Details

analyze108.0ms (4%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
0%	0%	100%	0%	0%	0%	0%	2
25%	25%	75%	0%	0%	0%	0%	3
28.6%	25%	62.5%	0%	0%	0%	12.5%	4
30.8%	25%	56.2%	0%	0%	0%	18.7%	5
36%	28.1%	50%	0%	0%	0%	21.9%	6
38.8%	29.7%	46.9%	0%	0%	0%	23.4%	7
40.2%	30.5%	45.3%	0%	0%	0%	24.2%	8
40.7%	30.8%	44.9%	0%	0%	0%	24.2%	9
41.2%	31.2%	44.5%	0%	0%	0%	24.2%	10
41.4%	31.3%	44.4%	0%	0%	0%	24.2%	11
41.5%	31.4%	44.3%	0%	0%	0%	24.3%	12

Compiler

Compiled 9 to 6 computations (33.3% saved)

sample1.8s (65.1%)

Results

1.2s	2727×	body	1024	valid
289.0ms	3873×	body	256	valid
225.0ms	1351×	body	512	valid
87.0ms	305×	body	2048	valid
0.0ms	4×	body	256	unsamplable
0.0ms	1×	body	2048	infinite

Bogosity

preprocess4.0ms (0.2%)

Algorithm

2×	egg-herbie

Rules

2×	`1-exp`
2×	`expm1-def`
2×	`sub-neg`
2×	`+-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	14	15
2	15	15
0	1	1

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0

Outputs
0

Call 2

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

Outputs
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify11.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

2×	`1-exp`
2×	`expm1-def`
2×	`sub-neg`
2×	`+-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	14	15
2	15	15

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

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

Outputs
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))

eval0.0ms (0%)

Compiler: Compiled 13 to 7 computations (46.2% saved)

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

1.0b

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	1.0b	(/.f64 (exp.f64 x) (expm1.f64 x))

Compiler

Compiled 6 to 4 computations (33.3% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	1.0b	(/.f64 (exp.f64 x) (expm1.f64 x))

Compiler

Compiled 11 to 4 computations (63.6% saved)

series1.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(/.f64 (exp.f64 x) (expm1.f64 x))
0.0ms	x	@	-inf	(/.f64 (exp.f64 x) (expm1.f64 x))
0.0ms	x	@	0	(/.f64 (exp.f64 x) (expm1.f64 x))

rewrite51.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

1394×	`add-sqr-sqrt`
1382×	`*-un-lft-identity`
1282×	`add-cube-cbrt`
1264×	`add-cbrt-cube`
1250×	`add-exp-log`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	15
1	137	15
2	1722	15

Stop Event

1×	node limit

Counts

1 → 31

Calls

Call 1

Inputs
(/.f64 (exp.f64 x) (expm1.f64 x))

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

Outputs

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

simplify51.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

1500×	`associate-r`
1276×	`associate-l`
1040×	`distribute-lft-in`
1024×	`distribute-rgt-in`
658×	`distribute-lft-neg-out`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	96	813
1	236	789
2	873	789
3	4944	789

Stop Event

1×	node limit

Counts

43 → 50

Calls

Call 1

Inputs
(/.f64 1 x)
(+.f64 1/2 (/.f64 1 x))
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
(+.f64 1/2 (+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x))))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(-.f64 (+.f64 1 (/.f64 (exp.f64 x) (expm1.f64 x))) 1)
(*.f64 (exp.f64 x) (/.f64 1 (expm1.f64 x)))
(*.f64 (/.f64 (exp.f64 x) (expm1.f64 x)) 1)
(*.f64 1 (/.f64 (exp.f64 x) (expm1.f64 x)))
(.f64 (sqrt.f64 (exp.f64 x)) (.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (expm1.f64 x))))
(*.f64 (sqrt.f64 (/.f64 (exp.f64 x) (expm1.f64 x))) (sqrt.f64 (/.f64 (exp.f64 x) (expm1.f64 x))))
(.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (.f64 (cbrt.f64 (exp.f64 x)) (/.f64 1 (expm1.f64 x))))
(*.f64 (cbrt.f64 (/.f64 (exp.f64 x) (expm1.f64 x))) (pow.f64 (cbrt.f64 (/.f64 (exp.f64 x) (expm1.f64 x))) 2))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 (exp.f64 x) (expm1.f64 x))) 2) (cbrt.f64 (/.f64 (exp.f64 x) (expm1.f64 x))))
(*.f64 (/.f64 1 (expm1.f64 x)) (exp.f64 x))
(*.f64 (neg.f64 (exp.f64 x)) (/.f64 1 (neg.f64 (expm1.f64 x))))
(*.f64 (/.f64 1 (sqrt.f64 (expm1.f64 x))) (/.f64 (exp.f64 x) (sqrt.f64 (expm1.f64 x))))
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (/.f64 (exp.f64 x) (cbrt.f64 (expm1.f64 x))))
(*.f64 (/.f64 (sqrt.f64 (exp.f64 x)) 1) (/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x)))
(*.f64 (/.f64 (sqrt.f64 (exp.f64 x)) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (/.f64 (sqrt.f64 (exp.f64 x)) (cbrt.f64 (expm1.f64 x))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) 1) (/.f64 (cbrt.f64 (exp.f64 x)) (expm1.f64 x)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (sqrt.f64 (expm1.f64 x))) (/.f64 (cbrt.f64 (exp.f64 x)) (sqrt.f64 (expm1.f64 x))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (cbrt.f64 (/.f64 (exp.f64 x) (expm1.f64 x))))
(pow.f64 (/.f64 (exp.f64 x) (expm1.f64 x)) 1)
(pow.f64 (sqrt.f64 (/.f64 (exp.f64 x) (expm1.f64 x))) 2)
(pow.f64 (cbrt.f64 (/.f64 (exp.f64 x) (expm1.f64 x))) 3)
(pow.f64 (pow.f64 (/.f64 (exp.f64 x) (expm1.f64 x)) 3) 1/3)
(pow.f64 (/.f64 (expm1.f64 x) (exp.f64 x)) -1)
(neg.f64 (/.f64 (exp.f64 x) (neg.f64 (expm1.f64 x))))
(sqrt.f64 (pow.f64 (/.f64 (exp.f64 x) (expm1.f64 x)) 2))
(log.f64 (exp.f64 (/.f64 (exp.f64 x) (expm1.f64 x))))
(cbrt.f64 (pow.f64 (/.f64 (exp.f64 x) (expm1.f64 x)) 3))
(expm1.f64 (log1p.f64 (/.f64 (exp.f64 x) (expm1.f64 x))))
(exp.f64 (-.f64 x (log.f64 (expm1.f64 x))))
(exp.f64 (*.f64 (-.f64 x (log.f64 (expm1.f64 x))) 1))
(log1p.f64 (expm1.f64 (/.f64 (exp.f64 x) (expm1.f64 x))))

Outputs
(/.f64 1 x)
(+.f64 1/2 (/.f64 1 x))
(+.f64 (/.f64 1 x) 1/2)
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
(+.f64 1/2 (fma.f64 1/12 x (/.f64 1 x)))
(+.f64 1/2 (fma.f64 x 1/12 (/.f64 1 x)))
(+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2))
(+.f64 1/2 (+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x))))
(+.f64 1/2 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 1/12 x (/.f64 1 x))))
(+.f64 1/2 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (/.f64 1 x))))
(+.f64 (fma.f64 x 1/12 (/.f64 1 x)) (fma.f64 -1/720 (pow.f64 x 3) 1/2))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(-.f64 (+.f64 1 (/.f64 (exp.f64 x) (expm1.f64 x))) 1)
(/.f64 (exp.f64 x) (expm1.f64 x))
(*.f64 (exp.f64 x) (/.f64 1 (expm1.f64 x)))
(/.f64 (exp.f64 x) (expm1.f64 x))
(*.f64 (/.f64 (exp.f64 x) (expm1.f64 x)) 1)
(/.f64 (exp.f64 x) (expm1.f64 x))
(*.f64 1 (/.f64 (exp.f64 x) (expm1.f64 x)))
(/.f64 (exp.f64 x) (expm1.f64 x))
(.f64 (sqrt.f64 (exp.f64 x)) (.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (expm1.f64 x))))
(/.f64 (exp.f64 x) (expm1.f64 x))
(*.f64 (sqrt.f64 (/.f64 (exp.f64 x) (expm1.f64 x))) (sqrt.f64 (/.f64 (exp.f64 x) (expm1.f64 x))))
(/.f64 (exp.f64 x) (expm1.f64 x))
(.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (.f64 (cbrt.f64 (exp.f64 x)) (/.f64 1 (expm1.f64 x))))
(/.f64 (exp.f64 x) (expm1.f64 x))
(*.f64 (cbrt.f64 (/.f64 (exp.f64 x) (expm1.f64 x))) (pow.f64 (cbrt.f64 (/.f64 (exp.f64 x) (expm1.f64 x))) 2))
(/.f64 (exp.f64 x) (expm1.f64 x))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 (exp.f64 x) (expm1.f64 x))) 2) (cbrt.f64 (/.f64 (exp.f64 x) (expm1.f64 x))))
(/.f64 (exp.f64 x) (expm1.f64 x))
(*.f64 (/.f64 1 (expm1.f64 x)) (exp.f64 x))
(/.f64 (exp.f64 x) (expm1.f64 x))
(*.f64 (neg.f64 (exp.f64 x)) (/.f64 1 (neg.f64 (expm1.f64 x))))
(/.f64 (exp.f64 x) (expm1.f64 x))
(*.f64 (/.f64 1 (sqrt.f64 (expm1.f64 x))) (/.f64 (exp.f64 x) (sqrt.f64 (expm1.f64 x))))
(/.f64 (/.f64 (exp.f64 x) (sqrt.f64 (expm1.f64 x))) (sqrt.f64 (expm1.f64 x)))
(/.f64 (exp.f64 x) (*.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 (expm1.f64 x))))
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (/.f64 (exp.f64 x) (cbrt.f64 (expm1.f64 x))))
(/.f64 (/.f64 (exp.f64 x) (cbrt.f64 (expm1.f64 x))) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2))
(/.f64 (exp.f64 x) (*.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (cbrt.f64 (expm1.f64 x))))
(*.f64 (/.f64 (sqrt.f64 (exp.f64 x)) 1) (/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x)))
(/.f64 (exp.f64 x) (expm1.f64 x))
(*.f64 (/.f64 (sqrt.f64 (exp.f64 x)) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (/.f64 (sqrt.f64 (exp.f64 x)) (cbrt.f64 (expm1.f64 x))))
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (/.f64 (exp.f64 x) (cbrt.f64 (expm1.f64 x))))
(/.f64 (/.f64 (exp.f64 x) (cbrt.f64 (expm1.f64 x))) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2))
(/.f64 (exp.f64 x) (*.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (cbrt.f64 (expm1.f64 x))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) 1) (/.f64 (cbrt.f64 (exp.f64 x)) (expm1.f64 x)))
(/.f64 (exp.f64 x) (expm1.f64 x))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (sqrt.f64 (expm1.f64 x))) (/.f64 (cbrt.f64 (exp.f64 x)) (sqrt.f64 (expm1.f64 x))))
(*.f64 (/.f64 1 (sqrt.f64 (expm1.f64 x))) (/.f64 (exp.f64 x) (sqrt.f64 (expm1.f64 x))))
(/.f64 (/.f64 (exp.f64 x) (sqrt.f64 (expm1.f64 x))) (sqrt.f64 (expm1.f64 x)))
(/.f64 (exp.f64 x) (*.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 (expm1.f64 x))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (cbrt.f64 (/.f64 (exp.f64 x) (expm1.f64 x))))
(*.f64 (cbrt.f64 (/.f64 (exp.f64 x) (expm1.f64 x))) (/.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)))
(/.f64 (cbrt.f64 (/.f64 (exp.f64 x) (expm1.f64 x))) (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (pow.f64 (cbrt.f64 (exp.f64 x)) 2)))
(pow.f64 (/.f64 (exp.f64 x) (expm1.f64 x)) 1)
(/.f64 (exp.f64 x) (expm1.f64 x))
(pow.f64 (sqrt.f64 (/.f64 (exp.f64 x) (expm1.f64 x))) 2)
(/.f64 (exp.f64 x) (expm1.f64 x))
(pow.f64 (cbrt.f64 (/.f64 (exp.f64 x) (expm1.f64 x))) 3)
(/.f64 (exp.f64 x) (expm1.f64 x))
(pow.f64 (pow.f64 (/.f64 (exp.f64 x) (expm1.f64 x)) 3) 1/3)
(/.f64 (exp.f64 x) (expm1.f64 x))
(pow.f64 (/.f64 (expm1.f64 x) (exp.f64 x)) -1)
(/.f64 (exp.f64 x) (expm1.f64 x))
(neg.f64 (/.f64 (exp.f64 x) (neg.f64 (expm1.f64 x))))
(/.f64 (exp.f64 x) (expm1.f64 x))
(sqrt.f64 (pow.f64 (/.f64 (exp.f64 x) (expm1.f64 x)) 2))
(/.f64 (exp.f64 x) (expm1.f64 x))
(log.f64 (exp.f64 (/.f64 (exp.f64 x) (expm1.f64 x))))
(/.f64 (exp.f64 x) (expm1.f64 x))
(cbrt.f64 (pow.f64 (/.f64 (exp.f64 x) (expm1.f64 x)) 3))
(/.f64 (exp.f64 x) (expm1.f64 x))
(expm1.f64 (log1p.f64 (/.f64 (exp.f64 x) (expm1.f64 x))))
(/.f64 (exp.f64 x) (expm1.f64 x))
(exp.f64 (-.f64 x (log.f64 (expm1.f64 x))))
(/.f64 (exp.f64 x) (expm1.f64 x))
(exp.f64 (*.f64 (-.f64 x (log.f64 (expm1.f64 x))) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(log1p.f64 (expm1.f64 (/.f64 (exp.f64 x) (expm1.f64 x))))
(/.f64 (exp.f64 x) (expm1.f64 x))

eval9.0ms (0.3%)

