Details

analyze0.0ms (0%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
100%	100%	0%	0%	0%	0%	0%	1

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample1.7s (40.6%)

Results

1.7s	8255×	body	256	valid
0.0ms	1×	body	256	infinite

Bogosity

preprocess213.0ms (5.2%)

Algorithm

2×	egg-herbie

Rules

2734×	`sqr-pow`
1306×	`cube-prod`
1044×	`pow-sqr`
884×	`associate-r`
868×	`unswap-sqr`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	14	17
2	25	17
3	46	17
4	106	17
5	329	17
6	1230	17
7	2094	17
8	2234	17
9	2402	17
10	2599	17
11	2878	17
12	3246	17
13	3692	17
14	4220	17
15	4862	17
16	5641	17
17	5967	17
18	6241	17
19	6447	17
20	6507	17
21	6537	17
22	7472	17
0	1	1

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0

Outputs
0

Call 2

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

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

Compiler

Compiled 8 to 7 computations (12.5% saved)

simplify207.0ms (5%)

Algorithm

1×	egg-herbie

Rules

2734×	`sqr-pow`
1306×	`cube-prod`
1044×	`pow-sqr`
884×	`associate-r`
868×	`unswap-sqr`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	14	17
2	25	17
3	46	17
4	106	17
5	329	17
6	1230	17
7	2094	17
8	2234	17
9	2402	17
10	2599	17
11	2878	17
12	3246	17
13	3692	17
14	4220	17
15	4862	17
16	5641	17
17	5967	17
18	6241	17
19	6447	17
20	6507	17
21	6537	17
22	7472	17

Stop Event

1×	node limit

Counts

1 → 2

Calls

Call 1

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

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

eval1.0ms (0%)

Compiler: Compiled 13 to 10 computations (23.1% saved)

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Accurracy

54.0%

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	54.0%	(sqrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 7 to 5 computations (28.6% saved)

localize26.0ms (0.6%)

Local Accuracy

Found 1 expressions with local accuracy:

New	Accuracy	Program
✓	54.0%	(sqrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 18 to 9 computations (50% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite61.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

1354×	`pow1`
1244×	`add-exp-log`
1244×	`log1p-expm1-u`
1244×	`expm1-log1p-u`
1214×	`add-log-exp`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	160	11
2	1810	11

Stop Event

1×	node limit

Counts

1 → 24

Calls

Call 1

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

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

simplify66.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

1366×	`log-prod`
812×	`associate-r`
808×	`distribute-rgt-in`
776×	`distribute-lft-in`
714×	`associate-l`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	61	504
1	138	504
2	486	504
3	2721	504
4	6903	504

Stop Event

1×	node limit

Counts

36 → 29

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

eval6.0ms (0.1%)

Compiler: Compiled 228 to 177 computations (22.4% saved)

prune11.0ms (0.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	22	7	29
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	22	8	30

Accurracy

99.7%

Counts

30 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	49.8%	(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
▶	50.4%	(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)
▶	50.2%	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
	25.5%	(.f64 (sqrt.f64 (cbrt.f64 (.f64 (pow.f64 x 4) 4))) (sqrt.f64 (cbrt.f64 (.f64 2 (.f64 x x)))))
▶	50.4%	(*.f64 (sqrt.f64 2) (neg.f64 x))
▶	51.1%	(*.f64 (sqrt.f64 2) x)
	28.0%	(.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (cbrt.f64 (.f64 2 (.f64 x x))))
✓	54.0%	(sqrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 135 to 109 computations (19.3% saved)

localize22.0ms (0.5%)

Local Accuracy

Found 1 expressions with local accuracy:

New	Accuracy	Program
✓	99.3%	(*.f64 (sqrt.f64 2) x)

Compiler

Compiled 10 to 8 computations (20% 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)

rewrite96.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

1182×	`pow1`
1084×	`add-exp-log`
1084×	`log1p-expm1-u`
1084×	`expm1-log1p-u`
1058×	`add-log-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	138	11
2	1508	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 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 3)
(pow.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3) 1/3)
(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 2)
(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)))

simplify61.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

1896×	`log-prod`
954×	`fma-neg`
806×	`*-commutative`
676×	`distribute-lft-out`
640×	`distribute-rgt-in`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	32	253
1	79	187
2	271	121
3	1535	121
4	4437	121
5	6814	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 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 3)
(pow.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3) 1/3)
(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 2)
(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 (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)
(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)
(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)

localize24.0ms (0.6%)

Local Accuracy

Found 1 expressions with local accuracy:

New	Accuracy	Program
✓	99.3%	(*.f64 (sqrt.f64 2) (neg.f64 x))

Compiler

Compiled 13 to 9 computations (30.8% 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))

rewrite49.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

1248×	`pow1`
1148×	`add-exp-log`
1146×	`log1p-expm1-u`
1146×	`expm1-log1p-u`
1120×	`add-log-exp`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	163	11
2	1913	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 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 3)
(pow.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3) 1/3)
(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 2)
(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)))

simplify76.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

1844×	`log-prod`
838×	`*-commutative`
656×	`distribute-rgt-in`
656×	`distribute-lft-out`
642×	`distribute-lft-in`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	37	463
1	91	397
2	335	331
3	1761	331
4	4925	331
5	7956	231

