Details

analyze3.0ms (0.2%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
0%	0%	100%	0%	0%	0%	0%	2
0%	0%	50%	0%	0%	50%	0%	3
50%	25%	25%	0%	0%	50%	0%	4
75%	37.5%	12.5%	0%	0%	50%	0%	5
87.5%	43.7%	6.2%	0%	0%	50%	0%	6
93.8%	46.9%	3.1%	0%	0%	50%	0%	7
96.9%	48.4%	1.6%	0%	0%	50%	0%	8
98.4%	49.2%	0.8%	0%	0%	50%	0%	9
99.2%	49.6%	0.4%	0%	0%	50%	0%	10
99.6%	49.8%	0.2%	0%	0%	50%	0%	11
99.8%	49.9%	0.1%	0%	0%	50%	0%	12

Compiler

Compiled 8 to 6 computations (25% saved)

sample932.0ms (52.1%)

Results

921.0ms	8256×	body	256	valid
0.0ms	4×	body	256	invalid

Bogosity

preprocess136.0ms (7.6%)

Algorithm

2×	egg-herbie

Rules

1212×	`+-commutative`
1106×	`distribute-lft-in`
1032×	`*-commutative`
962×	`distribute-rgt-in`
904×	`fma-def`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	15	17
2	23	17
3	34	17
4	50	17
5	87	17
6	141	17
7	312	17
8	892	17
9	1737	17
10	3073	17
11	5153	17
12	6204	17
13	6616	17
14	6904	17
15	7040	17
16	7117	17
17	7412	17
0	1	1

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0

Outputs
0

Call 2

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

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

Compiler

Compiled 8 to 6 computations (25% saved)

simplify142.0ms (7.9%)

Algorithm

1×	egg-herbie

Rules

1212×	`+-commutative`
1106×	`distribute-lft-in`
1032×	`*-commutative`
962×	`distribute-rgt-in`
904×	`fma-def`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	15	17
2	23	17
3	34	17
4	50	17
5	87	17
6	141	17
7	312	17
8	892	17
9	1737	17
10	3073	17
11	5153	17
12	6204	17
13	6616	17
14	6904	17
15	7040	17
16	7117	17
17	7412	17

Stop Event

1×	node limit

Counts

1 → 2

Calls

Call 1

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

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

eval1.0ms (0%)

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

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.0b

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.0b	(sqrt.f64 (-.f64 1 (*.f64 x x)))

Compiler

Compiled 7 to 5 computations (28.6% saved)

localize6.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (-.f64 1 (*.f64 x x)))

Compiler

Compiled 17 to 8 computations (52.9% saved)

series1.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	x	@	inf	(sqrt.f64 (-.f64 1 (*.f64 x x)))
0.0ms	x	@	-inf	(sqrt.f64 (-.f64 1 (*.f64 x x)))
0.0ms	x	@	0	(sqrt.f64 (-.f64 1 (*.f64 x x)))

rewrite51.0ms (2.9%)

Algorithm

1×	batch-egg-rewrite

Rules

1534×	`add-sqr-sqrt`
1512×	`*-un-lft-identity`
1410×	`add-cube-cbrt`
1400×	`add-cbrt-cube`
1394×	`add-exp-log`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	163	17
2	2006	17

Stop Event

1×	node limit

Counts

1 → 24

Calls

Call 1

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

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

Outputs

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

simplify71.0ms (4%)

Algorithm

1×	egg-herbie

Rules

998×	`associate-/r/`
738×	`*-commutative`
716×	`associate--r+`
680×	`unswap-sqr`
596×	`associate-*r/`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	112	1318
1	275	1170
2	790	1042
3	2409	994
4	6659	994

Stop Event

1×	node limit

Counts

36 → 86

Calls

Call 1

Inputs
1
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 -1/8 (pow.f64 x 4))))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (+.f64 (.f64 -1/16 (pow.f64 x 6)) (*.f64 -1/8 (pow.f64 x 4)))))
(*.f64 (sqrt.f64 -1) x)
(+.f64 (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 -1) x))) (*.f64 (sqrt.f64 -1) x))
(-.f64 (+.f64 (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 -1) x))) (.f64 (sqrt.f64 -1) x)) (.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))))
(-.f64 (+.f64 (.f64 1/16 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5)))) (+.f64 (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 -1) x))) (.f64 (sqrt.f64 -1) x))) (.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))))
(.f64 -1 (.f64 (sqrt.f64 -1) x))
(-.f64 (.f64 -1 (.f64 (sqrt.f64 -1) x)) (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 -1) x))))
(-.f64 (+.f64 (.f64 1/8 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))) (.f64 -1 (.f64 (sqrt.f64 -1) x))) (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 -1) x))))
(-.f64 (+.f64 (.f64 1/8 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))) (.f64 -1 (.f64 (sqrt.f64 -1) x))) (+.f64 (.f64 1/16 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5)))) (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 -1) x)))))
(-.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) 1)
(.f64 1 (sqrt.f64 (-.f64 1 (.f64 x x))))
(.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) 1)
(.f64 (pow.f64 (-.f64 1 (.f64 x x)) 1/4) (pow.f64 (-.f64 1 (*.f64 x x)) 1/4))
(.f64 (cbrt.f64 (sqrt.f64 (-.f64 1 (.f64 x x)))) (cbrt.f64 (-.f64 1 (*.f64 x x))))
(.f64 (cbrt.f64 (-.f64 1 (.f64 x x))) (cbrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))
(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (-.f64 1 (.f64 x x))) 2)) (sqrt.f64 (cbrt.f64 (-.f64 1 (*.f64 x x)))))
(.f64 (pow.f64 1 1/2) (sqrt.f64 (-.f64 1 (.f64 x x))))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (-.f64 1 (.f64 x x))) 2) 1/2) (pow.f64 (cbrt.f64 (-.f64 1 (*.f64 x x))) 1/2))
(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 6))) (sqrt.f64 (+.f64 1 (+.f64 (*.f64 x x) (pow.f64 x 4)))))
(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 4))) (sqrt.f64 (+.f64 1 (*.f64 x x))))
(pow.f64 (-.f64 1 (*.f64 x x)) 1/2)
(pow.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1)
(pow.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 1/4) 2)
(pow.f64 (cbrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) 3)
(pow.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 3/2) 1/3)
(fabs.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))))
(log.f64 (exp.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))
(cbrt.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))
(exp.f64 (log.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))
(exp.f64 (.f64 (log1p.f64 (.f64 x (neg.f64 x))) 1/2))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (-.f64 1 (.f64 x x)))) 1))
(log1p.f64 (expm1.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))