Compiler: Compiled 509 to 217 computations (57.4% saved)

prune7.0ms (0.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	46	4	50
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	46	5	51

Error

0.8b

Counts

51 → 5

Alt Table

Click to see full alt table

Status	Error	Program
✓	1.0b	(/.f64 (exp.f64 x) (expm1.f64 x))
▶	20.8b	(/.f64 1 x)
▶	20.4b	(+.f64 (/.f64 1 x) 1/2)
▶	20.4b	(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
▶	1.0b	(*.f64 (/.f64 1 (expm1.f64 x)) (exp.f64 x))

Compiler

Compiled 34 to 26 computations (23.5% saved)

localize7.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (expm1.f64 x))
✓	1.0b	(*.f64 (/.f64 1 (expm1.f64 x)) (exp.f64 x))

Compiler

Compiled 18 to 9 computations (50% saved)

series1.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

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

rewrite56.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

1546×	`add-sqr-sqrt`
1530×	`*-un-lft-identity`
1418×	`add-cube-cbrt`
1396×	`add-cbrt-cube`
1378×	`add-exp-log`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	26
1	171	26
2	1983	26

Stop Event

1×	node limit

Counts

2 → 44

Calls

Call 1

Inputs
(*.f64 (/.f64 1 (expm1.f64 x)) (exp.f64 x))
(/.f64 1 (expm1.f64 x))

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

Outputs

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

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

simplify58.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

1022×	`distribute-lft-in`
1016×	`distribute-rgt-in`
868×	`distribute-lft-neg-out`
864×	`unswap-sqr`
742×	`distribute-rgt-neg-out`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	120	980
1	281	968
2	933	968
3	4306	968

Stop Event

1×	node limit

Counts

68 → 70

Calls

Call 1

Inputs
(/.f64 1 x)
(+.f64 1/2 (/.f64 1 x))
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
(+.f64 1/2 (+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x))))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 1 x)
(-.f64 (/.f64 1 x) 1/2)
(-.f64 (+.f64 (*.f64 1/12 x) (/.f64 1 x)) 1/2)
(-.f64 (+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x))) 1/2)
(/.f64 1 (-.f64 (exp.f64 x) 1))
(/.f64 1 (-.f64 (exp.f64 x) 1))
(/.f64 1 (-.f64 (exp.f64 x) 1))
(/.f64 1 (-.f64 (exp.f64 x) 1))
(/.f64 1 (-.f64 (exp.f64 x) 1))
(/.f64 1 (-.f64 (exp.f64 x) 1))
(/.f64 1 (-.f64 (exp.f64 x) 1))
(/.f64 1 (-.f64 (exp.f64 x) 1))
(-.f64 (+.f64 1 (*.f64 (/.f64 1 (expm1.f64 x)) (exp.f64 x))) 1)
(/.f64 1 (/.f64 (expm1.f64 x) (exp.f64 x)))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (sqrt.f64 (exp.f64 x)) (/.f64 (expm1.f64 x) (sqrt.f64 (exp.f64 x))))
(/.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (/.f64 (expm1.f64 x) (cbrt.f64 (exp.f64 x))))
(/.f64 (*.f64 (exp.f64 x) -1) (neg.f64 (expm1.f64 x)))
(/.f64 (*.f64 -1 (exp.f64 x)) (neg.f64 (expm1.f64 x)))
(/.f64 (/.f64 (exp.f64 x) 1) (expm1.f64 x))
(/.f64 (/.f64 (exp.f64 x) (sqrt.f64 (expm1.f64 x))) (sqrt.f64 (expm1.f64 x)))
(/.f64 (/.f64 (exp.f64 x) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (cbrt.f64 (expm1.f64 x)))
(/.f64 (neg.f64 (exp.f64 x)) (neg.f64 (expm1.f64 x)))
(pow.f64 (*.f64 (/.f64 1 (expm1.f64 x)) (exp.f64 x)) 1)
(pow.f64 (sqrt.f64 (*.f64 (/.f64 1 (expm1.f64 x)) (exp.f64 x))) 2)
(pow.f64 (cbrt.f64 (*.f64 (/.f64 1 (expm1.f64 x)) (exp.f64 x))) 3)
(pow.f64 (pow.f64 (*.f64 (/.f64 1 (expm1.f64 x)) (exp.f64 x)) 3) 1/3)
(sqrt.f64 (pow.f64 (*.f64 (/.f64 1 (expm1.f64 x)) (exp.f64 x)) 2))
(log.f64 (exp.f64 (*.f64 (/.f64 1 (expm1.f64 x)) (exp.f64 x))))
(cbrt.f64 (pow.f64 (*.f64 (/.f64 1 (expm1.f64 x)) (exp.f64 x)) 3))
(expm1.f64 (log1p.f64 (*.f64 (/.f64 1 (expm1.f64 x)) (exp.f64 x))))
(exp.f64 (-.f64 x (log.f64 (expm1.f64 x))))
(exp.f64 (*.f64 (-.f64 x (log.f64 (expm1.f64 x))) 1))
(log1p.f64 (expm1.f64 (*.f64 (/.f64 1 (expm1.f64 x)) (exp.f64 x))))
(-.f64 (+.f64 1 (/.f64 1 (expm1.f64 x))) 1)
(*.f64 1 (/.f64 1 (expm1.f64 x)))
(*.f64 (/.f64 1 (expm1.f64 x)) 1)
(*.f64 (pow.f64 (expm1.f64 x) -1/2) (pow.f64 (expm1.f64 x) -1/2))
(*.f64 (/.f64 1 (cbrt.f64 (expm1.f64 x))) (cbrt.f64 (pow.f64 (expm1.f64 x) -2)))
(*.f64 (cbrt.f64 (pow.f64 (expm1.f64 x) -2)) (/.f64 1 (cbrt.f64 (expm1.f64 x))))
(*.f64 -1 (/.f64 1 (neg.f64 (expm1.f64 x))))
(*.f64 (pow.f64 (sqrt.f64 (expm1.f64 x)) -1) (pow.f64 (sqrt.f64 (expm1.f64 x)) -1))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) -1) (pow.f64 (cbrt.f64 (expm1.f64 x)) -1))
(pow.f64 (expm1.f64 x) -1)
(pow.f64 (/.f64 1 (expm1.f64 x)) 1)
(pow.f64 (pow.f64 (expm1.f64 x) -1/2) 2)
(pow.f64 (/.f64 1 (cbrt.f64 (expm1.f64 x))) 3)
(pow.f64 (pow.f64 (/.f64 1 (expm1.f64 x)) 3) 1/3)
(sqrt.f64 (pow.f64 (expm1.f64 x) -2))
(log.f64 (exp.f64 (/.f64 1 (expm1.f64 x))))
(cbrt.f64 (pow.f64 (/.f64 1 (expm1.f64 x)) 3))
(expm1.f64 (log1p.f64 (/.f64 1 (expm1.f64 x))))
(exp.f64 (neg.f64 (log.f64 (expm1.f64 x))))
(exp.f64 (*.f64 (log.f64 (expm1.f64 x)) -1))
(exp.f64 (*.f64 (neg.f64 (log.f64 (expm1.f64 x))) 1))
(log1p.f64 (expm1.f64 (/.f64 1 (expm1.f64 x))))

Outputs
(/.f64 1 x)
(+.f64 1/2 (/.f64 1 x))
(+.f64 (/.f64 1 x) 1/2)
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
(+.f64 1/2 (fma.f64 1/12 x (/.f64 1 x)))
(+.f64 1/2 (fma.f64 x 1/12 (/.f64 1 x)))
(+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2))
(+.f64 1/2 (+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x))))
(+.f64 1/2 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 1/12 x (/.f64 1 x))))
(+.f64 1/2 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (/.f64 1 x))))
(+.f64 (fma.f64 x 1/12 (/.f64 1 x)) (fma.f64 -1/720 (pow.f64 x 3) 1/2))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 1 x)
(-.f64 (/.f64 1 x) 1/2)
(+.f64 (/.f64 1 x) -1/2)
(-.f64 (+.f64 (*.f64 1/12 x) (/.f64 1 x)) 1/2)
(+.f64 (fma.f64 1/12 x (/.f64 1 x)) -1/2)
(+.f64 (fma.f64 x 1/12 (/.f64 1 x)) -1/2)
(+.f64 (/.f64 1 x) (fma.f64 x 1/12 -1/2))
(-.f64 (+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x))) 1/2)
(+.f64 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 1/12 x (/.f64 1 x))) -1/2)
(+.f64 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (/.f64 1 x))) -1/2)
(+.f64 (fma.f64 x 1/12 (/.f64 1 x)) (fma.f64 -1/720 (pow.f64 x 3) -1/2))
(+.f64 (fma.f64 x 1/12 -1/2) (fma.f64 -1/720 (pow.f64 x 3) (/.f64 1 x)))
(/.f64 1 (-.f64 (exp.f64 x) 1))
(/.f64 1 (expm1.f64 x))
(/.f64 1 (-.f64 (exp.f64 x) 1))
(/.f64 1 (expm1.f64 x))
(/.f64 1 (-.f64 (exp.f64 x) 1))
(/.f64 1 (expm1.f64 x))
(/.f64 1 (-.f64 (exp.f64 x) 1))
(/.f64 1 (expm1.f64 x))
(/.f64 1 (-.f64 (exp.f64 x) 1))
(/.f64 1 (expm1.f64 x))
(/.f64 1 (-.f64 (exp.f64 x) 1))
(/.f64 1 (expm1.f64 x))
(/.f64 1 (-.f64 (exp.f64 x) 1))
(/.f64 1 (expm1.f64 x))
(/.f64 1 (-.f64 (exp.f64 x) 1))
(/.f64 1 (expm1.f64 x))
(-.f64 (+.f64 1 (*.f64 (/.f64 1 (expm1.f64 x)) (exp.f64 x))) 1)
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 1 (/.f64 (expm1.f64 x) (exp.f64 x)))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (sqrt.f64 (exp.f64 x)) (/.f64 (expm1.f64 x) (sqrt.f64 (exp.f64 x))))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (/.f64 (expm1.f64 x) (cbrt.f64 (exp.f64 x))))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (*.f64 (exp.f64 x) -1) (neg.f64 (expm1.f64 x)))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (*.f64 -1 (exp.f64 x)) (neg.f64 (expm1.f64 x)))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (/.f64 (exp.f64 x) 1) (expm1.f64 x))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (/.f64 (exp.f64 x) (sqrt.f64 (expm1.f64 x))) (sqrt.f64 (expm1.f64 x)))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (/.f64 (exp.f64 x) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (cbrt.f64 (expm1.f64 x)))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (neg.f64 (exp.f64 x)) (neg.f64 (expm1.f64 x)))
(/.f64 (exp.f64 x) (expm1.f64 x))
(pow.f64 (*.f64 (/.f64 1 (expm1.f64 x)) (exp.f64 x)) 1)
(/.f64 (exp.f64 x) (expm1.f64 x))
(pow.f64 (sqrt.f64 (*.f64 (/.f64 1 (expm1.f64 x)) (exp.f64 x))) 2)
(/.f64 (exp.f64 x) (expm1.f64 x))
(pow.f64 (cbrt.f64 (*.f64 (/.f64 1 (expm1.f64 x)) (exp.f64 x))) 3)
(/.f64 (exp.f64 x) (expm1.f64 x))
(pow.f64 (pow.f64 (*.f64 (/.f64 1 (expm1.f64 x)) (exp.f64 x)) 3) 1/3)
(/.f64 (exp.f64 x) (expm1.f64 x))
(sqrt.f64 (pow.f64 (*.f64 (/.f64 1 (expm1.f64 x)) (exp.f64 x)) 2))
(/.f64 (exp.f64 x) (expm1.f64 x))
(log.f64 (exp.f64 (*.f64 (/.f64 1 (expm1.f64 x)) (exp.f64 x))))
(/.f64 (exp.f64 x) (expm1.f64 x))
(cbrt.f64 (pow.f64 (*.f64 (/.f64 1 (expm1.f64 x)) (exp.f64 x)) 3))
(/.f64 (exp.f64 x) (expm1.f64 x))
(expm1.f64 (log1p.f64 (*.f64 (/.f64 1 (expm1.f64 x)) (exp.f64 x))))
(/.f64 (exp.f64 x) (expm1.f64 x))
(exp.f64 (-.f64 x (log.f64 (expm1.f64 x))))
(/.f64 (exp.f64 x) (expm1.f64 x))
(exp.f64 (*.f64 (-.f64 x (log.f64 (expm1.f64 x))) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(log1p.f64 (expm1.f64 (*.f64 (/.f64 1 (expm1.f64 x)) (exp.f64 x))))
(/.f64 (exp.f64 x) (expm1.f64 x))
(-.f64 (+.f64 1 (/.f64 1 (expm1.f64 x))) 1)
(/.f64 1 (expm1.f64 x))
(*.f64 1 (/.f64 1 (expm1.f64 x)))
(/.f64 1 (expm1.f64 x))
(*.f64 (/.f64 1 (expm1.f64 x)) 1)
(/.f64 1 (expm1.f64 x))
(*.f64 (pow.f64 (expm1.f64 x) -1/2) (pow.f64 (expm1.f64 x) -1/2))
(/.f64 1 (expm1.f64 x))
(*.f64 (/.f64 1 (cbrt.f64 (expm1.f64 x))) (cbrt.f64 (pow.f64 (expm1.f64 x) -2)))
(/.f64 (cbrt.f64 (pow.f64 (expm1.f64 x) -2)) (cbrt.f64 (expm1.f64 x)))
(*.f64 (cbrt.f64 (pow.f64 (expm1.f64 x) -2)) (/.f64 1 (cbrt.f64 (expm1.f64 x))))
(*.f64 (/.f64 1 (cbrt.f64 (expm1.f64 x))) (cbrt.f64 (pow.f64 (expm1.f64 x) -2)))
(/.f64 (cbrt.f64 (pow.f64 (expm1.f64 x) -2)) (cbrt.f64 (expm1.f64 x)))
(*.f64 -1 (/.f64 1 (neg.f64 (expm1.f64 x))))
(/.f64 1 (expm1.f64 x))
(*.f64 (pow.f64 (sqrt.f64 (expm1.f64 x)) -1) (pow.f64 (sqrt.f64 (expm1.f64 x)) -1))
(/.f64 1 (expm1.f64 x))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) -1) (pow.f64 (cbrt.f64 (expm1.f64 x)) -1))
(/.f64 1 (expm1.f64 x))
(pow.f64 (expm1.f64 x) -1)
(/.f64 1 (expm1.f64 x))
(pow.f64 (/.f64 1 (expm1.f64 x)) 1)
(/.f64 1 (expm1.f64 x))
(pow.f64 (pow.f64 (expm1.f64 x) -1/2) 2)
(/.f64 1 (expm1.f64 x))
(pow.f64 (/.f64 1 (cbrt.f64 (expm1.f64 x))) 3)
(/.f64 1 (expm1.f64 x))
(pow.f64 (pow.f64 (/.f64 1 (expm1.f64 x)) 3) 1/3)
(/.f64 1 (expm1.f64 x))
(sqrt.f64 (pow.f64 (expm1.f64 x) -2))
(/.f64 1 (expm1.f64 x))
(log.f64 (exp.f64 (/.f64 1 (expm1.f64 x))))
(/.f64 1 (expm1.f64 x))
(cbrt.f64 (pow.f64 (/.f64 1 (expm1.f64 x)) 3))
(/.f64 1 (expm1.f64 x))
(expm1.f64 (log1p.f64 (/.f64 1 (expm1.f64 x))))
(/.f64 1 (expm1.f64 x))
(exp.f64 (neg.f64 (log.f64 (expm1.f64 x))))
(/.f64 1 (expm1.f64 x))
(exp.f64 (*.f64 (log.f64 (expm1.f64 x)) -1))
(/.f64 1 (expm1.f64 x))
(exp.f64 (*.f64 (neg.f64 (log.f64 (expm1.f64 x))) 1))
(/.f64 1 (expm1.f64 x))
(log1p.f64 (expm1.f64 (/.f64 1 (expm1.f64 x))))
(/.f64 1 (expm1.f64 x))