Stop Event

1×	node limit

Counts

25 → 20

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 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 3)
(pow.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3) 1/3)
(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 2)
(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))
(neg.f64 (hypot.f64 x x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(neg.f64 (hypot.f64 x x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(neg.f64 (hypot.f64 x x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(neg.f64 (hypot.f64 x x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(neg.f64 (hypot.f64 x x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(neg.f64 (hypot.f64 x x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(neg.f64 (hypot.f64 x x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(neg.f64 (hypot.f64 x x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(neg.f64 (hypot.f64 x x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(neg.f64 (hypot.f64 x x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(neg.f64 (hypot.f64 x x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(neg.f64 (hypot.f64 x x))
(-.f64 0 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(neg.f64 (hypot.f64 x x))
(-.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)
(hypot.f64 x 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)
(hypot.f64 x 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)
(hypot.f64 x 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)
(hypot.f64 x 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)
(hypot.f64 x x)
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(neg.f64 (hypot.f64 x 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)
(hypot.f64 x 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)
(hypot.f64 x 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)
(hypot.f64 x 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)
(hypot.f64 x 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)
(hypot.f64 x 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)
(hypot.f64 x x)

localize43.0ms (1%)

Local Accuracy

Found 1 expressions with local accuracy:

New	Accuracy	Program
✓	99.8%	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))

Compiler

Compiled 20 to 13 computations (35% 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 (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

1542×	`pow1`
1416×	`add-exp-log`
1416×	`log1p-expm1-u`
1416×	`expm1-log1p-u`
1382×	`add-log-exp`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	180	11
2	2032	11

Stop Event

1×	node limit

Counts

1 → 12

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 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 3)
(pow.f64 (.f64 2 (.f64 x x)) 1/2)
(pow.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3) 1/3)
(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 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)))
(log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 2) x)))

simplify64.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

1594×	`log-prod`
978×	`fma-neg`
744×	`exp-sum`
714×	`exp-prod`
690×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	320
1	94	320
2	330	320
3	1700	320
4	4103	320
5	6033	320

Stop Event

1×	node limit

Counts

24 → 17

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

localize118.0ms (2.9%)

Local Accuracy

Found 3 expressions with local accuracy:

New	Accuracy	Program
✓	99.3%	(*.f64 x (sqrt.f64 2))
✓	99.0%	(cbrt.f64 (*.f64 x (sqrt.f64 2)))
✓	98.9%	(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)

Compiler

Compiled 23 to 19 computations (17.4% saved)

series4.0ms (0.1%)

Counts

3 → 12

Calls

9 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)
1.0ms	x	@	0	(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)
1.0ms	x	@	inf	(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)
0.0ms	x	@	-inf	(cbrt.f64 (*.f64 x (sqrt.f64 2)))
0.0ms	x	@	inf	(cbrt.f64 (*.f64 x (sqrt.f64 2)))

rewrite60.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

1498×	`pow1`
1398×	`add-exp-log`
1396×	`log1p-expm1-u`
1396×	`expm1-log1p-u`
1370×	`add-log-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	37
1	205	37
2	2025	37

Stop Event

1×	node limit

Counts

3 → 64

Calls

Call 1

Inputs
(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)
(cbrt.f64 (*.f64 x (sqrt.f64 2)))
(*.f64 x (sqrt.f64 2))

Outputs
(-.f64 (+.f64 1 (*.f64 x (sqrt.f64 2))) 1)
(*.f64 x (sqrt.f64 2))
(*.f64 (sqrt.f64 2) x)
(.f64 (.f64 x (sqrt.f64 2)) 1)
(.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (cbrt.f64 (.f64 2 (.f64 x x))))
(.f64 1 (.f64 x (sqrt.f64 2)))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 2 (.f64 x x)))) (.f64 (cbrt.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))) (cbrt.f64 (.f64 2 (*.f64 x x)))))
(.f64 (cbrt.f64 2) (.f64 (cbrt.f64 (sqrt.f64 2)) x))
(.f64 (cbrt.f64 (.f64 2 (.f64 x x))) (cbrt.f64 (.f64 x (sqrt.f64 2))))
(.f64 (cbrt.f64 x) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (.f64 2 (.f64 x x)))))
(.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (sqrt.f64 2)))
(.f64 (pow.f64 (.f64 x (sqrt.f64 2)) 1/6) (.f64 (pow.f64 (.f64 x (sqrt.f64 2)) 1/6) (cbrt.f64 (.f64 2 (.f64 x x)))))
(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))
(.f64 (sqrt.f64 (.f64 x (sqrt.f64 2))) (sqrt.f64 (*.f64 x (sqrt.f64 2))))
(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (sqrt.f64 2)))
(.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 2 (.f64 x x)))) 3) (cbrt.f64 (.f64 x (sqrt.f64 2))))
(.f64 (pow.f64 (pow.f64 (.f64 x (sqrt.f64 2)) 1/6) 3) (pow.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 1/6) 3))
(.f64 (.f64 x (cbrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))
(.f64 (.f64 x (pow.f64 2 1/4)) (pow.f64 2 1/4))
(.f64 (.f64 (sqrt.f64 2) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))
(.f64 (.f64 (sqrt.f64 2) (sqrt.f64 x)) (sqrt.f64 x))
(.f64 (.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 1) (cbrt.f64 (*.f64 x (sqrt.f64 2))))
(.f64 (.f64 (cbrt.f64 (.f64 2 (.f64 x x))) (cbrt.f64 (cbrt.f64 (.f64 2 (.f64 x x))))) (cbrt.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2)))))
(.f64 (.f64 (cbrt.f64 (.f64 2 (.f64 x x))) (cbrt.f64 x)) (cbrt.f64 (sqrt.f64 2)))
(.f64 (.f64 (cbrt.f64 (.f64 2 (.f64 x x))) (pow.f64 (.f64 x (sqrt.f64 2)) 1/6)) (pow.f64 (.f64 x (sqrt.f64 2)) 1/6))
(sqrt.f64 (.f64 2 (.f64 x x)))
(log.f64 (pow.f64 (exp.f64 x) (sqrt.f64 2)))
(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))))
(log1p.f64 (expm1.f64 (*.f64 x (sqrt.f64 2))))
(-.f64 (+.f64 1 (cbrt.f64 (*.f64 x (sqrt.f64 2)))) 1)
(.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) 1)
(.f64 1 (cbrt.f64 (.f64 x (sqrt.f64 2))))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))) (cbrt.f64 (cbrt.f64 (.f64 2 (.f64 x x)))))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))) (pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 1/3))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 2 (.f64 x x)))) (cbrt.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))))
(*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 x))
(*.f64 (cbrt.f64 x) (cbrt.f64 (sqrt.f64 2)))
(.f64 (pow.f64 (.f64 x (sqrt.f64 2)) 1/6) (pow.f64 (*.f64 x (sqrt.f64 2)) 1/6))
(.f64 (pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 1/3) (cbrt.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))))
(.f64 (pow.f64 1 1/3) (cbrt.f64 (.f64 x (sqrt.f64 2))))
(.f64 (pow.f64 (sqrt.f64 (.f64 x (sqrt.f64 2))) 1/3) (pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 1/3))
(pow.f64 (*.f64 x (sqrt.f64 2)) 1/3)
(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 1)
(pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2)))) 3)
(pow.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 1/6) 2)
(sqrt.f64 (cbrt.f64 (.f64 2 (.f64 x x))))
(log.f64 (exp.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2)))))
(expm1.f64 (log1p.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2)))))
(exp.f64 (log.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2)))))
(log1p.f64 (expm1.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2)))))
(-.f64 (+.f64 1 (*.f64 x (sqrt.f64 2))) 1)
(pow.f64 (*.f64 x (sqrt.f64 2)) 1)
(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)
(pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 3/2)
(pow.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3) 1/3)
(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
(sqrt.f64 (.f64 2 (.f64 x x)))
(log.f64 (pow.f64 (exp.f64 x) (sqrt.f64 2)))
(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))))
(log1p.f64 (expm1.f64 (*.f64 x (sqrt.f64 2))))