Outputs
1
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 1 (.f64 -1/2 (.f64 x x)))
(fma.f64 -1/2 (*.f64 x x) 1)
(fma.f64 x (*.f64 -1/2 x) 1)
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 -1/8 (pow.f64 x 4))))
(+.f64 1 (fma.f64 -1/2 (.f64 x x) (.f64 -1/8 (pow.f64 x 4))))
(fma.f64 -1/2 (*.f64 x x) (fma.f64 -1/8 (pow.f64 x 4) 1))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (+.f64 (.f64 -1/16 (pow.f64 x 6)) (*.f64 -1/8 (pow.f64 x 4)))))
(+.f64 1 (fma.f64 -1/2 (.f64 x x) (fma.f64 -1/16 (pow.f64 x 6) (.f64 -1/8 (pow.f64 x 4)))))
(+.f64 1 (fma.f64 -1/2 (.f64 x x) (fma.f64 -1/8 (pow.f64 x 4) (.f64 -1/16 (pow.f64 x 6)))))
(+.f64 1 (fma.f64 -1/8 (pow.f64 x 4) (fma.f64 -1/16 (pow.f64 x 6) (.f64 x (.f64 -1/2 x)))))
(+.f64 (fma.f64 -1/2 (.f64 x x) 1) (fma.f64 -1/8 (pow.f64 x 4) (.f64 -1/16 (pow.f64 x 6))))
(*.f64 (sqrt.f64 -1) x)
(*.f64 x (sqrt.f64 -1))
(+.f64 (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 -1) x))) (*.f64 (sqrt.f64 -1) x))
(+.f64 (.f64 x (sqrt.f64 -1)) (/.f64 1/2 (.f64 x (sqrt.f64 -1))))
(fma.f64 x (sqrt.f64 -1) (/.f64 (/.f64 1/2 x) (sqrt.f64 -1)))
(fma.f64 x (sqrt.f64 -1) (/.f64 (/.f64 1/2 (sqrt.f64 -1)) x))
(-.f64 (+.f64 (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 -1) x))) (.f64 (sqrt.f64 -1) x)) (.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))))
(+.f64 (/.f64 1/2 (.f64 x (sqrt.f64 -1))) (-.f64 (.f64 x (sqrt.f64 -1)) (/.f64 1/8 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))))
(-.f64 (fma.f64 x (sqrt.f64 -1) (/.f64 (/.f64 1/2 x) (sqrt.f64 -1))) (/.f64 (/.f64 1/8 (pow.f64 x 3)) (neg.f64 (sqrt.f64 -1))))
(+.f64 (/.f64 (/.f64 1/2 x) (sqrt.f64 -1)) (fma.f64 x (sqrt.f64 -1) (/.f64 1/8 (*.f64 (sqrt.f64 -1) (pow.f64 x 3)))))
(+.f64 (/.f64 (/.f64 1/2 (sqrt.f64 -1)) x) (fma.f64 x (sqrt.f64 -1) (/.f64 (/.f64 1/8 (pow.f64 x 3)) (sqrt.f64 -1))))
(-.f64 (+.f64 (.f64 1/16 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5)))) (+.f64 (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 -1) x))) (.f64 (sqrt.f64 -1) x))) (.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))))
(+.f64 (/.f64 1/16 (.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5))) (+.f64 (/.f64 1/2 (.f64 x (sqrt.f64 -1))) (-.f64 (.f64 x (sqrt.f64 -1)) (/.f64 1/8 (.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3))))))
(+.f64 (fma.f64 x (sqrt.f64 -1) (/.f64 (/.f64 1/2 x) (sqrt.f64 -1))) (-.f64 (/.f64 (/.f64 1/16 (pow.f64 x 5)) (pow.f64 (sqrt.f64 -1) 5)) (/.f64 (/.f64 1/8 (pow.f64 x 3)) (neg.f64 (sqrt.f64 -1)))))
(+.f64 (/.f64 (/.f64 1/2 x) (sqrt.f64 -1)) (-.f64 (fma.f64 x (sqrt.f64 -1) (/.f64 1/16 (*.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5)))) (/.f64 (/.f64 -1/8 (sqrt.f64 -1)) (pow.f64 x 3))))
(-.f64 (fma.f64 x (sqrt.f64 -1) (/.f64 1/16 (.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5)))) (.f64 (/.f64 (/.f64 -1 x) (sqrt.f64 -1)) (+.f64 (/.f64 1/8 (*.f64 x x)) 1/2)))
(-.f64 (fma.f64 x (sqrt.f64 -1) (/.f64 1/16 (.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5)))) (.f64 (/.f64 (/.f64 -1 x) (sqrt.f64 -1)) (+.f64 1/2 (/.f64 1/8 (*.f64 x x)))))
(.f64 -1 (.f64 (sqrt.f64 -1) x))
(neg.f64 (*.f64 x (sqrt.f64 -1)))
(*.f64 x (neg.f64 (sqrt.f64 -1)))
(-.f64 (.f64 -1 (.f64 (sqrt.f64 -1) x)) (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 -1) x))))
(-.f64 (neg.f64 (.f64 x (sqrt.f64 -1))) (/.f64 1/2 (.f64 x (sqrt.f64 -1))))
(neg.f64 (fma.f64 x (sqrt.f64 -1) (/.f64 (/.f64 1/2 x) (sqrt.f64 -1))))
(-.f64 (/.f64 (/.f64 -1/2 x) (sqrt.f64 -1)) (*.f64 x (sqrt.f64 -1)))
(-.f64 (/.f64 -1/2 (.f64 x (sqrt.f64 -1))) (.f64 x (sqrt.f64 -1)))
(-.f64 (+.f64 (.f64 1/8 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))) (.f64 -1 (.f64 (sqrt.f64 -1) x))) (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 -1) x))))
(+.f64 (/.f64 1/8 (.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3))) (-.f64 (neg.f64 (.f64 x (sqrt.f64 -1))) (/.f64 1/2 (*.f64 x (sqrt.f64 -1)))))
(fma.f64 1/8 (/.f64 (/.f64 -1 (sqrt.f64 -1)) (pow.f64 x 3)) (neg.f64 (fma.f64 x (sqrt.f64 -1) (/.f64 (/.f64 1/2 x) (sqrt.f64 -1)))))
(-.f64 (/.f64 (/.f64 -1/8 (sqrt.f64 -1)) (pow.f64 x 3)) (fma.f64 x (sqrt.f64 -1) (/.f64 (/.f64 1/2 x) (sqrt.f64 -1))))
(-.f64 (/.f64 (/.f64 -1/8 (sqrt.f64 -1)) (pow.f64 x 3)) (fma.f64 x (sqrt.f64 -1) (/.f64 (/.f64 1/2 (sqrt.f64 -1)) x)))
(-.f64 (+.f64 (.f64 1/8 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))) (.f64 -1 (.f64 (sqrt.f64 -1) x))) (+.f64 (.f64 1/16 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5)))) (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 -1) x)))))
(-.f64 (+.f64 (/.f64 1/8 (.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3))) (neg.f64 (.f64 x (sqrt.f64 -1)))) (+.f64 (/.f64 1/2 (.f64 x (sqrt.f64 -1))) (/.f64 1/16 (.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5)))))
(-.f64 (fma.f64 1/8 (/.f64 (/.f64 -1 (sqrt.f64 -1)) (pow.f64 x 3)) (neg.f64 (fma.f64 x (sqrt.f64 -1) (/.f64 (/.f64 1/2 x) (sqrt.f64 -1))))) (/.f64 (/.f64 1/16 (pow.f64 x 5)) (pow.f64 (sqrt.f64 -1) 5)))
(+.f64 (-.f64 (/.f64 (/.f64 -1/8 (sqrt.f64 -1)) (pow.f64 x 3)) (fma.f64 x (sqrt.f64 -1) (/.f64 (/.f64 1/2 x) (sqrt.f64 -1)))) (/.f64 -1/16 (*.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5))))
(-.f64 (.f64 (/.f64 (/.f64 -1 x) (sqrt.f64 -1)) (+.f64 (/.f64 1/8 (.f64 x x)) 1/2)) (fma.f64 x (sqrt.f64 -1) (/.f64 1/16 (*.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5)))))
(-.f64 (.f64 (/.f64 (/.f64 -1 x) (sqrt.f64 -1)) (+.f64 1/2 (/.f64 1/8 (.f64 x x)))) (fma.f64 x (sqrt.f64 -1) (/.f64 1/16 (*.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5)))))
(-.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) 1)
(+.f64 1 (-.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1))
(+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 0)
(sqrt.f64 (fma.f64 x (neg.f64 x) 1))
(sqrt.f64 (neg.f64 (fma.f64 x x -1)))
(.f64 1 (sqrt.f64 (-.f64 1 (.f64 x x))))
(+.f64 1 (-.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1))
(+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 0)
(sqrt.f64 (fma.f64 x (neg.f64 x) 1))
(sqrt.f64 (neg.f64 (fma.f64 x x -1)))
