Details

analyze386.0ms (9.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
50%	50%	0%	4
62.5%	37.5%	0%	5
68.7%	31.2%	0%	6
71.8%	28.1%	0%	7
73.4%	26.5%	0%	8
74.2%	25.8%	0%	9
74.6%	25.4%	0%	10
74.8%	25.2%	0%	11
74.9%	25.1%	0%	12
74.9%	25%	0%	13
74.9%	25%	0%	14

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample3.1s (79.6%)

Results

1.5s	2561×	body	1024	valid
704.0ms	1232×	body	2048	valid
513.0ms	1387×	body	512	valid
258.0ms	2351×	body	128	valid
148.0ms	670×	body	256	valid
39.0ms	55×	body	4096	valid

Compiler

Compiled 22 to 16 computations (27.3% saved)

preprocess17.0ms (0.4%)

Algorithm

2×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`1-exp_binary64`
1×	`hypot-1-def_binary64`
1×	`fma-def_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	13	9
2	14	9
0	1	1

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0

Outputs
0

Call 2

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

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

Compiler

Compiled 10 to 7 computations (30% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`1-exp_binary64`
1×	`hypot-1-def_binary64`
1×	`fma-def_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	13	9
2	14	9

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

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

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

prune3.0ms (0.1%)

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

48.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	48.8b	(log.f64 (+.f64 x (hypot.f64 1 x)))

Compiler

Compiled 30 to 21 computations (30% saved)

localize4.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 1 x)
✓	0.7b	(+.f64 x (hypot.f64 1 x))
✓	4.5b	(log.f64 (+.f64 x (hypot.f64 1 x)))

series7.0ms (0.2%)

Counts

3 → 36

Calls

9 calls:

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

rewrite41.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

619×	`pow1_binary64`
575×	`add-log-exp_binary64`
575×	`log1p-expm1-u_binary64`
575×	`expm1-log1p-u_binary64`
62×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	20
1	121	20
2	1555	20

Stop Event

1×	node limit

Counts

3 → 75

Calls

Call 1

Inputs
(log.f64 (+.f64 x (hypot.f64 1 x)))
(+.f64 x (hypot.f64 1 x))
(hypot.f64 1 x)

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

Outputs

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

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

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

simplify37.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

447×	`cancel-sign-sub-inv_binary64`
436×	`fma-neg_binary64`
413×	`associate-/r*_binary64`
338×	`sub-neg_binary64`
314×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	98	569
1	306	549
2	863	537
3	2779	537

