Details

analyze4.0ms (0.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0.1%	14

Compiler

Compiled 10 to 5 computations (50% saved)

sample700.0ms (54.3%)

Results

687.0ms

8256×

body

128

valid

preprocess13.0ms (1%)

Algorithm

2×	egg-herbie

Rules

2×	`*-commutative_binary64`
2×	`associate-r_binary64`
2×	`count-2_binary64`
1×	`associate-l_binary64`
1×	`distribute-rgt-out_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	4
1	11	4
2	14	4
3	17	4
0	1	1

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0

Outputs
0

Call 2

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

Outputs
(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
(hypot.f64 x x)

Compiler

Compiled 9 to 4 computations (55.6% saved)

simplify6.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
2×	`associate-r_binary64`
2×	`count-2_binary64`
1×	`associate-l_binary64`
1×	`distribute-rgt-out_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	4
1	11	4
2	14	4
3	17	4

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

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

Outputs
(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
(hypot.f64 x x)

prune3.0ms (0.3%)

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

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(hypot.f64 x x)

Compiler

Compiled 20 to 9 computations (55% saved)

localize2.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(hypot.f64 x x)

series3.0ms (0.2%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(hypot.f64 x x)
1.0ms	x	@	inf	(hypot.f64 x x)
1.0ms	x	@	0	(hypot.f64 x x)

rewrite42.0ms (3.3%)

Algorithm

1×	batch-egg-rewrite

Rules

271×	`pow1_binary64`
260×	`add-sqr-sqrt_binary64`
255×	`*-un-lft-identity_binary64`
249×	`add-log-exp_binary64`
249×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	4
1	60	4
2	695	4

Stop Event

1×	node limit

Counts

1 → 20

Calls

Call 1

Inputs
(hypot.f64 x x)

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

Outputs

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

simplify11.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

38×	`fma-def_binary64`
9×	`sub-neg_binary64`
6×	`+-commutative_binary64`
4×	`*-commutative_binary64`
4×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	80
1	12	80
2	25	80
3	29	80
4	33	80
5	51	80
6	73	80
7	84	80
8	96	80
9	121	80

Stop Event

1×

saturated

Counts

32 → 23

Calls

Call 1

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

Outputs
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))

prune15.0ms (1.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	18	5	23
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	18	6	24

Error

0.0b

Counts

24 → 6

Alt Table

Status	Error	Program
▶	0.5b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
	28.5b	(*.f64 (sqrt.f64 2) (neg.f64 x))
	34.3b	(*.f64 (sqrt.f64 2) x)
	5.8b	(exp.f64 (log.f64 (hypot.f64 x x)))
✓	0.1b	(hypot.f64 x x)
	1.4b	(pow.f64 (cbrt.f64 (hypot.f64 x x)) 3)

Compiler

Compiled 236 to 115 computations (51.3% saved)

localize4.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (hypot.f64 x x))
	0.1b	(hypot.f64 x x)
✓	0.5b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))

series3.0ms (0.2%)

Counts

2 → 12

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(sqrt.f64 (hypot.f64 x x))
1.0ms	x	@	inf	(sqrt.f64 (hypot.f64 x x))
1.0ms	x	@	-inf	(sqrt.f64 (hypot.f64 x x))
0.0ms	x	@	0	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
0.0ms	x	@	inf	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))

rewrite29.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

352×	`pow1_binary64`
327×	`add-log-exp_binary64`
327×	`log1p-expm1-u_binary64`
327×	`expm1-log1p-u_binary64`
317×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	10
1	101	10
2	962	10

Stop Event

1×	node limit

Counts

2 → 35

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
(sqrt.f64 (hypot.f64 x x))

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

Outputs

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

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

simplify11.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

38×	`fma-def_binary64`
9×	`sub-neg_binary64`
6×	`+-commutative_binary64`
4×	`*-commutative_binary64`
4×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	80
1	12	80
2	25	80
3	29	80
4	33	80
5	51	80
6	73	80
7	84	80
8	96	80
9	121	80

Stop Event

1×

saturated

Counts

47 → 38

Calls

Call 1

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

Outputs
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))

prune49.0ms (3.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	102	3	105
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	102	9	111

