Details

analyze1.0ms (0%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	25.7%	74.3%	0%	0%	0%	0
100%	25.7%	0%	74.3%	0%	0%	0%	1

Compiler

Compiled 26 to 19 computations (26.9% saved)

sample1.7s (63.8%)

Results

930.0ms	6201×	body	256	valid
378.0ms	964×	body	1024	valid
324.0ms	1057×	body	512	valid
20.0ms	34×	body	2048	valid

Bogosity

preprocess45.0ms (1.7%)

Algorithm

2×	egg-herbie

Rules

498×	`associate-l_binary64`
451×	`distribute-rgt-neg-in_binary64`
426×	`distribute-lft-neg-in_binary64`
409×	`associate-r_binary64`
366×	`distribute-rgt-out_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	26
1	32	26
2	76	26
3	270	26
4	1173	20
5	4509	20
0	2	2

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0
1

Outputs
0
1

Call 2

Inputs
(-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2))
(-.f64 (pow.f64 (+.f64 eps x) 2) (pow.f64 eps 2))

Outputs
(-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2))
(-.f64 (pow.f64 (+.f64 x eps) 2) (*.f64 x x))
(*.f64 eps (+.f64 eps (+.f64 x x)))
(-.f64 (pow.f64 (+.f64 eps x) 2) (pow.f64 eps 2))
(-.f64 (pow.f64 (+.f64 x eps) 2) (*.f64 eps eps))
(*.f64 x (+.f64 x (+.f64 eps eps)))

Compiler

Compiled 13 to 10 computations (23.1% saved)

simplify55.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

563×	`distribute-rgt-in_binary64`
513×	`cancel-sign-sub-inv_binary64`
510×	`fma-neg_binary64`
463×	`distribute-lft-in_binary64`
412×	`fma-def_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	19	13
2	49	13
3	161	13
4	636	8
5	2828	8

Stop Event

1×	node limit

Counts

1 → 4

Calls

Call 1

Inputs
(-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2))

Outputs
(-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2))
(-.f64 (pow.f64 (+.f64 x eps) 2) (*.f64 x x))
(fma.f64 x (neg.f64 x) (pow.f64 (+.f64 x eps) 2))
(*.f64 eps (fma.f64 2 x eps))

eval1.0ms (0%)

Compiler: Compiled 35 to 19 computations (45.7% saved)

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	3	1	4
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	4	1	5

Error

0.0b

Counts

5 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.0b	(*.f64 eps (fma.f64 2 x eps))

Compiler

Compiled 8 to 5 computations (37.5% saved)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 eps (fma.f64 2 x eps))

Compiler

Compiled 15 to 8 computations (46.7% saved)

series4.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	eps	@	-inf	(*.f64 eps (fma.f64 2 x eps))
1.0ms	eps	@	0	(*.f64 eps (fma.f64 2 x eps))
1.0ms	x	@	0	(*.f64 eps (fma.f64 2 x eps))
1.0ms	eps	@	inf	(*.f64 eps (fma.f64 2 x eps))
1.0ms	x	@	inf	(*.f64 eps (fma.f64 2 x eps))

rewrite36.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

552×	`pow1_binary64`
531×	`add-sqr-sqrt_binary64`
507×	`add-log-exp_binary64`
507×	`log1p-expm1-u_binary64`
507×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	120	8
2	1364	8

Stop Event

1×	node limit

Counts

1 → 13

Calls

Call 1

Inputs
(*.f64 eps (fma.f64 2 x eps))

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

Outputs

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

simplify39.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

717×	`fma-def_binary64`
584×	`log-prod_binary64`
329×	`*-commutative_binary64`
314×	`associate-l_binary64`
273×	`associate-r_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	281
1	101	281
2	331	281
3	2324	281
4	5611	281

Stop Event

1×	node limit

Counts

37 → 19

Calls

Call 1

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

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

eval11.0ms (0.4%)

Compiler: Compiled 147 to 90 computations (38.8% saved)

prune4.0ms (0.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	16	3	19
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	16	4	20

Error

0.0b

Counts

20 → 4

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.0b	(+.f64 (.f64 (.f64 2 x) eps) (*.f64 eps eps))
✓	0.0b	(*.f64 eps (fma.f64 2 x eps))
▶	25.2b	(.f64 eps (.f64 2 x))
▶	16.4b	(*.f64 eps eps)