Stop Event

1×	node limit

Counts

111 → 139

Calls

Call 1

Inputs
x
(-.f64 x (*.f64 1/6 (pow.f64 x 3)))
(-.f64 (+.f64 (.f64 3/40 (pow.f64 x 5)) x) (.f64 1/6 (pow.f64 x 3)))
(-.f64 (+.f64 (.f64 3/40 (pow.f64 x 5)) x) (+.f64 (.f64 5/112 (pow.f64 x 7)) (*.f64 1/6 (pow.f64 x 3))))
(-.f64 (log.f64 2) (log.f64 (/.f64 1 x)))
(-.f64 (+.f64 (log.f64 2) (*.f64 1/4 (/.f64 1 (pow.f64 x 2)))) (log.f64 (/.f64 1 x)))
(-.f64 (+.f64 (log.f64 2) (.f64 1/4 (/.f64 1 (pow.f64 x 2)))) (+.f64 (.f64 3/32 (/.f64 1 (pow.f64 x 4))) (log.f64 (/.f64 1 x))))
(-.f64 (+.f64 (.f64 5/96 (/.f64 1 (pow.f64 x 6))) (+.f64 (log.f64 2) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))) (+.f64 (*.f64 3/32 (/.f64 1 (pow.f64 x 4))) (log.f64 (/.f64 1 x))))
(+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2))
(-.f64 (+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2)) (*.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (.f64 3/32 (/.f64 1 (pow.f64 x 4))) (+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2))) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (.f64 3/32 (/.f64 1 (pow.f64 x 4))) (+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2))) (+.f64 (.f64 5/96 (/.f64 1 (pow.f64 x 6))) (*.f64 1/4 (/.f64 1 (pow.f64 x 2)))))
1
(+.f64 1 x)
(+.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 2)) x))
(-.f64 (+.f64 1 (+.f64 (.f64 1/2 (pow.f64 x 2)) x)) (.f64 1/8 (pow.f64 x 4)))
(*.f64 2 x)
(+.f64 (.f64 1/2 (/.f64 1 x)) (.f64 2 x))
(-.f64 (+.f64 (.f64 1/2 (/.f64 1 x)) (.f64 2 x)) (*.f64 1/8 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 5))) (+.f64 (.f64 1/2 (/.f64 1 x)) (.f64 2 x))) (.f64 1/8 (/.f64 1 (pow.f64 x 3))))
(/.f64 -1/2 x)
(-.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(-.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 5))) (*.f64 1/2 (/.f64 1 x))))
(-.f64 (+.f64 (.f64 5/128 (/.f64 1 (pow.f64 x 7))) (.f64 1/8 (/.f64 1 (pow.f64 x 3)))) (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 5))) (.f64 1/2 (/.f64 1 x))))
1
(+.f64 1 (*.f64 1/2 (pow.f64 x 2)))
(-.f64 (+.f64 1 (.f64 1/2 (pow.f64 x 2))) (.f64 1/8 (pow.f64 x 4)))
(-.f64 (+.f64 1 (+.f64 (.f64 1/16 (pow.f64 x 6)) (.f64 1/2 (pow.f64 x 2)))) (*.f64 1/8 (pow.f64 x 4)))
x
(+.f64 (*.f64 1/2 (/.f64 1 x)) x)
(-.f64 (+.f64 (.f64 1/2 (/.f64 1 x)) x) (.f64 1/8 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 5))) (+.f64 (.f64 1/2 (/.f64 1 x)) x)) (*.f64 1/8 (/.f64 1 (pow.f64 x 3))))
(*.f64 -1 x)
(neg.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) x))
(-.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 1 x)) x))
(-.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 5))) (+.f64 (*.f64 1/2 (/.f64 1 x)) x)))