simplify79.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

1720×	`fma-def`
1492×	`log-prod`
700×	`sqr-pow`
656×	`cube-prod`
636×	`distribute-rgt-out`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	115	1244
1	252	1130
2	952	1016
3	2437	1016
4	5083	1016

Stop Event

1×	node limit

Counts

76 → 65

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)
(*.f64 x (sqrt.f64 2))
(*.f64 (sqrt.f64 2) x)
(.f64 (.f64 x (sqrt.f64 2)) 1)
(.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (cbrt.f64 (.f64 2 (.f64 x x))))
(.f64 1 (.f64 x (sqrt.f64 2)))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 2 (.f64 x x)))) (.f64 (cbrt.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))) (cbrt.f64 (.f64 2 (*.f64 x x)))))
(.f64 (cbrt.f64 2) (.f64 (cbrt.f64 (sqrt.f64 2)) x))
(.f64 (cbrt.f64 (.f64 2 (.f64 x x))) (cbrt.f64 (.f64 x (sqrt.f64 2))))
(.f64 (cbrt.f64 x) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (.f64 2 (.f64 x x)))))
(.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (sqrt.f64 2)))
(.f64 (pow.f64 (.f64 x (sqrt.f64 2)) 1/6) (.f64 (pow.f64 (.f64 x (sqrt.f64 2)) 1/6) (cbrt.f64 (.f64 2 (.f64 x x)))))
(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))
(.f64 (sqrt.f64 (.f64 x (sqrt.f64 2))) (sqrt.f64 (*.f64 x (sqrt.f64 2))))
(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (sqrt.f64 2)))
(.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 2 (.f64 x x)))) 3) (cbrt.f64 (.f64 x (sqrt.f64 2))))
(.f64 (pow.f64 (pow.f64 (.f64 x (sqrt.f64 2)) 1/6) 3) (pow.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 1/6) 3))
(.f64 (.f64 x (cbrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))
(.f64 (.f64 x (pow.f64 2 1/4)) (pow.f64 2 1/4))
(.f64 (.f64 (sqrt.f64 2) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))
(.f64 (.f64 (sqrt.f64 2) (sqrt.f64 x)) (sqrt.f64 x))
(.f64 (.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 1) (cbrt.f64 (*.f64 x (sqrt.f64 2))))
(.f64 (.f64 (cbrt.f64 (.f64 2 (.f64 x x))) (cbrt.f64 (cbrt.f64 (.f64 2 (.f64 x x))))) (cbrt.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2)))))
(.f64 (.f64 (cbrt.f64 (.f64 2 (.f64 x x))) (cbrt.f64 x)) (cbrt.f64 (sqrt.f64 2)))
(.f64 (.f64 (cbrt.f64 (.f64 2 (.f64 x x))) (pow.f64 (.f64 x (sqrt.f64 2)) 1/6)) (pow.f64 (.f64 x (sqrt.f64 2)) 1/6))
(sqrt.f64 (.f64 2 (.f64 x x)))
(log.f64 (pow.f64 (exp.f64 x) (sqrt.f64 2)))
(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))))
(log1p.f64 (expm1.f64 (*.f64 x (sqrt.f64 2))))
(-.f64 (+.f64 1 (cbrt.f64 (*.f64 x (sqrt.f64 2)))) 1)
(.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) 1)
(.f64 1 (cbrt.f64 (.f64 x (sqrt.f64 2))))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))) (cbrt.f64 (cbrt.f64 (.f64 2 (.f64 x x)))))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))) (pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 1/3))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 2 (.f64 x x)))) (cbrt.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))))
(*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 x))
(*.f64 (cbrt.f64 x) (cbrt.f64 (sqrt.f64 2)))
(.f64 (pow.f64 (.f64 x (sqrt.f64 2)) 1/6) (pow.f64 (*.f64 x (sqrt.f64 2)) 1/6))
(.f64 (pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 1/3) (cbrt.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))))
(.f64 (pow.f64 1 1/3) (cbrt.f64 (.f64 x (sqrt.f64 2))))
(.f64 (pow.f64 (sqrt.f64 (.f64 x (sqrt.f64 2))) 1/3) (pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 1/3))
(pow.f64 (*.f64 x (sqrt.f64 2)) 1/3)
(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 1)
(pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2)))) 3)
(pow.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 1/6) 2)
(sqrt.f64 (cbrt.f64 (.f64 2 (.f64 x x))))
(log.f64 (exp.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2)))))
(expm1.f64 (log1p.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2)))))
(exp.f64 (log.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2)))))
(log1p.f64 (expm1.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2)))))
(-.f64 (+.f64 1 (*.f64 x (sqrt.f64 2))) 1)
(pow.f64 (*.f64 x (sqrt.f64 2)) 1)
(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)
(pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 3/2)
(pow.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3) 1/3)
(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
(sqrt.f64 (.f64 2 (.f64 x x)))
(log.f64 (pow.f64 (exp.f64 x) (sqrt.f64 2)))
(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))))
(log1p.f64 (expm1.f64 (*.f64 x (sqrt.f64 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 (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)
(*.f64 x (sqrt.f64 2))
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(.f64 (.f64 x (sqrt.f64 2)) 1)
(*.f64 (sqrt.f64 2) x)
(.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (cbrt.f64 (.f64 2 (.f64 x x))))
(*.f64 (sqrt.f64 2) x)
(.f64 1 (.f64 x (sqrt.f64 2)))
(*.f64 (sqrt.f64 2) x)
(.f64 (cbrt.f64 (cbrt.f64 (.f64 2 (.f64 x x)))) (.f64 (cbrt.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))) (cbrt.f64 (.f64 2 (*.f64 x x)))))
(*.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 (.f64 2 (.f64 x x))) (cbrt.f64 (.f64 x (sqrt.f64 2))))
(*.f64 (sqrt.f64 2) x)
(.f64 (cbrt.f64 x) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (.f64 2 (.f64 x x)))))
(.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 x)) (cbrt.f64 (.f64 2 (.f64 x x))))
(.f64 (cbrt.f64 (.f64 2 (.f64 x x))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 x)))
(.f64 (cbrt.f64 x) (.f64 (cbrt.f64 (.f64 x (.f64 2 x))) (cbrt.f64 (sqrt.f64 2))))
(.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (sqrt.f64 2)))
(*.f64 (sqrt.f64 2) x)
(.f64 (pow.f64 (.f64 x (sqrt.f64 2)) 1/6) (.f64 (pow.f64 (.f64 x (sqrt.f64 2)) 1/6) (cbrt.f64 (.f64 2 (.f64 x x)))))
(*.f64 (sqrt.f64 2) x)
(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))
(*.f64 (sqrt.f64 2) x)
(.f64 (sqrt.f64 (.f64 x (sqrt.f64 2))) (sqrt.f64 (*.f64 x (sqrt.f64 2))))
(*.f64 (sqrt.f64 2) x)
(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (sqrt.f64 2)))
(*.f64 (sqrt.f64 2) x)
(.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 2 (.f64 x x)))) 3) (cbrt.f64 (.f64 x (sqrt.f64 2))))
(*.f64 (sqrt.f64 2) x)
(.f64 (pow.f64 (pow.f64 (.f64 x (sqrt.f64 2)) 1/6) 3) (pow.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 1/6) 3))
(*.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 (.f64 x (pow.f64 2 1/4)) (pow.f64 2 1/4))
(*.f64 (sqrt.f64 2) x)
