Details

analyze3.0ms (0.1%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
0%	0%	100%	0%	0%	0%	0%	2
50%	50%	50%	0%	0%	0%	0%	3
75%	75%	25%	0%	0%	0%	0%	4
87.5%	87.5%	12.5%	0%	0%	0%	0%	5
93.8%	93.7%	6.2%	0%	0%	0%	0%	6
96.9%	96.8%	3.1%	0%	0%	0%	0%	7
98.4%	98.4%	1.6%	0%	0%	0%	0%	8
99.2%	99.2%	0.8%	0%	0%	0%	0%	9
99.6%	99.6%	0.4%	0%	0%	0%	0%	10
99.8%	99.8%	0.2%	0%	0%	0%	0%	11
99.9%	99.9%	0.1%	0%	0%	0%	0%	12

Compiler

Compiled 8 to 6 computations (25% saved)

sample740.0ms (32.9%)

Results

731.0ms	8256×	body	256	valid
0.0ms	2×	body	256	infinite

Bogosity

preprocess4.0ms (0.2%)

Algorithm

2×	egg-herbie

Rules

6×	`*-commutative`
2×	`associate-l`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	12	17
2	13	17
0	1	1

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0

Outputs
0

Call 2

Inputs
(sqrt.f64 (.f64 (.f64 2 x) x))

Outputs
(sqrt.f64 (.f64 (.f64 2 x) x))
(sqrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 8 to 6 computations (25% saved)

simplify46.0ms (2%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative`
2×	`associate-l`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	12	17
2	13	17

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

Inputs
(sqrt.f64 (.f64 (.f64 2 x) x))

Outputs
(sqrt.f64 (.f64 (.f64 2 x) x))
(sqrt.f64 (.f64 2 (.f64 x x)))

eval0.0ms (0%)

Compiler: Compiled 13 to 9 computations (30.8% saved)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

29.8b

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	29.8b	(sqrt.f64 (.f64 (.f64 2 x) x))

Compiler

Compiled 7 to 5 computations (28.6% saved)

localize7.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	28.8b	(sqrt.f64 (.f64 (.f64 2 x) x))

Compiler

Compiled 17 to 11 computations (35.3% saved)

series1.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

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

rewrite49.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

1420×	`add-sqr-sqrt`
1402×	`*-un-lft-identity`
1302×	`add-cube-cbrt`
1286×	`add-cbrt-cube`
1272×	`add-exp-log`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	159	11
2	1814	11

Stop Event

1×	node limit

Counts

1 → 26

Calls

Call 1

Inputs
(sqrt.f64 (.f64 (.f64 2 x) x))

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

Outputs

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

simplify54.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

1274×	`associate-r`
1020×	`associate-l`
906×	`*-commutative`
682×	`log-prod`
570×	`associate-/l*`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	62	538
1	145	526
2	645	518
3	3236	478
4	7263	478

Stop Event

1×	node limit

Counts

38 → 32

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

eval6.0ms (0.3%)

Compiler: Compiled 267 to 198 computations (25.8% saved)

prune5.0ms (0.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	28	4	32
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	28	5	33

Error

0.2b

Counts

33 → 5

Alt Table

Click to see full alt table

Status	Error	Program
▶	31.8b	(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 2)
▶	31.7b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
▶	31.9b	(*.f64 (sqrt.f64 2) (neg.f64 x))
▶	30.9b	(*.f64 (sqrt.f64 2) x)
✓	29.8b	(sqrt.f64 (.f64 (.f64 2 x) x))

Compiler

Compiled 34 to 27 computations (20.6% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.4b	(*.f64 (sqrt.f64 2) x)

Compiler

Compiled 9 to 7 computations (22.2% saved)

series1.0ms (0%)

Counts

1 → 0

Calls

3 calls:

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

rewrite120.0ms (5.3%)

Algorithm

1×	batch-egg-rewrite

Rules

1198×	`add-sqr-sqrt`
1182×	`*-un-lft-identity`
1118×	`pow1`
1096×	`add-cube-cbrt`
1082×	`add-cbrt-cube`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	137	11
2	1511	11

Stop Event

1×	node limit

Counts

1 → 11

Calls

Call 1

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

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

Outputs

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

simplify61.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

1066×	`*-commutative`
886×	`log-prod`
738×	`associate--l+`
678×	`distribute-lft-out`
632×	`distribute-lft-in`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	32	253
1	79	187
2	273	121
3	1642	121
4	4568	121
5	6886	121

Stop Event

1×	node limit

Counts

11 → 14

Calls

Call 1

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

Outputs
(-.f64 (+.f64 1 (*.f64 (sqrt.f64 2) x)) 1)
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(pow.f64 (*.f64 (sqrt.f64 2) x) 1)
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 2)
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 3)
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(pow.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3) 1/3)
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(sqrt.f64 (.f64 2 (.f64 x x)))
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(log.f64 (pow.f64 (exp.f64 x) (sqrt.f64 2)))
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3))
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 2) x)))
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(exp.f64 (log.f64 (*.f64 (sqrt.f64 2) x)))
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 2) x)))
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.4b	(*.f64 (sqrt.f64 2) (neg.f64 x))

Compiler

Compiled 12 to 8 computations (33.3% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(*.f64 (sqrt.f64 2) (neg.f64 x))
0.0ms	x	@	inf	(*.f64 (sqrt.f64 2) (neg.f64 x))
0.0ms	x	@	-inf	(*.f64 (sqrt.f64 2) (neg.f64 x))

rewrite59.0ms (2.6%)