Outputs
x
(-.f64 x (*.f64 1/6 (pow.f64 x 3)))
(+.f64 x (*.f64 -1/6 (pow.f64 x 3)))
(+.f64 x (*.f64 (pow.f64 x 3) -1/6))
(fma.f64 (pow.f64 x 3) -1/6 x)
(-.f64 (+.f64 (.f64 3/40 (pow.f64 x 5)) x) (.f64 1/6 (pow.f64 x 3)))
(+.f64 (fma.f64 3/40 (pow.f64 x 5) x) (*.f64 -1/6 (pow.f64 x 3)))
(+.f64 (fma.f64 3/40 (pow.f64 x 5) x) (*.f64 (pow.f64 x 3) -1/6))
(fma.f64 (pow.f64 x 3) -1/6 (fma.f64 3/40 (pow.f64 x 5) x))
(fma.f64 3/40 (pow.f64 x 5) (fma.f64 (pow.f64 x 3) -1/6 x))
(-.f64 (+.f64 (.f64 3/40 (pow.f64 x 5)) x) (+.f64 (.f64 5/112 (pow.f64 x 7)) (*.f64 1/6 (pow.f64 x 3))))
(-.f64 (fma.f64 3/40 (pow.f64 x 5) x) (fma.f64 5/112 (pow.f64 x 7) (*.f64 1/6 (pow.f64 x 3))))
(-.f64 (fma.f64 3/40 (pow.f64 x 5) x) (fma.f64 1/6 (pow.f64 x 3) (*.f64 5/112 (pow.f64 x 7))))
(+.f64 x (fma.f64 3/40 (pow.f64 x 5) (fma.f64 (pow.f64 x 3) -1/6 (*.f64 (pow.f64 x 7) -5/112))))
(-.f64 (log.f64 2) (log.f64 (/.f64 1 x)))
(-.f64 (log.f64 2) (neg.f64 (log.f64 x)))
(+.f64 (log.f64 2) (log.f64 x))
(-.f64 (+.f64 (log.f64 2) (*.f64 1/4 (/.f64 1 (pow.f64 x 2)))) (log.f64 (/.f64 1 x)))
(-.f64 (+.f64 (log.f64 2) (/.f64 1/4 (*.f64 x x))) (neg.f64 (log.f64 x)))
(+.f64 (log.f64 2) (+.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 x)))
(-.f64 (+.f64 (log.f64 2) (.f64 1/4 (/.f64 1 (pow.f64 x 2)))) (+.f64 (.f64 3/32 (/.f64 1 (pow.f64 x 4))) (log.f64 (/.f64 1 x))))
(+.f64 (log.f64 2) (-.f64 (/.f64 1/4 (*.f64 x x)) (+.f64 (neg.f64 (log.f64 x)) (/.f64 3/32 (pow.f64 x 4)))))
(+.f64 (log.f64 2) (-.f64 (/.f64 1/4 (*.f64 x x)) (-.f64 (/.f64 3/32 (pow.f64 x 4)) (log.f64 x))))
(+.f64 (log.f64 2) (+.f64 (/.f64 1/4 (*.f64 x x)) (-.f64 (log.f64 x) (/.f64 3/32 (pow.f64 x 4)))))
(-.f64 (+.f64 (.f64 5/96 (/.f64 1 (pow.f64 x 6))) (+.f64 (log.f64 2) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))) (+.f64 (*.f64 3/32 (/.f64 1 (pow.f64 x 4))) (log.f64 (/.f64 1 x))))
(-.f64 (+.f64 (+.f64 (log.f64 2) (/.f64 1/4 (*.f64 x x))) (/.f64 5/96 (pow.f64 x 6))) (+.f64 (neg.f64 (log.f64 x)) (/.f64 3/32 (pow.f64 x 4))))
(+.f64 (+.f64 (log.f64 2) (/.f64 5/96 (pow.f64 x 6))) (-.f64 (/.f64 1/4 (*.f64 x x)) (-.f64 (/.f64 3/32 (pow.f64 x 4)) (log.f64 x))))
(+.f64 (log.f64 2) (+.f64 (/.f64 1/4 (*.f64 x x)) (+.f64 (/.f64 5/96 (pow.f64 x 6)) (-.f64 (log.f64 x) (/.f64 3/32 (pow.f64 x 4))))))
(+.f64 (log.f64 2) (+.f64 (/.f64 5/96 (pow.f64 x 6)) (+.f64 (/.f64 1/4 (*.f64 x x)) (-.f64 (log.f64 x) (/.f64 3/32 (pow.f64 x 4))))))
(+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2))
(-.f64 (+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2)) (*.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(+.f64 (log.f64 (/.f64 -1 x)) (-.f64 (log.f64 1/2) (/.f64 1/4 (*.f64 x x))))
(+.f64 (log.f64 (/.f64 -1 x)) (+.f64 (log.f64 1/2) (/.f64 -1/4 (*.f64 x x))))
(-.f64 (+.f64 (.f64 3/32 (/.f64 1 (pow.f64 x 4))) (+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2))) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(+.f64 (/.f64 3/32 (pow.f64 x 4)) (+.f64 (log.f64 (/.f64 -1 x)) (-.f64 (log.f64 1/2) (/.f64 1/4 (*.f64 x x)))))