(.f64 (.f64 (sqrt.f64 2) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))
(*.f64 (sqrt.f64 2) x)
(.f64 (.f64 (sqrt.f64 2) (sqrt.f64 x)) (sqrt.f64 x))
(*.f64 (sqrt.f64 2) x)
(.f64 (.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 1) (cbrt.f64 (*.f64 x (sqrt.f64 2))))
(*.f64 (sqrt.f64 2) x)
(.f64 (.f64 (cbrt.f64 (.f64 2 (.f64 x x))) (cbrt.f64 (cbrt.f64 (.f64 2 (.f64 x x))))) (cbrt.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2)))))
(*.f64 (sqrt.f64 2) x)
(.f64 (.f64 (cbrt.f64 (.f64 2 (.f64 x x))) (cbrt.f64 x)) (cbrt.f64 (sqrt.f64 2)))
(.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 x)) (cbrt.f64 (.f64 2 (.f64 x x))))
(.f64 (cbrt.f64 (.f64 2 (.f64 x x))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 x)))
(.f64 (cbrt.f64 x) (.f64 (cbrt.f64 (.f64 x (.f64 2 x))) (cbrt.f64 (sqrt.f64 2))))
(.f64 (.f64 (cbrt.f64 (.f64 2 (.f64 x x))) (pow.f64 (.f64 x (sqrt.f64 2)) 1/6)) (pow.f64 (.f64 x (sqrt.f64 2)) 1/6))
(*.f64 (sqrt.f64 2) x)
(sqrt.f64 (.f64 2 (.f64 x x)))
(*.f64 (sqrt.f64 2) x)
(log.f64 (pow.f64 (exp.f64 x) (sqrt.f64 2)))
(*.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)
(log1p.f64 (expm1.f64 (*.f64 x (sqrt.f64 2))))
(*.f64 (sqrt.f64 2) x)
(-.f64 (+.f64 1 (cbrt.f64 (*.f64 x (sqrt.f64 2)))) 1)
(+.f64 1 (-.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 1))
(+.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 0)
(cbrt.f64 (*.f64 (sqrt.f64 2) x))
(.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) 1)
(+.f64 1 (-.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 1))
(+.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 0)
(cbrt.f64 (*.f64 (sqrt.f64 2) x))
(.f64 1 (cbrt.f64 (.f64 x (sqrt.f64 2))))
(+.f64 1 (-.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 1))
(+.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 0)
(cbrt.f64 (*.f64 (sqrt.f64 2) x))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))) (cbrt.f64 (cbrt.f64 (.f64 2 (.f64 x x)))))
(+.f64 1 (-.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 1))
(+.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 0)
(cbrt.f64 (*.f64 (sqrt.f64 2) x))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))) (pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 1/3))
(+.f64 1 (-.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 1))
(+.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 0)
(cbrt.f64 (*.f64 (sqrt.f64 2) x))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 2 (.f64 x x)))) (cbrt.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))))
(+.f64 1 (-.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 1))
(+.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 0)
(cbrt.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 x))
(*.f64 (cbrt.f64 x) (cbrt.f64 (sqrt.f64 2)))
(*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 x))
(.f64 (pow.f64 (.f64 x (sqrt.f64 2)) 1/6) (pow.f64 (*.f64 x (sqrt.f64 2)) 1/6))
(+.f64 1 (-.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 1))
(+.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 0)
(cbrt.f64 (*.f64 (sqrt.f64 2) x))
(.f64 (pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 1/3) (cbrt.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))))
(+.f64 1 (-.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 1))
(+.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 0)
(cbrt.f64 (*.f64 (sqrt.f64 2) x))
(.f64 (pow.f64 1 1/3) (cbrt.f64 (.f64 x (sqrt.f64 2))))
(+.f64 1 (-.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 1))
(+.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 0)
(cbrt.f64 (*.f64 (sqrt.f64 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))
(+.f64 1 (-.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 1))
(+.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 0)
(cbrt.f64 (*.f64 (sqrt.f64 2) x))
(pow.f64 (*.f64 x (sqrt.f64 2)) 1/3)
(+.f64 1 (-.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 1))
(+.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 0)
(cbrt.f64 (*.f64 (sqrt.f64 2) x))
(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 1)
(+.f64 1 (-.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 1))
(+.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 0)
(cbrt.f64 (*.f64 (sqrt.f64 2) x))
(pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2)))) 3)
(+.f64 1 (-.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 1))
(+.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 0)
(cbrt.f64 (*.f64 (sqrt.f64 2) x))
(pow.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 1/6) 2)
(+.f64 1 (-.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 1))
(+.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 0)
(cbrt.f64 (*.f64 (sqrt.f64 2) x))
(sqrt.f64 (cbrt.f64 (.f64 2 (.f64 x x))))
(+.f64 1 (-.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 1))
(+.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 0)
(cbrt.f64 (*.f64 (sqrt.f64 2) x))
(log.f64 (exp.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2)))))
(+.f64 1 (-.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 1))
(+.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 0)
(cbrt.f64 (*.f64 (sqrt.f64 2) x))
(expm1.f64 (log1p.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2)))))
(+.f64 1 (-.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 1))
(+.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 0)
(cbrt.f64 (*.f64 (sqrt.f64 2) x))
(exp.f64 (log.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2)))))
(+.f64 1 (-.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 1))
(+.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 0)
(cbrt.f64 (*.f64 (sqrt.f64 2) x))
(log1p.f64 (expm1.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2)))))
(+.f64 1 (-.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 1))
(+.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 0)
(cbrt.f64 (*.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 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)
(*.f64 (sqrt.f64 2) x)
(pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 3/2)
(*.f64 (sqrt.f64 2) x)
(pow.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3) 1/3)
(*.f64 (sqrt.f64 2) x)
(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
(*.f64 (sqrt.f64 2) x)
(sqrt.f64 (.f64 2 (.f64 x x)))
(*.f64 (sqrt.f64 2) x)
(log.f64 (pow.f64 (exp.f64 x) (sqrt.f64 2)))
(*.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)
(log1p.f64 (expm1.f64 (*.f64 x (sqrt.f64 2))))
(*.f64 (sqrt.f64 2) x)