(.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) 1)
(+.f64 1 (-.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1))
(+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 0)
(sqrt.f64 (fma.f64 x (neg.f64 x) 1))
(sqrt.f64 (neg.f64 (fma.f64 x x -1)))
(.f64 (pow.f64 (-.f64 1 (.f64 x x)) 1/4) (pow.f64 (-.f64 1 (*.f64 x x)) 1/4))
(+.f64 1 (-.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1))
(+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 0)
(sqrt.f64 (fma.f64 x (neg.f64 x) 1))
(sqrt.f64 (neg.f64 (fma.f64 x x -1)))
(.f64 (cbrt.f64 (sqrt.f64 (-.f64 1 (.f64 x x)))) (cbrt.f64 (-.f64 1 (*.f64 x x))))
(*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x (neg.f64 x) 1))) (cbrt.f64 (fma.f64 x (neg.f64 x) 1)))
(*.f64 (cbrt.f64 (sqrt.f64 (neg.f64 (fma.f64 x x -1)))) (cbrt.f64 (neg.f64 (fma.f64 x x -1))))
(.f64 (cbrt.f64 (-.f64 1 (.f64 x x))) (cbrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))
(.f64 (cbrt.f64 (sqrt.f64 (-.f64 1 (.f64 x x)))) (cbrt.f64 (-.f64 1 (*.f64 x x))))
(*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x (neg.f64 x) 1))) (cbrt.f64 (fma.f64 x (neg.f64 x) 1)))
(*.f64 (cbrt.f64 (sqrt.f64 (neg.f64 (fma.f64 x x -1)))) (cbrt.f64 (neg.f64 (fma.f64 x x -1))))
(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (-.f64 1 (.f64 x x))) 2)) (sqrt.f64 (cbrt.f64 (-.f64 1 (*.f64 x x)))))
(.f64 (fabs.f64 (cbrt.f64 (-.f64 1 (.f64 x x)))) (sqrt.f64 (cbrt.f64 (-.f64 1 (*.f64 x x)))))
(*.f64 (cbrt.f64 (fma.f64 x (neg.f64 x) 1)) (sqrt.f64 (cbrt.f64 (fma.f64 x (neg.f64 x) 1))))
(pow.f64 (cbrt.f64 (neg.f64 (fma.f64 x x -1))) 3/2)
(.f64 (pow.f64 1 1/2) (sqrt.f64 (-.f64 1 (.f64 x x))))
(+.f64 1 (-.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1))
(+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 0)
(sqrt.f64 (fma.f64 x (neg.f64 x) 1))
(sqrt.f64 (neg.f64 (fma.f64 x x -1)))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (-.f64 1 (.f64 x x))) 2) 1/2) (pow.f64 (cbrt.f64 (-.f64 1 (*.f64 x x))) 1/2))
(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (-.f64 1 (.f64 x x))) 2)) (sqrt.f64 (cbrt.f64 (-.f64 1 (*.f64 x x)))))
(.f64 (fabs.f64 (cbrt.f64 (-.f64 1 (.f64 x x)))) (sqrt.f64 (cbrt.f64 (-.f64 1 (*.f64 x x)))))
(*.f64 (cbrt.f64 (fma.f64 x (neg.f64 x) 1)) (sqrt.f64 (cbrt.f64 (fma.f64 x (neg.f64 x) 1))))
(pow.f64 (cbrt.f64 (neg.f64 (fma.f64 x x -1))) 3/2)
(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 6))) (sqrt.f64 (+.f64 1 (+.f64 (*.f64 x x) (pow.f64 x 4)))))
(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 6))) (sqrt.f64 (+.f64 1 (fma.f64 x x (pow.f64 x 4)))))
(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 4))) (sqrt.f64 (+.f64 1 (*.f64 x x))))
(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 4))) (hypot.f64 1 x))
(pow.f64 (-.f64 1 (*.f64 x x)) 1/2)
(+.f64 1 (-.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1))
(+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 0)
(sqrt.f64 (fma.f64 x (neg.f64 x) 1))
(sqrt.f64 (neg.f64 (fma.f64 x x -1)))
(pow.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1)
(+.f64 1 (-.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1))
(+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 0)
(sqrt.f64 (fma.f64 x (neg.f64 x) 1))
(sqrt.f64 (neg.f64 (fma.f64 x x -1)))
(pow.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 1/4) 2)
(+.f64 1 (-.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1))
(+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 0)
(sqrt.f64 (fma.f64 x (neg.f64 x) 1))
(sqrt.f64 (neg.f64 (fma.f64 x x -1)))
(pow.f64 (cbrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) 3)
(+.f64 1 (-.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1))
(+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 0)
(sqrt.f64 (fma.f64 x (neg.f64 x) 1))
(sqrt.f64 (neg.f64 (fma.f64 x x -1)))
(pow.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 3/2) 1/3)
(cbrt.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 3/2))
(cbrt.f64 (pow.f64 (fma.f64 x (neg.f64 x) 1) 3/2))
(cbrt.f64 (pow.f64 (neg.f64 (fma.f64 x x -1)) 3/2))
(fabs.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))))
(+.f64 1 (-.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1))
(+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 0)
(sqrt.f64 (fma.f64 x (neg.f64 x) 1))
(sqrt.f64 (neg.f64 (fma.f64 x x -1)))
(log.f64 (exp.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))
(+.f64 1 (-.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1))
(+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 0)
(sqrt.f64 (fma.f64 x (neg.f64 x) 1))
(sqrt.f64 (neg.f64 (fma.f64 x x -1)))
(cbrt.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 3/2))
(cbrt.f64 (pow.f64 (fma.f64 x (neg.f64 x) 1) 3/2))
(cbrt.f64 (pow.f64 (neg.f64 (fma.f64 x x -1)) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))
(+.f64 1 (-.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1))
(+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 0)
(sqrt.f64 (fma.f64 x (neg.f64 x) 1))
(sqrt.f64 (neg.f64 (fma.f64 x x -1)))
(exp.f64 (log.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))
(+.f64 1 (-.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1))
(+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 0)
(sqrt.f64 (fma.f64 x (neg.f64 x) 1))
(sqrt.f64 (neg.f64 (fma.f64 x x -1)))
(exp.f64 (.f64 (log1p.f64 (.f64 x (neg.f64 x))) 1/2))
(+.f64 1 (-.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1))
(+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 0)
(sqrt.f64 (fma.f64 x (neg.f64 x) 1))
(sqrt.f64 (neg.f64 (fma.f64 x x -1)))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (-.f64 1 (.f64 x x)))) 1))
(+.f64 1 (-.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1))
(+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 0)
(sqrt.f64 (fma.f64 x (neg.f64 x) 1))
(sqrt.f64 (neg.f64 (fma.f64 x x -1)))
(log1p.f64 (expm1.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))
(+.f64 1 (-.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1))
(+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 0)
(sqrt.f64 (fma.f64 x (neg.f64 x) 1))
(sqrt.f64 (neg.f64 (fma.f64 x x -1)))