localize10.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (*.f64 1/12 x) (/.f64 1 x))
✓	0.3b	(*.f64 1/12 x)

Compiler

Compiled 27 to 20 computations (25.9% saved)

series1.0ms (0%)

Counts

2 → 9

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	x	@	inf	(*.f64 1/12 x)
0.0ms	x	@	-inf	(*.f64 1/12 x)
0.0ms	x	@	0	(*.f64 1/12 x)
0.0ms	x	@	0	(+.f64 (*.f64 1/12 x) (/.f64 1 x))
0.0ms	x	@	inf	(+.f64 (*.f64 1/12 x) (/.f64 1 x))

rewrite58.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

1742×	`add-sqr-sqrt`
1712×	`*-un-lft-identity`
1612×	`add-cube-cbrt`
1598×	`add-cbrt-cube`
164×	`pow1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	22
1	172	22
2	2161	22

Stop Event

1×	node limit

Counts

2 → 50

Calls

Call 1

Inputs
(*.f64 1/12 x)
(+.f64 (*.f64 1/12 x) (/.f64 1 x))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 1/12 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 1/12 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 1/12 x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 1/12 x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 1/1728 (pow.f64 x 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 1/144 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 1/12) x))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 1/12 x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 1/1728 (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 1/12 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 1/12 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 1/12 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 1/12 x)))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (*.f64 1/144 (*.f64 x x)) (-.f64 (*.f64 1/12 x) (/.f64 1 x))) (/.f64 (pow.f64 x -2) (-.f64 (*.f64 1/12 x) (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (*.f64 1/12 x) (/.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 (*.f64 1/12 x) (/.f64 1 x))) (sqrt.f64 (+.f64 (*.f64 1/12 x) (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 (*.f64 1/12 x) (/.f64 1 x))) (pow.f64 (cbrt.f64 (+.f64 (*.f64 1/12 x) (/.f64 1 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 (*.f64 1/12 x) (/.f64 1 x))) 2) (cbrt.f64 (+.f64 (*.f64 1/12 x) (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 1/144 (*.f64 x x)) (pow.f64 x -2)) (/.f64 1 (-.f64 (*.f64 1/12 x) (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (*.f64 1/1728 (pow.f64 x 3)) (pow.f64 x -3)) (/.f64 1 (+.f64 (*.f64 1/144 (*.f64 x x)) (-.f64 (pow.f64 x -2) (/.f64 (*.f64 1/12 x) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (*.f64 1/12 x) (/.f64 1 x)) (-.f64 (*.f64 1/144 (*.f64 x x)) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (*.f64 1/144 (*.f64 x x)) (-.f64 (pow.f64 x -2) (/.f64 (*.f64 1/12 x) x))) (+.f64 (*.f64 1/1728 (pow.f64 x 3)) (pow.f64 x -3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 1/144 (*.f64 x x)) (pow.f64 x -2)) (-.f64 (*.f64 1/12 x) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 1/1728 (pow.f64 x 3)) (pow.f64 x -3)) (+.f64 (*.f64 1/144 (*.f64 x x)) (-.f64 (pow.f64 x -2) (/.f64 (*.f64 1/12 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 1/1728 (pow.f64 x 3)) (pow.f64 x -3)) (+.f64 (pow.f64 x -2) (-.f64 (*.f64 1/144 (*.f64 x x)) (/.f64 (*.f64 1/12 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x -2) (*.f64 1/144 (*.f64 x x))) (-.f64 (/.f64 1 x) (*.f64 1/12 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (*.f64 1/144 (*.f64 x x)) (pow.f64 x -2))) (neg.f64 (-.f64 (*.f64 1/12 x) (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (*.f64 1/1728 (pow.f64 x 3)) (pow.f64 x -3))) (neg.f64 (+.f64 (*.f64 1/144 (*.f64 x x)) (-.f64 (pow.f64 x -2) (/.f64 (*.f64 1/12 x) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (*.f64 1/12 x) (/.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 (*.f64 1/12 x) (/.f64 1 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 (*.f64 1/12 x) (/.f64 1 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (*.f64 1/12 x) (/.f64 1 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 (*.f64 1/12 x) (/.f64 1 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 (*.f64 1/12 x) (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 (*.f64 1/12 x) (/.f64 1 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 (*.f64 1/12 x) (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 (*.f64 1/12 x) (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (+.f64 (*.f64 1/12 x) (/.f64 1 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 (*.f64 1/12 x) (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/12 x (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x 1/12 (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 1/12 x) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (/.f64 1 x) (*.f64 1/12 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 1/12 x)) (sqrt.f64 (*.f64 1/12 x)) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x -1/2) (pow.f64 x -1/2) (*.f64 1/12 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 1/12 x)) 2) (cbrt.f64 (*.f64 1/12 x)) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x -2)) (/.f64 1 (cbrt.f64 x)) (*.f64 1/12 x))))))

simplify57.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

1222×	`associate-r`
1096×	`associate-+r+`
1034×	`associate-l`
852×	`associate-+l+`
406×	`associate-*r/`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	122	1291
1	284	1177
2	1034	1147
3	5366	1147

