Details

analyze4.0ms (0.2%)

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)

sample871.0ms (36%)

Results

861.0ms	8256×	body	256	valid
0.0ms	4×	body	256	infinite

Bogosity

preprocess14.0ms (0.6%)

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)

simplify11.0ms (0.4%)

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)))

eval5.0ms (0.2%)

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

prune1.0ms (0.1%)

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

Accurracy

53.7%

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	53.7%	(sqrt.f64 (.f64 (.f64 2 x) x))

Compiler

Compiled 7 to 5 computations (28.6% saved)

localize7.0ms (0.3%)

Local Accuracy

Found 1 expressions with local accuracy:

New	Accuracy	Program
✓	55.5%	(sqrt.f64 (.f64 (.f64 2 x) x))

Compiler

Compiled 17 to 11 computations (35.3% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	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))

rewrite54.0ms (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
((-.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 (+.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))))

simplify57.0ms (2.3%)

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 (0.2%)

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

prune10.0ms (0.4%)

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

Accurracy

99.8%

Counts

33 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	47.6%	(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 2)
▶	47.8%	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
▶	52.6%	(*.f64 (sqrt.f64 2) (neg.f64 x))
▶	48.9%	(*.f64 (sqrt.f64 2) x)
✓	53.7%	(sqrt.f64 (.f64 (.f64 2 x) x))

Compiler

Compiled 34 to 27 computations (20.6% saved)

localize4.0ms (0.2%)

Local Accuracy

Found 1 expressions with local accuracy:

New	Accuracy	Program
✓	99.4%	(*.f64 (sqrt.f64 2) x)

Compiler

Compiled 9 to 7 computations (22.2% saved)

series0.0ms (0%)

Counts

1 → 0

Calls

3 calls:

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

rewrite46.0ms (1.9%)

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
((-.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) (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))))

simplify63.0ms (2.6%)

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)

localize6.0ms (0.2%)

Local Accuracy

Found 1 expressions with local accuracy:

New	Accuracy	Program
✓	99.4%	(*.f64 (sqrt.f64 2) (neg.f64 x))

Compiler

Compiled 12 to 8 computations (33.3% saved)

series0.0ms (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))

rewrite52.0ms (2.1%)

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

((-.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))))

simplify67.0ms (2.8%)

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 Accuracy

Found 1 expressions with local accuracy:

New	Accuracy	Program
✓	99.7%	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))

Compiler

Compiled 19 to 12 computations (36.8% saved)

series1.0ms (0%)

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 (2.2%)

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

((-.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))))

simplify67.0ms (2.7%)

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)

localize10.0ms (0.4%)

Local Accuracy

Found 3 expressions with local accuracy:

New	Accuracy	Program
✓	99.9%	(sqrt.f64 (*.f64 (sqrt.f64 2) x))
✓	99.6%	(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 2)
	99.4%	(*.f64 (sqrt.f64 2) x)

Compiler

Compiled 21 to 17 computations (19% saved)

series4.0ms (0.2%)

Counts

2 → 0

Calls

6 calls:

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

rewrite92.0ms (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

((-.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)))))

simplify63.0ms (2.6%)

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))

eval27.0ms (1.1%)

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

prune13.0ms (0.5%)

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

Accurracy

99.8%

Counts

135 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	48.8%	(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))
✓	47.8%	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
✓	52.6%	(*.f64 (sqrt.f64 2) (neg.f64 x))
✓	48.9%	(*.f64 (sqrt.f64 2) x)
✓	53.7%	(sqrt.f64 (.f64 (.f64 2 x) x))

Compiler

Compiled 36 to 29 computations (19.4% saved)

localize10.0ms (0.4%)

Local Accuracy

Found 2 expressions with local accuracy:

New	Accuracy	Program
✓	99.7%	(*.f64 (pow.f64 2 1/4) x)
✓	99.6%	(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))

Compiler

Compiled 21 to 18 computations (14.3% saved)

series52.0ms (2.1%)

Counts

2 → 12

Calls

6 calls:

Time	Variable		Point	Expression
50.0ms	x	@	0	(*.f64 (pow.f64 2 1/4) x)
0.0ms	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))

rewrite54.0ms (2.2%)

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

((-.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))))

simplify46.0ms (1.9%)