Compiler

Compiled 31 to 20 computations (35.5% saved)

localize3.0ms (0.1%)

Compiler: Compiled 6 to 3 computations (50% saved)

localize5.0ms (0.2%)

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

localize9.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 (.f64 2 x) eps) (*.f64 eps eps))

Compiler

Compiled 25 to 13 computations (48% saved)

series3.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

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

rewrite67.0ms (2.6%)

Algorithm

1×	batch-egg-rewrite

Rules

890×	`pow1_binary64`
828×	`add-log-exp_binary64`
827×	`log1p-expm1-u_binary64`
827×	`expm1-log1p-u_binary64`
809×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	174	8
2	2324	8

Stop Event

1×	node limit

Counts

1 → 40

Calls

Call 1

Inputs
(+.f64 (.f64 (.f64 2 x) eps) (*.f64 eps eps))

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

Outputs

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

simplify47.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

887×	`fma-neg_binary64`
700×	`div-sub_binary64`
609×	`times-frac_binary64`
271×	`fma-def_binary64`
250×	`log-prod_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	106	963
1	287	810
2	980	773
3	5246	773

Stop Event

1×	node limit

Counts

64 → 56

Calls

Call 1

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

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

eval16.0ms (0.6%)

Compiler: Compiled 835 to 518 computations (38% saved)

prune12.0ms (0.5%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	55	1	56
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	55	5	60

Error

Counts

60 → 5

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.0b	(fma.f64 (.f64 2 x) eps (.f64 eps eps))
✓	0.0b	(+.f64 (.f64 (.f64 2 x) eps) (*.f64 eps eps))
✓	0.0b	(*.f64 eps (fma.f64 2 x eps))
✓	25.2b	(.f64 eps (.f64 2 x))
✓	16.4b	(*.f64 eps eps)

Compiler

Compiled 41 to 26 computations (36.6% saved)

localize7.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (.f64 2 x) eps (.f64 eps eps))

Compiler

Compiled 19 to 9 computations (52.6% saved)

series2.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	x	@	-inf	(fma.f64 (.f64 2 x) eps (.f64 eps eps))
0.0ms	x	@	inf	(fma.f64 (.f64 2 x) eps (.f64 eps eps))
0.0ms	x	@	0	(fma.f64 (.f64 2 x) eps (.f64 eps eps))
0.0ms	eps	@	0	(fma.f64 (.f64 2 x) eps (.f64 eps eps))
0.0ms	eps	@	-inf	(fma.f64 (.f64 2 x) eps (.f64 eps eps))

rewrite61.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

618×	`pow1_binary64`
567×	`add-log-exp_binary64`
567×	`log1p-expm1-u_binary64`
567×	`expm1-log1p-u_binary64`
553×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	139	10
2	1582	10

Stop Event

1×	node limit

Counts

1 → 22

Calls

Call 1

Inputs
(fma.f64 (.f64 2 x) eps (.f64 eps eps))

Outputs

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

simplify60.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

739×	`fma-neg_binary64`
637×	`associate-/l*_binary64`
357×	`associate-/r*_binary64`
273×	`*-commutative_binary64`
255×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	60	426
1	178	413
2	763	409
3	2949	389
4	7874	389

Stop Event

1×	node limit

Counts

46 → 36

Calls

Call 1

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

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

eval8.0ms (0.3%)

Compiler: Compiled 510 to 300 computations (41.2% saved)

prune14.0ms (0.5%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	35	1	36
Fresh	0	0	0
Picked	0	1	1
Done	1	3	4
Total	36	5	41

Error

Counts

41 → 5

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.0b	(fma.f64 (.f64 2 x) eps (.f64 eps eps))
✓	0.0b	(+.f64 (.f64 (.f64 2 x) eps) (*.f64 eps eps))
▶	0.0b	(.f64 eps (+.f64 (.f64 2 x) eps))
✓	25.2b	(.f64 eps (.f64 2 x))
✓	16.4b	(*.f64 eps eps)

Compiler

Compiled 42 to 27 computations (35.7% saved)

localize8.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 eps (+.f64 (.f64 2 x) eps))