eval25.0ms (1.4%)

Compiler: Compiled 1270 to 986 computations (22.4% saved)

prune177.0ms (9.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	84	2	86
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	84	3	87

Error

Counts

87 → 3

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.2b	(+.f64 1 (.f64 -1/2 (.f64 x x)))
✓	0.0b	(sqrt.f64 (-.f64 1 (*.f64 x x)))
	0.5b	1

Compiler

Compiled 17 to 13 computations (23.5% saved)

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (.f64 -1/2 (.f64 x x)))
✓	0.0b	(.f64 -1/2 (.f64 x x))

Compiler

Compiled 19 to 10 computations (47.4% saved)

series1.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	x	@	inf	(.f64 -1/2 (.f64 x x))
0.0ms	x	@	0	(.f64 -1/2 (.f64 x x))
0.0ms	x	@	inf	(+.f64 1 (.f64 -1/2 (.f64 x x)))
0.0ms	x	@	0	(+.f64 1 (.f64 -1/2 (.f64 x x)))
0.0ms	x	@	-inf	(.f64 -1/2 (.f64 x x))

rewrite98.0ms (5.5%)

Algorithm

1×	batch-egg-rewrite

Rules

1564×	`add-sqr-sqrt`
1540×	`*-un-lft-identity`
1444×	`add-cube-cbrt`
1434×	`add-cbrt-cube`
1424×	`add-exp-log`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	32
1	165	28
2	2004	28

Stop Event

1×	node limit

Counts

2 → 46

Calls

Call 1

Inputs
(.f64 -1/2 (.f64 x x))
(+.f64 1 (.f64 -1/2 (.f64 x x)))

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

Outputs

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

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

simplify64.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

1516×	`associate-/r*`
1062×	`associate-r`
798×	`associate-l`
658×	`distribute-lft-neg-in`
640×	`associate-+r+`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	108	1500
1	251	1408
2	838	1340
3	3896	1340