(+.f64 (+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2)) (-.f64 (/.f64 3/32 (pow.f64 x 4)) (/.f64 1/4 (*.f64 x x))))
(+.f64 (log.f64 (/.f64 -1 x)) (-.f64 (+.f64 (/.f64 3/32 (pow.f64 x 4)) (log.f64 1/2)) (/.f64 1/4 (*.f64 x x))))
(+.f64 (log.f64 (/.f64 -1 x)) (+.f64 (+.f64 (/.f64 3/32 (pow.f64 x 4)) (log.f64 1/2)) (/.f64 -1/4 (*.f64 x x))))
(-.f64 (+.f64 (.f64 3/32 (/.f64 1 (pow.f64 x 4))) (+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2))) (+.f64 (.f64 5/96 (/.f64 1 (pow.f64 x 6))) (*.f64 1/4 (/.f64 1 (pow.f64 x 2)))))
(+.f64 (/.f64 3/32 (pow.f64 x 4)) (-.f64 (+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2)) (+.f64 (/.f64 1/4 (*.f64 x x)) (/.f64 5/96 (pow.f64 x 6)))))
(+.f64 (log.f64 (/.f64 -1 x)) (-.f64 (+.f64 (/.f64 3/32 (pow.f64 x 4)) (log.f64 1/2)) (+.f64 (/.f64 1/4 (*.f64 x x)) (/.f64 5/96 (pow.f64 x 6)))))
(+.f64 (/.f64 3/32 (pow.f64 x 4)) (+.f64 (log.f64 (/.f64 -1 x)) (+.f64 (log.f64 1/2) (+.f64 (/.f64 -1/4 (*.f64 x x)) (/.f64 -5/96 (pow.f64 x 6))))))
1
(+.f64 1 x)
(+.f64 x 1)
(+.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 2)) x))
(+.f64 1 (fma.f64 1/2 (*.f64 x x) x))
(+.f64 x (fma.f64 (*.f64 x x) 1/2 1))
(+.f64 1 (fma.f64 (*.f64 x x) 1/2 x))
(-.f64 (+.f64 1 (+.f64 (.f64 1/2 (pow.f64 x 2)) x)) (.f64 1/8 (pow.f64 x 4)))
(+.f64 1 (-.f64 (fma.f64 1/2 (.f64 x x) x) (.f64 (pow.f64 x 4) 1/8)))
(+.f64 1 (+.f64 (fma.f64 (.f64 x x) 1/2 x) (.f64 (pow.f64 x 4) -1/8)))
(+.f64 x (fma.f64 (pow.f64 x 4) -1/8 (fma.f64 (*.f64 x x) 1/2 1)))
(-.f64 (fma.f64 (*.f64 x x) 1/2 x) (fma.f64 (pow.f64 x 4) 1/8 -1))
(*.f64 2 x)
(*.f64 x 2)
(+.f64 (.f64 1/2 (/.f64 1 x)) (.f64 2 x))
(+.f64 (*.f64 x 2) (/.f64 1/2 x))
(fma.f64 x 2 (/.f64 1/2 x))
(-.f64 (+.f64 (.f64 1/2 (/.f64 1 x)) (.f64 2 x)) (*.f64 1/8 (/.f64 1 (pow.f64 x 3))))
(+.f64 (/.f64 1/2 x) (-.f64 (*.f64 x 2) (/.f64 1/8 (pow.f64 x 3))))
(+.f64 (fma.f64 x 2 (/.f64 1/2 x)) (/.f64 -1/8 (pow.f64 x 3)))
(-.f64 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 5))) (+.f64 (.f64 1/2 (/.f64 1 x)) (.f64 2 x))) (.f64 1/8 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 (+.f64 (*.f64 x 2) (/.f64 1/2 x)) (/.f64 1/16 (pow.f64 x 5))) (/.f64 1/8 (pow.f64 x 3)))
(+.f64 (fma.f64 x 2 (/.f64 1/2 x)) (-.f64 (/.f64 1/16 (pow.f64 x 5)) (/.f64 1/8 (pow.f64 x 3))))
(+.f64 (+.f64 (/.f64 1/2 x) (fma.f64 x 2 (/.f64 1/16 (pow.f64 x 5)))) (/.f64 -1/8 (pow.f64 x 3)))
(+.f64 (/.f64 1/2 x) (-.f64 (fma.f64 x 2 (/.f64 1/16 (pow.f64 x 5))) (/.f64 1/8 (pow.f64 x 3))))
(/.f64 -1/2 x)
(-.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(-.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x))
(+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x))
(-.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 5))) (*.f64 1/2 (/.f64 1 x))))
(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))
(+.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/16 (pow.f64 x 5))) (/.f64 -1/2 x))
(+.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 -1/2 x) (/.f64 -1/16 (pow.f64 x 5))))
(-.f64 (+.f64 (.f64 5/128 (/.f64 1 (pow.f64 x 7))) (.f64 1/8 (/.f64 1 (pow.f64 x 3)))) (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 5))) (.f64 1/2 (/.f64 1 x))))
