Details

analyze4.0ms (0.2%)

Algorithm

1×

Search

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

Compiler

Compiled 8 to 6 computations (25% saved)

sample748.0ms (47.8%)

Results

736.0ms

8256×

body

128

valid

Compiler

Compiled 16 to 12 computations (25% saved)

preprocess20.0ms (1.2%)

Algorithm

2×	egg-herbie

Rules

3×	`*-commutative_binary64`
1×	`associate-r_binary64`
1×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	9	9
2	12	9
0	1	1

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0

Outputs
0

Call 2

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

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

Compiler

Compiled 7 to 5 computations (28.6% saved)

simplify6.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
1×	`associate-r_binary64`
1×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	9	9
2	12	9

Stop Event

1×

saturated

Counts

1 → 1

Calls

Call 1

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

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

prune4.0ms (0.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

28.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	28.2b	(sqrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 21 to 15 computations (28.6% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 2 (.f64 x x))
✓	27.2b	(sqrt.f64 (.f64 2 (.f64 x x)))

series3.0ms (0.2%)

Counts

2 → 24

Calls

6 calls:

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

rewrite32.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

503×	`pow1_binary64`
466×	`add-log-exp_binary64`
466×	`log1p-expm1-u_binary64`
466×	`expm1-log1p-u_binary64`
454×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	16
1	122	13
2	1363	13

Stop Event

1×	node limit

Counts

2 → 36

Calls

Call 1

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

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

simplify49.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

964×	`fma-def_binary64`
286×	`distribute-rgt-in_binary64`
242×	`unswap-sqr_binary64`
225×	`fma-neg_binary64`
201×	`fabs-mul_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	164
1	20	164
2	43	164
3	83	164
4	203	164
5	607	164
6	959	164
7	1606	164
8	2009	164
9	2876	164
10	3703	164
11	4514	164

Stop Event

1×	node limit

Counts

60 → 40

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

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

prune25.0ms (1.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	34	6	40
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	34	7	41

Error

0.2b

Counts

41 → 7

Alt Table

Status	Error	Program
	34.1b	(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
	45.8b	(.f64 (sqrt.f64 (cbrt.f64 (.f64 4 (pow.f64 x 4)))) (sqrt.f64 (cbrt.f64 (.f64 2 (.f64 x x)))))
	33.9b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
▶	29.8b	(*.f64 (sqrt.f64 2) (neg.f64 x))
	33.2b	(*.f64 (sqrt.f64 2) x)
✓	28.2b	(sqrt.f64 (.f64 2 (.f64 x x)))
	30.7b	(sqrt.f64 (exp.f64 (log.f64 (.f64 2 (.f64 x x)))))

Compiler

Compiled 424 to 325 computations (23.3% saved)

localize3.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series2.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	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))

rewrite31.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

450×	`pow1_binary64`
418×	`add-log-exp_binary64`
417×	`log1p-expm1-u_binary64`
417×	`expm1-log1p-u_binary64`
410×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	125	6
2	1472	6

Stop Event

1×	node limit

Counts

1 → 15

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

simplify11.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×

saturated

Counts

27 → 17

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))

Outputs
(.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 -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 -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))

prune13.0ms (0.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	17	0	17
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	17	7	24

Error

0.2b

Counts

24 → 7

Alt Table

Status	Error	Program
	34.1b	(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
	45.8b	(.f64 (sqrt.f64 (cbrt.f64 (.f64 4 (pow.f64 x 4)))) (sqrt.f64 (cbrt.f64 (.f64 2 (.f64 x x)))))
	33.9b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
✓	29.8b	(*.f64 (sqrt.f64 2) (neg.f64 x))
	33.2b	(*.f64 (sqrt.f64 2) x)
✓	28.2b	(sqrt.f64 (.f64 2 (.f64 x x)))
▶	30.7b	(sqrt.f64 (exp.f64 (log.f64 (.f64 2 (.f64 x x)))))