Algorithm

1×	batch-egg-rewrite

Rules

1266×	`add-sqr-sqrt`
1248×	`*-un-lft-identity`
1162×	`add-cube-cbrt`
1148×	`add-cbrt-cube`
1134×	`add-exp-log`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	162	11
2	1917	11

Stop Event

1×	node limit

Counts

1 → 13

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 2) (neg.f64 x))

Outputs

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

simplify67.0ms (3%)

Algorithm

1×	egg-herbie

Rules

1082×	`*-commutative`
878×	`log-prod`
650×	`distribute-lft-in`
648×	`distribute-rgt-in`
646×	`distribute-lft-out`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	37	463
1	90	397
2	331	331
3	1789	331
4	4954	331
5	7952	331

Stop Event

1×	node limit

Counts

25 → 19

Calls

Call 1

Inputs
(.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))
(.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))
(.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))
(-.f64 0 (*.f64 (sqrt.f64 2) x))
(-.f64 (+.f64 1 (*.f64 (sqrt.f64 2) x)) 1)
(pow.f64 (*.f64 (sqrt.f64 2) x) 1)
(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 2)
(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 3)
(pow.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3) 1/3)
(neg.f64 (*.f64 (sqrt.f64 2) x))
(sqrt.f64 (.f64 2 (.f64 x x)))
(log.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))
(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3))
(expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 2) x)))
(exp.f64 (log.f64 (*.f64 (sqrt.f64 2) x)))
(log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 2) x)))

Outputs
(.f64 -1 (.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(*.f64 x (neg.f64 (sqrt.f64 2)))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(*.f64 x (neg.f64 (sqrt.f64 2)))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(*.f64 x (neg.f64 (sqrt.f64 2)))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(*.f64 x (neg.f64 (sqrt.f64 2)))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(*.f64 x (neg.f64 (sqrt.f64 2)))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(*.f64 x (neg.f64 (sqrt.f64 2)))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(*.f64 x (neg.f64 (sqrt.f64 2)))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(*.f64 x (neg.f64 (sqrt.f64 2)))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(*.f64 x (neg.f64 (sqrt.f64 2)))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(*.f64 x (neg.f64 (sqrt.f64 2)))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(*.f64 x (neg.f64 (sqrt.f64 2)))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(*.f64 x (neg.f64 (sqrt.f64 2)))
(-.f64 0 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(*.f64 x (neg.f64 (sqrt.f64 2)))
(-.f64 (+.f64 1 (*.f64 (sqrt.f64 2) x)) 1)
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(pow.f64 (*.f64 (sqrt.f64 2) x) 1)
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 2)
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 3)
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(pow.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3) 1/3)
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(*.f64 x (neg.f64 (sqrt.f64 2)))
(sqrt.f64 (.f64 2 (.f64 x x)))
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(log.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3))
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 2) x)))
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(exp.f64 (log.f64 (*.f64 (sqrt.f64 2) x)))
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 2) x)))
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)

localize8.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))

Compiler

Compiled 19 to 12 computations (36.8% saved)

series2.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

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

rewrite54.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

1556×	`add-sqr-sqrt`
1542×	`*-un-lft-identity`
1430×	`add-cube-cbrt`
1410×	`add-cbrt-cube`
1396×	`add-exp-log`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	178	11
2	2019	11

Stop Event

1×	node limit

Counts

1 → 13

Calls

Call 1

Inputs
(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))

Outputs

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

simplify63.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

908×	`*-commutative`
860×	`log-prod`
848×	`associate-*r/`
618×	`associate--l+`
592×	`associate-*l/`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	331
1	97	331
2	342	331
3	1801	331
4	4297	331
5	6385	331

Stop Event

1×	node limit

Counts

25 → 18

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

localize9.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (*.f64 (sqrt.f64 2) x))
✓	0.2b	(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 2)
	0.4b	(*.f64 (sqrt.f64 2) x)

Compiler

Compiled 21 to 17 computations (19% saved)

series5.0ms (0.2%)

Counts

2 → 0

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 2)
1.0ms	x	@	0	(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 2)
1.0ms	x	@	inf	(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 2)
1.0ms	x	@	inf	(sqrt.f64 (*.f64 (sqrt.f64 2) x))
0.0ms	x	@	-inf	(sqrt.f64 (*.f64 (sqrt.f64 2) x))

rewrite84.0ms (3.8%)

Algorithm

1×	batch-egg-rewrite

Rules

1346×	`add-sqr-sqrt`
1328×	`*-un-lft-identity`
1232×	`add-cube-cbrt`
1218×	`add-cbrt-cube`
1206×	`add-exp-log`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	26
1	180	26
2	1765	26

Stop Event

1×	node limit

Counts

2 → 50

Calls

Call 1

Inputs
(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 2)
(sqrt.f64 (*.f64 (sqrt.f64 2) x))

Outputs

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

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

simplify60.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

952×	`distribute-lft-in`
914×	`distribute-rgt-in`
852×	`associate-+r+`
770×	`associate-+l+`
746×	`fma-def`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	107	1324
1	216	1102
2	838	880
3	2458	878
4	7035	878