Compiler

Compiled 20 to 12 computations (40% saved)

series2.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

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

rewrite62.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

813×	`pow1_binary64`
758×	`add-log-exp_binary64`
757×	`log1p-expm1-u_binary64`
757×	`expm1-log1p-u_binary64`
742×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	8
1	154	8
2	2090	8

Stop Event

1×	node limit

Counts

1 → 24

Calls

Call 1

Inputs
(.f64 eps (+.f64 (.f64 2 x) eps))

Outputs

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

simplify41.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

481×	`times-frac_binary64`
390×	`associate-/l/_binary64`
389×	`fma-neg_binary64`
346×	`fma-def_binary64`
305×	`associate-/r/_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	83	708
1	253	468
2	999	462
3	4627	435

Stop Event

1×	node limit

Counts

48 → 35

Calls

Call 1

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

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

eval8.0ms (0.3%)

Compiler: Compiled 477 to 274 computations (42.6% saved)

prune18.0ms (0.7%)

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	35	0	35
Fresh	0	0	0
Picked	0	1	1
Done	0	4	4
Total	35	5	40

Error

Counts

40 → 5

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.0b	(fma.f64 (.f64 2 x) eps (.f64 eps eps))
✓	0.0b	(+.f64 (.f64 (.f64 2 x) eps) (*.f64 eps eps))
✓	0.0b	(.f64 eps (+.f64 (.f64 2 x) eps))
✓	25.2b	(.f64 eps (.f64 2 x))
✓	16.4b	(*.f64 eps eps)

Compiler

Compiled 42 to 27 computations (35.7% saved)

regimes13.0ms (0.5%)

Counts

7 → 1

Calls

Call 1

Inputs
(*.f64 eps eps)
(.f64 eps (.f64 2 x))
(.f64 eps (+.f64 (.f64 2 x) eps))
(+.f64 (.f64 (.f64 2 x) eps) (*.f64 eps eps))
(*.f64 eps (fma.f64 2 x eps))
(fma.f64 (.f64 2 x) eps (.f64 eps eps))
(-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2))

Outputs
(fma.f64 (.f64 2 x) eps (.f64 eps eps))

Calls

3 calls:

5.0ms	eps
5.0ms	x
3.0ms	(-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2))

Results

Error	Segments	Branch
0.0b	1	`x`
0.0b	1	`eps`
0.0b	1	`(-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2))`

Compiler

Compiled 66 to 38 computations (42.4% saved)

regimes18.0ms (0.7%)

Counts

5 → 1

Calls

Call 1

Inputs
(*.f64 eps eps)
(.f64 eps (.f64 2 x))
(.f64 eps (+.f64 (.f64 2 x) eps))
(+.f64 (.f64 (.f64 2 x) eps) (*.f64 eps eps))
(*.f64 eps (fma.f64 2 x eps))

Outputs
(+.f64 (.f64 (.f64 2 x) eps) (*.f64 eps eps))

Calls

2 calls:

4.0ms	eps
4.0ms	x

Results

Error	Segments	Branch
0.0b	1	`x`
0.0b	1	`eps`

Compiler

Compiled 38 to 21 computations (44.7% saved)

regimes24.0ms (0.9%)

Counts

3 → 1

Calls

Call 1

Inputs
(*.f64 eps eps)
(.f64 eps (.f64 2 x))
(.f64 eps (+.f64 (.f64 2 x) eps))

Outputs
(.f64 eps (+.f64 (.f64 2 x) eps))

Calls

2 calls:

19.0ms	eps
3.0ms	x

Results

Error	Segments	Branch
0.0b	1	`x`
0.0b	1	`eps`

Compiler

Compiled 23 to 14 computations (39.1% saved)

regimes50.0ms (1.9%)

Accuracy

Total -36.8b remaining (-891.7%)

Threshold costs -36.8b (-891.7%)

Counts

2 → 3

Calls

Call 1

Inputs
(*.f64 eps eps)
(.f64 eps (.f64 2 x))

Outputs
(.f64 eps (.f64 2 x))
(*.f64 eps eps)
(.f64 eps (.f64 2 x))

Calls

2 calls:

11.0ms	eps
8.0ms	x

Results

Error	Segments	Branch
4.1b	3	`x`
6.1b	3	`eps`

Compiler

Compiled 16 to 10 computations (37.5% saved)

bsearch46.0ms (1.7%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
16.0ms	3.5816474663417894e-86	1.6911767046543522e-84
29.0ms	-1.6119078894958e-98	-9.855121632632252e-100

Results

30.0ms	105×	body	512	valid
13.0ms	116×	body	256	valid
1.0ms	3×	body	1024	valid

Compiler

Compiled 212 to 152 computations (28.3% saved)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
2×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	68
1	24	68

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(fma.f64 (.f64 2 x) eps (.f64 eps eps))
(+.f64 (.f64 (.f64 2 x) eps) (*.f64 eps eps))
(.f64 eps (+.f64 (.f64 2 x) eps))
(if (<=.f64 x -8003532508642629/615656346818663737691860001564743965704370926101022604186692084441339402679643915803347910232576806887603562348544) (.f64 eps (.f64 2 x)) (if (<=.f64 x 3079649020494481/69992023193056381579920071267763883691301421788582797965624659405118495974380029543152421664737722368) (.f64 eps eps) (.f64 eps (*.f64 2 x))))
(*.f64 eps eps)

Outputs
(fma.f64 (.f64 2 x) eps (.f64 eps eps))
(+.f64 (.f64 (.f64 2 x) eps) (*.f64 eps eps))
(+.f64 (.f64 eps eps) (.f64 (*.f64 2 x) eps))
(.f64 eps (+.f64 (.f64 2 x) eps))
(if (<=.f64 x -8003532508642629/615656346818663737691860001564743965704370926101022604186692084441339402679643915803347910232576806887603562348544) (.f64 eps (.f64 2 x)) (if (<=.f64 x 3079649020494481/69992023193056381579920071267763883691301421788582797965624659405118495974380029543152421664737722368) (.f64 eps eps) (.f64 eps (*.f64 2 x))))
(if (<=.f64 x -8003532508642629/615656346818663737691860001564743965704370926101022604186692084441339402679643915803347910232576806887603562348544) (.f64 (.f64 2 x) eps) (if (<=.f64 x 3079649020494481/69992023193056381579920071267763883691301421788582797965624659405118495974380029543152421664737722368) (.f64 eps eps) (.f64 (*.f64 2 x) eps)))
(*.f64 eps eps)

Compiler

Compiled 58 to 37 computations (36.2% saved)

soundness103.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

563×	`distribute-rgt-in_binary64`
513×	`cancel-sign-sub-inv_binary64`
510×	`fma-neg_binary64`
463×	`distribute-lft-in_binary64`
412×	`fma-def_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	19	13
2	49	13
3	161	13
4	636	8
5	2828	8

Stop Event

1×	node limit

Compiler

Compiled 212 to 127 computations (40.1% saved)

end33.0ms (1.3%)

Compiler: Compiled 50 to 26 computations (48% saved)

Details

analyze1.0ms (0%)

sample1.7s (63.8%)

preprocess45.0ms (1.7%)

simplify55.0ms (2.1%)

eval1.0ms (0%)

prune1.0ms (0%)

localize6.0ms (0.2%)

series4.0ms (0.1%)

rewrite36.0ms (1.4%)

simplify39.0ms (1.5%)

eval11.0ms (0.4%)

prune4.0ms (0.1%)

localize3.0ms (0.1%)

localize5.0ms (0.2%)

localize9.0ms (0.3%)

series3.0ms (0.1%)

rewrite67.0ms (2.6%)

simplify47.0ms (1.8%)

eval16.0ms (0.6%)

prune12.0ms (0.5%)

localize7.0ms (0.3%)

series2.0ms (0.1%)

rewrite61.0ms (2.4%)

simplify60.0ms (2.3%)

eval8.0ms (0.3%)

prune14.0ms (0.5%)

localize8.0ms (0.3%)

series2.0ms (0.1%)

rewrite62.0ms (2.4%)

simplify41.0ms (1.6%)

eval8.0ms (0.3%)

prune18.0ms (0.7%)

regimes13.0ms (0.5%)

regimes18.0ms (0.7%)

regimes24.0ms (0.9%)

regimes50.0ms (1.9%)

bsearch46.0ms (1.7%)

simplify4.0ms (0.2%)

soundness103.0ms (3.9%)

end33.0ms (1.3%)

Profiling