localize39.0ms (1%)

Local Accuracy

Found 3 expressions with local accuracy:

New	Accuracy	Program
✓	99.9%	(sqrt.f64 (*.f64 x (sqrt.f64 2)))
	99.7%	(*.f64 x (sqrt.f64 2))
✓	99.6%	(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)

Compiler

Compiled 22 to 18 computations (18.2% saved)

series4.0ms (0.1%)

Counts

2 → 0

Calls

6 calls:

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

rewrite52.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

1328×	`pow1`
1220×	`add-exp-log`
1220×	`log1p-expm1-u`
1220×	`expm1-log1p-u`
1190×	`add-log-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	26
1	182	26
2	1761	26

Stop Event

1×	node limit

Counts

2 → 50

Calls

Call 1

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

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

simplify70.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

1478×	`exp-sum`
1026×	`fma-def`
870×	`distribute-rgt-in`
848×	`distribute-lft-in`
756×	`associate-+r+`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	107	1308
1	215	1074
2	761	840
3	2626	838
4	7133	838

Stop Event

1×	node limit

Counts

50 → 65

Calls

Call 1

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

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

eval42.0ms (1%)

Compiler: Compiled 1724 to 1382 computations (19.8% saved)

prune17.0ms (0.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	186	1	187
Fresh	2	0	2
Picked	1	0	1
Done	2	3	5
Total	191	4	195

Accurracy

100.0%

Counts

195 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(hypot.f64 x x)
✓	50.2%	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
✓	50.4%	(*.f64 (sqrt.f64 2) (neg.f64 x))
✓	54.0%	(sqrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 25 to 18 computations (28% saved)

localize19.0ms (0.5%)

Local Accuracy

Found 1 expressions with local accuracy:

New	Accuracy	Program
✓	100.0%	(hypot.f64 x x)

Compiler

Compiled 6 to 3 computations (50% saved)

series3.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

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

rewrite85.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

738×	`pow1`
704×	`add-sqr-sqrt`
696×	`*-un-lft-identity`
674×	`add-exp-log`
674×	`log1p-expm1-u`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	7
1	80	7
2	933	7

Stop Event

1×	node limit

Counts

1 → 41

Calls

Call 1

Inputs
(hypot.f64 x x)

Outputs
(+.f64 0 (hypot.f64 x x))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 x x)))) (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 x x)))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (hypot.f64 x x))) 2)) (log.f64 (cbrt.f64 (exp.f64 (hypot.f64 x x)))))
(-.f64 (+.f64 1 (hypot.f64 x x)) 1)
(*.f64 (hypot.f64 x x) 1)
(*.f64 1 (hypot.f64 x x))
(*.f64 (cbrt.f64 (hypot.f64 x x)) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))
(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (cbrt.f64 (hypot.f64 x x)))
(*.f64 (sqrt.f64 x) (pow.f64 (+.f64 x x) 1/2))
(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)) (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 4) 1/2))
(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (pow.f64 (hypot.f64 x x) 3/2) 1/2))
(*.f64 (cbrt.f64 (pow.f64 (hypot.f64 x x) 5/2)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))
(.f64 (cbrt.f64 (pow.f64 (.f64 (hypot.f64 x x) (cbrt.f64 (hypot.f64 x x))) 2)) (cbrt.f64 (cbrt.f64 (hypot.f64 x x))))
(*.f64 (pow.f64 1 1/3) (hypot.f64 x x))
(*.f64 (pow.f64 1 1/2) (hypot.f64 x x))
(*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) 3))
(.f64 (pow.f64 (pow.f64 (.f64 (hypot.f64 x x) (cbrt.f64 (hypot.f64 x x))) 2) 1/3) (cbrt.f64 (cbrt.f64 (hypot.f64 x x))))
(*.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 5/2) 1/3) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 4) 1/2) (sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)))
(*.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 3/2) 1/2) (sqrt.f64 (sqrt.f64 (hypot.f64 x x))))
(*.f64 (pow.f64 2 1/2) x)
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5) 1/2) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))
(pow.f64 (hypot.f64 x x) 1)
(pow.f64 (cbrt.f64 (hypot.f64 x x)) 3)
(pow.f64 (pow.f64 (hypot.f64 x x) 3) 1/3)
(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)
(pow.f64 (*.f64 x (+.f64 x x)) 1/2)
(pow.f64 (E.f64) (log.f64 (hypot.f64 x x)))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (hypot.f64 x x))) 2)) (cbrt.f64 (log.f64 (hypot.f64 x x))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (hypot.f64 x x)))) (sqrt.f64 (log.f64 (hypot.f64 x x))))
(sqrt.f64 (*.f64 x (+.f64 x x)))
(log.f64 (exp.f64 (hypot.f64 x x)))
(cbrt.f64 (pow.f64 (hypot.f64 x x) 3))
(expm1.f64 (log1p.f64 (hypot.f64 x x)))
(exp.f64 (log.f64 (hypot.f64 x x)))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (hypot.f64 x x))) 3))
(exp.f64 (.f64 (.f64 3 (log.f64 (hypot.f64 x x))) 1/3))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (hypot.f64 x x))) 2))
(exp.f64 (.f64 (.f64 2 (log.f64 (hypot.f64 x x))) 1/2))
(log1p.f64 (expm1.f64 (hypot.f64 x x)))

simplify50.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

924×	`associate-r`
884×	`log-prod`
766×	`associate-l`
738×	`associate-+r+`
718×	`associate-+l+`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	116	717
1	249	681
2	686	669
3	4006	669

