 (pow.f64 x 3) x)
(+.f64 (*.f64 -1/4 (pow.f64 x 3)) x)
(fma.f64 -1/4 (pow.f64 x 3) x)
(+.f64 (*.f64 -1/4 (pow.f64 x 3)) x)
(fma.f64 -1/4 (pow.f64 x 3) x)
(*.f64 -1/4 (pow.f64 x 3))
(+.f64 (*.f64 -1/4 (pow.f64 x 3)) x)
(fma.f64 -1/4 (pow.f64 x 3) x)
(+.f64 (*.f64 -1/4 (pow.f64 x 3)) x)
(fma.f64 -1/4 (pow.f64 x 3) x)
(+.f64 (*.f64 -1/4 (pow.f64 x 3)) x)
(fma.f64 -1/4 (pow.f64 x 3) x)
(*.f64 -1/4 (pow.f64 x 3))
(+.f64 (*.f64 -1/4 (pow.f64 x 3)) x)
(fma.f64 -1/4 (pow.f64 x 3) x)
(+.f64 (*.f64 -1/4 (pow.f64 x 3)) x)
(fma.f64 -1/4 (pow.f64 x 3) x)
(+.f64 (*.f64 -1/4 (pow.f64 x 3)) x)
(fma.f64 -1/4 (pow.f64 x 3) x)

eval130.0ms (1.8%)

Compiler: Compiled 4587 to 3658 computations (20.3% saved)

prune56.0ms (0.8%)

Pruning

16 alts after pruning (10 fresh and 6 done)

	Pruned	Kept	Total
New	316	9	325
Fresh	4	1	5
Picked	0	1	1
Done	4	5	9
Total	324	16	340

Error

0.0b

Counts

340 → 16

Alt Table

Click to see full alt table

Status	Error	Program
✓	29.1b	(-.f64 (-.f64 (+.f64 1 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2))))) 1) 1)
✓	29.1b	(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)
✓	59.8b	(+.f64 1 (+.f64 x -1))
✓	32.3b	(.f64 (.f64 (+.f64 x 2) x) (+.f64 1/2 (*.f64 -1/4 x)))
✓	32.2b	(+.f64 (*.f64 -1/3 (pow.f64 x 3)) x)
	60.3b	(.f64 (.f64 x 2) (+.f64 (/.f64 1 x) (/.f64 (/.f64 -2 x) x)))
	47.4b	-1
	32.3b	(.f64 (+.f64 (.f64 x x) (.f64 x 2)) (+.f64 1/2 (.f64 -1/4 x)))
	29.4b	(/.f64 2 (/.f64 (+.f64 x 2) x))
	61.3b	(.f64 (-.f64 (+.f64 1 (.f64 x (+.f64 x 2))) 1) (+.f64 1/2 (*.f64 -1/4 x)))
	60.1b	(+.f64 2 (/.f64 -4 x))
	59.5b	2
	59.5b	(.f64 (.f64 x 2) (/.f64 1 x))
	29.1b	(-.f64 (.f64 (exp.f64 (neg.f64 (log1p.f64 (exp.f64 (.f64 x -2))))) 2) 1)
✓	59.7b	(-.f64 (+.f64 x 1) 1)
	30.7b	x

Compiler

Compiled 158 to 131 computations (17.1% saved)

regimes457.0ms (6.4%)