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))

eval8.0ms (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

Accurracy

99.8%

Counts

36 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	48.8%	(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))
▶	53.6%	(.f64 (pow.f64 2 1/4) (sqrt.f64 (.f64 (sqrt.f64 2) (*.f64 x x))))
✓	47.8%	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
✓	52.6%	(*.f64 (sqrt.f64 2) (neg.f64 x))
✓	48.9%	(*.f64 (sqrt.f64 2) x)
✓	53.7%	(sqrt.f64 (.f64 (.f64 2 x) x))

Compiler

Compiled 48 to 39 computations (18.8% saved)

localize21.0ms (0.9%)

Local Accuracy

Found 3 expressions with local accuracy:

New	Accuracy	Program
✓	99.6%	(.f64 (sqrt.f64 2) (.f64 x x))
✓	99.6%	(.f64 (pow.f64 2 1/4) (sqrt.f64 (.f64 (sqrt.f64 2) (*.f64 x x))))
✓	55.5%	(sqrt.f64 (.f64 (sqrt.f64 2) (.f64 x x)))

Compiler

Compiled 36 to 24 computations (33.3% saved)

series2.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

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

rewrite79.0ms (3.3%)

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

((-.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))))))

simplify56.0ms (2.3%)

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)))

eval66.0ms (2.7%)

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

prune11.0ms (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

Accurracy

99.9%

Counts

77 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	48.8%	(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))
	52.6%	(.f64 (pow.f64 2 1/4) (.f64 (sqrt.f64 (sqrt.f64 2)) (neg.f64 x)))
✓	47.8%	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
✓	52.6%	(*.f64 (sqrt.f64 2) (neg.f64 x))
✓	48.9%	(*.f64 (sqrt.f64 2) x)
✓	53.7%	(sqrt.f64 (.f64 (.f64 2 x) x))

Compiler

Compiled 47 to 39 computations (17% saved)

regimes34.0ms (1.4%)

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 2) x)

Calls

3 calls:

11.0ms	x
10.0ms	(sqrt.f64 (.f64 (.f64 2 x) x))
10.0ms	(.f64 (.f64 2 x) x)

Results

Accuracy	Segments	Branch
99.4%	2	`x`
79.9%	3	`(sqrt.f64 (.f64 (.f64 2 x) x))`
79.9%	3	`(.f64 (.f64 2 x) x)`

Compiler

Compiled 75 to 58 computations (22.7% saved)

bsearch14.0ms (0.6%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
14.0ms	-1.7031926117110213e-305	1.2582354217461972e-306

Results

12.0ms

144×

body

256

valid

Compiler

Compiled 173 to 152 computations (12.1% saved)

regimes62.0ms (2.6%)

Accuracy

Total -63.0b remaining (-15499.9%)

Threshold costs -63b (-15499.9%)

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 2) x)

Calls

3 calls:

42.0ms	(.f64 (.f64 2 x) x)
10.0ms	(sqrt.f64 (.f64 (.f64 2 x) x))
8.0ms	x

Results

Accuracy	Segments	Branch
99.4%	2	`x`
79.9%	3	`(sqrt.f64 (.f64 (.f64 2 x) x))`
79.9%	3	`(.f64 (.f64 2 x) x)`

Compiler

Compiled 54 to 41 computations (24.1% saved)

bsearch33.0ms (1.4%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
33.0ms	-1.7031926117110213e-305	1.2582354217461972e-306

Results

31.0ms

144×

body

256

valid

Compiler

Compiled 128 to 107 computations (16.4% saved)

simplify8.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	97
1	32	97
2	48	97
3	63	97
4	73	97
5	78	97
6	79	97

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs

(if (<=.f64 x -20240225330731/101201126653655309176247673359458653524778324882071059178450679013715169783997673445980191850718562247593538932158405955694904368692896738433506699970369254960758712138283180682233453871046608170619883839236372534281003741712346349309051677824579778170405028256179384776166707307615251266093163754323003131653853870546747392) (*.f64 (pow.f64 2 1/4) (*.f64 (sqrt.f64 (sqrt.f64 2)) (neg.f64 x))) (*.f64 (sqrt.f64 2) x))

(if (<=.f64 x -20240225330731/101201126653655309176247673359458653524778324882071059178450679013715169783997673445980191850718562247593538932158405955694904368692896738433506699970369254960758712138283180682233453871046608170619883839236372534281003741712346349309051677824579778170405028256179384776166707307615251266093163754323003131653853870546747392) (*.f64 (sqrt.f64 2) (neg.f64 x)) (*.f64 (sqrt.f64 2) x))