Error

0.0b

Counts

111 → 9

Alt Table

Status	Error	Program
▶	0.6b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 2))
✓	0.5b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
	22.0b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (cbrt.f64 (pow.f64 (hypot.f64 x x) 3/2)))
	1.4b	(pow.f64 (cbrt.f64 (hypot.f64 x x)) 3)
	28.5b	(*.f64 (sqrt.f64 2) (neg.f64 x))
	34.3b	(*.f64 (sqrt.f64 2) x)
	0.9b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))))
	5.8b	(exp.f64 (log.f64 (hypot.f64 x x)))
✓	0.1b	(hypot.f64 x x)

Compiler

Compiled 1371 to 481 computations (64.9% saved)

localize8.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(sqrt.f64 (hypot.f64 x x))
	0.1b	(hypot.f64 x x)
✓	0.5b	(pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 2)
✓	0.5b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 2))

series44.0ms (3.5%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
27.0ms	x	@	0	(pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 2)
9.0ms	x	@	-inf	(pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 2)
7.0ms	x	@	inf	(pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 2)
0.0ms	x	@	0	(*.f64 (sqrt.f64 (hypot.f64 x x)) (pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 2))
0.0ms	x	@	-inf	(*.f64 (sqrt.f64 (hypot.f64 x x)) (pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 2))

rewrite36.0ms (2.8%)

Algorithm

1×	batch-egg-rewrite

Rules

558×	`pow1_binary64`
521×	`add-log-exp_binary64`
521×	`log1p-expm1-u_binary64`
521×	`expm1-log1p-u_binary64`
507×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	10
1	194	10
2	1583	10

Stop Event

1×	node limit

Counts

2 → 34

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 (hypot.f64 x x)) (pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 2))
(pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 2)

Outputs

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

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

simplify25.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

578×	`associate-l_binary64`
506×	`unswap-sqr_binary64`
497×	`associate-r_binary64`
271×	`fma-def_binary64`
102×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	29	312
1	81	308
2	193	272
3	459	188
4	1409	184

Stop Event

1×	node limit

Counts

58 → 42

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x)))) 2)
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x)))) 2)
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x)))) 2)
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x)))) 2)
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 (sqrt.f64 2))))) 2)
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 (sqrt.f64 2))))) 2)
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 (sqrt.f64 2))))) 2)
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 (sqrt.f64 2))))) 2)
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 (sqrt.f64 2))))) 2)
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 (sqrt.f64 2))))) 2)
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 (sqrt.f64 2))))) 2)
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 (sqrt.f64 2))))) 2)

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

prune58.0ms (4.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	108	1	109
Fresh	1	5	6
Picked	1	0	1
Done	0	2	2
Total	110	8	118

Error

0.0b

Counts

118 → 8

Alt Table

Status	Error	Program
▶	0.9b	(pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 4)
	28.5b	(*.f64 (sqrt.f64 2) (neg.f64 x))
✓	0.5b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
	34.3b	(*.f64 (sqrt.f64 2) x)
	0.9b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))))
	5.8b	(exp.f64 (log.f64 (hypot.f64 x x)))
✓	0.1b	(hypot.f64 x x)
	22.0b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (cbrt.f64 (pow.f64 (hypot.f64 x x) 3/2)))

Compiler

Compiled 1658 to 781 computations (52.9% saved)

localize6.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(pow.f64 (hypot.f64 x x) 1/4)
	0.1b	(hypot.f64 x x)
✓	0.9b	(pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 4)

series4.0ms (0.3%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(pow.f64 (hypot.f64 x x) 1/4)
1.0ms	x	@	0	(pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 4)
1.0ms	x	@	inf	(pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 4)
1.0ms	x	@	-inf	(pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 4)
0.0ms	x	@	-inf	(pow.f64 (hypot.f64 x x) 1/4)

rewrite32.0ms (2.5%)

Algorithm

1×	batch-egg-rewrite

Rules

510×	`pow1_binary64`
478×	`add-log-exp_binary64`
478×	`log1p-expm1-u_binary64`
478×	`expm1-log1p-u_binary64`
466×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	156	11
2	1420	11

Stop Event

1×	node limit

Counts

2 → 30

Calls

Call 1

Inputs
(pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 4)
(pow.f64 (hypot.f64 x x) 1/4)