Stop Event

1×	node limit

Counts

50 → 65

Calls

Call 1

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

Outputs
(-.f64 (+.f64 1 (*.f64 (sqrt.f64 2) x)) 1)
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 x (sqrt.f64 2))
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(.f64 (.f64 (sqrt.f64 2) x) 1)
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(.f64 (sqrt.f64 (.f64 (sqrt.f64 2) x)) (sqrt.f64 (*.f64 (sqrt.f64 2) x)))
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(.f64 1 (.f64 (sqrt.f64 2) x))
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(.f64 (pow.f64 (.f64 (sqrt.f64 2) x) 1/4) (.f64 (pow.f64 (.f64 (sqrt.f64 2) x) 1/4) (sqrt.f64 (*.f64 (sqrt.f64 2) x))))
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(.f64 (pow.f64 2 1/4) (.f64 (sqrt.f64 x) (sqrt.f64 (*.f64 (sqrt.f64 2) x))))
(.f64 (pow.f64 2 1/4) (.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) (sqrt.f64 x)))
(.f64 (sqrt.f64 (.f64 (sqrt.f64 2) x)) (*.f64 (pow.f64 2 1/4) (sqrt.f64 x)))
(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (sqrt.f64 2)))
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(.f64 (cbrt.f64 2) (.f64 (cbrt.f64 (sqrt.f64 2)) x))
(.f64 (cbrt.f64 2) (.f64 x (cbrt.f64 (sqrt.f64 2))))
(.f64 x (.f64 (cbrt.f64 2) (cbrt.f64 (sqrt.f64 2))))
(.f64 (cbrt.f64 (sqrt.f64 2)) (.f64 x (cbrt.f64 2)))
(.f64 (cbrt.f64 (.f64 x x)) (*.f64 (cbrt.f64 x) (sqrt.f64 2)))
(.f64 (cbrt.f64 (.f64 x x)) (*.f64 (sqrt.f64 2) (cbrt.f64 x)))
(.f64 (sqrt.f64 2) (.f64 (cbrt.f64 (*.f64 x x)) (cbrt.f64 x)))
(.f64 (cbrt.f64 (.f64 (sqrt.f64 2) x)) (cbrt.f64 (.f64 2 (.f64 x x))))
(.f64 (cbrt.f64 (.f64 x (.f64 2 x))) (cbrt.f64 (.f64 (sqrt.f64 2) x)))
(.f64 (cbrt.f64 (.f64 (sqrt.f64 2) x)) (.f64 (cbrt.f64 (sqrt.f64 (.f64 (sqrt.f64 2) x))) (sqrt.f64 (*.f64 (sqrt.f64 2) x))))
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(.f64 (cbrt.f64 (.f64 2 (.f64 x x))) (cbrt.f64 (.f64 (sqrt.f64 2) x)))
(.f64 (cbrt.f64 (.f64 (sqrt.f64 2) x)) (cbrt.f64 (.f64 2 (.f64 x x))))
(.f64 (cbrt.f64 (.f64 x (.f64 2 x))) (cbrt.f64 (.f64 (sqrt.f64 2) x)))
(.f64 (.f64 (sqrt.f64 (.f64 (sqrt.f64 2) x)) (pow.f64 (.f64 (sqrt.f64 2) x) 1/4)) (pow.f64 (*.f64 (sqrt.f64 2) x) 1/4))
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(.f64 (.f64 (sqrt.f64 2) (sqrt.f64 x)) (sqrt.f64 x))
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(.f64 (.f64 (sqrt.f64 2) (cbrt.f64 (*.f64 x x))) (cbrt.f64 x))
(.f64 (cbrt.f64 (.f64 x x)) (*.f64 (sqrt.f64 2) (cbrt.f64 x)))
(.f64 (sqrt.f64 2) (.f64 (cbrt.f64 (*.f64 x x)) (cbrt.f64 x)))
(.f64 (.f64 x (pow.f64 2 1/4)) (pow.f64 2 1/4))
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(.f64 (.f64 x (cbrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))
(.f64 (cbrt.f64 2) (.f64 x (cbrt.f64 (sqrt.f64 2))))
(.f64 x (.f64 (cbrt.f64 2) (cbrt.f64 (sqrt.f64 2))))
(.f64 (cbrt.f64 (sqrt.f64 2)) (.f64 x (cbrt.f64 2)))
(.f64 (.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) (pow.f64 2 1/4)) (sqrt.f64 x))
(.f64 (pow.f64 2 1/4) (.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) (sqrt.f64 x)))
(.f64 (sqrt.f64 (.f64 (sqrt.f64 2) x)) (*.f64 (pow.f64 2 1/4) (sqrt.f64 x)))
(.f64 (.f64 (sqrt.f64 (.f64 (sqrt.f64 2) x)) (cbrt.f64 (.f64 (sqrt.f64 2) x))) (cbrt.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x))))
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(sqrt.f64 (.f64 2 (.f64 x x)))
(fabs.f64 (*.f64 (sqrt.f64 2) x))
(log.f64 (pow.f64 (exp.f64 x) (sqrt.f64 2)))
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3))
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 2) x)))
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(exp.f64 (log.f64 (*.f64 (sqrt.f64 2) x)))
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 2) x)))
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(-.f64 (+.f64 1 (sqrt.f64 (*.f64 (sqrt.f64 2) x))) 1)
(+.f64 1 (-.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 1))
(+.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 0)
(sqrt.f64 (*.f64 (sqrt.f64 2) x))
(.f64 (sqrt.f64 (.f64 (sqrt.f64 2) x)) 1)
(+.f64 1 (-.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 1))
(+.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 0)
(sqrt.f64 (*.f64 (sqrt.f64 2) x))
(.f64 1 (sqrt.f64 (.f64 (sqrt.f64 2) x)))
(+.f64 1 (-.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 1))
(+.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 0)
(sqrt.f64 (*.f64 (sqrt.f64 2) x))
(.f64 (pow.f64 (.f64 (sqrt.f64 2) x) 1/4) (pow.f64 (*.f64 (sqrt.f64 2) x) 1/4))
(+.f64 1 (-.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 1))
(+.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 0)
(sqrt.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (pow.f64 2 1/4) (sqrt.f64 x))
(*.f64 (sqrt.f64 x) (pow.f64 2 1/4))
(*.f64 (pow.f64 2 1/4) (sqrt.f64 x))
(.f64 (cbrt.f64 (sqrt.f64 (.f64 (sqrt.f64 2) x))) (cbrt.f64 (*.f64 (sqrt.f64 2) x)))
(+.f64 1 (-.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 1))
(+.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 0)
(sqrt.f64 (*.f64 (sqrt.f64 2) x))
(.f64 (cbrt.f64 (.f64 (sqrt.f64 2) x)) (cbrt.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x))))
(+.f64 1 (-.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 1))
(+.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 0)
(sqrt.f64 (*.f64 (sqrt.f64 2) x))
(.f64 (sqrt.f64 (cbrt.f64 (.f64 2 (.f64 x x)))) (sqrt.f64 (cbrt.f64 (.f64 (sqrt.f64 2) x))))
(.f64 (sqrt.f64 (cbrt.f64 (.f64 x (.f64 2 x)))) (sqrt.f64 (cbrt.f64 (.f64 (sqrt.f64 2) x))))
(.f64 (pow.f64 1 1/2) (sqrt.f64 (.f64 (sqrt.f64 2) x)))
(+.f64 1 (-.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 1))
(+.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 0)
(sqrt.f64 (*.f64 (sqrt.f64 2) x))
(.f64 (pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 1/2) (pow.f64 (cbrt.f64 (.f64 (sqrt.f64 2) x)) 1/2))
(.f64 (sqrt.f64 (cbrt.f64 (.f64 2 (.f64 x x)))) (sqrt.f64 (cbrt.f64 (.f64 (sqrt.f64 2) x))))
(.f64 (sqrt.f64 (cbrt.f64 (.f64 x (.f64 2 x)))) (sqrt.f64 (cbrt.f64 (.f64 (sqrt.f64 2) x))))
(pow.f64 (*.f64 (sqrt.f64 2) x) 1/2)
(+.f64 1 (-.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 1))
(+.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 0)
(sqrt.f64 (*.f64 (sqrt.f64 2) x))
(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 1)
(+.f64 1 (-.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 1))
(+.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 0)
(sqrt.f64 (*.f64 (sqrt.f64 2) x))
(pow.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 1/4) 2)
(+.f64 1 (-.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 1))
(+.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 0)
(sqrt.f64 (*.f64 (sqrt.f64 2) x))
(pow.f64 (cbrt.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x))) 3)
(+.f64 1 (-.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 1))
(+.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 0)
(sqrt.f64 (*.f64 (sqrt.f64 2) x))
(pow.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3/2) 1/3)
(+.f64 1 (-.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 1))
(+.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 0)
(sqrt.f64 (*.f64 (sqrt.f64 2) x))
(fabs.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)))
(+.f64 1 (-.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 1))
(+.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 0)
(sqrt.f64 (*.f64 (sqrt.f64 2) x))
(log.f64 (exp.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x))))
(+.f64 1 (-.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 1))
(+.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 0)
(sqrt.f64 (*.f64 (sqrt.f64 2) x))
(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3/2))
(+.f64 1 (-.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 1))
(+.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 0)
(sqrt.f64 (*.f64 (sqrt.f64 2) x))
(expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x))))
(+.f64 1 (-.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 1))
(+.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 0)
(sqrt.f64 (*.f64 (sqrt.f64 2) x))
(exp.f64 (log.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x))))
(+.f64 1 (-.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 1))
(+.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 0)
(sqrt.f64 (*.f64 (sqrt.f64 2) x))
(log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x))))
(+.f64 1 (-.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 1))
(+.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 0)
(sqrt.f64 (*.f64 (sqrt.f64 2) x))