Counts

34 → 3

Calls

Call 1

Inputs
2
x
x
x
-1
x
(-.f64 1 1)
(+.f64 2 (/.f64 -4 x))
(/.f64 1 (/.f64 1 x))
(+.f64 1 (+.f64 x -1))
(-.f64 (+.f64 x 1) 1)
(/.f64 2 (/.f64 (+.f64 x 2) x))
(.f64 (.f64 x 2) (/.f64 1 x))
(.f64 (/.f64 1 x) (.f64 x x))
(.f64 x (.f64 x (/.f64 1 x)))
(neg.f64 (/.f64 (*.f64 x x) (neg.f64 x)))
(/.f64 1 (/.f64 (+.f64 x 2) (*.f64 x 2)))
(.f64 (.f64 x 2) (/.f64 1 (+.f64 x 2)))
(/.f64 (-.f64 (*.f64 x x) 0) (-.f64 x 0))
(-.f64 (/.f64 2 (+.f64 2 (*.f64 -2 x))) 1)
(.f64 (.f64 (+.f64 x 2) x) (+.f64 1/2 (*.f64 -1/4 x)))
(/.f64 1 (/.f64 (+.f64 x 2) (*.f64 (+.f64 x 2) x)))
(.f64 (.f64 (+.f64 x 2) x) (/.f64 1 (+.f64 x 2)))
(.f64 (.f64 x 2) (+.f64 (/.f64 1 x) (/.f64 (/.f64 -2 x) x)))
(.f64 (+.f64 (.f64 x x) (.f64 x 2)) (+.f64 1/2 (.f64 -1/4 x)))
(.f64 (-.f64 (+.f64 1 (.f64 x (+.f64 x 2))) 1) (+.f64 1/2 (*.f64 -1/4 x)))
(+.f64 (*.f64 -1/3 (pow.f64 x 3)) x)
(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)
(-.f64 (-.f64 (+.f64 1 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2))))) 1) 1)
(-.f64 (-.f64 (+.f64 1 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2)))) 1) 1)
(-.f64 (.f64 (exp.f64 (neg.f64 (log1p.f64 (exp.f64 (.f64 x -2))))) 2) 1)
(-.f64 (*.f64 (exp.f64 (neg.f64 (log1p.f64 (pow.f64 (exp.f64 -2) x)))) 2) 1)
(-.f64 (/.f64 (/.f64 2 (hypot.f64 1 (exp.f64 (neg.f64 x)))) (hypot.f64 1 (exp.f64 (neg.f64 x)))) 1)
(expm1.f64 (-.f64 (log1p.f64 1) (log1p.f64 (pow.f64 (exp.f64 x) -2))))

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

Calls

12 calls:

237.0ms	y
47.0ms	(*.f64 -2 x)
46.0ms	(*.f64 -2 x)
45.0ms	x
10.0ms	(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))

Results

Error	Segments	Branch
0.0b	3	`x`
18.8b	12	`y`
0.0b	3	`(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)`
0.0b	3	`(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)`
0.0b	3	`(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))`
0.0b	3	`(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))`
0.0b	3	`(+.f64 1 (exp.f64 (*.f64 -2 x)))`
0.0b	3	`(+.f64 1 (exp.f64 (*.f64 -2 x)))`
0.0b	3	`(exp.f64 (*.f64 -2 x))`
0.0b	3	`(exp.f64 (*.f64 -2 x))`
0.0b	3	`(*.f64 -2 x)`
0.0b	3	`(*.f64 -2 x)`

Compiler

Compiled 355 to 277 computations (22% saved)

bsearch1.0ms (0%)

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	9.644449601046783e-5	0.06818362329695954
0.0ms	-12.371098015332015	-1.4202774702027883e-12

Compiler

Compiled 17 to 15 computations (11.8% saved)

regimes569.0ms (7.9%)

Counts

30 → 3

Calls

Call 1

Inputs
2
x
x
x
-1
x
(-.f64 1 1)
(+.f64 2 (/.f64 -4 x))
(/.f64 1 (/.f64 1 x))
(+.f64 1 (+.f64 x -1))
(-.f64 (+.f64 x 1) 1)
(/.f64 2 (/.f64 (+.f64 x 2) x))
(.f64 (.f64 x 2) (/.f64 1 x))
(.f64 (/.f64 1 x) (.f64 x x))
(.f64 x (.f64 x (/.f64 1 x)))
(neg.f64 (/.f64 (*.f64 x x) (neg.f64 x)))
(/.f64 1 (/.f64 (+.f64 x 2) (*.f64 x 2)))
(.f64 (.f64 x 2) (/.f64 1 (+.f64 x 2)))
(/.f64 (-.f64 (*.f64 x x) 0) (-.f64 x 0))
(-.f64 (/.f64 2 (+.f64 2 (*.f64 -2 x))) 1)
(.f64 (.f64 (+.f64 x 2) x) (+.f64 1/2 (*.f64 -1/4 x)))
(/.f64 1 (/.f64 (+.f64 x 2) (*.f64 (+.f64 x 2) x)))
(.f64 (.f64 (+.f64 x 2) x) (/.f64 1 (+.f64 x 2)))
(.f64 (.f64 x 2) (+.f64 (/.f64 1 x) (/.f64 (/.f64 -2 x) x)))
(.f64 (+.f64 (.f64 x x) (.f64 x 2)) (+.f64 1/2 (.f64 -1/4 x)))
(.f64 (-.f64 (+.f64 1 (.f64 x (+.f64 x 2))) 1) (+.f64 1/2 (*.f64 -1/4 x)))
(+.f64 (*.f64 -1/3 (pow.f64 x 3)) x)
(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)
(-.f64 (-.f64 (+.f64 1 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2))))) 1) 1)
(-.f64 (-.f64 (+.f64 1 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2)))) 1) 1)