Outputs

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

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

simplify36.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

322×	`fma-neg_binary64`
284×	`prod-exp_binary64`
219×	`div-sub_binary64`
192×	`*-commutative_binary64`
189×	`fma-def_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	28	428
1	72	420
2	162	348
3	371	240
4	1243	204
5	3481	204

Stop Event

1×	node limit

Counts

54 → 40

Calls

Call 1

Inputs
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x)))) 4)
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x)))) 4)
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x)))) 4)
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x)))) 4)
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 (sqrt.f64 2))))) 4)
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 (sqrt.f64 2))))) 4)
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 (sqrt.f64 2))))) 4)
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 (sqrt.f64 2))))) 4)
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 (sqrt.f64 2))))) 4)
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 (sqrt.f64 2))))) 4)
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 (sqrt.f64 2))))) 4)
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 (sqrt.f64 2))))) 4)
(exp.f64 (*.f64 1/4 (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x))))
(exp.f64 (*.f64 1/4 (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x))))
(exp.f64 (*.f64 1/4 (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x))))
(exp.f64 (*.f64 1/4 (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x))))
(exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 (sqrt.f64 2)))))
(exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 (sqrt.f64 2)))))
(exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 (sqrt.f64 2)))))
(exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 (sqrt.f64 2)))))
(exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 (sqrt.f64 2)))))
(exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 (sqrt.f64 2)))))
(exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 (sqrt.f64 2)))))
(exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 (sqrt.f64 2)))))