eval28.0ms (1.2%)

Compiler: Compiled 1111 to 907 computations (18.4% saved)

prune12.0ms (0.6%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	129	1	130
Fresh	0	0	0
Picked	1	0	1
Done	0	4	4
Total	130	5	135

Error

0.1b

Counts

135 → 5

Alt Table

Click to see full alt table

Status	Error	Program
▶	30.9b	(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))
✓	31.7b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
✓	31.9b	(*.f64 (sqrt.f64 2) (neg.f64 x))
✓	30.9b	(*.f64 (sqrt.f64 2) x)
✓	29.8b	(sqrt.f64 (.f64 (.f64 2 x) x))

Compiler

Compiled 36 to 29 computations (19.4% saved)

localize10.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (pow.f64 2 1/4) x)
✓	0.3b	(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))

Compiler

Compiled 21 to 18 computations (14.3% saved)

series33.0ms (1.5%)

Counts

2 → 12

Calls

6 calls:

Time	Variable		Point	Expression
31.0ms	x	@	0	(*.f64 (pow.f64 2 1/4) x)
1.0ms	x	@	inf	(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))
0.0ms	x	@	-inf	(*.f64 (pow.f64 2 1/4) x)
0.0ms	x	@	inf	(*.f64 (pow.f64 2 1/4) x)
0.0ms	x	@	-inf	(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))

rewrite55.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

1434×	`add-sqr-sqrt`
1414×	`*-un-lft-identity`
1324×	`add-cube-cbrt`
1304×	`add-cbrt-cube`
1286×	`add-exp-log`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	38
1	168	24
2	1899	24