Outputs
(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)
(+.f64 (*.f64 -1/3 (pow.f64 x 3)) x)
(-.f64 (-.f64 (+.f64 1 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2))))) 1) 1)

Calls

12 calls:

317.0ms	y
83.0ms	x
41.0ms	(*.f64 -2 x)
41.0ms	(*.f64 -2 x)
18.0ms	(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)

Results

Error	Segments	Branch
0.0b	3	`x`
18.9b	12	`y`
0.0b	3	`(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)`
0.0b	3	`(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)`
0.0b	3	`(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))`
0.0b	3	`(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))`
0.0b	3	`(+.f64 1 (exp.f64 (*.f64 -2 x)))`
0.0b	3	`(+.f64 1 (exp.f64 (*.f64 -2 x)))`
0.0b	3	`(exp.f64 (*.f64 -2 x))`
0.0b	3	`(exp.f64 (*.f64 -2 x))`
0.0b	3	`(*.f64 -2 x)`
0.0b	3	`(*.f64 -2 x)`

Compiler

Compiled 309 to 240 computations (22.3% saved)

bsearch1.0ms (0%)

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	9.644449601046783e-5	0.06818362329695954
0.0ms	-12.371098015332015	-1.4202774702027883e-12

Compiler

Compiled 17 to 15 computations (11.8% saved)

regimes551.0ms (7.7%)

Counts

28 → 3

Calls

Call 1

Inputs
2
x
x
x
-1
x
(-.f64 1 1)
(+.f64 2 (/.f64 -4 x))
(/.f64 1 (/.f64 1 x))
(+.f64 1 (+.f64 x -1))
(-.f64 (+.f64 x 1) 1)
(/.f64 2 (/.f64 (+.f64 x 2) x))
(.f64 (.f64 x 2) (/.f64 1 x))
(.f64 (/.f64 1 x) (.f64 x x))
(.f64 x (.f64 x (/.f64 1 x)))
(neg.f64 (/.f64 (*.f64 x x) (neg.f64 x)))
(/.f64 1 (/.f64 (+.f64 x 2) (*.f64 x 2)))
(.f64 (.f64 x 2) (/.f64 1 (+.f64 x 2)))
(/.f64 (-.f64 (*.f64 x x) 0) (-.f64 x 0))
(-.f64 (/.f64 2 (+.f64 2 (*.f64 -2 x))) 1)
(.f64 (.f64 (+.f64 x 2) x) (+.f64 1/2 (*.f64 -1/4 x)))
(/.f64 1 (/.f64 (+.f64 x 2) (*.f64 (+.f64 x 2) x)))
(.f64 (.f64 (+.f64 x 2) x) (/.f64 1 (+.f64 x 2)))
(.f64 (.f64 x 2) (+.f64 (/.f64 1 x) (/.f64 (/.f64 -2 x) x)))
(.f64 (+.f64 (.f64 x x) (.f64 x 2)) (+.f64 1/2 (.f64 -1/4 x)))
(.f64 (-.f64 (+.f64 1 (.f64 x (+.f64 x 2))) 1) (+.f64 1/2 (*.f64 -1/4 x)))
(+.f64 (*.f64 -1/3 (pow.f64 x 3)) x)
(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)

Outputs
(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)
(+.f64 (*.f64 -1/3 (pow.f64 x 3)) x)
(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)

Calls

12 calls:

220.0ms	y
77.0ms	(*.f64 -2 x)
75.0ms	(*.f64 -2 x)
39.0ms	x
18.0ms	(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)