Stop Event

1×	node limit

Counts

59 → 64

Calls

Call 1

Inputs
(/.f64 1 x)
(*.f64 1/12 x)
(+.f64 (/.f64 1 x) (*.f64 1/12 x))
(+.f64 (/.f64 1 x) (*.f64 1/12 x))
(+.f64 (/.f64 1 x) (*.f64 1/12 x))
(*.f64 1/12 x)
(+.f64 (/.f64 1 x) (*.f64 1/12 x))
(+.f64 (/.f64 1 x) (*.f64 1/12 x))
(+.f64 (/.f64 1 x) (*.f64 1/12 x))
(-.f64 (exp.f64 (log1p.f64 (*.f64 1/12 x))) 1)
(pow.f64 (*.f64 1/12 x) 1)
(pow.f64 (sqrt.f64 (*.f64 1/12 x)) 2)
(pow.f64 (cbrt.f64 (*.f64 1/12 x)) 3)
(pow.f64 (*.f64 1/1728 (pow.f64 x 3)) 1/3)
(sqrt.f64 (.f64 1/144 (.f64 x x)))
(log.f64 (pow.f64 (exp.f64 1/12) x))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 1/12 x))))
(cbrt.f64 (*.f64 1/1728 (pow.f64 x 3)))
(expm1.f64 (log1p.f64 (*.f64 1/12 x)))
(exp.f64 (log.f64 (*.f64 1/12 x)))
(exp.f64 (.f64 (log.f64 (.f64 1/12 x)) 1))
(log1p.f64 (expm1.f64 (*.f64 1/12 x)))
(-.f64 (exp.f64 (log1p.f64 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))) 1)
(-.f64 (/.f64 (.f64 1/144 (.f64 x x)) (-.f64 (.f64 1/12 x) (/.f64 1 x))) (/.f64 (pow.f64 x -2) (-.f64 (.f64 1/12 x) (/.f64 1 x))))
(.f64 1 (+.f64 (.f64 1/12 x) (/.f64 1 x)))
(.f64 (+.f64 (.f64 1/12 x) (/.f64 1 x)) 1)
(.f64 (sqrt.f64 (+.f64 (.f64 1/12 x) (/.f64 1 x))) (sqrt.f64 (+.f64 (*.f64 1/12 x) (/.f64 1 x))))
(.f64 (cbrt.f64 (+.f64 (.f64 1/12 x) (/.f64 1 x))) (pow.f64 (cbrt.f64 (+.f64 (*.f64 1/12 x) (/.f64 1 x))) 2))
(.f64 (pow.f64 (cbrt.f64 (+.f64 (.f64 1/12 x) (/.f64 1 x))) 2) (cbrt.f64 (+.f64 (*.f64 1/12 x) (/.f64 1 x))))
(.f64 (-.f64 (.f64 1/144 (.f64 x x)) (pow.f64 x -2)) (/.f64 1 (-.f64 (.f64 1/12 x) (/.f64 1 x))))
(.f64 (+.f64 (.f64 1/1728 (pow.f64 x 3)) (pow.f64 x -3)) (/.f64 1 (+.f64 (.f64 1/144 (.f64 x x)) (-.f64 (pow.f64 x -2) (/.f64 (*.f64 1/12 x) x)))))
(/.f64 1 (/.f64 (-.f64 (.f64 1/12 x) (/.f64 1 x)) (-.f64 (.f64 1/144 (*.f64 x x)) (pow.f64 x -2))))
(/.f64 1 (/.f64 (+.f64 (.f64 1/144 (.f64 x x)) (-.f64 (pow.f64 x -2) (/.f64 (.f64 1/12 x) x))) (+.f64 (.f64 1/1728 (pow.f64 x 3)) (pow.f64 x -3))))
(/.f64 (-.f64 (.f64 1/144 (.f64 x x)) (pow.f64 x -2)) (-.f64 (*.f64 1/12 x) (/.f64 1 x)))
(/.f64 (+.f64 (.f64 1/1728 (pow.f64 x 3)) (pow.f64 x -3)) (+.f64 (.f64 1/144 (.f64 x x)) (-.f64 (pow.f64 x -2) (/.f64 (.f64 1/12 x) x))))
(/.f64 (+.f64 (.f64 1/1728 (pow.f64 x 3)) (pow.f64 x -3)) (+.f64 (pow.f64 x -2) (-.f64 (.f64 1/144 (.f64 x x)) (/.f64 (.f64 1/12 x) x))))
(/.f64 (-.f64 (pow.f64 x -2) (.f64 1/144 (.f64 x x))) (-.f64 (/.f64 1 x) (*.f64 1/12 x)))
(/.f64 (neg.f64 (-.f64 (.f64 1/144 (.f64 x x)) (pow.f64 x -2))) (neg.f64 (-.f64 (*.f64 1/12 x) (/.f64 1 x))))
(/.f64 (neg.f64 (+.f64 (.f64 1/1728 (pow.f64 x 3)) (pow.f64 x -3))) (neg.f64 (+.f64 (.f64 1/144 (.f64 x x)) (-.f64 (pow.f64 x -2) (/.f64 (.f64 1/12 x) x)))))
(pow.f64 (+.f64 (*.f64 1/12 x) (/.f64 1 x)) 1)
(pow.f64 (sqrt.f64 (+.f64 (*.f64 1/12 x) (/.f64 1 x))) 2)
(pow.f64 (cbrt.f64 (+.f64 (*.f64 1/12 x) (/.f64 1 x))) 3)
(pow.f64 (pow.f64 (+.f64 (*.f64 1/12 x) (/.f64 1 x)) 3) 1/3)
(sqrt.f64 (pow.f64 (+.f64 (*.f64 1/12 x) (/.f64 1 x)) 2))
(log.f64 (exp.f64 (+.f64 (*.f64 1/12 x) (/.f64 1 x))))
(log.f64 (+.f64 1 (expm1.f64 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))))
(cbrt.f64 (pow.f64 (+.f64 (*.f64 1/12 x) (/.f64 1 x)) 3))
(expm1.f64 (log1p.f64 (+.f64 (*.f64 1/12 x) (/.f64 1 x))))
(exp.f64 (log.f64 (+.f64 (*.f64 1/12 x) (/.f64 1 x))))
(exp.f64 (.f64 (log.f64 (+.f64 (.f64 1/12 x) (/.f64 1 x))) 1))
(log1p.f64 (expm1.f64 (+.f64 (*.f64 1/12 x) (/.f64 1 x))))
(fma.f64 1/12 x (/.f64 1 x))
(fma.f64 x 1/12 (/.f64 1 x))
(fma.f64 1 (*.f64 1/12 x) (/.f64 1 x))
(fma.f64 1 (/.f64 1 x) (*.f64 1/12 x))
(fma.f64 (sqrt.f64 (.f64 1/12 x)) (sqrt.f64 (.f64 1/12 x)) (/.f64 1 x))
(fma.f64 (pow.f64 x -1/2) (pow.f64 x -1/2) (*.f64 1/12 x))
(fma.f64 (pow.f64 (cbrt.f64 (.f64 1/12 x)) 2) (cbrt.f64 (.f64 1/12 x)) (/.f64 1 x))
(fma.f64 (cbrt.f64 (pow.f64 x -2)) (/.f64 1 (cbrt.f64 x)) (*.f64 1/12 x))

Outputs
(/.f64 1 x)
(*.f64 1/12 x)
(*.f64 x 1/12)
(+.f64 (/.f64 1 x) (*.f64 1/12 x))
(fma.f64 x 1/12 (/.f64 1 x))
(+.f64 (/.f64 1 x) (*.f64 1/12 x))
(fma.f64 x 1/12 (/.f64 1 x))
(+.f64 (/.f64 1 x) (*.f64 1/12 x))
(fma.f64 x 1/12 (/.f64 1 x))
(*.f64 1/12 x)
(*.f64 x 1/12)
(+.f64 (/.f64 1 x) (*.f64 1/12 x))
(fma.f64 x 1/12 (/.f64 1 x))
(+.f64 (/.f64 1 x) (*.f64 1/12 x))
(fma.f64 x 1/12 (/.f64 1 x))
(+.f64 (/.f64 1 x) (*.f64 1/12 x))
(fma.f64 x 1/12 (/.f64 1 x))
(-.f64 (exp.f64 (log1p.f64 (*.f64 1/12 x))) 1)
(*.f64 x 1/12)
(pow.f64 (*.f64 1/12 x) 1)
(*.f64 x 1/12)
(pow.f64 (sqrt.f64 (*.f64 1/12 x)) 2)
(*.f64 x 1/12)
(pow.f64 (cbrt.f64 (*.f64 1/12 x)) 3)
(*.f64 x 1/12)
(pow.f64 (*.f64 1/1728 (pow.f64 x 3)) 1/3)
(cbrt.f64 (*.f64 1/1728 (pow.f64 x 3)))
(sqrt.f64 (.f64 1/144 (.f64 x x)))
(sqrt.f64 (.f64 x (.f64 x 1/144)))
(log.f64 (pow.f64 (exp.f64 1/12) x))
(*.f64 x 1/12)
(log.f64 (+.f64 1 (expm1.f64 (*.f64 1/12 x))))
(*.f64 x 1/12)
(cbrt.f64 (*.f64 1/1728 (pow.f64 x 3)))
(expm1.f64 (log1p.f64 (*.f64 1/12 x)))
(*.f64 x 1/12)
(exp.f64 (log.f64 (*.f64 1/12 x)))
(*.f64 x 1/12)
(exp.f64 (.f64 (log.f64 (.f64 1/12 x)) 1))
(*.f64 x 1/12)
(log1p.f64 (expm1.f64 (*.f64 1/12 x)))
(*.f64 x 1/12)
(-.f64 (exp.f64 (log1p.f64 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))) 1)
(fma.f64 x 1/12 (/.f64 1 x))
(-.f64 (/.f64 (.f64 1/144 (.f64 x x)) (-.f64 (.f64 1/12 x) (/.f64 1 x))) (/.f64 (pow.f64 x -2) (-.f64 (.f64 1/12 x) (/.f64 1 x))))
(/.f64 (-.f64 (.f64 1/144 (.f64 x x)) (pow.f64 x -2)) (-.f64 (*.f64 x 1/12) (/.f64 1 x)))
(/.f64 (-.f64 (.f64 x (.f64 x 1/144)) (pow.f64 x -2)) (fma.f64 x 1/12 (/.f64 -1 x)))
(/.f64 (fma.f64 (*.f64 x x) -1/144 (pow.f64 x -2)) (fma.f64 x -1/12 (/.f64 1 x)))
(.f64 1 (+.f64 (.f64 1/12 x) (/.f64 1 x)))
(fma.f64 x 1/12 (/.f64 1 x))
(.f64 (+.f64 (.f64 1/12 x) (/.f64 1 x)) 1)
(fma.f64 x 1/12 (/.f64 1 x))
(.f64 (sqrt.f64 (+.f64 (.f64 1/12 x) (/.f64 1 x))) (sqrt.f64 (+.f64 (*.f64 1/12 x) (/.f64 1 x))))
(fma.f64 x 1/12 (/.f64 1 x))
(.f64 (cbrt.f64 (+.f64 (.f64 1/12 x) (/.f64 1 x))) (pow.f64 (cbrt.f64 (+.f64 (*.f64 1/12 x) (/.f64 1 x))) 2))
(fma.f64 x 1/12 (/.f64 1 x))
(.f64 (pow.f64 (cbrt.f64 (+.f64 (.f64 1/12 x) (/.f64 1 x))) 2) (cbrt.f64 (+.f64 (*.f64 1/12 x) (/.f64 1 x))))
(fma.f64 x 1/12 (/.f64 1 x))
(.f64 (-.f64 (.f64 1/144 (.f64 x x)) (pow.f64 x -2)) (/.f64 1 (-.f64 (.f64 1/12 x) (/.f64 1 x))))
(/.f64 (-.f64 (.f64 1/144 (.f64 x x)) (pow.f64 x -2)) (-.f64 (*.f64 x 1/12) (/.f64 1 x)))
(/.f64 (-.f64 (.f64 x (.f64 x 1/144)) (pow.f64 x -2)) (fma.f64 x 1/12 (/.f64 -1 x)))
(/.f64 (fma.f64 (*.f64 x x) -1/144 (pow.f64 x -2)) (fma.f64 x -1/12 (/.f64 1 x)))
(.f64 (+.f64 (.f64 1/1728 (pow.f64 x 3)) (pow.f64 x -3)) (/.f64 1 (+.f64 (.f64 1/144 (.f64 x x)) (-.f64 (pow.f64 x -2) (/.f64 (*.f64 1/12 x) x)))))
(/.f64 (.f64 (fma.f64 1/1728 (pow.f64 x 3) (pow.f64 x -3)) 1) (fma.f64 1/144 (.f64 x x) (-.f64 (pow.f64 x -2) (/.f64 1/12 (/.f64 x x)))))
(/.f64 (fma.f64 1/1728 (pow.f64 x 3) (pow.f64 x -3)) (fma.f64 1/144 (*.f64 x x) (+.f64 (pow.f64 x -2) -1/12)))
(/.f64 (fma.f64 1/1728 (pow.f64 x 3) (pow.f64 x -3)) (+.f64 (pow.f64 x -2) (fma.f64 1/144 (*.f64 x x) -1/12)))
(/.f64 (fma.f64 1/1728 (pow.f64 x 3) (pow.f64 x -3)) (+.f64 (pow.f64 x -2) (fma.f64 x (*.f64 x 1/144) -1/12)))
(/.f64 1 (/.f64 (-.f64 (.f64 1/12 x) (/.f64 1 x)) (-.f64 (.f64 1/144 (*.f64 x x)) (pow.f64 x -2))))
(/.f64 (-.f64 (.f64 1/144 (.f64 x x)) (pow.f64 x -2)) (-.f64 (*.f64 x 1/12) (/.f64 1 x)))
(/.f64 (-.f64 (.f64 x (.f64 x 1/144)) (pow.f64 x -2)) (fma.f64 x 1/12 (/.f64 -1 x)))
(/.f64 (fma.f64 (*.f64 x x) -1/144 (pow.f64 x -2)) (fma.f64 x -1/12 (/.f64 1 x)))
(/.f64 1 (/.f64 (+.f64 (.f64 1/144 (.f64 x x)) (-.f64 (pow.f64 x -2) (/.f64 (.f64 1/12 x) x))) (+.f64 (.f64 1/1728 (pow.f64 x 3)) (pow.f64 x -3))))
(/.f64 (.f64 (fma.f64 1/1728 (pow.f64 x 3) (pow.f64 x -3)) 1) (fma.f64 1/144 (.f64 x x) (-.f64 (pow.f64 x -2) (/.f64 1/12 (/.f64 x x)))))
(/.f64 (fma.f64 1/1728 (pow.f64 x 3) (pow.f64 x -3)) (fma.f64 1/144 (*.f64 x x) (+.f64 (pow.f64 x -2) -1/12)))
(/.f64 (fma.f64 1/1728 (pow.f64 x 3) (pow.f64 x -3)) (+.f64 (pow.f64 x -2) (fma.f64 1/144 (*.f64 x x) -1/12)))
(/.f64 (fma.f64 1/1728 (pow.f64 x 3) (pow.f64 x -3)) (+.f64 (pow.f64 x -2) (fma.f64 x (*.f64 x 1/144) -1/12)))
(/.f64 (-.f64 (.f64 1/144 (.f64 x x)) (pow.f64 x -2)) (-.f64 (*.f64 1/12 x) (/.f64 1 x)))
(/.f64 (-.f64 (.f64 1/144 (.f64 x x)) (pow.f64 x -2)) (-.f64 (*.f64 x 1/12) (/.f64 1 x)))
(/.f64 (-.f64 (.f64 x (.f64 x 1/144)) (pow.f64 x -2)) (fma.f64 x 1/12 (/.f64 -1 x)))
(/.f64 (fma.f64 (*.f64 x x) -1/144 (pow.f64 x -2)) (fma.f64 x -1/12 (/.f64 1 x)))
(/.f64 (+.f64 (.f64 1/1728 (pow.f64 x 3)) (pow.f64 x -3)) (+.f64 (.f64 1/144 (.f64 x x)) (-.f64 (pow.f64 x -2) (/.f64 (.f64 1/12 x) x))))
(/.f64 (.f64 (fma.f64 1/1728 (pow.f64 x 3) (pow.f64 x -3)) 1) (fma.f64 1/144 (.f64 x x) (-.f64 (pow.f64 x -2) (/.f64 1/12 (/.f64 x x)))))
(/.f64 (fma.f64 1/1728 (pow.f64 x 3) (pow.f64 x -3)) (fma.f64 1/144 (*.f64 x x) (+.f64 (pow.f64 x -2) -1/12)))
(/.f64 (fma.f64 1/1728 (pow.f64 x 3) (pow.f64 x -3)) (+.f64 (pow.f64 x -2) (fma.f64 1/144 (*.f64 x x) -1/12)))
(/.f64 (fma.f64 1/1728 (pow.f64 x 3) (pow.f64 x -3)) (+.f64 (pow.f64 x -2) (fma.f64 x (*.f64 x 1/144) -1/12)))
(/.f64 (+.f64 (.f64 1/1728 (pow.f64 x 3)) (pow.f64 x -3)) (+.f64 (pow.f64 x -2) (-.f64 (.f64 1/144 (.f64 x x)) (/.f64 (.f64 1/12 x) x))))
(/.f64 (.f64 (fma.f64 1/1728 (pow.f64 x 3) (pow.f64 x -3)) 1) (fma.f64 1/144 (.f64 x x) (-.f64 (pow.f64 x -2) (/.f64 1/12 (/.f64 x x)))))
(/.f64 (fma.f64 1/1728 (pow.f64 x 3) (pow.f64 x -3)) (fma.f64 1/144 (*.f64 x x) (+.f64 (pow.f64 x -2) -1/12)))
(/.f64 (fma.f64 1/1728 (pow.f64 x 3) (pow.f64 x -3)) (+.f64 (pow.f64 x -2) (fma.f64 1/144 (*.f64 x x) -1/12)))
(/.f64 (fma.f64 1/1728 (pow.f64 x 3) (pow.f64 x -3)) (+.f64 (pow.f64 x -2) (fma.f64 x (*.f64 x 1/144) -1/12)))
(/.f64 (-.f64 (pow.f64 x -2) (.f64 1/144 (.f64 x x))) (-.f64 (/.f64 1 x) (*.f64 1/12 x)))
(/.f64 (-.f64 (.f64 1/144 (.f64 x x)) (pow.f64 x -2)) (-.f64 (*.f64 x 1/12) (/.f64 1 x)))
(/.f64 (-.f64 (.f64 x (.f64 x 1/144)) (pow.f64 x -2)) (fma.f64 x 1/12 (/.f64 -1 x)))
(/.f64 (fma.f64 (*.f64 x x) -1/144 (pow.f64 x -2)) (fma.f64 x -1/12 (/.f64 1 x)))
(/.f64 (neg.f64 (-.f64 (.f64 1/144 (.f64 x x)) (pow.f64 x -2))) (neg.f64 (-.f64 (*.f64 1/12 x) (/.f64 1 x))))
(/.f64 (-.f64 (.f64 1/144 (.f64 x x)) (pow.f64 x -2)) (-.f64 (*.f64 x 1/12) (/.f64 1 x)))
(/.f64 (-.f64 (.f64 x (.f64 x 1/144)) (pow.f64 x -2)) (fma.f64 x 1/12 (/.f64 -1 x)))
(/.f64 (fma.f64 (*.f64 x x) -1/144 (pow.f64 x -2)) (fma.f64 x -1/12 (/.f64 1 x)))
(/.f64 (neg.f64 (+.f64 (.f64 1/1728 (pow.f64 x 3)) (pow.f64 x -3))) (neg.f64 (+.f64 (.f64 1/144 (.f64 x x)) (-.f64 (pow.f64 x -2) (/.f64 (.f64 1/12 x) x)))))
(/.f64 (.f64 (fma.f64 1/1728 (pow.f64 x 3) (pow.f64 x -3)) 1) (fma.f64 1/144 (.f64 x x) (-.f64 (pow.f64 x -2) (/.f64 1/12 (/.f64 x x)))))
(/.f64 (fma.f64 1/1728 (pow.f64 x 3) (pow.f64 x -3)) (fma.f64 1/144 (*.f64 x x) (+.f64 (pow.f64 x -2) -1/12)))
(/.f64 (fma.f64 1/1728 (pow.f64 x 3) (pow.f64 x -3)) (+.f64 (pow.f64 x -2) (fma.f64 1/144 (*.f64 x x) -1/12)))
(/.f64 (fma.f64 1/1728 (pow.f64 x 3) (pow.f64 x -3)) (+.f64 (pow.f64 x -2) (fma.f64 x (*.f64 x 1/144) -1/12)))
(pow.f64 (+.f64 (*.f64 1/12 x) (/.f64 1 x)) 1)
(fma.f64 x 1/12 (/.f64 1 x))
(pow.f64 (sqrt.f64 (+.f64 (*.f64 1/12 x) (/.f64 1 x))) 2)
(fma.f64 x 1/12 (/.f64 1 x))
(pow.f64 (cbrt.f64 (+.f64 (*.f64 1/12 x) (/.f64 1 x))) 3)
(fma.f64 x 1/12 (/.f64 1 x))
(pow.f64 (pow.f64 (+.f64 (*.f64 1/12 x) (/.f64 1 x)) 3) 1/3)
(fma.f64 x 1/12 (/.f64 1 x))
(sqrt.f64 (pow.f64 (+.f64 (*.f64 1/12 x) (/.f64 1 x)) 2))
(fma.f64 x 1/12 (/.f64 1 x))
(log.f64 (exp.f64 (+.f64 (*.f64 1/12 x) (/.f64 1 x))))
(fma.f64 x 1/12 (/.f64 1 x))
(log.f64 (+.f64 1 (expm1.f64 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))))
(fma.f64 x 1/12 (/.f64 1 x))
(cbrt.f64 (pow.f64 (+.f64 (*.f64 1/12 x) (/.f64 1 x)) 3))
(fma.f64 x 1/12 (/.f64 1 x))
(expm1.f64 (log1p.f64 (+.f64 (*.f64 1/12 x) (/.f64 1 x))))
(fma.f64 x 1/12 (/.f64 1 x))
(exp.f64 (log.f64 (+.f64 (*.f64 1/12 x) (/.f64 1 x))))
(fma.f64 x 1/12 (/.f64 1 x))
(exp.f64 (.f64 (log.f64 (+.f64 (.f64 1/12 x) (/.f64 1 x))) 1))
(fma.f64 x 1/12 (/.f64 1 x))
(log1p.f64 (expm1.f64 (+.f64 (*.f64 1/12 x) (/.f64 1 x))))
(fma.f64 x 1/12 (/.f64 1 x))
(fma.f64 1/12 x (/.f64 1 x))
(fma.f64 x 1/12 (/.f64 1 x))
(fma.f64 x 1/12 (/.f64 1 x))
(fma.f64 1 (*.f64 1/12 x) (/.f64 1 x))
(fma.f64 x 1/12 (/.f64 1 x))
(fma.f64 1 (/.f64 1 x) (*.f64 1/12 x))
(fma.f64 x 1/12 (/.f64 1 x))
(fma.f64 (sqrt.f64 (.f64 1/12 x)) (sqrt.f64 (.f64 1/12 x)) (/.f64 1 x))
(fma.f64 x 1/12 (/.f64 1 x))
(fma.f64 (pow.f64 x -1/2) (pow.f64 x -1/2) (*.f64 1/12 x))
(fma.f64 x 1/12 (/.f64 1 x))
(fma.f64 (pow.f64 (cbrt.f64 (.f64 1/12 x)) 2) (cbrt.f64 (.f64 1/12 x)) (/.f64 1 x))
(fma.f64 x 1/12 (/.f64 1 x))
(fma.f64 (cbrt.f64 (pow.f64 x -2)) (/.f64 1 (cbrt.f64 x)) (*.f64 1/12 x))
(fma.f64 (cbrt.f64 (pow.f64 x -2)) (/.f64 1 (cbrt.f64 x)) (*.f64 x 1/12))
(fma.f64 x 1/12 (/.f64 (cbrt.f64 (pow.f64 x -2)) (cbrt.f64 x)))