Stop Event

1×	node limit

Counts

2 → 24

Calls

Call 1

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

Outputs

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

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

simplify57.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

1686×	`log-prod`
1240×	`associate-r`
1078×	`associate-l`
990×	`fma-def`
876×	`associate-+r+`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	64	566
1	151	500
2	574	434
3	3510	432

Stop Event

1×	node limit

Counts

36 → 31

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 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(-.f64 (+.f64 1 (*.f64 x (sqrt.f64 2))) 1)
(pow.f64 (*.f64 x (sqrt.f64 2)) 1)
(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)
(pow.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3) 1/3)
(sqrt.f64 (.f64 2 (.f64 x x)))
(log.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))
(cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3))
(expm1.f64 (log1p.f64 (*.f64 x (sqrt.f64 2))))
(exp.f64 (log.f64 (*.f64 x (sqrt.f64 2))))
(exp.f64 (.f64 (log.f64 (.f64 x (sqrt.f64 2))) 1))
(log1p.f64 (expm1.f64 (*.f64 x (sqrt.f64 2))))
(-.f64 (+.f64 1 (*.f64 (pow.f64 2 1/4) x)) 1)
(pow.f64 (*.f64 (pow.f64 2 1/4) x) 1)
(pow.f64 (*.f64 (pow.f64 2 1/8) (sqrt.f64 x)) 2)
(pow.f64 (cbrt.f64 (*.f64 (pow.f64 2 1/4) x)) 3)
(pow.f64 (pow.f64 (*.f64 (pow.f64 2 1/4) x) 3) 1/3)
(sqrt.f64 (.f64 x (.f64 x (sqrt.f64 2))))
(log.f64 (pow.f64 (exp.f64 (pow.f64 2 1/4)) x))
(cbrt.f64 (pow.f64 (*.f64 (pow.f64 2 1/4) x) 3))
(expm1.f64 (log1p.f64 (*.f64 (pow.f64 2 1/4) x)))
(exp.f64 (log.f64 (*.f64 (pow.f64 2 1/4) x)))
(exp.f64 (.f64 (log.f64 (.f64 (pow.f64 2 1/4) x)) 1))
(log1p.f64 (expm1.f64 (*.f64 (pow.f64 2 1/4) 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 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(-.f64 (+.f64 1 (*.f64 x (sqrt.f64 2))) 1)
(*.f64 (sqrt.f64 2) x)
(pow.f64 (*.f64 x (sqrt.f64 2)) 1)
(*.f64 (sqrt.f64 2) x)
(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
(*.f64 (sqrt.f64 2) x)
(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)
(*.f64 (sqrt.f64 2) x)
(pow.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3) 1/3)
(*.f64 (sqrt.f64 2) x)
(sqrt.f64 (.f64 2 (.f64 x x)))
(fabs.f64 (*.f64 (sqrt.f64 2) x))
(log.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))
(*.f64 (sqrt.f64 2) x)
(cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3))
(*.f64 (sqrt.f64 2) x)
(expm1.f64 (log1p.f64 (*.f64 x (sqrt.f64 2))))
(*.f64 (sqrt.f64 2) x)
(exp.f64 (log.f64 (*.f64 x (sqrt.f64 2))))
(*.f64 (sqrt.f64 2) x)
(exp.f64 (.f64 (log.f64 (.f64 x (sqrt.f64 2))) 1))
(*.f64 (sqrt.f64 2) x)
(log1p.f64 (expm1.f64 (*.f64 x (sqrt.f64 2))))
(*.f64 (sqrt.f64 2) x)
(-.f64 (+.f64 1 (*.f64 (pow.f64 2 1/4) x)) 1)
(+.f64 1 (-.f64 (*.f64 x (pow.f64 2 1/4)) 1))
(+.f64 (*.f64 x (pow.f64 2 1/4)) 0)
(*.f64 x (pow.f64 2 1/4))
(pow.f64 (*.f64 (pow.f64 2 1/4) x) 1)
(+.f64 1 (-.f64 (*.f64 x (pow.f64 2 1/4)) 1))
(+.f64 (*.f64 x (pow.f64 2 1/4)) 0)
(*.f64 x (pow.f64 2 1/4))
(pow.f64 (*.f64 (pow.f64 2 1/8) (sqrt.f64 x)) 2)
(+.f64 1 (-.f64 (*.f64 x (pow.f64 2 1/4)) 1))
(+.f64 (*.f64 x (pow.f64 2 1/4)) 0)
(*.f64 x (pow.f64 2 1/4))
(pow.f64 (cbrt.f64 (*.f64 (pow.f64 2 1/4) x)) 3)
(+.f64 1 (-.f64 (*.f64 x (pow.f64 2 1/4)) 1))
(+.f64 (*.f64 x (pow.f64 2 1/4)) 0)
(*.f64 x (pow.f64 2 1/4))
(pow.f64 (pow.f64 (*.f64 (pow.f64 2 1/4) x) 3) 1/3)
(+.f64 1 (-.f64 (*.f64 x (pow.f64 2 1/4)) 1))
(+.f64 (*.f64 x (pow.f64 2 1/4)) 0)
(*.f64 x (pow.f64 2 1/4))
(sqrt.f64 (.f64 x (.f64 x (sqrt.f64 2))))
(sqrt.f64 (.f64 x (.f64 (sqrt.f64 2) x)))
(sqrt.f64 (.f64 (sqrt.f64 2) (.f64 x x)))
(log.f64 (pow.f64 (exp.f64 (pow.f64 2 1/4)) x))
(+.f64 1 (-.f64 (*.f64 x (pow.f64 2 1/4)) 1))
(+.f64 (*.f64 x (pow.f64 2 1/4)) 0)
(*.f64 x (pow.f64 2 1/4))
(cbrt.f64 (pow.f64 (*.f64 (pow.f64 2 1/4) x) 3))
(+.f64 1 (-.f64 (*.f64 x (pow.f64 2 1/4)) 1))
(+.f64 (*.f64 x (pow.f64 2 1/4)) 0)
(*.f64 x (pow.f64 2 1/4))
(expm1.f64 (log1p.f64 (*.f64 (pow.f64 2 1/4) x)))
(+.f64 1 (-.f64 (*.f64 x (pow.f64 2 1/4)) 1))
(+.f64 (*.f64 x (pow.f64 2 1/4)) 0)
(*.f64 x (pow.f64 2 1/4))
(exp.f64 (log.f64 (*.f64 (pow.f64 2 1/4) x)))
(+.f64 1 (-.f64 (*.f64 x (pow.f64 2 1/4)) 1))
(+.f64 (*.f64 x (pow.f64 2 1/4)) 0)
(*.f64 x (pow.f64 2 1/4))
(exp.f64 (.f64 (log.f64 (.f64 (pow.f64 2 1/4) x)) 1))
(+.f64 1 (-.f64 (*.f64 x (pow.f64 2 1/4)) 1))
(+.f64 (*.f64 x (pow.f64 2 1/4)) 0)
(*.f64 x (pow.f64 2 1/4))
(log1p.f64 (expm1.f64 (*.f64 (pow.f64 2 1/4) x)))
(+.f64 1 (-.f64 (*.f64 x (pow.f64 2 1/4)) 1))
(+.f64 (*.f64 x (pow.f64 2 1/4)) 0)
(*.f64 x (pow.f64 2 1/4))