Results

Error	Segments	Branch
0.0b	3	`x`
18.9b	12	`y`
0.0b	3	`(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)`
0.0b	3	`(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)`
0.0b	3	`(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))`
0.0b	3	`(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))`
0.0b	3	`(+.f64 1 (exp.f64 (*.f64 -2 x)))`
0.0b	3	`(+.f64 1 (exp.f64 (*.f64 -2 x)))`
0.0b	3	`(exp.f64 (*.f64 -2 x))`
0.0b	3	`(exp.f64 (*.f64 -2 x))`
0.0b	3	`(*.f64 -2 x)`
0.0b	3	`(*.f64 -2 x)`

Compiler

Compiled 281 to 214 computations (23.8% saved)

bsearch1.0ms (0%)

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	9.644449601046783e-5	0.06818362329695954
0.0ms	-12.371098015332015	-1.4202774702027883e-12

Compiler

Compiled 17 to 15 computations (11.8% saved)

regimes129.0ms (1.8%)

Counts

27 → 2

Calls

Call 1

Inputs
2
x
x
x
-1
x
(-.f64 1 1)
(+.f64 2 (/.f64 -4 x))
(/.f64 1 (/.f64 1 x))
(+.f64 1 (+.f64 x -1))
(-.f64 (+.f64 x 1) 1)
(/.f64 2 (/.f64 (+.f64 x 2) x))
(.f64 (.f64 x 2) (/.f64 1 x))
(.f64 (/.f64 1 x) (.f64 x x))
(.f64 x (.f64 x (/.f64 1 x)))
(neg.f64 (/.f64 (*.f64 x x) (neg.f64 x)))
(/.f64 1 (/.f64 (+.f64 x 2) (*.f64 x 2)))
(.f64 (.f64 x 2) (/.f64 1 (+.f64 x 2)))
(/.f64 (-.f64 (*.f64 x x) 0) (-.f64 x 0))
(-.f64 (/.f64 2 (+.f64 2 (*.f64 -2 x))) 1)
(.f64 (.f64 (+.f64 x 2) x) (+.f64 1/2 (*.f64 -1/4 x)))
(/.f64 1 (/.f64 (+.f64 x 2) (*.f64 (+.f64 x 2) x)))
(.f64 (.f64 (+.f64 x 2) x) (/.f64 1 (+.f64 x 2)))
(.f64 (.f64 x 2) (+.f64 (/.f64 1 x) (/.f64 (/.f64 -2 x) x)))
(.f64 (+.f64 (.f64 x x) (.f64 x 2)) (+.f64 1/2 (.f64 -1/4 x)))
(.f64 (-.f64 (+.f64 1 (.f64 x (+.f64 x 2))) 1) (+.f64 1/2 (*.f64 -1/4 x)))
(+.f64 (*.f64 -1/3 (pow.f64 x 3)) x)

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

Calls

4 calls:

39.0ms	y
27.0ms	x
27.0ms	(*.f64 -2 x)
27.0ms	(*.f64 -2 x)

Results

Error	Segments	Branch
14.6b	2	`x`
27.4b	3	`y`
14.6b	2	`(*.f64 -2 x)`
14.6b	2	`(*.f64 -2 x)`

Compiler

Compiled 199 to 141 computations (29.1% saved)

bsearch0.0ms (0%)

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.7277824039384374	1073788571.5866737

Compiler

Compiled 17 to 15 computations (11.8% saved)

regimes61.0ms (0.9%)

Counts

17 → 2

Calls

Call 1

Inputs
2
x
x
x
-1
x
(-.f64 1 1)
(+.f64 2 (/.f64 -4 x))
(/.f64 1 (/.f64 1 x))
(+.f64 1 (+.f64 x -1))
(-.f64 (+.f64 x 1) 1)
(/.f64 2 (/.f64 (+.f64 x 2) x))
(.f64 (.f64 x 2) (/.f64 1 x))
(.f64 (/.f64 1 x) (.f64 x x))
(.f64 x (.f64 x (/.f64 1 x)))
(neg.f64 (/.f64 (*.f64 x x) (neg.f64 x)))
(/.f64 1 (/.f64 (+.f64 x 2) (*.f64 x 2)))

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

Calls

2 calls:

37.0ms	y
19.0ms	x

Results

Error	Segments	Branch
14.7b	2	`x`
27.6b	3	`y`

Compiler

Compiled 81 to 55 computations (32.1% saved)

bsearch24.0ms (0.3%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
24.0ms	-536894285.7933369	-0.3638912019692187

Compiler

Compiled 17 to 15 computations (11.8% saved)

regimes51.0ms (0.7%)

Counts

11 → 3

Calls

Call 1

Inputs
2
x
x
x
-1
x
(-.f64 1 1)
(+.f64 2 (/.f64 -4 x))
(/.f64 1 (/.f64 1 x))
(+.f64 1 (+.f64 x -1))
(-.f64 (+.f64 x 1) 1)

Outputs
-1
x
(+.f64 2 (/.f64 -4 x))

Calls

2 calls:

28.0ms	y
20.0ms	x

Results

Error	Segments	Branch
14.2b	3	`x`
29.0b	3	`y`

Compiler

Compiled 37 to 27 computations (27% saved)

bsearch45.0ms (0.6%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
22.0ms	7.101387351013941e-13	6.185549007666007
23.0ms	-536894285.7933369	-0.3638912019692187

Compiler

Compiled 17 to 15 computations (11.8% saved)

regimes34.0ms (0.5%)

Counts

7 → 3

Calls

Call 1

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

Outputs
-1
x
2

Calls

2 calls:

18.0ms	y
14.0ms	x

Results

Error	Segments	Branch
14.3b	3	`x`
29.0b	3	`y`

Compiler

Compiled 17 to 11 computations (35.3% saved)

bsearch46.0ms (0.6%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
22.0ms	7.101387351013941e-13	6.185549007666007
24.0ms	-536894285.7933369	-0.3638912019692187

Compiler

Compiled 17 to 15 computations (11.8% saved)

regimes14.0ms (0.2%)

Accuracy

Total -33.2b remaining (-116.7%)

Threshold costs -33.2b (-116.7%)

Counts

4 → 2

Calls

Call 1

Inputs
2
x
x
x

Outputs
x
2

Calls

2 calls:

8.0ms	x
5.0ms	y

Results

Error	Segments	Branch
28.5b	2	`x`
30.7b	1	`y`

Compiler

Compiled 12 to 7 computations (41.7% saved)

bsearch23.0ms (0.3%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
23.0ms	7.101387351013941e-13	6.185549007666007

Compiler

Compiled 17 to 15 computations (11.8% saved)

simplify14.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	274
1	79	274
2	85	274
3	86	274

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(if (<=.f64 (.f64 -2 x) -10) (-.f64 (.f64 (exp.f64 (neg.f64 (log1p.f64 (exp.f64 (.f64 x -2))))) 2) 1) (if (<=.f64 (.f64 -2 x) 7378697629483821/73786976294838206464) (+.f64 (.f64 -1/3 (pow.f64 x 3)) x) (-.f64 (-.f64 (+.f64 1 (/.f64 2 (+.f64 1 (exp.f64 (.f64 x -2))))) 1) 1)))
(if (<=.f64 (.f64 -2 x) -10) (-.f64 (/.f64 2 (+.f64 1 (exp.f64 (.f64 -2 x)))) 1) (if (<=.f64 (.f64 -2 x) 7378697629483821/73786976294838206464) (+.f64 (.f64 -1/3 (pow.f64 x 3)) x) (-.f64 (-.f64 (+.f64 1 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2))))) 1) 1)))
(if (<=.f64 (.f64 -2 x) -10) (-.f64 (/.f64 2 (+.f64 1 (exp.f64 (.f64 -2 x)))) 1) (if (<=.f64 (.f64 -2 x) 7378697629483821/73786976294838206464) (+.f64 (.f64 -1/3 (pow.f64 x 3)) x) (-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)))
(if (<=.f64 (.f64 -2 x) 1) (.f64 (*.f64 x 2) (/.f64 1 (+.f64 x 2))) -1)
(if (<=.f64 x -281487231310017/524288) -1 (/.f64 2 (/.f64 (+.f64 x 2) x)))
(if (<=.f64 x -281487231310017/524288) -1 (if (<=.f64 x 7032873389035921/9903520314283042199192993792) x (+.f64 2 (/.f64 -4 x))))
(if (<=.f64 x -281487231310017/524288) -1 (if (<=.f64 x 7032873389035921/9903520314283042199192993792) x 2))
(if (<=.f64 x 7032873389035921/9903520314283042199192993792) x 2)
2