Compiler

Compiled 219 to 180 computations (17.8% saved)

localize7.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(.f64 2 (.f64 x x))
✓	3.1b	(exp.f64 (log.f64 (.f64 2 (.f64 x x))))
✓	27.2b	(sqrt.f64 (exp.f64 (log.f64 (.f64 2 (.f64 x x)))))
✓	28.0b	(log.f64 (.f64 2 (.f64 x x)))

series34.0ms (2.2%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
25.0ms	x	@	0	(log.f64 (.f64 2 (.f64 x x)))
7.0ms	x	@	inf	(log.f64 (.f64 2 (.f64 x x)))
0.0ms	x	@	-inf	(log.f64 (.f64 2 (.f64 x x)))
0.0ms	x	@	0	(sqrt.f64 (exp.f64 (log.f64 (.f64 2 (.f64 x x)))))
0.0ms	x	@	inf	(sqrt.f64 (exp.f64 (log.f64 (.f64 2 (.f64 x x)))))

rewrite40.0ms (2.6%)

Algorithm

1×	batch-egg-rewrite

Rules

587×	`pow1_binary64`
543×	`add-log-exp_binary64`
543×	`log1p-expm1-u_binary64`
543×	`expm1-log1p-u_binary64`
529×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	25
1	146	22
2	1560	22

Stop Event

1×	node limit

Counts

3 → 81

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 x (sqrt.f64 2))) (log.f64 (*.f64 x (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 2) (*.f64 2 (log.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 2 (log.f64 x)) (log.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (cbrt.f64 (*.f64 4 (pow.f64 x 4)))) (log.f64 (cbrt.f64 (*.f64 x (*.f64 2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 2 x)) (log.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (log.f64 (*.f64 x (*.f64 2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (log.f64 2) 1) (*.f64 2 (log.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (log.f64 (*.f64 x (*.f64 2 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (log.f64 (*.f64 x (*.f64 2 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (log.f64 (*.f64 x (*.f64 2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (log.f64 (*.f64 x (*.f64 2 x)))) (pow.f64 (cbrt.f64 (log.f64 (*.f64 x (*.f64 2 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 x (*.f64 2 x)))) 2) (cbrt.f64 (log.f64 (*.f64 x (*.f64 2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (log.f64 (*.f64 x (*.f64 2 x)))) (sqrt.f64 (log.f64 (*.f64 x (*.f64 2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (log.f64 2) 3) (pow.f64 (*.f64 2 (log.f64 x)) 3)) (+.f64 (*.f64 (log.f64 2) (log.f64 2)) (-.f64 (*.f64 (*.f64 2 (log.f64 x)) (*.f64 2 (log.f64 x))) (*.f64 (log.f64 2) (*.f64 2 (log.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (log.f64 2) (log.f64 2)) (*.f64 (*.f64 2 (log.f64 x)) (*.f64 2 (log.f64 x)))) (-.f64 (log.f64 2) (*.f64 2 (log.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (log.f64 (*.f64 x (*.f64 2 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (log.f64 (*.f64 x (*.f64 2 x))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (log.f64 (*.f64 x (*.f64 2 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (log.f64 (*.f64 x (*.f64 2 x)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (log.f64 (*.f64 x (*.f64 2 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (log.f64 (*.f64 x (*.f64 2 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (log.f64 (*.f64 x (*.f64 2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (log.f64 (*.f64 x (*.f64 2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (-.f64 (*.f64 x (*.f64 2 x)) 1))))))

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

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

simplify32.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

326×	`fma-def_binary64`
242×	`unswap-sqr_binary64`
213×	`unsub-neg_binary64`
177×	`distribute-neg-in_binary64`
176×	`associate-l_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	22	292
1	54	292
2	98	284
3	207	284
4	510	284
5	1360	284
6	3481	284

Stop Event

1×	node limit

Counts

117 → 88

Calls

Call 1

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

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

prune46.0ms (3%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	101	1	102
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	102	7	109

Error

0.1b

Counts

109 → 7

Alt Table

Status	Error	Program
	34.1b	(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
	33.9b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
✓	29.8b	(*.f64 (sqrt.f64 2) (neg.f64 x))
▶	28.4b	(sqrt.f64 (.f64 (cbrt.f64 (.f64 x (.f64 2 x))) (.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (.f64 x (sqrt.f64 2)))))
	33.2b	(*.f64 (sqrt.f64 2) x)
✓	28.2b	(sqrt.f64 (.f64 2 (.f64 x x)))
✓	30.7b	(sqrt.f64 (exp.f64 (log.f64 (.f64 2 (.f64 x x)))))