Outputs
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x)))) 4)
(pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x))) 4)
(pow.f64 (*.f64 (pow.f64 (sqrt.f64 2) 1/4) (pow.f64 x 1/4)) 4)
(pow.f64 (*.f64 (sqrt.f64 2) x) 1)
(*.f64 (sqrt.f64 2) x)
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x)))) 4)
(pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x))) 4)
(pow.f64 (*.f64 (pow.f64 (sqrt.f64 2) 1/4) (pow.f64 x 1/4)) 4)
(pow.f64 (*.f64 (sqrt.f64 2) x) 1)
(*.f64 (sqrt.f64 2) x)
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x)))) 4)
(pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x))) 4)
(pow.f64 (*.f64 (pow.f64 (sqrt.f64 2) 1/4) (pow.f64 x 1/4)) 4)
(pow.f64 (*.f64 (sqrt.f64 2) x) 1)
(*.f64 (sqrt.f64 2) x)
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x)))) 4)
(pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x))) 4)
(pow.f64 (*.f64 (pow.f64 (sqrt.f64 2) 1/4) (pow.f64 x 1/4)) 4)
(pow.f64 (*.f64 (sqrt.f64 2) x) 1)
(*.f64 (sqrt.f64 2) x)
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 (sqrt.f64 2))))) 4)
(pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x))) 4)
(pow.f64 (*.f64 (pow.f64 (sqrt.f64 2) 1/4) (pow.f64 x 1/4)) 4)
(pow.f64 (*.f64 (sqrt.f64 2) x) 1)
(*.f64 (sqrt.f64 2) x)
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 (sqrt.f64 2))))) 4)
(pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x))) 4)
(pow.f64 (*.f64 (pow.f64 (sqrt.f64 2) 1/4) (pow.f64 x 1/4)) 4)
(pow.f64 (*.f64 (sqrt.f64 2) x) 1)
(*.f64 (sqrt.f64 2) x)
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 (sqrt.f64 2))))) 4)
(pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x))) 4)
(pow.f64 (*.f64 (pow.f64 (sqrt.f64 2) 1/4) (pow.f64 x 1/4)) 4)
(pow.f64 (*.f64 (sqrt.f64 2) x) 1)
(*.f64 (sqrt.f64 2) x)
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 (sqrt.f64 2))))) 4)
(pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x))) 4)
(pow.f64 (*.f64 (pow.f64 (sqrt.f64 2) 1/4) (pow.f64 x 1/4)) 4)
(pow.f64 (*.f64 (sqrt.f64 2) x) 1)
(*.f64 (sqrt.f64 2) x)
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 (sqrt.f64 2))))) 4)
(pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 (sqrt.f64 2)))) 4)
(pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 (sqrt.f64 2)) (log.f64 (/.f64 -1 x)))) 4)
(pow.f64 (*.f64 (pow.f64 (sqrt.f64 2) 1/4) (pow.f64 (/.f64 -1 x) -1/4)) 4)
(pow.f64 (/.f64 (sqrt.f64 2) (/.f64 -1 x)) 1)
(.f64 -1 (.f64 (sqrt.f64 2) x))
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 (sqrt.f64 2))))) 4)
(pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 (sqrt.f64 2)))) 4)
(pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 (sqrt.f64 2)) (log.f64 (/.f64 -1 x)))) 4)
(pow.f64 (*.f64 (pow.f64 (sqrt.f64 2) 1/4) (pow.f64 (/.f64 -1 x) -1/4)) 4)
(pow.f64 (/.f64 (sqrt.f64 2) (/.f64 -1 x)) 1)
(.f64 -1 (.f64 (sqrt.f64 2) x))
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 (sqrt.f64 2))))) 4)
(pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 (sqrt.f64 2)))) 4)
(pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 (sqrt.f64 2)) (log.f64 (/.f64 -1 x)))) 4)
(pow.f64 (*.f64 (pow.f64 (sqrt.f64 2) 1/4) (pow.f64 (/.f64 -1 x) -1/4)) 4)
(pow.f64 (/.f64 (sqrt.f64 2) (/.f64 -1 x)) 1)
(.f64 -1 (.f64 (sqrt.f64 2) x))
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 (sqrt.f64 2))))) 4)
(pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 (sqrt.f64 2)))) 4)
(pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 (sqrt.f64 2)) (log.f64 (/.f64 -1 x)))) 4)
(pow.f64 (*.f64 (pow.f64 (sqrt.f64 2) 1/4) (pow.f64 (/.f64 -1 x) -1/4)) 4)
(pow.f64 (/.f64 (sqrt.f64 2) (/.f64 -1 x)) 1)
(.f64 -1 (.f64 (sqrt.f64 2) x))
(exp.f64 (*.f64 1/4 (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x)))
(*.f64 (pow.f64 (sqrt.f64 2) 1/4) (pow.f64 x 1/4))
(pow.f64 (*.f64 (sqrt.f64 2) x) 1/4)
(exp.f64 (*.f64 1/4 (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x)))
(*.f64 (pow.f64 (sqrt.f64 2) 1/4) (pow.f64 x 1/4))
(pow.f64 (*.f64 (sqrt.f64 2) x) 1/4)
(exp.f64 (*.f64 1/4 (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x)))
(*.f64 (pow.f64 (sqrt.f64 2) 1/4) (pow.f64 x 1/4))
(pow.f64 (*.f64 (sqrt.f64 2) x) 1/4)
(exp.f64 (*.f64 1/4 (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x)))
(*.f64 (pow.f64 (sqrt.f64 2) 1/4) (pow.f64 x 1/4))
(pow.f64 (*.f64 (sqrt.f64 2) x) 1/4)
(exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 (sqrt.f64 2)))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x)))
(*.f64 (pow.f64 (sqrt.f64 2) 1/4) (pow.f64 x 1/4))
(pow.f64 (*.f64 (sqrt.f64 2) x) 1/4)
(exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 (sqrt.f64 2)))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x)))
(*.f64 (pow.f64 (sqrt.f64 2) 1/4) (pow.f64 x 1/4))
(pow.f64 (*.f64 (sqrt.f64 2) x) 1/4)
(exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 (sqrt.f64 2)))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x)))
(*.f64 (pow.f64 (sqrt.f64 2) 1/4) (pow.f64 x 1/4))
(pow.f64 (*.f64 (sqrt.f64 2) x) 1/4)
(exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 (sqrt.f64 2)))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x)))
(*.f64 (pow.f64 (sqrt.f64 2) 1/4) (pow.f64 x 1/4))
(pow.f64 (*.f64 (sqrt.f64 2) x) 1/4)
(exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 (sqrt.f64 2)))))
(pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 (sqrt.f64 2))))
(pow.f64 (exp.f64 1/4) (-.f64 (log.f64 (sqrt.f64 2)) (log.f64 (/.f64 -1 x))))
(*.f64 (pow.f64 (sqrt.f64 2) 1/4) (pow.f64 (/.f64 -1 x) -1/4))
(pow.f64 (/.f64 (sqrt.f64 2) (/.f64 -1 x)) 1/4)
(pow.f64 (.f64 -1 (.f64 (sqrt.f64 2) x)) 1/4)
(exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 (sqrt.f64 2)))))
(pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 (sqrt.f64 2))))
(pow.f64 (exp.f64 1/4) (-.f64 (log.f64 (sqrt.f64 2)) (log.f64 (/.f64 -1 x))))
(*.f64 (pow.f64 (sqrt.f64 2) 1/4) (pow.f64 (/.f64 -1 x) -1/4))
(pow.f64 (/.f64 (sqrt.f64 2) (/.f64 -1 x)) 1/4)
(pow.f64 (.f64 -1 (.f64 (sqrt.f64 2) x)) 1/4)
(exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 (sqrt.f64 2)))))
(pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 (sqrt.f64 2))))
(pow.f64 (exp.f64 1/4) (-.f64 (log.f64 (sqrt.f64 2)) (log.f64 (/.f64 -1 x))))
(*.f64 (pow.f64 (sqrt.f64 2) 1/4) (pow.f64 (/.f64 -1 x) -1/4))
(pow.f64 (/.f64 (sqrt.f64 2) (/.f64 -1 x)) 1/4)
(pow.f64 (.f64 -1 (.f64 (sqrt.f64 2) x)) 1/4)
(exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 (sqrt.f64 2)))))
(pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 (sqrt.f64 2))))
(pow.f64 (exp.f64 1/4) (-.f64 (log.f64 (sqrt.f64 2)) (log.f64 (/.f64 -1 x))))
(*.f64 (pow.f64 (sqrt.f64 2) 1/4) (pow.f64 (/.f64 -1 x) -1/4))
(pow.f64 (/.f64 (sqrt.f64 2) (/.f64 -1 x)) 1/4)
(pow.f64 (.f64 -1 (.f64 (sqrt.f64 2) x)) 1/4)