Outputs
(if (<=.f64 (.f64 -2 x) -10) (-.f64 (.f64 (exp.f64 (neg.f64 (log1p.f64 (exp.f64 (.f64 x -2))))) 2) 1) (if (<=.f64 (.f64 -2 x) 7378697629483821/73786976294838206464) (+.f64 (.f64 -1/3 (pow.f64 x 3)) x) (-.f64 (-.f64 (+.f64 1 (/.f64 2 (+.f64 1 (exp.f64 (.f64 x -2))))) 1) 1)))
(if (<=.f64 (.f64 -2 x) -10) (+.f64 (.f64 (exp.f64 (neg.f64 (log1p.f64 (exp.f64 (.f64 -2 x))))) 2) -1) (if (<=.f64 (.f64 -2 x) 7378697629483821/73786976294838206464) (+.f64 x (.f64 -1/3 (pow.f64 x 3))) (+.f64 (+.f64 (+.f64 1 (/.f64 2 (+.f64 (exp.f64 (.f64 -2 x)) 1))) -1) -1)))
(if (<=.f64 (.f64 -2 x) -10) (-.f64 (/.f64 2 (+.f64 1 (exp.f64 (.f64 -2 x)))) 1) (if (<=.f64 (.f64 -2 x) 7378697629483821/73786976294838206464) (+.f64 (.f64 -1/3 (pow.f64 x 3)) x) (-.f64 (-.f64 (+.f64 1 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2))))) 1) 1)))
(if (<=.f64 (.f64 -2 x) -10) (+.f64 (/.f64 2 (+.f64 (exp.f64 (.f64 -2 x)) 1)) -1) (if (<=.f64 (.f64 -2 x) 7378697629483821/73786976294838206464) (+.f64 x (.f64 -1/3 (pow.f64 x 3))) (+.f64 (+.f64 (+.f64 1 (/.f64 2 (+.f64 (exp.f64 (*.f64 -2 x)) 1))) -1) -1)))
(if (<=.f64 (.f64 -2 x) -10) (-.f64 (/.f64 2 (+.f64 1 (exp.f64 (.f64 -2 x)))) 1) (if (<=.f64 (.f64 -2 x) 7378697629483821/73786976294838206464) (+.f64 (.f64 -1/3 (pow.f64 x 3)) x) (-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)))
(if (<=.f64 (.f64 -2 x) -10) (+.f64 (/.f64 2 (+.f64 (exp.f64 (.f64 -2 x)) 1)) -1) (if (<=.f64 (.f64 -2 x) 7378697629483821/73786976294838206464) (+.f64 x (.f64 -1/3 (pow.f64 x 3))) (+.f64 (/.f64 2 (+.f64 (exp.f64 (*.f64 -2 x)) 1)) -1)))
(if (<=.f64 (.f64 -2 x) 1) (.f64 (*.f64 x 2) (/.f64 1 (+.f64 x 2))) -1)
(if (<=.f64 x -281487231310017/524288) -1 (/.f64 2 (/.f64 (+.f64 x 2) x)))
(if (<=.f64 x -281487231310017/524288) -1 (if (<=.f64 x 7032873389035921/9903520314283042199192993792) x (+.f64 2 (/.f64 -4 x))))
(if (<=.f64 x -281487231310017/524288) -1 (if (<=.f64 x 7032873389035921/9903520314283042199192993792) x 2))
(if (<=.f64 x 7032873389035921/9903520314283042199192993792) x 2)
2

Compiler

Compiled 205 to 172 computations (16.1% saved)

soundness83.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

531×	`associate-l_binary64`
420×	`associate-r_binary64`
279×	`fma-def_binary64`
277×	`associate-+l+_binary64`
276×	`distribute-rgt-out_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	61	468
1	168	356
2	506	338
3	1413	338
4	5081	338

Stop Event

1×	node limit

Compiler

Compiled 23 to 20 computations (13% saved)

end114.0ms (1.6%)

Compiler: Compiled 189 to 156 computations (17.5% saved)