Compiler

Compiled 1162 to 913 computations (21.4% saved)

localize10.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(*.f64 x (sqrt.f64 2))
✓	0.6b	(cbrt.f64 (*.f64 x (sqrt.f64 2)))
✓	27.2b	(sqrt.f64 (.f64 (cbrt.f64 (.f64 x (.f64 2 x))) (.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (.f64 x (sqrt.f64 2)))))
✓	28.1b	(cbrt.f64 (.f64 x (.f64 2 x)))

series17.0ms (1.1%)

Counts

4 → 24

Calls

12 calls:

Time	Variable		Point	Expression
5.0ms	x	@	-inf	(sqrt.f64 (.f64 (cbrt.f64 (.f64 x (.f64 2 x))) (.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (.f64 x (sqrt.f64 2)))))
4.0ms	x	@	0	(sqrt.f64 (.f64 (cbrt.f64 (.f64 x (.f64 2 x))) (.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (.f64 x (sqrt.f64 2)))))
1.0ms	x	@	0	(cbrt.f64 (.f64 x (.f64 2 x)))
1.0ms	x	@	-inf	(cbrt.f64 (*.f64 x (sqrt.f64 2)))
1.0ms	x	@	inf	(sqrt.f64 (.f64 (cbrt.f64 (.f64 x (.f64 2 x))) (.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (.f64 x (sqrt.f64 2)))))

rewrite47.0ms (3%)

Algorithm

1×	batch-egg-rewrite

Rules

771×	`log1p-expm1-u_binary64`
771×	`expm1-log1p-u_binary64`
140×	`associate-r_binary64`
113×	`add-sqr-sqrt_binary64`
109×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	75
1	242	29
2	2958	29

Stop Event

1×	node limit

Counts

4 → 115

Calls

Call 1

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

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

simplify37.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

737×	`fma-def_binary64`
454×	`unswap-sqr_binary64`
347×	`cancel-sign-sub-inv_binary64`
339×	`distribute-rgt-neg-in_binary64`
334×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	23	324
1	56	264
2	149	264
3	357	256
4	1238	240
5	2357	240
6	3975	240

Stop Event

1×	node limit

Counts

139 → 102

Calls

Call 1

Inputs
(.f64 (pow.f64 (pow.f64 (sqrt.f64 2) 2) 1/3) (.f64 (sqrt.f64 (cbrt.f64 2)) x))
(.f64 (pow.f64 (pow.f64 (sqrt.f64 2) 2) 1/3) (.f64 (sqrt.f64 (cbrt.f64 2)) x))
(.f64 (pow.f64 (pow.f64 (sqrt.f64 2) 2) 1/3) (.f64 (sqrt.f64 (cbrt.f64 2)) x))
(.f64 (pow.f64 (pow.f64 (sqrt.f64 2) 2) 1/3) (.f64 (sqrt.f64 (cbrt.f64 2)) x))
(.f64 (pow.f64 (pow.f64 (sqrt.f64 2) 2) 1/3) (.f64 (sqrt.f64 (cbrt.f64 2)) x))
(.f64 (pow.f64 (pow.f64 (sqrt.f64 2) 2) 1/3) (.f64 (sqrt.f64 (cbrt.f64 2)) x))
(.f64 (pow.f64 (pow.f64 (sqrt.f64 2) 2) 1/3) (.f64 (sqrt.f64 (cbrt.f64 2)) x))
(.f64 (pow.f64 (pow.f64 (sqrt.f64 2) 2) 1/3) (.f64 (sqrt.f64 (cbrt.f64 2)) x))
(.f64 -1 (.f64 (sqrt.f64 (.f64 -1 (.f64 (*.f64 (cbrt.f64 -1) (cbrt.f64 2)) (pow.f64 (pow.f64 (sqrt.f64 2) 4) 1/3)))) x))
(.f64 -1 (.f64 (sqrt.f64 (.f64 -1 (.f64 (*.f64 (cbrt.f64 -1) (cbrt.f64 2)) (pow.f64 (pow.f64 (sqrt.f64 2) 4) 1/3)))) x))
(.f64 -1 (.f64 (sqrt.f64 (.f64 -1 (.f64 (*.f64 (cbrt.f64 -1) (cbrt.f64 2)) (pow.f64 (pow.f64 (sqrt.f64 2) 4) 1/3)))) x))
(.f64 -1 (.f64 (sqrt.f64 (.f64 -1 (.f64 (*.f64 (cbrt.f64 -1) (cbrt.f64 2)) (pow.f64 (pow.f64 (sqrt.f64 2) 4) 1/3)))) 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 (sqrt.f64 2) x)