Stop Event

1×	node limit

Counts

53 → 55

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 0 (hypot.f64 x x))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 x x)))) (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 x x)))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (hypot.f64 x x))) 2)) (log.f64 (cbrt.f64 (exp.f64 (hypot.f64 x x)))))
(-.f64 (+.f64 1 (hypot.f64 x x)) 1)
(*.f64 (hypot.f64 x x) 1)
(*.f64 1 (hypot.f64 x x))
(*.f64 (cbrt.f64 (hypot.f64 x x)) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))
(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (cbrt.f64 (hypot.f64 x x)))
(*.f64 (sqrt.f64 x) (pow.f64 (+.f64 x x) 1/2))
(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)) (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 4) 1/2))
(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (pow.f64 (hypot.f64 x x) 3/2) 1/2))
(*.f64 (cbrt.f64 (pow.f64 (hypot.f64 x x) 5/2)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))
(.f64 (cbrt.f64 (pow.f64 (.f64 (hypot.f64 x x) (cbrt.f64 (hypot.f64 x x))) 2)) (cbrt.f64 (cbrt.f64 (hypot.f64 x x))))
(*.f64 (pow.f64 1 1/3) (hypot.f64 x x))
(*.f64 (pow.f64 1 1/2) (hypot.f64 x x))
(*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) 3))
(.f64 (pow.f64 (pow.f64 (.f64 (hypot.f64 x x) (cbrt.f64 (hypot.f64 x x))) 2) 1/3) (cbrt.f64 (cbrt.f64 (hypot.f64 x x))))
(*.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 5/2) 1/3) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 4) 1/2) (sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)))
(*.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 3/2) 1/2) (sqrt.f64 (sqrt.f64 (hypot.f64 x x))))
(*.f64 (pow.f64 2 1/2) x)
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5) 1/2) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))
(pow.f64 (hypot.f64 x x) 1)
(pow.f64 (cbrt.f64 (hypot.f64 x x)) 3)
(pow.f64 (pow.f64 (hypot.f64 x x) 3) 1/3)
(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)
(pow.f64 (*.f64 x (+.f64 x x)) 1/2)
(pow.f64 (E.f64) (log.f64 (hypot.f64 x x)))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (hypot.f64 x x))) 2)) (cbrt.f64 (log.f64 (hypot.f64 x x))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (hypot.f64 x x)))) (sqrt.f64 (log.f64 (hypot.f64 x x))))
(sqrt.f64 (*.f64 x (+.f64 x x)))
(log.f64 (exp.f64 (hypot.f64 x x)))
(cbrt.f64 (pow.f64 (hypot.f64 x x) 3))
(expm1.f64 (log1p.f64 (hypot.f64 x x)))
(exp.f64 (log.f64 (hypot.f64 x x)))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (hypot.f64 x x))) 3))
(exp.f64 (.f64 (.f64 3 (log.f64 (hypot.f64 x x))) 1/3))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (hypot.f64 x x))) 2))
(exp.f64 (.f64 (.f64 2 (log.f64 (hypot.f64 x x))) 1/2))
(log1p.f64 (expm1.f64 (hypot.f64 x x)))

Outputs
(*.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 0 (hypot.f64 x x))
(hypot.f64 x x)
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 x x)))) (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 x x)))))
(hypot.f64 x x)
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (hypot.f64 x x))) 2)) (log.f64 (cbrt.f64 (exp.f64 (hypot.f64 x x)))))
(+.f64 (*.f64 2 (log.f64 (cbrt.f64 (exp.f64 (hypot.f64 x x))))) (log.f64 (cbrt.f64 (exp.f64 (hypot.f64 x x)))))
(*.f64 3 (log.f64 (cbrt.f64 (exp.f64 (hypot.f64 x x)))))
(*.f64 (log.f64 (cbrt.f64 (exp.f64 (hypot.f64 x x)))) 3)
(-.f64 (+.f64 1 (hypot.f64 x x)) 1)
(hypot.f64 x x)
(*.f64 (hypot.f64 x x) 1)
(hypot.f64 x x)
(*.f64 1 (hypot.f64 x x))
(hypot.f64 x x)
(*.f64 (cbrt.f64 (hypot.f64 x x)) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))
(hypot.f64 x x)
(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (cbrt.f64 (hypot.f64 x x)))