localize5.0ms (0.2%)

Compiler: Compiled 12 to 9 computations (25% saved)

localize2.0ms (0.1%)

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

eval31.0ms (1.1%)

Compiler: Compiled 1664 to 1140 computations (31.5% saved)

prune17.0ms (0.6%)

Pruning

7 alts after pruning (2 fresh and 5 done)

	Pruned	Kept	Total
New	132	2	134
Fresh	0	0	0
Picked	0	1	1
Done	0	4	4
Total	132	7	139

Error

0.8b

Counts

139 → 7

Alt Table

Click to see full alt table

Status	Error	Program
✓	1.0b	(/.f64 (exp.f64 x) (expm1.f64 x))
✓	20.8b	(/.f64 1 x)
✓	20.4b	(+.f64 (/.f64 1 x) 1/2)
✓	20.4b	(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
▶	62.0b	(+.f64 1/2 (*.f64 x 1/12))
✓	1.0b	(*.f64 (/.f64 1 (expm1.f64 x)) (exp.f64 x))
▶	1.7b	(*.f64 (-.f64 (/.f64 1 x) 1/2) (exp.f64 x))

Compiler

Compiled 49 to 38 computations (22.4% saved)

localize9.0ms (0.3%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 22 to 15 computations (31.8% saved)

series1.0ms (0.1%)

Counts

2 → 15

Calls

6 calls:

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

rewrite65.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

1994×	`add-sqr-sqrt`
1964×	`*-un-lft-identity`
1838×	`add-cube-cbrt`
1818×	`add-cbrt-cube`
194×	`pow1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	36
1	207	36
2	2478	36

Stop Event

1×	node limit

Counts

2 → 51

Calls

Call 1

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

Outputs

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

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

simplify61.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

1000×	`times-frac`
938×	`associate-/l*`
778×	`associate-+r+`
762×	`*-commutative`
688×	`unswap-sqr`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	138	1606
1	313	1462
2	1108	1460
3	3882	1460