Outputs
(.f64 (pow.f64 (pow.f64 (sqrt.f64 2) 2) 1/3) (.f64 (sqrt.f64 (cbrt.f64 2)) x))
(.f64 (cbrt.f64 (pow.f64 (sqrt.f64 2) 2)) (.f64 (sqrt.f64 (cbrt.f64 2)) x))
(.f64 (cbrt.f64 2) (.f64 (sqrt.f64 (cbrt.f64 2)) x))
(.f64 (cbrt.f64 2) (.f64 x (pow.f64 2 1/6)))
(*.f64 x (pow.f64 (pow.f64 2 1/6) 3))
(.f64 (pow.f64 (pow.f64 (sqrt.f64 2) 2) 1/3) (.f64 (sqrt.f64 (cbrt.f64 2)) x))
(.f64 (cbrt.f64 (pow.f64 (sqrt.f64 2) 2)) (.f64 (sqrt.f64 (cbrt.f64 2)) x))
(.f64 (cbrt.f64 2) (.f64 (sqrt.f64 (cbrt.f64 2)) x))
(.f64 (cbrt.f64 2) (.f64 x (pow.f64 2 1/6)))
(*.f64 x (pow.f64 (pow.f64 2 1/6) 3))
(.f64 (pow.f64 (pow.f64 (sqrt.f64 2) 2) 1/3) (.f64 (sqrt.f64 (cbrt.f64 2)) x))
(.f64 (cbrt.f64 (pow.f64 (sqrt.f64 2) 2)) (.f64 (sqrt.f64 (cbrt.f64 2)) x))
(.f64 (cbrt.f64 2) (.f64 (sqrt.f64 (cbrt.f64 2)) x))
(.f64 (cbrt.f64 2) (.f64 x (pow.f64 2 1/6)))
(*.f64 x (pow.f64 (pow.f64 2 1/6) 3))
(.f64 (pow.f64 (pow.f64 (sqrt.f64 2) 2) 1/3) (.f64 (sqrt.f64 (cbrt.f64 2)) x))
(.f64 (cbrt.f64 (pow.f64 (sqrt.f64 2) 2)) (.f64 (sqrt.f64 (cbrt.f64 2)) x))
(.f64 (cbrt.f64 2) (.f64 (sqrt.f64 (cbrt.f64 2)) x))
(.f64 (cbrt.f64 2) (.f64 x (pow.f64 2 1/6)))
(*.f64 x (pow.f64 (pow.f64 2 1/6) 3))
(.f64 (pow.f64 (pow.f64 (sqrt.f64 2) 2) 1/3) (.f64 (sqrt.f64 (cbrt.f64 2)) x))
(.f64 (cbrt.f64 (pow.f64 (sqrt.f64 2) 2)) (.f64 (sqrt.f64 (cbrt.f64 2)) x))
(.f64 (cbrt.f64 2) (.f64 (sqrt.f64 (cbrt.f64 2)) x))
(.f64 (cbrt.f64 2) (.f64 x (pow.f64 2 1/6)))
(*.f64 x (pow.f64 (pow.f64 2 1/6) 3))
(.f64 (pow.f64 (pow.f64 (sqrt.f64 2) 2) 1/3) (.f64 (sqrt.f64 (cbrt.f64 2)) x))
(.f64 (cbrt.f64 (pow.f64 (sqrt.f64 2) 2)) (.f64 (sqrt.f64 (cbrt.f64 2)) x))
(.f64 (cbrt.f64 2) (.f64 (sqrt.f64 (cbrt.f64 2)) x))
(.f64 (cbrt.f64 2) (.f64 x (pow.f64 2 1/6)))
(*.f64 x (pow.f64 (pow.f64 2 1/6) 3))
(.f64 (pow.f64 (pow.f64 (sqrt.f64 2) 2) 1/3) (.f64 (sqrt.f64 (cbrt.f64 2)) x))
(.f64 (cbrt.f64 (pow.f64 (sqrt.f64 2) 2)) (.f64 (sqrt.f64 (cbrt.f64 2)) x))
(.f64 (cbrt.f64 2) (.f64 (sqrt.f64 (cbrt.f64 2)) x))
(.f64 (cbrt.f64 2) (.f64 x (pow.f64 2 1/6)))
(*.f64 x (pow.f64 (pow.f64 2 1/6) 3))