eval7.0ms (0.3%)

Compiler: Compiled 287 to 251 computations (12.5% saved)

prune6.0ms (0.2%)

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	30	1	31
Fresh	0	0	0
Picked	0	1	1
Done	0	4	4
Total	30	6	36

Error

0.1b

Counts

36 → 6

Alt Table

Click to see full alt table

Status	Error	Program
✓	30.9b	(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))
▶	30.0b	(.f64 (pow.f64 2 1/4) (sqrt.f64 (.f64 (sqrt.f64 2) (*.f64 x x))))
✓	31.7b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
✓	31.9b	(*.f64 (sqrt.f64 2) (neg.f64 x))
✓	30.9b	(*.f64 (sqrt.f64 2) x)
✓	29.8b	(sqrt.f64 (.f64 (.f64 2 x) x))

Compiler

Compiled 48 to 39 computations (18.8% saved)

localize19.0ms (0.9%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (sqrt.f64 2) (.f64 x x))
✓	0.3b	(.f64 (pow.f64 2 1/4) (sqrt.f64 (.f64 (sqrt.f64 2) (*.f64 x x))))
✓	28.8b	(sqrt.f64 (.f64 (sqrt.f64 2) (.f64 x x)))

Compiler

Compiled 36 to 24 computations (33.3% saved)

series3.0ms (0.2%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(sqrt.f64 (.f64 (sqrt.f64 2) (.f64 x x)))
0.0ms	x	@	0	(.f64 (sqrt.f64 2) (.f64 x x))
0.0ms	x	@	0	(.f64 (pow.f64 2 1/4) (sqrt.f64 (.f64 (sqrt.f64 2) (*.f64 x x))))
0.0ms	x	@	inf	(sqrt.f64 (.f64 (sqrt.f64 2) (.f64 x x)))
0.0ms	x	@	inf	(.f64 (pow.f64 2 1/4) (sqrt.f64 (.f64 (sqrt.f64 2) (*.f64 x x))))

rewrite64.0ms (2.9%)

Algorithm

1×	batch-egg-rewrite

Rules

1962×	`add-sqr-sqrt`
1940×	`*-un-lft-identity`
1806×	`add-cube-cbrt`
1780×	`add-cbrt-cube`
220×	`pow1`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	71
1	243	41
2	2793	41

Stop Event

1×	node limit

Counts

3 → 54

Calls

Call 1

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

Outputs

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

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

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

simplify54.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

1596×	`associate-+r+`
1450×	`associate-+l+`
1036×	`unswap-sqr`
462×	`*-commutative`
428×	`distribute-lft-neg-in`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	122	1636
1	265	1636
2	1138	1632
3	4114	1632

Stop Event

1×	node limit

Counts

90 → 71

Calls

Call 1

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

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

eval20.0ms (0.9%)

Compiler: Compiled 796 to 711 computations (10.7% saved)

prune10.0ms (0.4%)

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	70	1	71
Fresh	0	0	0
Picked	1	0	1
Done	0	5	5
Total	71	6	77

Error

0.0b

Counts

77 → 6

Alt Table

Click to see full alt table

Status	Error	Program
✓	30.9b	(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))
	31.9b	(.f64 (pow.f64 2 1/4) (.f64 (sqrt.f64 (sqrt.f64 2)) (neg.f64 x)))
✓	31.7b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
✓	31.9b	(*.f64 (sqrt.f64 2) (neg.f64 x))
✓	30.9b	(*.f64 (sqrt.f64 2) x)
✓	29.8b	(sqrt.f64 (.f64 (.f64 2 x) x))

Compiler

Compiled 47 to 39 computations (17% saved)

regimes30.0ms (1.3%)