(+.f64 (/.f64 5/128 (pow.f64 x 7)) (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
(+.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (-.f64 (/.f64 5/128 (pow.f64 x 7)) (/.f64 1/16 (pow.f64 x 5)))) (/.f64 -1/2 x))
(+.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 5/128 (pow.f64 x 7)) (+.f64 (/.f64 -1/2 x) (/.f64 -1/16 (pow.f64 x 5)))))
(+.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (-.f64 (/.f64 5/128 (pow.f64 x 7)) (/.f64 1/16 (pow.f64 x 5))) (/.f64 -1/2 x)))
1
(+.f64 1 (*.f64 1/2 (pow.f64 x 2)))
(+.f64 1 (.f64 (.f64 x x) 1/2))
(fma.f64 (*.f64 x x) 1/2 1)
(-.f64 (+.f64 1 (.f64 1/2 (pow.f64 x 2))) (.f64 1/8 (pow.f64 x 4)))
(+.f64 1 (-.f64 (.f64 (.f64 x x) 1/2) (*.f64 (pow.f64 x 4) 1/8)))
(+.f64 (fma.f64 (.f64 x x) 1/2 1) (.f64 (pow.f64 x 4) -1/8))
(fma.f64 (pow.f64 x 4) -1/8 (fma.f64 (*.f64 x x) 1/2 1))
(-.f64 (+.f64 1 (+.f64 (.f64 1/16 (pow.f64 x 6)) (.f64 1/2 (pow.f64 x 2)))) (*.f64 1/8 (pow.f64 x 4)))
(+.f64 1 (-.f64 (fma.f64 1/16 (pow.f64 x 6) (.f64 (.f64 x x) 1/2)) (*.f64 (pow.f64 x 4) 1/8)))
(+.f64 (fma.f64 (.f64 x x) 1/2 (.f64 (pow.f64 x 6) 1/16)) (-.f64 1 (*.f64 (pow.f64 x 4) 1/8)))
(fma.f64 (pow.f64 x 4) -1/8 (fma.f64 x (*.f64 x 1/2) (fma.f64 (pow.f64 x 6) 1/16 1)))
(fma.f64 (pow.f64 x 4) -1/8 (fma.f64 (pow.f64 x 6) 1/16 (fma.f64 (*.f64 x x) 1/2 1)))
x
(+.f64 (*.f64 1/2 (/.f64 1 x)) x)
(+.f64 x (/.f64 1/2 x))
(-.f64 (+.f64 (.f64 1/2 (/.f64 1 x)) x) (.f64 1/8 (/.f64 1 (pow.f64 x 3))))
(+.f64 (/.f64 1/2 x) (-.f64 x (/.f64 1/8 (pow.f64 x 3))))
(+.f64 x (-.f64 (/.f64 1/2 x) (/.f64 1/8 (pow.f64 x 3))))
(+.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 -1/8 (pow.f64 x 3)))
(-.f64 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 5))) (+.f64 (.f64 1/2 (/.f64 1 x)) x)) (*.f64 1/8 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 (/.f64 1/16 (pow.f64 x 5)) (+.f64 x (/.f64 1/2 x))) (/.f64 1/8 (pow.f64 x 3)))
(+.f64 (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))) (+.f64 x (/.f64 -1/8 (pow.f64 x 3))))
(+.f64 (+.f64 (/.f64 1/2 x) (+.f64 x (/.f64 1/16 (pow.f64 x 5)))) (/.f64 -1/8 (pow.f64 x 3)))
(+.f64 (/.f64 1/2 x) (-.f64 (+.f64 x (/.f64 1/16 (pow.f64 x 5))) (/.f64 1/8 (pow.f64 x 3))))
(*.f64 -1 x)
(neg.f64 x)
(neg.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) x))
(neg.f64 (+.f64 x (/.f64 1/2 x)))
(-.f64 (/.f64 -1/2 x) x)
(-.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 1 x)) x))
(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 x (/.f64 1/2 x)))
(+.f64 (/.f64 1/8 (pow.f64 x 3)) (-.f64 (/.f64 -1/2 x) x))
(-.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 5))) (+.f64 (*.f64 1/2 (/.f64 1 x)) x)))
(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/16 (pow.f64 x 5)) (+.f64 x (/.f64 1/2 x))))
(+.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/16 (pow.f64 x 5))) (-.f64 (/.f64 -1/2 x) x))
(+.f64 (/.f64 1/8 (pow.f64 x 3)) (-.f64 (+.f64 (/.f64 -1/2 x) (/.f64 -1/16 (pow.f64 x 5))) x))
(+.f64 (/.f64 1/8 (pow.f64 x 3)) (-.f64 (/.f64 -1/2 x) (+.f64 x (/.f64 1/16 (pow.f64 x 5)))))