(.f64 (pow.f64 (pow.f64 (sqrt.f64 2) 2) 1/3) (.f64 (sqrt.f64 (cbrt.f64 2)) x))
(.f64 (cbrt.f64 (pow.f64 (sqrt.f64 2) 2)) (.f64 (sqrt.f64 (cbrt.f64 2)) x))
(.f64 (cbrt.f64 2) (.f64 (sqrt.f64 (cbrt.f64 2)) x))
(.f64 (cbrt.f64 2) (.f64 x (pow.f64 2 1/6)))
(*.f64 x (pow.f64 (pow.f64 2 1/6) 3))
(.f64 -1 (.f64 (sqrt.f64 (.f64 -1 (.f64 (*.f64 (cbrt.f64 -1) (cbrt.f64 2)) (pow.f64 (pow.f64 (sqrt.f64 2) 4) 1/3)))) x))
(neg.f64 (.f64 x (sqrt.f64 (neg.f64 (.f64 (*.f64 (cbrt.f64 2) (cbrt.f64 -1)) (cbrt.f64 (pow.f64 (sqrt.f64 2) 4)))))))
(.f64 x (neg.f64 (sqrt.f64 (.f64 (*.f64 (cbrt.f64 2) (cbrt.f64 -1)) (neg.f64 (cbrt.f64 4))))))
(.f64 x (neg.f64 (sqrt.f64 (.f64 (cbrt.f64 -1) (*.f64 (cbrt.f64 4) (neg.f64 (cbrt.f64 2)))))))
(.f64 -1 (.f64 (sqrt.f64 (.f64 -1 (.f64 (*.f64 (cbrt.f64 -1) (cbrt.f64 2)) (pow.f64 (pow.f64 (sqrt.f64 2) 4) 1/3)))) x))
(neg.f64 (.f64 x (sqrt.f64 (neg.f64 (.f64 (*.f64 (cbrt.f64 2) (cbrt.f64 -1)) (cbrt.f64 (pow.f64 (sqrt.f64 2) 4)))))))
(.f64 x (neg.f64 (sqrt.f64 (.f64 (*.f64 (cbrt.f64 2) (cbrt.f64 -1)) (neg.f64 (cbrt.f64 4))))))
(.f64 x (neg.f64 (sqrt.f64 (.f64 (cbrt.f64 -1) (*.f64 (cbrt.f64 4) (neg.f64 (cbrt.f64 2)))))))
(.f64 -1 (.f64 (sqrt.f64 (.f64 -1 (.f64 (*.f64 (cbrt.f64 -1) (cbrt.f64 2)) (pow.f64 (pow.f64 (sqrt.f64 2) 4) 1/3)))) x))
(neg.f64 (.f64 x (sqrt.f64 (neg.f64 (.f64 (*.f64 (cbrt.f64 2) (cbrt.f64 -1)) (cbrt.f64 (pow.f64 (sqrt.f64 2) 4)))))))
(.f64 x (neg.f64 (sqrt.f64 (.f64 (*.f64 (cbrt.f64 2) (cbrt.f64 -1)) (neg.f64 (cbrt.f64 4))))))
(.f64 x (neg.f64 (sqrt.f64 (.f64 (cbrt.f64 -1) (*.f64 (cbrt.f64 4) (neg.f64 (cbrt.f64 2)))))))
(.f64 -1 (.f64 (sqrt.f64 (.f64 -1 (.f64 (*.f64 (cbrt.f64 -1) (cbrt.f64 2)) (pow.f64 (pow.f64 (sqrt.f64 2) 4) 1/3)))) x))
(neg.f64 (.f64 x (sqrt.f64 (neg.f64 (.f64 (*.f64 (cbrt.f64 2) (cbrt.f64 -1)) (cbrt.f64 (pow.f64 (sqrt.f64 2) 4)))))))
(.f64 x (neg.f64 (sqrt.f64 (.f64 (*.f64 (cbrt.f64 2) (cbrt.f64 -1)) (neg.f64 (cbrt.f64 4))))))
(.f64 x (neg.f64 (sqrt.f64 (.f64 (cbrt.f64 -1) (*.f64 (cbrt.f64 4) (neg.f64 (cbrt.f64 2)))))))
(*.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)