Counts

8 → 2

Calls

Call 1

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

Outputs
(.f64 (pow.f64 2 1/4) (.f64 (sqrt.f64 (sqrt.f64 2)) (neg.f64 x)))
(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))

Calls

3 calls:

10.0ms	(sqrt.f64 (.f64 (.f64 2 x) x))
9.0ms	x
9.0ms	(.f64 (.f64 2 x) x)

Results

Error	Segments	Branch
0.4b	2	`x`
13.2b	3	`(sqrt.f64 (.f64 (.f64 2 x) x))`
13.2b	3	`(.f64 (.f64 2 x) x)`

Compiler

Compiled 75 to 58 computations (22.7% saved)

bsearch14.0ms (0.6%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
14.0ms	-1.5135243257979747e-308	1.5858643378806048e-303

Results

12.0ms

144×

body

256

valid

Compiler

Compiled 200 to 170 computations (15% saved)

regimes28.0ms (1.2%)

Counts

6 → 2

Calls

Call 1

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

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

Calls

3 calls:

9.0ms	(sqrt.f64 (.f64 (.f64 2 x) x))
9.0ms	x
8.0ms	(.f64 (.f64 2 x) x)

Results

Error	Segments	Branch
0.4b	2	`x`
13.2b	3	`(sqrt.f64 (.f64 (.f64 2 x) x))`
13.2b	3	`(.f64 (.f64 2 x) x)`

Compiler

Compiled 54 to 41 computations (24.1% saved)

bsearch13.0ms (0.6%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
13.0ms	-1.5135243257979747e-308	1.5858643378806048e-303

Results

12.0ms

144×

body

256

valid

Compiler

Compiled 155 to 125 computations (19.4% saved)

regimes49.0ms (2.2%)

Accuracy

Total -62.0b remaining (-14173.5%)

Threshold costs -62.0b (-14173.5%)

Counts

3 → 2

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) (neg.f64 x))
(sqrt.f64 (.f64 (.f64 2 x) x))

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

Calls

3 calls:

36.0ms	(sqrt.f64 (.f64 (.f64 2 x) x))
7.0ms	(.f64 (.f64 2 x) x)
6.0ms	x

Results

Error	Segments	Branch
0.4b	2	`x`
13.3b	3	`(sqrt.f64 (.f64 (.f64 2 x) x))`
13.3b	3	`(.f64 (.f64 2 x) x)`

Compiler

Compiled 31 to 22 computations (29% saved)

bsearch14.0ms (0.6%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
14.0ms	-1.5135243257979747e-308	1.5858643378806048e-303

Results

12.0ms

144×

body

256

valid

Compiler

Compiled 128 to 107 computations (16.4% saved)

simplify9.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

32×	`*-commutative`
14×	`neg-mul-1`
14×	`+-commutative`
14×	`neg-sub0`
8×	`sub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	152
1	39	152
2	55	152
3	70	152
4	80	152
5	85	152
6	86	152

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(if (<=.f64 x -20240225330731/50600563326827654588123836679729326762389162441035529589225339506857584891998836722990095925359281123796769466079202977847452184346448369216753349985184627480379356069141590341116726935523304085309941919618186267140501870856173174654525838912289889085202514128089692388083353653807625633046581877161501565826926935273373696) (.f64 (pow.f64 2 1/4) (.f64 (sqrt.f64 (sqrt.f64 2)) (neg.f64 x))) (.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x)))
(if (<=.f64 x -20240225330731/50600563326827654588123836679729326762389162441035529589225339506857584891998836722990095925359281123796769466079202977847452184346448369216753349985184627480379356069141590341116726935523304085309941919618186267140501870856173174654525838912289889085202514128089692388083353653807625633046581877161501565826926935273373696) (.f64 (sqrt.f64 2) (neg.f64 x)) (.f64 (sqrt.f64 (*.f64 2 x)) (sqrt.f64 x)))
(if (<=.f64 x -20240225330731/50600563326827654588123836679729326762389162441035529589225339506857584891998836722990095925359281123796769466079202977847452184346448369216753349985184627480379356069141590341116726935523304085309941919618186267140501870856173174654525838912289889085202514128089692388083353653807625633046581877161501565826926935273373696) (.f64 (sqrt.f64 2) (neg.f64 x)) (.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) x)