Stop Event

1×	node limit

Counts

66 → 77

Calls

Call 1

Inputs
(/.f64 1 x)
(+.f64 1/2 (/.f64 1 x))
(+.f64 1/2 (+.f64 (*.f64 -1/12 (pow.f64 x 2)) (/.f64 1 x)))
(+.f64 (.f64 -1/24 (pow.f64 x 3)) (+.f64 1/2 (+.f64 (.f64 -1/12 (pow.f64 x 2)) (/.f64 1 x))))
(*.f64 -1/2 (exp.f64 x))
(+.f64 (/.f64 (exp.f64 x) x) (*.f64 -1/2 (exp.f64 x)))
(+.f64 (/.f64 (exp.f64 x) x) (*.f64 -1/2 (exp.f64 x)))
(+.f64 (/.f64 (exp.f64 x) x) (*.f64 -1/2 (exp.f64 x)))
(*.f64 -1/2 (exp.f64 x))
(+.f64 (/.f64 (exp.f64 x) x) (*.f64 -1/2 (exp.f64 x)))
(+.f64 (/.f64 (exp.f64 x) x) (*.f64 -1/2 (exp.f64 x)))
(+.f64 (/.f64 (exp.f64 x) x) (*.f64 -1/2 (exp.f64 x)))
(/.f64 1 x)
-1/2
-1/2
(+.f64 (.f64 (exp.f64 x) (/.f64 1 x)) (.f64 (exp.f64 x) -1/2))
(+.f64 (.f64 (/.f64 1 x) (exp.f64 x)) (.f64 -1/2 (exp.f64 x)))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (-.f64 (/.f64 1 x) 1/2) (exp.f64 x)))) 1)
(/.f64 (*.f64 (exp.f64 x) (+.f64 (pow.f64 x -2) -1/4)) (+.f64 (/.f64 1 x) 1/2))
(/.f64 (*.f64 (exp.f64 x) (+.f64 (pow.f64 x -3) -1/8)) (+.f64 (pow.f64 x -2) (+.f64 1/4 (/.f64 1/2 x))))
(/.f64 (*.f64 (+.f64 (pow.f64 x -2) -1/4) (exp.f64 x)) (+.f64 (/.f64 1 x) 1/2))
(/.f64 (*.f64 (+.f64 (pow.f64 x -3) -1/8) (exp.f64 x)) (+.f64 (pow.f64 x -2) (+.f64 1/4 (/.f64 1/2 x))))
(pow.f64 (*.f64 (-.f64 (/.f64 1 x) 1/2) (exp.f64 x)) 1)
(pow.f64 (sqrt.f64 (*.f64 (-.f64 (/.f64 1 x) 1/2) (exp.f64 x))) 2)
(pow.f64 (cbrt.f64 (*.f64 (-.f64 (/.f64 1 x) 1/2) (exp.f64 x))) 3)
(pow.f64 (pow.f64 (*.f64 (-.f64 (/.f64 1 x) 1/2) (exp.f64 x)) 3) 1/3)
(sqrt.f64 (pow.f64 (*.f64 (-.f64 (/.f64 1 x) 1/2) (exp.f64 x)) 2))
(log.f64 (pow.f64 (exp.f64 (exp.f64 x)) (-.f64 (/.f64 1 x) 1/2)))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (-.f64 (/.f64 1 x) 1/2) (exp.f64 x)))))
(cbrt.f64 (pow.f64 (*.f64 (-.f64 (/.f64 1 x) 1/2) (exp.f64 x)) 3))
(expm1.f64 (log1p.f64 (*.f64 (-.f64 (/.f64 1 x) 1/2) (exp.f64 x))))
(exp.f64 (+.f64 x (log.f64 (-.f64 (/.f64 1 x) 1/2))))
(exp.f64 (*.f64 (+.f64 x (log.f64 (-.f64 (/.f64 1 x) 1/2))) 1))
(log1p.f64 (expm1.f64 (*.f64 (-.f64 (/.f64 1 x) 1/2) (exp.f64 x))))
(+.f64 (/.f64 1 x) -1/2)
(+.f64 -1/2 (/.f64 1 x))
(*.f64 1 (-.f64 (/.f64 1 x) 1/2))
(*.f64 (-.f64 (/.f64 1 x) 1/2) 1)
(*.f64 (sqrt.f64 (-.f64 (/.f64 1 x) 1/2)) (sqrt.f64 (-.f64 (/.f64 1 x) 1/2)))
(*.f64 (cbrt.f64 (-.f64 (/.f64 1 x) 1/2)) (pow.f64 (cbrt.f64 (-.f64 (/.f64 1 x) 1/2)) 2))
(*.f64 (pow.f64 (cbrt.f64 (-.f64 (/.f64 1 x) 1/2)) 2) (cbrt.f64 (-.f64 (/.f64 1 x) 1/2)))
(*.f64 (+.f64 (pow.f64 x -2) -1/4) (/.f64 1 (+.f64 (/.f64 1 x) 1/2)))
(*.f64 (+.f64 (pow.f64 x -3) -1/8) (/.f64 1 (+.f64 (pow.f64 x -2) (+.f64 1/4 (/.f64 1/2 x)))))
(/.f64 1 (/.f64 (+.f64 (/.f64 1 x) 1/2) (+.f64 (pow.f64 x -2) -1/4)))
(/.f64 1 (/.f64 (+.f64 (pow.f64 x -2) (+.f64 1/4 (/.f64 1/2 x))) (+.f64 (pow.f64 x -3) -1/8)))
(/.f64 (+.f64 (pow.f64 x -2) -1/4) (+.f64 (/.f64 1 x) 1/2))
(/.f64 (+.f64 (pow.f64 x -2) -1/4) (-.f64 (/.f64 1 x) -1/2))
(/.f64 (+.f64 (pow.f64 x -3) -1/8) (+.f64 (pow.f64 x -2) (+.f64 1/4 (/.f64 1/2 x))))
(/.f64 (+.f64 (pow.f64 x -3) -1/8) (+.f64 (pow.f64 x -2) (-.f64 1/4 (*.f64 (/.f64 1 x) -1/2))))
(/.f64 (neg.f64 (+.f64 (pow.f64 x -2) -1/4)) (neg.f64 (+.f64 (/.f64 1 x) 1/2)))
(/.f64 (neg.f64 (+.f64 (pow.f64 x -3) -1/8)) (neg.f64 (+.f64 (pow.f64 x -2) (+.f64 1/4 (/.f64 1/2 x)))))
(pow.f64 (-.f64 (/.f64 1 x) 1/2) 1)
(pow.f64 (sqrt.f64 (-.f64 (/.f64 1 x) 1/2)) 2)
(pow.f64 (cbrt.f64 (-.f64 (/.f64 1 x) 1/2)) 3)
(pow.f64 (pow.f64 (-.f64 (/.f64 1 x) 1/2) 3) 1/3)
(sqrt.f64 (pow.f64 (-.f64 (/.f64 1 x) 1/2) 2))
(log.f64 (exp.f64 (-.f64 (/.f64 1 x) 1/2)))
(log.f64 (+.f64 1 (expm1.f64 (-.f64 (/.f64 1 x) 1/2))))
(cbrt.f64 (pow.f64 (-.f64 (/.f64 1 x) 1/2) 3))
(expm1.f64 (log1p.f64 (-.f64 (/.f64 1 x) 1/2)))
(exp.f64 (log.f64 (-.f64 (/.f64 1 x) 1/2)))
(exp.f64 (*.f64 (log.f64 (-.f64 (/.f64 1 x) 1/2)) 1))
(log1p.f64 (expm1.f64 (-.f64 (/.f64 1 x) 1/2)))
(fma.f64 1 (/.f64 1 x) -1/2)
(fma.f64 (pow.f64 x -1/2) (pow.f64 x -1/2) -1/2)
(fma.f64 (cbrt.f64 (pow.f64 x -2)) (/.f64 1 (cbrt.f64 x)) -1/2)