(hypot.f64 x x)
(*.f64 (sqrt.f64 x) (pow.f64 (+.f64 x x) 1/2))
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
(hypot.f64 x x)
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)) (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 4) 1/2))
(hypot.f64 x x)
(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (pow.f64 (hypot.f64 x x) 3/2) 1/2))
(hypot.f64 x x)
(*.f64 (cbrt.f64 (pow.f64 (hypot.f64 x x) 5/2)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))
(*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (cbrt.f64 (pow.f64 (hypot.f64 x x) 5/2)))
(.f64 (cbrt.f64 (pow.f64 (.f64 (hypot.f64 x x) (cbrt.f64 (hypot.f64 x x))) 2)) (cbrt.f64 (cbrt.f64 (hypot.f64 x x))))
(.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) (cbrt.f64 (pow.f64 (.f64 (hypot.f64 x x) (cbrt.f64 (hypot.f64 x x))) 2)))
(*.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) (cbrt.f64 (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 4) 2)))
(*.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) (cbrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 8)))
(*.f64 (pow.f64 1 1/3) (hypot.f64 x x))
(hypot.f64 x x)
(*.f64 (pow.f64 1 1/2) (hypot.f64 x x))
(hypot.f64 x x)
(*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) 3))
(hypot.f64 x x)
(.f64 (pow.f64 (pow.f64 (.f64 (hypot.f64 x x) (cbrt.f64 (hypot.f64 x x))) 2) 1/3) (cbrt.f64 (cbrt.f64 (hypot.f64 x x))))
(.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) (cbrt.f64 (pow.f64 (.f64 (hypot.f64 x x) (cbrt.f64 (hypot.f64 x x))) 2)))
(*.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) (cbrt.f64 (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 4) 2)))
(*.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) (cbrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 8)))
(*.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 5/2) 1/3) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))
(*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (cbrt.f64 (pow.f64 (hypot.f64 x x) 5/2)))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 4) 1/2) (sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)))
(hypot.f64 x x)
(*.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 3/2) 1/2) (sqrt.f64 (sqrt.f64 (hypot.f64 x x))))
(hypot.f64 x x)
(*.f64 (pow.f64 2 1/2) x)
(*.f64 x (sqrt.f64 2))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5) 1/2) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))
(hypot.f64 x x)
(pow.f64 (hypot.f64 x x) 1)
(hypot.f64 x x)
(pow.f64 (cbrt.f64 (hypot.f64 x x)) 3)
(hypot.f64 x x)
(pow.f64 (pow.f64 (hypot.f64 x x) 3) 1/3)
(hypot.f64 x x)
(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)
(hypot.f64 x x)
(pow.f64 (*.f64 x (+.f64 x x)) 1/2)
(hypot.f64 x x)
(pow.f64 (E.f64) (log.f64 (hypot.f64 x x)))
(hypot.f64 x x)
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (hypot.f64 x x))) 2)) (cbrt.f64 (log.f64 (hypot.f64 x x))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (hypot.f64 x x)))) (sqrt.f64 (log.f64 (hypot.f64 x x))))
(sqrt.f64 (*.f64 x (+.f64 x x)))
(hypot.f64 x x)
(log.f64 (exp.f64 (hypot.f64 x x)))
(hypot.f64 x x)
(cbrt.f64 (pow.f64 (hypot.f64 x x) 3))
(hypot.f64 x x)
(expm1.f64 (log1p.f64 (hypot.f64 x x)))
(hypot.f64 x x)
(exp.f64 (log.f64 (hypot.f64 x x)))
(hypot.f64 x x)
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (hypot.f64 x x))) 3))
(hypot.f64 x x)
(exp.f64 (.f64 (.f64 3 (log.f64 (hypot.f64 x x))) 1/3))
(hypot.f64 x x)
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (hypot.f64 x x))) 2))
(hypot.f64 x x)
(exp.f64 (.f64 (.f64 2 (log.f64 (hypot.f64 x x))) 1/2))
(hypot.f64 x x)
(log1p.f64 (expm1.f64 (hypot.f64 x x)))
(hypot.f64 x x)