Outputs
(if (<=.f64 x -20240225330731/50600563326827654588123836679729326762389162441035529589225339506857584891998836722990095925359281123796769466079202977847452184346448369216753349985184627480379356069141590341116726935523304085309941919618186267140501870856173174654525838912289889085202514128089692388083353653807625633046581877161501565826926935273373696) (.f64 (pow.f64 2 1/4) (.f64 (sqrt.f64 (sqrt.f64 2)) (neg.f64 x))) (.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x)))
(if (<=.f64 x -20240225330731/50600563326827654588123836679729326762389162441035529589225339506857584891998836722990095925359281123796769466079202977847452184346448369216753349985184627480379356069141590341116726935523304085309941919618186267140501870856173174654525838912289889085202514128089692388083353653807625633046581877161501565826926935273373696) (.f64 (pow.f64 2 1/4) (.f64 (sqrt.f64 (sqrt.f64 2)) (neg.f64 x))) (.f64 (sqrt.f64 (.f64 x 2)) (sqrt.f64 x)))
(if (<=.f64 x -20240225330731/50600563326827654588123836679729326762389162441035529589225339506857584891998836722990095925359281123796769466079202977847452184346448369216753349985184627480379356069141590341116726935523304085309941919618186267140501870856173174654525838912289889085202514128089692388083353653807625633046581877161501565826926935273373696) (.f64 (pow.f64 2 1/4) (.f64 x (neg.f64 (sqrt.f64 (sqrt.f64 2))))) (.f64 (sqrt.f64 (.f64 x 2)) (sqrt.f64 x)))
(if (<=.f64 x -20240225330731/50600563326827654588123836679729326762389162441035529589225339506857584891998836722990095925359281123796769466079202977847452184346448369216753349985184627480379356069141590341116726935523304085309941919618186267140501870856173174654525838912289889085202514128089692388083353653807625633046581877161501565826926935273373696) (.f64 (sqrt.f64 2) (neg.f64 x)) (.f64 (sqrt.f64 (*.f64 2 x)) (sqrt.f64 x)))
(if (<=.f64 x -20240225330731/50600563326827654588123836679729326762389162441035529589225339506857584891998836722990095925359281123796769466079202977847452184346448369216753349985184627480379356069141590341116726935523304085309941919618186267140501870856173174654525838912289889085202514128089692388083353653807625633046581877161501565826926935273373696) (.f64 (sqrt.f64 2) (neg.f64 x)) (.f64 (sqrt.f64 (*.f64 x 2)) (sqrt.f64 x)))
(if (<=.f64 x -20240225330731/50600563326827654588123836679729326762389162441035529589225339506857584891998836722990095925359281123796769466079202977847452184346448369216753349985184627480379356069141590341116726935523304085309941919618186267140501870856173174654525838912289889085202514128089692388083353653807625633046581877161501565826926935273373696) (.f64 x (neg.f64 (sqrt.f64 2))) (.f64 (sqrt.f64 (*.f64 x 2)) (sqrt.f64 x)))
(if (<=.f64 x -20240225330731/50600563326827654588123836679729326762389162441035529589225339506857584891998836722990095925359281123796769466079202977847452184346448369216753349985184627480379356069141590341116726935523304085309941919618186267140501870856173174654525838912289889085202514128089692388083353653807625633046581877161501565826926935273373696) (.f64 (sqrt.f64 2) (neg.f64 x)) (.f64 (sqrt.f64 2) x))
(if (<=.f64 x -20240225330731/50600563326827654588123836679729326762389162441035529589225339506857584891998836722990095925359281123796769466079202977847452184346448369216753349985184627480379356069141590341116726935523304085309941919618186267140501870856173174654525838912289889085202514128089692388083353653807625633046581877161501565826926935273373696) (.f64 (sqrt.f64 2) (neg.f64 x)) (.f64 x (sqrt.f64 2)))
(if (<=.f64 x -20240225330731/50600563326827654588123836679729326762389162441035529589225339506857584891998836722990095925359281123796769466079202977847452184346448369216753349985184627480379356069141590341116726935523304085309941919618186267140501870856173174654525838912289889085202514128089692388083353653807625633046581877161501565826926935273373696) (.f64 x (neg.f64 (sqrt.f64 2))) (.f64 x (sqrt.f64 2)))
(*.f64 (sqrt.f64 2) x)
(*.f64 x (sqrt.f64 2))

Compiler

Compiled 58 to 46 computations (20.7% saved)

soundness148.0ms (6.6%)

Algorithm

2×	egg-herbie

Rules

1686×	`log-prod`
1596×	`associate-+r+`
1450×	`associate-+l+`
1240×	`associate-r`
1078×	`associate-l`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	64	566
1	151	500
2	574	434
3	3510	432
0	122	1636
1	265	1636
2	1138	1632
3	4114	1632

Stop Event

1×	node limit
1×	node limit

Compiler

Compiled 66 to 56 computations (15.2% saved)

end40.0ms (1.8%)

Compiler: Compiled 55 to 42 computations (23.6% saved)

Details

analyze3.0ms (0.1%)

sample740.0ms (32.9%)

preprocess4.0ms (0.2%)

simplify46.0ms (2%)

eval0.0ms (0%)

prune1.0ms (0%)

localize7.0ms (0.3%)

series1.0ms (0.1%)

rewrite49.0ms (2.2%)

simplify54.0ms (2.4%)

eval6.0ms (0.3%)

prune5.0ms (0.2%)

localize4.0ms (0.2%)

series1.0ms (0%)

rewrite120.0ms (5.3%)

simplify61.0ms (2.7%)

localize5.0ms (0.2%)

series1.0ms (0%)

rewrite59.0ms (2.6%)

simplify67.0ms (3%)

localize8.0ms (0.3%)

series2.0ms (0.1%)

rewrite54.0ms (2.4%)

simplify63.0ms (2.8%)

localize9.0ms (0.4%)

series5.0ms (0.2%)

rewrite84.0ms (3.8%)

simplify60.0ms (2.7%)

eval28.0ms (1.2%)

prune12.0ms (0.6%)

localize10.0ms (0.4%)

series33.0ms (1.5%)

rewrite55.0ms (2.4%)

simplify57.0ms (2.5%)

eval7.0ms (0.3%)

prune6.0ms (0.2%)

localize19.0ms (0.9%)

series3.0ms (0.2%)

rewrite64.0ms (2.9%)

simplify54.0ms (2.4%)

eval20.0ms (0.9%)

prune10.0ms (0.4%)

regimes30.0ms (1.3%)

bsearch14.0ms (0.6%)

regimes28.0ms (1.2%)

bsearch13.0ms (0.6%)

regimes49.0ms (2.2%)

bsearch14.0ms (0.6%)

simplify9.0ms (0.4%)

soundness148.0ms (6.6%)

end40.0ms (1.8%)

Profiling