Outputs
(/.f64 1 x)
(+.f64 1/2 (/.f64 1 x))
(+.f64 (/.f64 1 x) 1/2)
(+.f64 1/2 (+.f64 (*.f64 -1/12 (pow.f64 x 2)) (/.f64 1 x)))
(+.f64 1/2 (fma.f64 -1/12 (*.f64 x x) (/.f64 1 x)))
(+.f64 1/2 (fma.f64 x (*.f64 x -1/12) (/.f64 1 x)))
(fma.f64 x (*.f64 x -1/12) (+.f64 (/.f64 1 x) 1/2))
(+.f64 (.f64 -1/24 (pow.f64 x 3)) (+.f64 1/2 (+.f64 (.f64 -1/12 (pow.f64 x 2)) (/.f64 1 x))))
(fma.f64 -1/24 (pow.f64 x 3) (+.f64 1/2 (fma.f64 -1/12 (*.f64 x x) (/.f64 1 x))))
(+.f64 (fma.f64 -1/12 (*.f64 x x) (/.f64 1 x)) (fma.f64 -1/24 (pow.f64 x 3) 1/2))
(+.f64 1/2 (fma.f64 -1/24 (pow.f64 x 3) (fma.f64 x (*.f64 x -1/12) (/.f64 1 x))))
(+.f64 (fma.f64 x (*.f64 x -1/12) (/.f64 1 x)) (fma.f64 -1/24 (pow.f64 x 3) 1/2))
(*.f64 -1/2 (exp.f64 x))
(+.f64 (/.f64 (exp.f64 x) x) (*.f64 -1/2 (exp.f64 x)))
(+.f64 (*.f64 -1/2 (exp.f64 x)) (/.f64 (exp.f64 x) x))
(*.f64 (exp.f64 x) (+.f64 (/.f64 1 x) -1/2))
(+.f64 (/.f64 (exp.f64 x) x) (*.f64 -1/2 (exp.f64 x)))
(+.f64 (*.f64 -1/2 (exp.f64 x)) (/.f64 (exp.f64 x) x))
(*.f64 (exp.f64 x) (+.f64 (/.f64 1 x) -1/2))
(+.f64 (/.f64 (exp.f64 x) x) (*.f64 -1/2 (exp.f64 x)))
(+.f64 (*.f64 -1/2 (exp.f64 x)) (/.f64 (exp.f64 x) x))
(*.f64 (exp.f64 x) (+.f64 (/.f64 1 x) -1/2))
(*.f64 -1/2 (exp.f64 x))
(+.f64 (/.f64 (exp.f64 x) x) (*.f64 -1/2 (exp.f64 x)))
(+.f64 (*.f64 -1/2 (exp.f64 x)) (/.f64 (exp.f64 x) x))
(*.f64 (exp.f64 x) (+.f64 (/.f64 1 x) -1/2))
(+.f64 (/.f64 (exp.f64 x) x) (*.f64 -1/2 (exp.f64 x)))
(+.f64 (*.f64 -1/2 (exp.f64 x)) (/.f64 (exp.f64 x) x))
(*.f64 (exp.f64 x) (+.f64 (/.f64 1 x) -1/2))
(+.f64 (/.f64 (exp.f64 x) x) (*.f64 -1/2 (exp.f64 x)))
(+.f64 (*.f64 -1/2 (exp.f64 x)) (/.f64 (exp.f64 x) x))
(*.f64 (exp.f64 x) (+.f64 (/.f64 1 x) -1/2))
(/.f64 1 x)
-1/2
-1/2
(+.f64 (.f64 (exp.f64 x) (/.f64 1 x)) (.f64 (exp.f64 x) -1/2))
(+.f64 (*.f64 -1/2 (exp.f64 x)) (/.f64 (exp.f64 x) x))
(*.f64 (exp.f64 x) (+.f64 (/.f64 1 x) -1/2))
(+.f64 (.f64 (/.f64 1 x) (exp.f64 x)) (.f64 -1/2 (exp.f64 x)))
(+.f64 (*.f64 -1/2 (exp.f64 x)) (/.f64 (exp.f64 x) x))
(*.f64 (exp.f64 x) (+.f64 (/.f64 1 x) -1/2))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (-.f64 (/.f64 1 x) 1/2) (exp.f64 x)))) 1)
(+.f64 (*.f64 -1/2 (exp.f64 x)) (/.f64 (exp.f64 x) x))
(*.f64 (exp.f64 x) (+.f64 (/.f64 1 x) -1/2))
(/.f64 (*.f64 (exp.f64 x) (+.f64 (pow.f64 x -2) -1/4)) (+.f64 (/.f64 1 x) 1/2))
(/.f64 (exp.f64 x) (/.f64 (+.f64 (/.f64 1 x) 1/2) (+.f64 (pow.f64 x -2) -1/4)))
(*.f64 (/.f64 (exp.f64 x) (+.f64 (/.f64 1 x) 1/2)) (+.f64 (pow.f64 x -2) -1/4))
(*.f64 (exp.f64 x) (/.f64 (+.f64 (pow.f64 x -2) -1/4) (+.f64 (/.f64 1 x) 1/2)))
(/.f64 (*.f64 (exp.f64 x) (+.f64 (pow.f64 x -3) -1/8)) (+.f64 (pow.f64 x -2) (+.f64 1/4 (/.f64 1/2 x))))
(/.f64 (+.f64 (pow.f64 x -3) -1/8) (/.f64 (+.f64 (pow.f64 x -2) (+.f64 1/4 (/.f64 1/2 x))) (exp.f64 x)))
(*.f64 (exp.f64 x) (/.f64 (+.f64 (pow.f64 x -3) -1/8) (+.f64 (pow.f64 x -2) (+.f64 1/4 (/.f64 1/2 x)))))
(*.f64 (exp.f64 x) (/.f64 (+.f64 (pow.f64 x -3) -1/8) (-.f64 (pow.f64 x -2) (-.f64 -1/4 (/.f64 1/2 x)))))
(/.f64 (*.f64 (+.f64 (pow.f64 x -2) -1/4) (exp.f64 x)) (+.f64 (/.f64 1 x) 1/2))
(/.f64 (exp.f64 x) (/.f64 (+.f64 (/.f64 1 x) 1/2) (+.f64 (pow.f64 x -2) -1/4)))
(*.f64 (/.f64 (exp.f64 x) (+.f64 (/.f64 1 x) 1/2)) (+.f64 (pow.f64 x -2) -1/4))
(*.f64 (exp.f64 x) (/.f64 (+.f64 (pow.f64 x -2) -1/4) (+.f64 (/.f64 1 x) 1/2)))
(/.f64 (*.f64 (+.f64 (pow.f64 x -3) -1/8) (exp.f64 x)) (+.f64 (pow.f64 x -2) (+.f64 1/4 (/.f64 1/2 x))))
(/.f64 (+.f64 (pow.f64 x -3) -1/8) (/.f64 (+.f64 (pow.f64 x -2) (+.f64 1/4 (/.f64 1/2 x))) (exp.f64 x)))
(*.f64 (exp.f64 x) (/.f64 (+.f64 (pow.f64 x -3) -1/8) (+.f64 (pow.f64 x -2) (+.f64 1/4 (/.f64 1/2 x)))))
(*.f64 (exp.f64 x) (/.f64 (+.f64 (pow.f64 x -3) -1/8) (-.f64 (pow.f64 x -2) (-.f64 -1/4 (/.f64 1/2 x)))))
(pow.f64 (*.f64 (-.f64 (/.f64 1 x) 1/2) (exp.f64 x)) 1)
(+.f64 (*.f64 -1/2 (exp.f64 x)) (/.f64 (exp.f64 x) x))
(*.f64 (exp.f64 x) (+.f64 (/.f64 1 x) -1/2))
(pow.f64 (sqrt.f64 (*.f64 (-.f64 (/.f64 1 x) 1/2) (exp.f64 x))) 2)
(+.f64 (*.f64 -1/2 (exp.f64 x)) (/.f64 (exp.f64 x) x))
(*.f64 (exp.f64 x) (+.f64 (/.f64 1 x) -1/2))
(pow.f64 (cbrt.f64 (*.f64 (-.f64 (/.f64 1 x) 1/2) (exp.f64 x))) 3)
(+.f64 (*.f64 -1/2 (exp.f64 x)) (/.f64 (exp.f64 x) x))
(*.f64 (exp.f64 x) (+.f64 (/.f64 1 x) -1/2))
(pow.f64 (pow.f64 (*.f64 (-.f64 (/.f64 1 x) 1/2) (exp.f64 x)) 3) 1/3)
(+.f64 (*.f64 -1/2 (exp.f64 x)) (/.f64 (exp.f64 x) x))
(*.f64 (exp.f64 x) (+.f64 (/.f64 1 x) -1/2))
(sqrt.f64 (pow.f64 (*.f64 (-.f64 (/.f64 1 x) 1/2) (exp.f64 x)) 2))
(+.f64 (*.f64 -1/2 (exp.f64 x)) (/.f64 (exp.f64 x) x))
(*.f64 (exp.f64 x) (+.f64 (/.f64 1 x) -1/2))
(log.f64 (pow.f64 (exp.f64 (exp.f64 x)) (-.f64 (/.f64 1 x) 1/2)))
(+.f64 (*.f64 -1/2 (exp.f64 x)) (/.f64 (exp.f64 x) x))
(*.f64 (exp.f64 x) (+.f64 (/.f64 1 x) -1/2))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (-.f64 (/.f64 1 x) 1/2) (exp.f64 x)))))
(+.f64 (*.f64 -1/2 (exp.f64 x)) (/.f64 (exp.f64 x) x))
(*.f64 (exp.f64 x) (+.f64 (/.f64 1 x) -1/2))
(cbrt.f64 (pow.f64 (*.f64 (-.f64 (/.f64 1 x) 1/2) (exp.f64 x)) 3))
(+.f64 (*.f64 -1/2 (exp.f64 x)) (/.f64 (exp.f64 x) x))
(*.f64 (exp.f64 x) (+.f64 (/.f64 1 x) -1/2))
(expm1.f64 (log1p.f64 (*.f64 (-.f64 (/.f64 1 x) 1/2) (exp.f64 x))))
(+.f64 (*.f64 -1/2 (exp.f64 x)) (/.f64 (exp.f64 x) x))
(*.f64 (exp.f64 x) (+.f64 (/.f64 1 x) -1/2))
(exp.f64 (+.f64 x (log.f64 (-.f64 (/.f64 1 x) 1/2))))
(+.f64 (*.f64 -1/2 (exp.f64 x)) (/.f64 (exp.f64 x) x))
(*.f64 (exp.f64 x) (+.f64 (/.f64 1 x) -1/2))
(exp.f64 (*.f64 (+.f64 x (log.f64 (-.f64 (/.f64 1 x) 1/2))) 1))
(+.f64 (*.f64 -1/2 (exp.f64 x)) (/.f64 (exp.f64 x) x))
(*.f64 (exp.f64 x) (+.f64 (/.f64 1 x) -1/2))
(log1p.f64 (expm1.f64 (*.f64 (-.f64 (/.f64 1 x) 1/2) (exp.f64 x))))
(+.f64 (*.f64 -1/2 (exp.f64 x)) (/.f64 (exp.f64 x) x))
(*.f64 (exp.f64 x) (+.f64 (/.f64 1 x) -1/2))
(+.f64 (/.f64 1 x) -1/2)
(+.f64 -1/2 (/.f64 1 x))
(+.f64 (/.f64 1 x) -1/2)
(*.f64 1 (-.f64 (/.f64 1 x) 1/2))
(+.f64 (/.f64 1 x) -1/2)
(*.f64 (-.f64 (/.f64 1 x) 1/2) 1)
(+.f64 (/.f64 1 x) -1/2)
(*.f64 (sqrt.f64 (-.f64 (/.f64 1 x) 1/2)) (sqrt.f64 (-.f64 (/.f64 1 x) 1/2)))
(+.f64 (/.f64 1 x) -1/2)
(*.f64 (cbrt.f64 (-.f64 (/.f64 1 x) 1/2)) (pow.f64 (cbrt.f64 (-.f64 (/.f64 1 x) 1/2)) 2))
(+.f64 (/.f64 1 x) -1/2)
(*.f64 (pow.f64 (cbrt.f64 (-.f64 (/.f64 1 x) 1/2)) 2) (cbrt.f64 (-.f64 (/.f64 1 x) 1/2)))
(+.f64 (/.f64 1 x) -1/2)
(*.f64 (+.f64 (pow.f64 x -2) -1/4) (/.f64 1 (+.f64 (/.f64 1 x) 1/2)))
(/.f64 (+.f64 (pow.f64 x -2) -1/4) (+.f64 (/.f64 1 x) 1/2))
(*.f64 (+.f64 (pow.f64 x -3) -1/8) (/.f64 1 (+.f64 (pow.f64 x -2) (+.f64 1/4 (/.f64 1/2 x)))))
(/.f64 (*.f64 (+.f64 (pow.f64 x -3) -1/8) 1) (+.f64 (pow.f64 x -2) (+.f64 1/4 (/.f64 1/2 x))))
(/.f64 (+.f64 (pow.f64 x -3) -1/8) (+.f64 (pow.f64 x -2) (+.f64 1/4 (/.f64 1/2 x))))
(/.f64 (+.f64 (pow.f64 x -3) -1/8) (-.f64 (pow.f64 x -2) (-.f64 -1/4 (/.f64 1/2 x))))
(/.f64 1 (/.f64 (+.f64 (/.f64 1 x) 1/2) (+.f64 (pow.f64 x -2) -1/4)))
(*.f64 (+.f64 (pow.f64 x -2) -1/4) (/.f64 1 (+.f64 (/.f64 1 x) 1/2)))
(/.f64 (+.f64 (pow.f64 x -2) -1/4) (+.f64 (/.f64 1 x) 1/2))
(/.f64 1 (/.f64 (+.f64 (pow.f64 x -2) (+.f64 1/4 (/.f64 1/2 x))) (+.f64 (pow.f64 x -3) -1/8)))
(/.f64 (*.f64 (+.f64 (pow.f64 x -3) -1/8) 1) (+.f64 (pow.f64 x -2) (+.f64 1/4 (/.f64 1/2 x))))
(/.f64 (+.f64 (pow.f64 x -3) -1/8) (+.f64 (pow.f64 x -2) (+.f64 1/4 (/.f64 1/2 x))))
(/.f64 (+.f64 (pow.f64 x -3) -1/8) (-.f64 (pow.f64 x -2) (-.f64 -1/4 (/.f64 1/2 x))))
(/.f64 (+.f64 (pow.f64 x -2) -1/4) (+.f64 (/.f64 1 x) 1/2))
(*.f64 (+.f64 (pow.f64 x -2) -1/4) (/.f64 1 (+.f64 (/.f64 1 x) 1/2)))
(/.f64 (+.f64 (pow.f64 x -2) -1/4) (-.f64 (/.f64 1 x) -1/2))
(*.f64 (+.f64 (pow.f64 x -2) -1/4) (/.f64 1 (+.f64 (/.f64 1 x) 1/2)))
(/.f64 (+.f64 (pow.f64 x -2) -1/4) (+.f64 (/.f64 1 x) 1/2))
(/.f64 (+.f64 (pow.f64 x -3) -1/8) (+.f64 (pow.f64 x -2) (+.f64 1/4 (/.f64 1/2 x))))
(/.f64 (*.f64 (+.f64 (pow.f64 x -3) -1/8) 1) (+.f64 (pow.f64 x -2) (+.f64 1/4 (/.f64 1/2 x))))
(/.f64 (+.f64 (pow.f64 x -3) -1/8) (-.f64 (pow.f64 x -2) (-.f64 -1/4 (/.f64 1/2 x))))
(/.f64 (+.f64 (pow.f64 x -3) -1/8) (+.f64 (pow.f64 x -2) (-.f64 1/4 (*.f64 (/.f64 1 x) -1/2))))
(/.f64 (*.f64 (+.f64 (pow.f64 x -3) -1/8) 1) (+.f64 (pow.f64 x -2) (+.f64 1/4 (/.f64 1/2 x))))
(/.f64 (+.f64 (pow.f64 x -3) -1/8) (+.f64 (pow.f64 x -2) (+.f64 1/4 (/.f64 1/2 x))))
(/.f64 (+.f64 (pow.f64 x -3) -1/8) (-.f64 (pow.f64 x -2) (-.f64 -1/4 (/.f64 1/2 x))))
(/.f64 (neg.f64 (+.f64 (pow.f64 x -2) -1/4)) (neg.f64 (+.f64 (/.f64 1 x) 1/2)))
(*.f64 (+.f64 (pow.f64 x -2) -1/4) (/.f64 1 (+.f64 (/.f64 1 x) 1/2)))
(/.f64 (+.f64 (pow.f64 x -2) -1/4) (+.f64 (/.f64 1 x) 1/2))
(/.f64 (neg.f64 (+.f64 (pow.f64 x -3) -1/8)) (neg.f64 (+.f64 (pow.f64 x -2) (+.f64 1/4 (/.f64 1/2 x)))))
(/.f64 (*.f64 (+.f64 (pow.f64 x -3) -1/8) 1) (+.f64 (pow.f64 x -2) (+.f64 1/4 (/.f64 1/2 x))))
(/.f64 (+.f64 (pow.f64 x -3) -1/8) (+.f64 (pow.f64 x -2) (+.f64 1/4 (/.f64 1/2 x))))
(/.f64 (+.f64 (pow.f64 x -3) -1/8) (-.f64 (pow.f64 x -2) (-.f64 -1/4 (/.f64 1/2 x))))
(pow.f64 (-.f64 (/.f64 1 x) 1/2) 1)
(+.f64 (/.f64 1 x) -1/2)
(pow.f64 (sqrt.f64 (-.f64 (/.f64 1 x) 1/2)) 2)
(+.f64 (/.f64 1 x) -1/2)
(pow.f64 (cbrt.f64 (-.f64 (/.f64 1 x) 1/2)) 3)
(+.f64 (/.f64 1 x) -1/2)
(pow.f64 (pow.f64 (-.f64 (/.f64 1 x) 1/2) 3) 1/3)
(+.f64 (/.f64 1 x) -1/2)
(sqrt.f64 (pow.f64 (-.f64 (/.f64 1 x) 1/2) 2))
(+.f64 (/.f64 1 x) -1/2)
(log.f64 (exp.f64 (-.f64 (/.f64 1 x) 1/2)))
(+.f64 (/.f64 1 x) -1/2)
(log.f64 (+.f64 1 (expm1.f64 (-.f64 (/.f64 1 x) 1/2))))
(+.f64 (/.f64 1 x) -1/2)
(cbrt.f64 (pow.f64 (-.f64 (/.f64 1 x) 1/2) 3))
(+.f64 (/.f64 1 x) -1/2)
(expm1.f64 (log1p.f64 (-.f64 (/.f64 1 x) 1/2)))
(+.f64 (/.f64 1 x) -1/2)
(exp.f64 (log.f64 (-.f64 (/.f64 1 x) 1/2)))
(+.f64 (/.f64 1 x) -1/2)
(exp.f64 (*.f64 (log.f64 (-.f64 (/.f64 1 x) 1/2)) 1))
(+.f64 (/.f64 1 x) -1/2)
(log1p.f64 (expm1.f64 (-.f64 (/.f64 1 x) 1/2)))
(+.f64 (/.f64 1 x) -1/2)
(fma.f64 1 (/.f64 1 x) -1/2)
(+.f64 (/.f64 1 x) -1/2)
(fma.f64 (pow.f64 x -1/2) (pow.f64 x -1/2) -1/2)
(+.f64 (/.f64 1 x) -1/2)
(fma.f64 (cbrt.f64 (pow.f64 x -2)) (/.f64 1 (cbrt.f64 x)) -1/2)
(+.f64 -1/2 (/.f64 (cbrt.f64 (pow.f64 x -2)) (cbrt.f64 x)))

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 x 1/12)

Compiler

Compiled 12 to 9 computations (25% saved)

series0.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(*.f64 x 1/12)
0.0ms	x	@	inf	(*.f64 x 1/12)
0.0ms	x	@	-inf	(*.f64 x 1/12)

rewrite45.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

924×	`associate-l`
902×	`add-sqr-sqrt`
884×	`*-un-lft-identity`
842×	`pow1`
826×	`add-cube-cbrt`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	100	7
2	1110	7

Stop Event

1×	node limit

Counts

1 → 11

Calls

Call 1

Inputs
(*.f64 x 1/12)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (*.f64 x 1/12) 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x 1/12) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 x 1/12)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x 1/12)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x 1/12) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 x (*.f64 x 1/144)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 x) 1/12))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x 1/12) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x 1/12)))))))

simplify62.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

844×	`log-prod`
822×	`distribute-rgt-out`
778×	`+-commutative`
690×	`fma-def`
650×	`associate-+r-`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	161
1	85	161
2	260	161
3	1791	161
4	3939	161
5	6098	161