eval9.0ms (0.2%)

Compiler: Compiled 507 to 205 computations (59.6% saved)

prune16.0ms (0.4%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	55	0	55
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	55	4	59

Accurracy

100.0%

Counts

59 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
✓	50.2%	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
✓	50.4%	(*.f64 (sqrt.f64 2) (neg.f64 x))
✓	54.0%	(sqrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 25 to 18 computations (28% saved)

regimes51.0ms (1.2%)

Accuracy

Total -63.3b remaining (-539739.4%)

Threshold costs -63.3b (-539739.4%)

Counts

10 → 1

Calls

Call 1

Inputs
(hypot.f64 x x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) (neg.f64 x))
(sqrt.f64 (.f64 2 (.f64 x x)))
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)
(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
(.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (cbrt.f64 (.f64 2 (.f64 x x))))
(.f64 (sqrt.f64 (cbrt.f64 (.f64 (pow.f64 x 4) 4))) (sqrt.f64 (cbrt.f64 (.f64 2 (.f64 x x)))))

Outputs
(hypot.f64 x x)

Calls

4 calls:

35.0ms	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
6.0ms	x
4.0ms	(pow.f64 x 2)
4.0ms	(*.f64 2 (pow.f64 x 2))

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(sqrt.f64 (*.f64 2 (pow.f64 x 2)))`
100.0%	1	`(*.f64 2 (pow.f64 x 2))`
100.0%	1	`(pow.f64 x 2)`

Compiler

Compiled 92 to 69 computations (25% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	7

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(hypot.f64 x x)

Outputs
(hypot.f64 x x)

Compiler

Compiled 4 to 2 computations (50% saved)

soundness614.0ms (14.9%)

Rules

2734×	`sqr-pow`
1844×	`log-prod`
1366×	`log-prod`
1306×	`cube-prod`
1248×	`pow1`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	14	17
2	25	17
3	46	17
4	106	17
5	329	17
6	1230	17
7	2094	17
8	2234	17
9	2402	17
10	2599	17
11	2878	17
12	3246	17
13	3692	17
14	4220	17
15	4862	17
16	5641	17
17	5967	17
18	6241	17
19	6447	17
20	6507	17
21	6537	17
22	7472	17
0	61	504
1	138	504
2	486	504
3	2721	504
4	6903	504
0	8	15
1	163	11
2	1913	11
0	37	463
1	91	397
2	335	331
3	1761	331
4	4925	331
5	7956	231

Stop Event

1×	node limit
1×	node limit
1×	node limit
1×	node limit

Compiler

Compiled 353 to 290 computations (17.8% saved)

end24.0ms (0.6%)

Compiler: Compiled 22 to 16 computations (27.3% saved)

Details

analyze0.0ms (0%)

sample1.7s (40.6%)

preprocess213.0ms (5.2%)

simplify207.0ms (5%)

eval1.0ms (0%)

prune1.0ms (0%)

localize26.0ms (0.6%)

series1.0ms (0%)

rewrite61.0ms (1.5%)

simplify66.0ms (1.6%)

eval6.0ms (0.1%)

prune11.0ms (0.3%)

localize22.0ms (0.5%)

series0.0ms (0%)

rewrite96.0ms (2.3%)

simplify61.0ms (1.5%)

localize24.0ms (0.6%)

series0.0ms (0%)

rewrite49.0ms (1.2%)

simplify76.0ms (1.8%)

localize43.0ms (1%)

series1.0ms (0%)

rewrite54.0ms (1.3%)

simplify64.0ms (1.6%)

localize118.0ms (2.9%)

series4.0ms (0.1%)

rewrite60.0ms (1.5%)

simplify79.0ms (1.9%)

localize39.0ms (1%)

series4.0ms (0.1%)

rewrite52.0ms (1.3%)

simplify70.0ms (1.7%)

eval42.0ms (1%)

prune17.0ms (0.4%)

localize19.0ms (0.5%)

series3.0ms (0.1%)

rewrite85.0ms (2.1%)

simplify50.0ms (1.2%)

eval9.0ms (0.2%)

prune16.0ms (0.4%)

regimes51.0ms (1.2%)

simplify4.0ms (0.1%)

soundness614.0ms (14.9%)

end24.0ms (0.6%)

Profiling