prune30.0ms (2.3%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	62	1	63
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	62	9	71

Error

0.0b

Counts

71 → 9

Alt Table

Status	Error	Program
✓	0.9b	(pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 4)
	28.5b	(*.f64 (sqrt.f64 2) (neg.f64 x))
✓	0.5b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
	1.4b	(*.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 1/8) 4) (pow.f64 (pow.f64 (hypot.f64 x x) 1/8) 4))
	34.3b	(*.f64 (sqrt.f64 2) x)
	0.9b	(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))))
	5.8b	(exp.f64 (log.f64 (hypot.f64 x x)))
✓	0.1b	(hypot.f64 x x)
	22.0b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (cbrt.f64 (pow.f64 (hypot.f64 x x) 3/2)))

Compiler

Compiled 729 to 445 computations (39% saved)

regimes37.0ms (2.9%)

Accuracy

Total -62.4b remaining (-51127.8%)

Threshold costs -62.4b (-51127.8%)

Counts

19 → 1

Compiler

Compiled 200 to 82 computations (59% saved)

simplify1.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	4

Stop Event

1×

saturated

Calls

Call 1

Inputs
(hypot.f64 x x)

Outputs
(hypot.f64 x x)

end77.0ms (6%)

Stop Event

1×

fuel

Compiler

Compiled 82 to 36 computations (56.1% saved)

Details

analyze4.0ms (0.3%)

sample700.0ms (54.3%)

preprocess13.0ms (1%)

simplify6.0ms (0.5%)

prune3.0ms (0.3%)

localize2.0ms (0.1%)

series3.0ms (0.2%)

rewrite42.0ms (3.3%)

simplify11.0ms (0.8%)

prune15.0ms (1.2%)

localize4.0ms (0.3%)

series3.0ms (0.2%)

rewrite29.0ms (2.3%)

simplify11.0ms (0.8%)

prune49.0ms (3.8%)

localize8.0ms (0.6%)

series44.0ms (3.5%)

rewrite36.0ms (2.8%)

simplify25.0ms (1.9%)

prune58.0ms (4.5%)

localize6.0ms (0.4%)

series4.0ms (0.3%)

rewrite32.0ms (2.5%)

simplify36.0ms (2.8%)

prune30.0ms (2.3%)

regimes37.0ms (2.9%)

simplify1.0ms (0.1%)

end77.0ms (6%)

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