Stop Event

1×	node limit

Counts

23 → 12

Calls

Call 1

Inputs
(*.f64 1/12 x)
(*.f64 1/12 x)
(*.f64 1/12 x)
(*.f64 1/12 x)
(*.f64 1/12 x)
(*.f64 1/12 x)
(*.f64 1/12 x)
(*.f64 1/12 x)
(*.f64 1/12 x)
(*.f64 1/12 x)
(*.f64 1/12 x)
(*.f64 1/12 x)
(-.f64 (+.f64 (*.f64 x 1/12) 1) 1)
(pow.f64 (*.f64 x 1/12) 1)
(pow.f64 (sqrt.f64 (*.f64 x 1/12)) 2)
(pow.f64 (cbrt.f64 (*.f64 x 1/12)) 3)
(pow.f64 (pow.f64 (*.f64 x 1/12) 3) 1/3)
(sqrt.f64 (.f64 x (.f64 x 1/144)))
(log.f64 (pow.f64 (exp.f64 x) 1/12))
(cbrt.f64 (pow.f64 (*.f64 x 1/12) 3))
(expm1.f64 (log1p.f64 (*.f64 x 1/12)))
(exp.f64 (log.f64 (*.f64 x 1/12)))
(log1p.f64 (expm1.f64 (*.f64 x 1/12)))

Outputs
(*.f64 1/12 x)
(*.f64 1/12 x)
(*.f64 1/12 x)
(*.f64 1/12 x)
(*.f64 1/12 x)
(*.f64 1/12 x)
(*.f64 1/12 x)
(*.f64 1/12 x)
(*.f64 1/12 x)
(*.f64 1/12 x)
(*.f64 1/12 x)
(*.f64 1/12 x)
(-.f64 (+.f64 (*.f64 x 1/12) 1) 1)
(*.f64 1/12 x)
(pow.f64 (*.f64 x 1/12) 1)
(*.f64 1/12 x)
(pow.f64 (sqrt.f64 (*.f64 x 1/12)) 2)
(*.f64 1/12 x)
(pow.f64 (cbrt.f64 (*.f64 x 1/12)) 3)
(*.f64 1/12 x)
(pow.f64 (pow.f64 (*.f64 x 1/12) 3) 1/3)
(*.f64 1/12 x)
(sqrt.f64 (.f64 x (.f64 x 1/144)))
(*.f64 1/12 x)
(log.f64 (pow.f64 (exp.f64 x) 1/12))
(*.f64 1/12 x)
(cbrt.f64 (pow.f64 (*.f64 x 1/12) 3))
(*.f64 1/12 x)
(expm1.f64 (log1p.f64 (*.f64 x 1/12)))
(*.f64 1/12 x)
(exp.f64 (log.f64 (*.f64 x 1/12)))
(*.f64 1/12 x)
(log1p.f64 (expm1.f64 (*.f64 x 1/12)))
(*.f64 1/12 x)

eval20.0ms (0.7%)

Compiler: Compiled 1053 to 764 computations (27.4% saved)

prune13.0ms (0.5%)

Pruning

8 alts after pruning (1 fresh and 7 done)

	Pruned	Kept	Total
New	88	1	89
Fresh	0	0	0
Picked	0	1	1
Done	0	6	6
Total	88	8	96

Error

0.8b

Counts

96 → 8

Alt Table

Click to see full alt table

Status	Error	Program
✓	1.0b	(/.f64 (exp.f64 x) (expm1.f64 x))
✓	20.8b	(/.f64 1 x)
✓	20.4b	(+.f64 (/.f64 1 x) 1/2)
✓	20.4b	(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
✓	62.0b	(+.f64 1/2 (*.f64 x 1/12))
✓	1.0b	(*.f64 (/.f64 1 (expm1.f64 x)) (exp.f64 x))
✓	1.7b	(*.f64 (-.f64 (/.f64 1 x) 1/2) (exp.f64 x))
▶	43.0b	(*.f64 -1/2 (exp.f64 x))

Compiler

Compiled 54 to 42 computations (22.2% saved)

localize4.0ms (0.1%)

Compiler: Compiled 9 to 5 computations (44.4% saved)

eval0.0ms (0%)

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

prune3.0ms (0.1%)

Pruning

8 alts after pruning (0 fresh and 8 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	1	1
Done	7	7
Total	8	8

Error

0.8b

Counts

8 → 8

Alt Table

Click to see full alt table

Status	Error	Program
✓	1.0b	(/.f64 (exp.f64 x) (expm1.f64 x))
✓	20.8b	(/.f64 1 x)
✓	20.4b	(+.f64 (/.f64 1 x) 1/2)
✓	20.4b	(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
✓	62.0b	(+.f64 1/2 (*.f64 x 1/12))
✓	1.0b	(*.f64 (/.f64 1 (expm1.f64 x)) (exp.f64 x))
✓	1.7b	(*.f64 (-.f64 (/.f64 1 x) 1/2) (exp.f64 x))
✓	43.0b	(*.f64 -1/2 (exp.f64 x))

Compiler

Compiled 54 to 42 computations (22.2% saved)

regimes12.0ms (0.5%)

Counts

9 → 1

Calls

Call 1

Inputs
(/.f64 1 x)
(+.f64 1/2 (*.f64 x 1/12))
(+.f64 (/.f64 1 x) 1/2)
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
(*.f64 -1/2 (exp.f64 x))
(*.f64 (-.f64 (/.f64 1 x) 1/2) (exp.f64 x))
(/.f64 (exp.f64 x) (expm1.f64 x))
(*.f64 (/.f64 1 (expm1.f64 x)) (exp.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))

Outputs
(*.f64 (/.f64 1 (expm1.f64 x)) (exp.f64 x))

Calls

3 calls:

6.0ms	x
2.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
2.0ms	(exp.f64 x)

Results

Error	Segments	Branch
1.0b	1	`x`
1.0b	1	`(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))`
1.0b	1	`(exp.f64 x)`

Compiler

Compiled 67 to 42 computations (37.3% saved)

regimes8.0ms (0.3%)

Counts

7 → 1

Calls

Call 1

Inputs
(/.f64 1 x)
(+.f64 1/2 (*.f64 x 1/12))
(+.f64 (/.f64 1 x) 1/2)
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
(*.f64 -1/2 (exp.f64 x))
(*.f64 (-.f64 (/.f64 1 x) 1/2) (exp.f64 x))
(/.f64 (exp.f64 x) (expm1.f64 x))

Outputs
(/.f64 (exp.f64 x) (expm1.f64 x))

Calls

2 calls:

5.0ms	x
2.0ms	(exp.f64 x)

Results

Error	Segments	Branch
1.0b	1	`x`
1.0b	1	`(exp.f64 x)`

Compiler

Compiled 45 to 31 computations (31.1% saved)

regimes8.0ms (0.3%)

Counts

6 → 1

Calls

Call 1

Inputs
(/.f64 1 x)
(+.f64 1/2 (*.f64 x 1/12))
(+.f64 (/.f64 1 x) 1/2)
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
(*.f64 -1/2 (exp.f64 x))
(*.f64 (-.f64 (/.f64 1 x) 1/2) (exp.f64 x))

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

Calls

2 calls:

4.0ms	x
2.0ms	(exp.f64 x)

Results

Error	Segments	Branch
1.7b	1	`x`
1.7b	1	`(exp.f64 x)`

Compiler

Compiled 40 to 29 computations (27.5% saved)

regimes13.0ms (0.5%)

Counts

5 → 2

Calls

Call 1

Inputs
(/.f64 1 x)
(+.f64 1/2 (*.f64 x 1/12))
(+.f64 (/.f64 1 x) 1/2)
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
(*.f64 -1/2 (exp.f64 x))

Outputs
(*.f64 -1/2 (exp.f64 x))
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))

Calls

2 calls:

8.0ms	x
4.0ms	(exp.f64 x)

Results

Error	Segments	Branch
1.3b	2	`x`
1.3b	2	`(exp.f64 x)`

Compiler

Compiled 32 to 24 computations (25% saved)

bsearch0.0ms (0%)

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	6.474454530446885e-26	0.9994705335708898

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes5.0ms (0.2%)

Counts

4 → 1

Calls

Call 1

Inputs
(/.f64 1 x)
(+.f64 1/2 (*.f64 x 1/12))
(+.f64 (/.f64 1 x) 1/2)
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))

Outputs
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))

Calls

1 calls:

4.0ms

Results

Error	Segments	Branch
20.4b	1	`x`

Compiler

Compiled 25 to 19 computations (24% saved)

regimes4.0ms (0.2%)

Counts

3 → 1

Calls

Call 1

Inputs
(/.f64 1 x)
(+.f64 1/2 (*.f64 x 1/12))
(+.f64 (/.f64 1 x) 1/2)

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

Calls

1 calls:

3.0ms

Results

Error	Segments	Branch
20.4b	1	`x`

Compiler

Compiled 16 to 12 computations (25% saved)

regimes5.0ms (0.2%)

Accuracy

Total -41.2b remaining (-198.3%)

Threshold costs -41.2b (-198.3%)

Counts

2 → 1

Calls

Call 1

Inputs
(/.f64 1 x)
(+.f64 1/2 (*.f64 x 1/12))

Outputs
(/.f64 1 x)

Calls

1 calls:

5.0ms

Results

Error	Segments	Branch
20.8b	1	`x`

Compiler

Compiled 11 to 8 computations (27.3% saved)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	153
1	38	153
2	39	153

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(*.f64 (/.f64 1 (expm1.f64 x)) (exp.f64 x))
(/.f64 (exp.f64 x) (expm1.f64 x))
(*.f64 (-.f64 (/.f64 1 x) 1/2) (exp.f64 x))
(if (<=.f64 (exp.f64 x) 8711228593176025/87112285931760246646623899502532662132736) (.f64 -1/2 (exp.f64 x)) (+.f64 1/2 (+.f64 (.f64 1/12 x) (/.f64 1 x))))
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
(+.f64 (/.f64 1 x) 1/2)
(/.f64 1 x)

Outputs
(*.f64 (/.f64 1 (expm1.f64 x)) (exp.f64 x))
(/.f64 (exp.f64 x) (expm1.f64 x))
(*.f64 (-.f64 (/.f64 1 x) 1/2) (exp.f64 x))
(*.f64 (exp.f64 x) (+.f64 (/.f64 1 x) -1/2))
(if (<=.f64 (exp.f64 x) 8711228593176025/87112285931760246646623899502532662132736) (.f64 -1/2 (exp.f64 x)) (+.f64 1/2 (+.f64 (.f64 1/12 x) (/.f64 1 x))))
(if (<=.f64 (exp.f64 x) 8711228593176025/87112285931760246646623899502532662132736) (.f64 (exp.f64 x) -1/2) (+.f64 1/2 (+.f64 (/.f64 1 x) (.f64 x 1/12))))
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
(+.f64 1/2 (+.f64 (/.f64 1 x) (*.f64 x 1/12)))
(+.f64 (/.f64 1 x) 1/2)
(/.f64 1 x)

Compiler

Compiled 62 to 47 computations (24.2% saved)

soundness11.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

2×	`1-exp`
2×	`expm1-def`
2×	`sub-neg`
2×	`+-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	14	15
2	15	15

Stop Event

1×

saturated

Compiler

Compiled 13 to 7 computations (46.2% saved)

end39.0ms (1.4%)

Compiler: Compiled 56 to 37 computations (33.9% saved)

Details

analyze108.0ms (4%)

sample1.8s (65.1%)

preprocess4.0ms (0.2%)

simplify11.0ms (0.4%)

eval0.0ms (0%)

prune1.0ms (0%)

localize5.0ms (0.2%)

series1.0ms (0.1%)

rewrite51.0ms (1.9%)

simplify51.0ms (1.9%)

eval9.0ms (0.3%)

prune7.0ms (0.2%)

localize7.0ms (0.3%)

series1.0ms (0.1%)

rewrite56.0ms (2.1%)

simplify58.0ms (2.1%)

localize10.0ms (0.4%)

series1.0ms (0%)

rewrite58.0ms (2.1%)

simplify57.0ms (2.1%)

localize5.0ms (0.2%)

localize2.0ms (0.1%)

eval31.0ms (1.1%)

prune17.0ms (0.6%)

localize9.0ms (0.3%)

series1.0ms (0.1%)

rewrite65.0ms (2.4%)

simplify61.0ms (2.3%)

localize5.0ms (0.2%)

series0.0ms (0%)

rewrite45.0ms (1.6%)

simplify62.0ms (2.3%)

eval20.0ms (0.7%)

prune13.0ms (0.5%)

localize4.0ms (0.1%)

eval0.0ms (0%)

prune3.0ms (0.1%)

regimes12.0ms (0.5%)

regimes8.0ms (0.3%)

regimes8.0ms (0.3%)

regimes13.0ms (0.5%)

bsearch0.0ms (0%)

regimes5.0ms (0.2%)

regimes4.0ms (0.2%)

regimes5.0ms (0.2%)

simplify7.0ms (0.2%)

soundness11.0ms (0.4%)

end39.0ms (1.4%)

Profiling