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

Outputs
(if (<=.f64 x -20240225330731/101201126653655309176247673359458653524778324882071059178450679013715169783997673445980191850718562247593538932158405955694904368692896738433506699970369254960758712138283180682233453871046608170619883839236372534281003741712346349309051677824579778170405028256179384776166707307615251266093163754323003131653853870546747392) (.f64 (pow.f64 2 1/4) (.f64 (sqrt.f64 (sqrt.f64 2)) (neg.f64 x))) (*.f64 (sqrt.f64 2) x))
(if (<=.f64 x -20240225330731/101201126653655309176247673359458653524778324882071059178450679013715169783997673445980191850718562247593538932158405955694904368692896738433506699970369254960758712138283180682233453871046608170619883839236372534281003741712346349309051677824579778170405028256179384776166707307615251266093163754323003131653853870546747392) (.f64 (pow.f64 2 1/4) (.f64 (sqrt.f64 (sqrt.f64 2)) (neg.f64 x))) (*.f64 x (sqrt.f64 2)))
(if (<=.f64 x -20240225330731/101201126653655309176247673359458653524778324882071059178450679013715169783997673445980191850718562247593538932158405955694904368692896738433506699970369254960758712138283180682233453871046608170619883839236372534281003741712346349309051677824579778170405028256179384776166707307615251266093163754323003131653853870546747392) (.f64 (sqrt.f64 2) (neg.f64 x)) (.f64 (sqrt.f64 2) x))
(if (<=.f64 x -20240225330731/101201126653655309176247673359458653524778324882071059178450679013715169783997673445980191850718562247593538932158405955694904368692896738433506699970369254960758712138283180682233453871046608170619883839236372534281003741712346349309051677824579778170405028256179384776166707307615251266093163754323003131653853870546747392) (.f64 (sqrt.f64 2) (neg.f64 x)) (.f64 x (sqrt.f64 2)))
(if (<=.f64 x -20240225330731/101201126653655309176247673359458653524778324882071059178450679013715169783997673445980191850718562247593538932158405955694904368692896738433506699970369254960758712138283180682233453871046608170619883839236372534281003741712346349309051677824579778170405028256179384776166707307615251266093163754323003131653853870546747392) (.f64 x (neg.f64 (sqrt.f64 2))) (.f64 x (sqrt.f64 2)))
(*.f64 (sqrt.f64 2) x)
(*.f64 x (sqrt.f64 2))

Compiler

Compiled 38 to 31 computations (18.4% saved)

soundness216.0ms (8.9%)

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)

end30.0ms (1.2%)

Compiler: Compiled 36 to 29 computations (19.4% saved)

Details

analyze4.0ms (0.2%)

sample871.0ms (36%)

preprocess14.0ms (0.6%)

simplify11.0ms (0.4%)

eval5.0ms (0.2%)

prune1.0ms (0.1%)

localize7.0ms (0.3%)

series1.0ms (0%)

rewrite54.0ms (2.2%)

simplify57.0ms (2.3%)

eval6.0ms (0.2%)

prune10.0ms (0.4%)

localize4.0ms (0.2%)

series0.0ms (0%)

rewrite46.0ms (1.9%)

simplify63.0ms (2.6%)

localize6.0ms (0.2%)

series0.0ms (0%)

rewrite52.0ms (2.1%)

simplify67.0ms (2.8%)

localize8.0ms (0.3%)

series1.0ms (0%)

rewrite54.0ms (2.2%)

simplify67.0ms (2.7%)

localize10.0ms (0.4%)

series4.0ms (0.2%)

rewrite92.0ms (3.8%)

simplify63.0ms (2.6%)

eval27.0ms (1.1%)

prune13.0ms (0.5%)

localize10.0ms (0.4%)

series52.0ms (2.1%)

rewrite54.0ms (2.2%)

simplify46.0ms (1.9%)

eval8.0ms (0.3%)

prune6.0ms (0.2%)

localize21.0ms (0.9%)

series2.0ms (0.1%)

rewrite79.0ms (3.3%)

simplify56.0ms (2.3%)

eval66.0ms (2.7%)

prune11.0ms (0.4%)

regimes34.0ms (1.4%)

bsearch14.0ms (0.6%)

regimes62.0ms (2.6%)

bsearch33.0ms (1.4%)

simplify8.0ms (0.3%)

soundness216.0ms (8.9%)

end30.0ms (1.2%)

Profiling