Stop Event

1×	node limit

Counts

70 → 63

Calls

Call 1

Inputs
(*.f64 -1/2 (pow.f64 x 2))
(*.f64 -1/2 (pow.f64 x 2))
(*.f64 -1/2 (pow.f64 x 2))
(*.f64 -1/2 (pow.f64 x 2))
(*.f64 -1/2 (pow.f64 x 2))
(*.f64 -1/2 (pow.f64 x 2))
(*.f64 -1/2 (pow.f64 x 2))
(*.f64 -1/2 (pow.f64 x 2))
(*.f64 -1/2 (pow.f64 x 2))
(*.f64 -1/2 (pow.f64 x 2))
(*.f64 -1/2 (pow.f64 x 2))
(*.f64 -1/2 (pow.f64 x 2))
1
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(*.f64 -1/2 (pow.f64 x 2))
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(*.f64 -1/2 (pow.f64 x 2))
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(-.f64 (fma.f64 -1/2 (*.f64 x x) 1) 1)
(pow.f64 (.f64 -1/2 (.f64 x x)) 1)
(pow.f64 (*.f64 x (sqrt.f64 -1/2)) 2)
(pow.f64 (cbrt.f64 (.f64 -1/2 (.f64 x x))) 3)
(pow.f64 (.f64 (pow.f64 (.f64 x x) 3) -1/8) 1/3)
(sqrt.f64 (*.f64 (pow.f64 x 4) 1/4))
(log.f64 (pow.f64 (exp.f64 -1/2) (*.f64 x x)))
(cbrt.f64 (.f64 (pow.f64 (.f64 x x) 3) -1/8))
(expm1.f64 (log1p.f64 (.f64 -1/2 (.f64 x x))))
(exp.f64 (log.f64 (.f64 -1/2 (.f64 x x))))
(exp.f64 (.f64 (log.f64 (.f64 -1/2 (*.f64 x x))) 1))
(log1p.f64 (expm1.f64 (.f64 -1/2 (.f64 x x))))
(-.f64 (+.f64 1 (fma.f64 -1/2 (*.f64 x x) 1)) 1)
(-.f64 (/.f64 1 (-.f64 1 (.f64 -1/2 (.f64 x x)))) (/.f64 (.f64 (pow.f64 x 4) 1/4) (-.f64 1 (.f64 -1/2 (*.f64 x x)))))
(.f64 1 (fma.f64 -1/2 (.f64 x x) 1))
(.f64 (fma.f64 -1/2 (.f64 x x) 1) 1)
(.f64 (hypot.f64 1 (.f64 x (sqrt.f64 -1/2))) (hypot.f64 1 (*.f64 x (sqrt.f64 -1/2))))
(.f64 (cbrt.f64 (fma.f64 -1/2 (.f64 x x) 1)) (pow.f64 (cbrt.f64 (fma.f64 -1/2 (*.f64 x x) 1)) 2))
(.f64 (pow.f64 (cbrt.f64 (fma.f64 -1/2 (.f64 x x) 1)) 2) (cbrt.f64 (fma.f64 -1/2 (*.f64 x x) 1)))
(.f64 (-.f64 1 (.f64 (pow.f64 x 4) 1/4)) (/.f64 1 (-.f64 1 (.f64 -1/2 (.f64 x x)))))
(.f64 (+.f64 1 (.f64 (pow.f64 (.f64 x x) 3) -1/8)) (/.f64 1 (+.f64 1 (+.f64 (.f64 (pow.f64 x 4) 1/4) (.f64 1/2 (.f64 x x))))))
(/.f64 1 (/.f64 (-.f64 1 (.f64 -1/2 (.f64 x x))) (-.f64 1 (*.f64 (pow.f64 x 4) 1/4))))
(/.f64 1 (/.f64 (+.f64 1 (+.f64 (.f64 (pow.f64 x 4) 1/4) (.f64 1/2 (.f64 x x)))) (+.f64 1 (.f64 (pow.f64 (*.f64 x x) 3) -1/8))))
(/.f64 (-.f64 1 (.f64 (pow.f64 x 4) 1/4)) (-.f64 1 (.f64 -1/2 (*.f64 x x))))
(/.f64 (+.f64 1 (.f64 (pow.f64 (.f64 x x) 3) -1/8)) (+.f64 1 (+.f64 (.f64 (pow.f64 x 4) 1/4) (.f64 1/2 (*.f64 x x)))))
(/.f64 (+.f64 1 (.f64 (pow.f64 (.f64 x x) 3) -1/8)) (+.f64 (.f64 (pow.f64 x 4) 1/4) (-.f64 1 (.f64 -1/2 (*.f64 x x)))))
(/.f64 (-.f64 (.f64 (pow.f64 x 4) 1/4) 1) (-.f64 (.f64 -1/2 (*.f64 x x)) 1))
(/.f64 (neg.f64 (-.f64 1 (.f64 (pow.f64 x 4) 1/4))) (neg.f64 (-.f64 1 (.f64 -1/2 (*.f64 x x)))))
(/.f64 (neg.f64 (+.f64 1 (.f64 (pow.f64 (.f64 x x) 3) -1/8))) (neg.f64 (+.f64 1 (+.f64 (.f64 (pow.f64 x 4) 1/4) (.f64 1/2 (*.f64 x x))))))
(pow.f64 (fma.f64 -1/2 (*.f64 x x) 1) 1)
(pow.f64 (hypot.f64 1 (*.f64 x (sqrt.f64 -1/2))) 2)
(pow.f64 (cbrt.f64 (fma.f64 -1/2 (*.f64 x x) 1)) 3)
(pow.f64 (pow.f64 (fma.f64 -1/2 (*.f64 x x) 1) 3) 1/3)
(sqrt.f64 (pow.f64 (fma.f64 -1/2 (*.f64 x x) 1) 2))
(log.f64 (exp.f64 (fma.f64 -1/2 (*.f64 x x) 1)))
(cbrt.f64 (pow.f64 (fma.f64 -1/2 (*.f64 x x) 1) 3))
(expm1.f64 (log1p.f64 (fma.f64 -1/2 (*.f64 x x) 1)))
(exp.f64 (log1p.f64 (.f64 -1/2 (.f64 x x))))
(exp.f64 (.f64 (log1p.f64 (.f64 -1/2 (*.f64 x x))) 1))
(log1p.f64 (expm1.f64 (fma.f64 -1/2 (*.f64 x x) 1)))
(fma.f64 -1/2 (*.f64 x x) 1)
(fma.f64 (*.f64 x x) -1/2 1)
(fma.f64 1 (.f64 -1/2 (.f64 x x)) 1)
(fma.f64 (.f64 x (sqrt.f64 -1/2)) (.f64 x (sqrt.f64 -1/2)) 1)
(fma.f64 (cbrt.f64 (.f64 (pow.f64 x 4) 1/4)) (cbrt.f64 (.f64 -1/2 (*.f64 x x))) 1)
(fma.f64 (*.f64 -1/2 x) x 1)