prune63.0ms (4%)

Pruning

10 alts after pruning (6 fresh and 4 done)

	Pruned	Kept	Total
New	100	4	104
Fresh	1	2	3
Picked	0	1	1
Done	0	3	3
Total	101	10	111

Error

0.1b

Counts

111 → 10

Alt Table

Status	Error	Program
	33.2b	(*.f64 (sqrt.f64 2) x)
	28.6b	(sqrt.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 x (.f64 x 2)))) 3) (.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (.f64 x (sqrt.f64 2)))))
	28.5b	(sqrt.f64 (.f64 (cbrt.f64 (.f64 x (.f64 2 x))) (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 (sqrt.f64 2))) (.f64 x (sqrt.f64 2)))))
	33.9b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
	33.1b	(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))
✓	29.8b	(*.f64 (sqrt.f64 2) (neg.f64 x))
✓	28.4b	(sqrt.f64 (.f64 (cbrt.f64 (.f64 x (.f64 2 x))) (.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (.f64 x (sqrt.f64 2)))))
	33.2b	(.f64 (pow.f64 (pow.f64 (sqrt.f64 2) 2) 1/3) (.f64 (sqrt.f64 (cbrt.f64 2)) x))
✓	28.2b	(sqrt.f64 (.f64 2 (.f64 x x)))
✓	30.7b	(sqrt.f64 (exp.f64 (log.f64 (.f64 2 (.f64 x x)))))

Compiler

Compiled 1889 to 1514 computations (19.9% saved)

regimes129.0ms (8.3%)

Accuracy

Total 0.3b remaining (71.8%)

Threshold costs 0.3b (71.8%)

Counts

21 → 2

Compiler

Compiled 251 to 189 computations (24.7% saved)

bsearch14.0ms (0.9%)

Algorithm

1×	binary-search

Calls

1 calls:

14.0ms

Steps

Iters	Point		Range
0.0	∈ [	-2.5582476213369104e-308	,	5.5531564092997706e-300	]

Compiler

Compiled 2 to 1 computations (50% saved)

simplify2.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

7×	`*-commutative_binary64`
3×	`+-commutative_binary64`
3×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	27
1	22	27
2	30	27
3	36	27
4	39	27
5	40	27

Stop Event

1×

saturated

Calls

Call 1

Inputs
(if (<=.f64 x 0) (.f64 (sqrt.f64 2) (neg.f64 x)) (.f64 (pow.f64 2 1/4) (*.f64 (pow.f64 2 1/4) x)))

Outputs

(if (<=.f64 x 0) (*.f64 (sqrt.f64 2) (neg.f64 x)) (*.f64 (pow.f64 2 1/4) (*.f64 (pow.f64 2 1/4) x)))

(if (<=.f64 x 0) (neg.f64 (*.f64 (sqrt.f64 2) x)) (*.f64 (pow.f64 2 1/4) (*.f64 x (pow.f64 2 1/4))))

(if (<=.f64 x 0) (neg.f64 (*.f64 x (sqrt.f64 2))) (*.f64 (pow.f64 2 1/4) (*.f64 x (pow.f64 2 1/4))))

end131.0ms (8.4%)

Stop Event

1×

fuel

Compiler

Compiled 157 to 129 computations (17.8% saved)

Details

analyze4.0ms (0.2%)

sample748.0ms (47.8%)

preprocess20.0ms (1.2%)

simplify6.0ms (0.4%)

prune4.0ms (0.2%)

localize4.0ms (0.2%)

series3.0ms (0.2%)

rewrite32.0ms (2.1%)

simplify49.0ms (3.1%)

prune25.0ms (1.6%)

localize3.0ms (0.2%)

series2.0ms (0.1%)

rewrite31.0ms (2%)

simplify11.0ms (0.7%)

prune13.0ms (0.8%)

localize7.0ms (0.4%)

series34.0ms (2.2%)

rewrite40.0ms (2.6%)

simplify32.0ms (2.1%)

prune46.0ms (3%)

localize10.0ms (0.6%)

series17.0ms (1.1%)

rewrite47.0ms (3%)

simplify37.0ms (2.4%)

prune63.0ms (4%)

regimes129.0ms (8.3%)

bsearch14.0ms (0.9%)

simplify2.0ms (0.2%)

end131.0ms (8.4%)

Profiling