prune60.0ms (1.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	137	2	139
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	137	3	140

Error

Counts

140 → 3

Alt Table

Status	Error	Program
▶	29.6b	(fma.f64 (pow.f64 x 3) -1/6 x)
✓	48.8b	(log.f64 (+.f64 x (hypot.f64 1 x)))
	46.3b	(log.f64 (/.f64 -1/2 x))

Compiler

Compiled 1852 to 1401 computations (24.4% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (pow.f64 x 3) -1/6 x)

series3.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
2.0ms	x	@	0	(fma.f64 (pow.f64 x 3) -1/6 x)
1.0ms	x	@	-inf	(fma.f64 (pow.f64 x 3) -1/6 x)
1.0ms	x	@	inf	(fma.f64 (pow.f64 x 3) -1/6 x)

rewrite28.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

522×	`pow1_binary64`
493×	`add-log-exp_binary64`
493×	`log1p-expm1-u_binary64`
493×	`expm1-log1p-u_binary64`
483×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	130	8
2	1342	8

Stop Event

1×	node limit

Counts

1 → 21

Calls

Call 1

Inputs
(fma.f64 (pow.f64 x 3) -1/6 x)

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

Outputs

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

simplify28.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

1047×	`fma-def_binary64`
818×	`unswap-sqr_binary64`
241×	`associate-l_binary64`
194×	`fma-neg_binary64`
174×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	105
1	23	105
2	61	87
3	194	87
4	429	87
5	1190	87
6	2374	87
7	3266	87

Stop Event

1×	node limit

Counts

33 → 26

Calls

Call 1

Inputs
x
(-.f64 x (*.f64 1/6 (pow.f64 x 3)))
(-.f64 x (*.f64 1/6 (pow.f64 x 3)))
(-.f64 x (*.f64 1/6 (pow.f64 x 3)))
(*.f64 -1/6 (pow.f64 x 3))
(-.f64 x (*.f64 1/6 (pow.f64 x 3)))
(-.f64 x (*.f64 1/6 (pow.f64 x 3)))
(-.f64 x (*.f64 1/6 (pow.f64 x 3)))
(*.f64 -1/6 (pow.f64 x 3))
(-.f64 x (*.f64 1/6 (pow.f64 x 3)))
(-.f64 x (*.f64 1/6 (pow.f64 x 3)))
(-.f64 x (*.f64 1/6 (pow.f64 x 3)))

Outputs
x
(-.f64 x (*.f64 1/6 (pow.f64 x 3)))
(+.f64 x (*.f64 (pow.f64 x 3) -1/6))
(fma.f64 (pow.f64 x 3) -1/6 x)
(-.f64 x (*.f64 1/6 (pow.f64 x 3)))
(+.f64 x (*.f64 (pow.f64 x 3) -1/6))
(fma.f64 (pow.f64 x 3) -1/6 x)
(-.f64 x (*.f64 1/6 (pow.f64 x 3)))
(+.f64 x (*.f64 (pow.f64 x 3) -1/6))
(fma.f64 (pow.f64 x 3) -1/6 x)
(*.f64 -1/6 (pow.f64 x 3))
(*.f64 (pow.f64 x 3) -1/6)
(-.f64 x (*.f64 1/6 (pow.f64 x 3)))
(+.f64 x (*.f64 (pow.f64 x 3) -1/6))
(fma.f64 (pow.f64 x 3) -1/6 x)
(-.f64 x (*.f64 1/6 (pow.f64 x 3)))
(+.f64 x (*.f64 (pow.f64 x 3) -1/6))
(fma.f64 (pow.f64 x 3) -1/6 x)
(-.f64 x (*.f64 1/6 (pow.f64 x 3)))
(+.f64 x (*.f64 (pow.f64 x 3) -1/6))
(fma.f64 (pow.f64 x 3) -1/6 x)
(*.f64 -1/6 (pow.f64 x 3))
(*.f64 (pow.f64 x 3) -1/6)
(-.f64 x (*.f64 1/6 (pow.f64 x 3)))
(+.f64 x (*.f64 (pow.f64 x 3) -1/6))
(fma.f64 (pow.f64 x 3) -1/6 x)
(-.f64 x (*.f64 1/6 (pow.f64 x 3)))
(+.f64 x (*.f64 (pow.f64 x 3) -1/6))
(fma.f64 (pow.f64 x 3) -1/6 x)
(-.f64 x (*.f64 1/6 (pow.f64 x 3)))
(+.f64 x (*.f64 (pow.f64 x 3) -1/6))
(fma.f64 (pow.f64 x 3) -1/6 x)