Outputs
(*.f64 -1/2 (pow.f64 x 2))
(.f64 -1/2 (.f64 x x))
(.f64 x (.f64 -1/2 x))
(*.f64 -1/2 (pow.f64 x 2))
(.f64 -1/2 (.f64 x x))
(.f64 x (.f64 -1/2 x))
(*.f64 -1/2 (pow.f64 x 2))
(.f64 -1/2 (.f64 x x))
(.f64 x (.f64 -1/2 x))
(*.f64 -1/2 (pow.f64 x 2))
(.f64 -1/2 (.f64 x x))
(.f64 x (.f64 -1/2 x))
(*.f64 -1/2 (pow.f64 x 2))
(.f64 -1/2 (.f64 x x))
(.f64 x (.f64 -1/2 x))
(*.f64 -1/2 (pow.f64 x 2))
(.f64 -1/2 (.f64 x x))
(.f64 x (.f64 -1/2 x))
(*.f64 -1/2 (pow.f64 x 2))
(.f64 -1/2 (.f64 x x))
(.f64 x (.f64 -1/2 x))
(*.f64 -1/2 (pow.f64 x 2))
(.f64 -1/2 (.f64 x x))
(.f64 x (.f64 -1/2 x))
(*.f64 -1/2 (pow.f64 x 2))
(.f64 -1/2 (.f64 x x))
(.f64 x (.f64 -1/2 x))
(*.f64 -1/2 (pow.f64 x 2))
(.f64 -1/2 (.f64 x x))
(.f64 x (.f64 -1/2 x))
(*.f64 -1/2 (pow.f64 x 2))
(.f64 -1/2 (.f64 x x))
(.f64 x (.f64 -1/2 x))
(*.f64 -1/2 (pow.f64 x 2))
(.f64 -1/2 (.f64 x x))
(.f64 x (.f64 -1/2 x))
1
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(fma.f64 -1/2 (*.f64 x x) 1)
(fma.f64 x (*.f64 -1/2 x) 1)
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(fma.f64 -1/2 (*.f64 x x) 1)
(fma.f64 x (*.f64 -1/2 x) 1)
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(fma.f64 -1/2 (*.f64 x x) 1)
(fma.f64 x (*.f64 -1/2 x) 1)
(*.f64 -1/2 (pow.f64 x 2))
(.f64 -1/2 (.f64 x x))
(.f64 x (.f64 -1/2 x))
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(fma.f64 -1/2 (*.f64 x x) 1)
(fma.f64 x (*.f64 -1/2 x) 1)
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(fma.f64 -1/2 (*.f64 x x) 1)
(fma.f64 x (*.f64 -1/2 x) 1)
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(fma.f64 -1/2 (*.f64 x x) 1)
(fma.f64 x (*.f64 -1/2 x) 1)
(*.f64 -1/2 (pow.f64 x 2))
(.f64 -1/2 (.f64 x x))
(.f64 x (.f64 -1/2 x))
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(fma.f64 -1/2 (*.f64 x x) 1)
(fma.f64 x (*.f64 -1/2 x) 1)
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(fma.f64 -1/2 (*.f64 x x) 1)
(fma.f64 x (*.f64 -1/2 x) 1)
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(fma.f64 -1/2 (*.f64 x x) 1)
(fma.f64 x (*.f64 -1/2 x) 1)
(-.f64 (fma.f64 -1/2 (*.f64 x x) 1) 1)
(.f64 -1/2 (.f64 x x))
(.f64 x (.f64 -1/2 x))
(pow.f64 (.f64 -1/2 (.f64 x x)) 1)
(.f64 -1/2 (.f64 x x))
(.f64 x (.f64 -1/2 x))
(pow.f64 (*.f64 x (sqrt.f64 -1/2)) 2)
(.f64 -1/2 (.f64 x x))
(.f64 x (.f64 -1/2 x))
(pow.f64 (cbrt.f64 (.f64 -1/2 (.f64 x x))) 3)
(.f64 -1/2 (.f64 x x))
(.f64 x (.f64 -1/2 x))
(pow.f64 (.f64 (pow.f64 (.f64 x x) 3) -1/8) 1/3)
(cbrt.f64 (.f64 (pow.f64 (.f64 x x) 3) -1/8))
(cbrt.f64 (*.f64 (pow.f64 x 6) -1/8))
(sqrt.f64 (*.f64 (pow.f64 x 4) 1/4))
(log.f64 (pow.f64 (exp.f64 -1/2) (*.f64 x x)))
(.f64 -1/2 (.f64 x x))
(.f64 x (.f64 -1/2 x))
(cbrt.f64 (.f64 (pow.f64 (.f64 x x) 3) -1/8))
(cbrt.f64 (*.f64 (pow.f64 x 6) -1/8))
(expm1.f64 (log1p.f64 (.f64 -1/2 (.f64 x x))))
(.f64 -1/2 (.f64 x x))
(.f64 x (.f64 -1/2 x))
(exp.f64 (log.f64 (.f64 -1/2 (.f64 x x))))
(.f64 -1/2 (.f64 x x))
(.f64 x (.f64 -1/2 x))
(exp.f64 (.f64 (log.f64 (.f64 -1/2 (*.f64 x x))) 1))
(.f64 -1/2 (.f64 x x))
(.f64 x (.f64 -1/2 x))
(log1p.f64 (expm1.f64 (.f64 -1/2 (.f64 x x))))
(.f64 -1/2 (.f64 x x))
(.f64 x (.f64 -1/2 x))
(-.f64 (+.f64 1 (fma.f64 -1/2 (*.f64 x x) 1)) 1)
(fma.f64 -1/2 (*.f64 x x) 1)
(fma.f64 x (*.f64 -1/2 x) 1)
(-.f64 (/.f64 1 (-.f64 1 (.f64 -1/2 (.f64 x x)))) (/.f64 (.f64 (pow.f64 x 4) 1/4) (-.f64 1 (.f64 -1/2 (*.f64 x x)))))
(/.f64 (-.f64 1 (.f64 (pow.f64 x 4) 1/4)) (+.f64 1 (.f64 (*.f64 x x) 1/2)))
(/.f64 (+.f64 1 (.f64 (pow.f64 x 4) -1/4)) (+.f64 1 (.f64 (*.f64 x x) 1/2)))
(/.f64 (fma.f64 (pow.f64 x 4) -1/4 1) (fma.f64 x (*.f64 x 1/2) 1))
(/.f64 (fma.f64 (pow.f64 x 4) 1/4 -1) (fma.f64 x (*.f64 -1/2 x) -1))
(.f64 1 (fma.f64 -1/2 (.f64 x x) 1))
(fma.f64 -1/2 (*.f64 x x) 1)
(fma.f64 x (*.f64 -1/2 x) 1)
(.f64 (fma.f64 -1/2 (.f64 x x) 1) 1)
(fma.f64 -1/2 (*.f64 x x) 1)
(fma.f64 x (*.f64 -1/2 x) 1)
(.f64 (hypot.f64 1 (.f64 x (sqrt.f64 -1/2))) (hypot.f64 1 (*.f64 x (sqrt.f64 -1/2))))
(pow.f64 (hypot.f64 1 (*.f64 x (sqrt.f64 -1/2))) 2)
(.f64 (cbrt.f64 (fma.f64 -1/2 (.f64 x x) 1)) (pow.f64 (cbrt.f64 (fma.f64 -1/2 (*.f64 x x) 1)) 2))
(fma.f64 -1/2 (*.f64 x x) 1)
(fma.f64 x (*.f64 -1/2 x) 1)
(.f64 (pow.f64 (cbrt.f64 (fma.f64 -1/2 (.f64 x x) 1)) 2) (cbrt.f64 (fma.f64 -1/2 (*.f64 x x) 1)))
(fma.f64 -1/2 (*.f64 x x) 1)
(fma.f64 x (*.f64 -1/2 x) 1)
(.f64 (-.f64 1 (.f64 (pow.f64 x 4) 1/4)) (/.f64 1 (-.f64 1 (.f64 -1/2 (.f64 x x)))))
(/.f64 (-.f64 1 (.f64 (pow.f64 x 4) 1/4)) (+.f64 1 (.f64 (*.f64 x x) 1/2)))
(/.f64 (+.f64 1 (.f64 (pow.f64 x 4) -1/4)) (+.f64 1 (.f64 (*.f64 x x) 1/2)))
(/.f64 (fma.f64 (pow.f64 x 4) -1/4 1) (fma.f64 x (*.f64 x 1/2) 1))
(/.f64 (fma.f64 (pow.f64 x 4) 1/4 -1) (fma.f64 x (*.f64 -1/2 x) -1))
(.f64 (+.f64 1 (.f64 (pow.f64 (.f64 x x) 3) -1/8)) (/.f64 1 (+.f64 1 (+.f64 (.f64 (pow.f64 x 4) 1/4) (.f64 1/2 (.f64 x x))))))
(.f64 (+.f64 1 (.f64 (pow.f64 (.f64 x x) 3) -1/8)) (/.f64 1 (+.f64 1 (fma.f64 (pow.f64 x 4) 1/4 (.f64 (*.f64 x x) 1/2)))))
(/.f64 (fma.f64 (pow.f64 x 6) -1/8 1) (+.f64 1 (fma.f64 (pow.f64 x 4) 1/4 (.f64 (.f64 x x) 1/2))))
(/.f64 (fma.f64 (pow.f64 x 6) -1/8 1) (fma.f64 x (*.f64 x 1/2) (fma.f64 (pow.f64 x 4) 1/4 1)))
(/.f64 1 (/.f64 (-.f64 1 (.f64 -1/2 (.f64 x x))) (-.f64 1 (*.f64 (pow.f64 x 4) 1/4))))
(/.f64 (-.f64 1 (.f64 (pow.f64 x 4) 1/4)) (+.f64 1 (.f64 (*.f64 x x) 1/2)))
(/.f64 (+.f64 1 (.f64 (pow.f64 x 4) -1/4)) (+.f64 1 (.f64 (*.f64 x x) 1/2)))
(/.f64 (fma.f64 (pow.f64 x 4) -1/4 1) (fma.f64 x (*.f64 x 1/2) 1))
(/.f64 (fma.f64 (pow.f64 x 4) 1/4 -1) (fma.f64 x (*.f64 -1/2 x) -1))
(/.f64 1 (/.f64 (+.f64 1 (+.f64 (.f64 (pow.f64 x 4) 1/4) (.f64 1/2 (.f64 x x)))) (+.f64 1 (.f64 (pow.f64 (*.f64 x x) 3) -1/8))))
(.f64 (+.f64 1 (.f64 (pow.f64 (.f64 x x) 3) -1/8)) (/.f64 1 (+.f64 1 (fma.f64 (pow.f64 x 4) 1/4 (.f64 (*.f64 x x) 1/2)))))
(/.f64 (fma.f64 (pow.f64 x 6) -1/8 1) (+.f64 1 (fma.f64 (pow.f64 x 4) 1/4 (.f64 (.f64 x x) 1/2))))
(/.f64 (fma.f64 (pow.f64 x 6) -1/8 1) (fma.f64 x (*.f64 x 1/2) (fma.f64 (pow.f64 x 4) 1/4 1)))
(/.f64 (-.f64 1 (.f64 (pow.f64 x 4) 1/4)) (-.f64 1 (.f64 -1/2 (*.f64 x x))))
(/.f64 (-.f64 1 (.f64 (pow.f64 x 4) 1/4)) (+.f64 1 (.f64 (*.f64 x x) 1/2)))
(/.f64 (+.f64 1 (.f64 (pow.f64 x 4) -1/4)) (+.f64 1 (.f64 (*.f64 x x) 1/2)))
(/.f64 (fma.f64 (pow.f64 x 4) -1/4 1) (fma.f64 x (*.f64 x 1/2) 1))
(/.f64 (fma.f64 (pow.f64 x 4) 1/4 -1) (fma.f64 x (*.f64 -1/2 x) -1))
(/.f64 (+.f64 1 (.f64 (pow.f64 (.f64 x x) 3) -1/8)) (+.f64 1 (+.f64 (.f64 (pow.f64 x 4) 1/4) (.f64 1/2 (*.f64 x x)))))
(.f64 (+.f64 1 (.f64 (pow.f64 (.f64 x x) 3) -1/8)) (/.f64 1 (+.f64 1 (fma.f64 (pow.f64 x 4) 1/4 (.f64 (*.f64 x x) 1/2)))))
(/.f64 (fma.f64 (pow.f64 x 6) -1/8 1) (+.f64 1 (fma.f64 (pow.f64 x 4) 1/4 (.f64 (.f64 x x) 1/2))))
(/.f64 (fma.f64 (pow.f64 x 6) -1/8 1) (fma.f64 x (*.f64 x 1/2) (fma.f64 (pow.f64 x 4) 1/4 1)))
(/.f64 (+.f64 1 (.f64 (pow.f64 (.f64 x x) 3) -1/8)) (+.f64 (.f64 (pow.f64 x 4) 1/4) (-.f64 1 (.f64 -1/2 (*.f64 x x)))))
(.f64 (+.f64 1 (.f64 (pow.f64 (.f64 x x) 3) -1/8)) (/.f64 1 (+.f64 1 (fma.f64 (pow.f64 x 4) 1/4 (.f64 (*.f64 x x) 1/2)))))
(/.f64 (fma.f64 (pow.f64 x 6) -1/8 1) (+.f64 1 (fma.f64 (pow.f64 x 4) 1/4 (.f64 (.f64 x x) 1/2))))
(/.f64 (fma.f64 (pow.f64 x 6) -1/8 1) (fma.f64 x (*.f64 x 1/2) (fma.f64 (pow.f64 x 4) 1/4 1)))
(/.f64 (-.f64 (.f64 (pow.f64 x 4) 1/4) 1) (-.f64 (.f64 -1/2 (*.f64 x x)) 1))
(/.f64 (-.f64 1 (.f64 (pow.f64 x 4) 1/4)) (+.f64 1 (.f64 (*.f64 x x) 1/2)))
(/.f64 (+.f64 1 (.f64 (pow.f64 x 4) -1/4)) (+.f64 1 (.f64 (*.f64 x x) 1/2)))
(/.f64 (fma.f64 (pow.f64 x 4) -1/4 1) (fma.f64 x (*.f64 x 1/2) 1))
(/.f64 (fma.f64 (pow.f64 x 4) 1/4 -1) (fma.f64 x (*.f64 -1/2 x) -1))
(/.f64 (neg.f64 (-.f64 1 (.f64 (pow.f64 x 4) 1/4))) (neg.f64 (-.f64 1 (.f64 -1/2 (*.f64 x x)))))
(/.f64 (-.f64 1 (.f64 (pow.f64 x 4) 1/4)) (+.f64 1 (.f64 (*.f64 x x) 1/2)))
(/.f64 (+.f64 1 (.f64 (pow.f64 x 4) -1/4)) (+.f64 1 (.f64 (*.f64 x x) 1/2)))
(/.f64 (fma.f64 (pow.f64 x 4) -1/4 1) (fma.f64 x (*.f64 x 1/2) 1))
(/.f64 (fma.f64 (pow.f64 x 4) 1/4 -1) (fma.f64 x (*.f64 -1/2 x) -1))
(/.f64 (neg.f64 (+.f64 1 (.f64 (pow.f64 (.f64 x x) 3) -1/8))) (neg.f64 (+.f64 1 (+.f64 (.f64 (pow.f64 x 4) 1/4) (.f64 1/2 (*.f64 x x))))))
(.f64 (+.f64 1 (.f64 (pow.f64 (.f64 x x) 3) -1/8)) (/.f64 1 (+.f64 1 (fma.f64 (pow.f64 x 4) 1/4 (.f64 (*.f64 x x) 1/2)))))
(/.f64 (fma.f64 (pow.f64 x 6) -1/8 1) (+.f64 1 (fma.f64 (pow.f64 x 4) 1/4 (.f64 (.f64 x x) 1/2))))
(/.f64 (fma.f64 (pow.f64 x 6) -1/8 1) (fma.f64 x (*.f64 x 1/2) (fma.f64 (pow.f64 x 4) 1/4 1)))
(pow.f64 (fma.f64 -1/2 (*.f64 x x) 1) 1)
(fma.f64 -1/2 (*.f64 x x) 1)
(fma.f64 x (*.f64 -1/2 x) 1)
(pow.f64 (hypot.f64 1 (*.f64 x (sqrt.f64 -1/2))) 2)
(pow.f64 (cbrt.f64 (fma.f64 -1/2 (*.f64 x x) 1)) 3)
(fma.f64 -1/2 (*.f64 x x) 1)
(fma.f64 x (*.f64 -1/2 x) 1)
(pow.f64 (pow.f64 (fma.f64 -1/2 (*.f64 x x) 1) 3) 1/3)
(fma.f64 -1/2 (*.f64 x x) 1)
(fma.f64 x (*.f64 -1/2 x) 1)
(sqrt.f64 (pow.f64 (fma.f64 -1/2 (*.f64 x x) 1) 2))
(fma.f64 -1/2 (*.f64 x x) 1)
(fma.f64 x (*.f64 -1/2 x) 1)
(log.f64 (exp.f64 (fma.f64 -1/2 (*.f64 x x) 1)))
(fma.f64 -1/2 (*.f64 x x) 1)
(fma.f64 x (*.f64 -1/2 x) 1)
(cbrt.f64 (pow.f64 (fma.f64 -1/2 (*.f64 x x) 1) 3))
(fma.f64 -1/2 (*.f64 x x) 1)
(fma.f64 x (*.f64 -1/2 x) 1)
(expm1.f64 (log1p.f64 (fma.f64 -1/2 (*.f64 x x) 1)))
(fma.f64 -1/2 (*.f64 x x) 1)
(fma.f64 x (*.f64 -1/2 x) 1)
(exp.f64 (log1p.f64 (.f64 -1/2 (.f64 x x))))
(exp.f64 (log1p.f64 (.f64 x (.f64 -1/2 x))))
(exp.f64 (.f64 (log1p.f64 (.f64 -1/2 (*.f64 x x))) 1))
(exp.f64 (log1p.f64 (.f64 -1/2 (.f64 x x))))
(exp.f64 (log1p.f64 (.f64 x (.f64 -1/2 x))))
(log1p.f64 (expm1.f64 (fma.f64 -1/2 (*.f64 x x) 1)))
(fma.f64 -1/2 (*.f64 x x) 1)
(fma.f64 x (*.f64 -1/2 x) 1)
(fma.f64 -1/2 (*.f64 x x) 1)
(fma.f64 x (*.f64 -1/2 x) 1)
(fma.f64 (*.f64 x x) -1/2 1)
(fma.f64 -1/2 (*.f64 x x) 1)
(fma.f64 x (*.f64 -1/2 x) 1)
(fma.f64 1 (.f64 -1/2 (.f64 x x)) 1)
(fma.f64 -1/2 (*.f64 x x) 1)
(fma.f64 x (*.f64 -1/2 x) 1)
(fma.f64 (.f64 x (sqrt.f64 -1/2)) (.f64 x (sqrt.f64 -1/2)) 1)
(fma.f64 -1/2 (*.f64 x x) 1)
(fma.f64 x (*.f64 -1/2 x) 1)
(fma.f64 (cbrt.f64 (.f64 (pow.f64 x 4) 1/4)) (cbrt.f64 (.f64 -1/2 (*.f64 x x))) 1)
(fma.f64 (cbrt.f64 (.f64 -1/2 (.f64 x x))) (cbrt.f64 (*.f64 (pow.f64 x 4) 1/4)) 1)
(fma.f64 (cbrt.f64 (.f64 x (.f64 -1/2 x))) (cbrt.f64 (*.f64 (pow.f64 x 4) 1/4)) 1)
(fma.f64 (*.f64 -1/2 x) x 1)
(fma.f64 -1/2 (*.f64 x x) 1)
(fma.f64 x (*.f64 -1/2 x) 1)