prune11.0ms (0.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	26	0	26
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	26	3	29

Error

Counts

29 → 3

Alt Table

Status	Error	Program
✓	29.6b	(fma.f64 (pow.f64 x 3) -1/6 x)
✓	48.8b	(log.f64 (+.f64 x (hypot.f64 1 x)))
▶	46.3b	(log.f64 (/.f64 -1/2 x))

Compiler

Compiled 291 to 219 computations (24.7% saved)

localize3.0ms (0.1%)

prune1.0ms (0%)

Pruning

3 alts after pruning (0 fresh and 3 done)

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

Error

Counts

3 → 3

Alt Table

Status	Error	Program
✓	29.6b	(fma.f64 (pow.f64 x 3) -1/6 x)
✓	48.8b	(log.f64 (+.f64 x (hypot.f64 1 x)))
✓	46.3b	(log.f64 (/.f64 -1/2 x))

Compiler

Compiled 19 to 14 computations (26.3% saved)

regimes41.0ms (1%)

Accuracy

Total 0.3b remaining (82.4%)

Threshold costs 0.3b (82.4%)

Counts

10 → 3

Compiler

Compiled 75 to 53 computations (29.3% saved)

bsearch41.0ms (1%)

Algorithm

2×	binary-search

Calls

2 calls:

23.0ms	x
18.0ms	x

Steps

Iters	Point		Range
1.25	∈ [	2.570748069662957e-5	,	287812918.615438	]
-1.25	∈ [	-163613986247.7313	,	-1.8685778706959397e-14	]

Compiler

Compiled 2 to 1 computations (50% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	32
1	20	32

Stop Event

1×

saturated

Calls

Call 1

Inputs
(if (<=.f64 x -5/4) (log.f64 (/.f64 -1/2 x)) (if (<=.f64 x 5/4) (fma.f64 (pow.f64 x 3) -1/6 x) (log.f64 (*.f64 x 2))))

Outputs
(if (<=.f64 x -5/4) (log.f64 (/.f64 -1/2 x)) (if (<=.f64 x 5/4) (fma.f64 (pow.f64 x 3) -1/6 x) (log.f64 (*.f64 x 2))))

end83.0ms (2.1%)

Stop Event

1×

done

Compiler

Compiled 65 to 48 computations (26.2% saved)

Details

analyze386.0ms (9.8%)

sample3.1s (79.6%)

preprocess17.0ms (0.4%)

simplify6.0ms (0.1%)

prune3.0ms (0.1%)

localize4.0ms (0.1%)

series7.0ms (0.2%)

rewrite41.0ms (1%)

simplify37.0ms (0.9%)

prune60.0ms (1.5%)

localize3.0ms (0.1%)

series3.0ms (0.1%)

rewrite28.0ms (0.7%)

simplify28.0ms (0.7%)

prune11.0ms (0.3%)

localize3.0ms (0.1%)

prune1.0ms (0%)

regimes41.0ms (1%)

bsearch41.0ms (1%)

simplify2.0ms (0.1%)

end83.0ms (2.1%)

Profiling