eval16.0ms (0.9%)

Compiler: Compiled 750 to 537 computations (28.4% saved)

prune7.0ms (0.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	63	0	63
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	63	3	66

Error

Counts

66 → 3

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.2b	(+.f64 1 (.f64 -1/2 (.f64 x x)))
✓	0.0b	(sqrt.f64 (-.f64 1 (*.f64 x x)))
	0.5b	1

Compiler

Compiled 17 to 13 computations (23.5% saved)

eval0.0ms (0%)

Compiler: Compiled 1 to 1 computations (0% saved)

prune1.0ms (0.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

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

Error

Counts

3 → 3

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.2b	(+.f64 1 (.f64 -1/2 (.f64 x x)))
✓	0.0b	(sqrt.f64 (-.f64 1 (*.f64 x x)))
	0.5b	1

Compiler

Compiled 17 to 13 computations (23.5% saved)

eval0.0ms (0%)

Compiler: Compiled 1 to 1 computations (0% saved)

prune1.0ms (0.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

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

Error

Counts

3 → 3

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.2b	(+.f64 1 (.f64 -1/2 (.f64 x x)))
✓	0.0b	(sqrt.f64 (-.f64 1 (*.f64 x x)))
	0.5b	1

Compiler

Compiled 17 to 13 computations (23.5% saved)

regimes9.0ms (0.5%)

Counts

3 → 1

Calls

Call 1

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

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

Calls

4 calls:

3.0ms	x
2.0ms	(*.f64 x x)
2.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))
2.0ms	(-.f64 1 (*.f64 x x))

Results

Error	Segments	Branch
0.0b	1	`x`
0.0b	1	`(sqrt.f64 (-.f64 1 (*.f64 x x)))`
0.0b	1	`(-.f64 1 (*.f64 x x))`
0.0b	1	`(*.f64 x x)`

Compiler

Compiled 34 to 22 computations (35.3% saved)

regimes15.0ms (0.9%)

Accuracy

Total -0.3b remaining (-131.7%)

Threshold costs -0.3b (-131.7%)

Counts

2 → 1

Calls

Call 1

Inputs
1
(+.f64 1 (.f64 -1/2 (.f64 x x)))

Outputs
(+.f64 1 (.f64 -1/2 (.f64 x x)))

Calls

2 calls:

12.0ms	(*.f64 x x)
3.0ms	x

Results

Error	Segments	Branch
0.2b	1	`x`
0.2b	1	`(*.f64 x x)`

Compiler

Compiled 15 to 10 computations (33.3% saved)

simplify5.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

10×	`+-commutative`
8×	`*-commutative`
4×	`sub-neg`
4×	`neg-mul-1`
4×	`cancel-sign-sub-inv`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	37
1	20	37
2	28	37
3	32	37
4	34	37

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

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

Outputs
(sqrt.f64 (-.f64 1 (*.f64 x x)))
(+.f64 1 (.f64 -1/2 (.f64 x x)))
(+.f64 1 (.f64 (.f64 x x) -1/2))
1

Compiler

Compiled 17 to 13 computations (23.5% saved)

soundness0.0ms (0%)

end18.0ms (1%)

Compiler: Compiled 15 to 10 computations (33.3% saved)

Details

analyze3.0ms (0.2%)

sample932.0ms (52.1%)

preprocess136.0ms (7.6%)

simplify142.0ms (7.9%)

eval1.0ms (0%)

prune1.0ms (0%)

localize6.0ms (0.3%)

series1.0ms (0.1%)

rewrite51.0ms (2.9%)

simplify71.0ms (4%)

eval25.0ms (1.4%)

prune177.0ms (9.9%)

localize6.0ms (0.3%)

series1.0ms (0.1%)

rewrite98.0ms (5.5%)

simplify64.0ms (3.6%)

eval16.0ms (0.9%)

prune7.0ms (0.4%)

eval0.0ms (0%)

prune1.0ms (0.1%)

eval0.0ms (0%)

prune1.0ms (0.1%)

regimes9.0ms (0.5%)

regimes15.0ms (0.9%)

simplify5.0ms (0.3%)

soundness0.0ms (0%)

end18.0ms (1%)

Profiling