Details

analyze17.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	25%	75%	0
0%	25%	75%	1
0%	25%	75%	2
0%	12.5%	87.5%	3
0%	6.3%	93.7%	4
0%	3.1%	96.9%	5
0%	1.6%	98.4%	6
0%	0.8%	99.2%	7
0%	0.4%	99.6%	8
0.1%	0.2%	99.7%	9
0.1%	0.1%	99.8%	10
0.1%	0%	99.8%	11
0.1%	0%	99.8%	12
0.1%	0%	99.9%	13
0.1%	0%	99.9%	14

Compiler

Compiled 107 to 71 computations (33.6% saved)

sample3.7s (53.8%)

Results

3.5s	8256×	body	128	valid
109.0ms	331×	body	128	invalid

Compiler

Compiled 214 to 142 computations (33.6% saved)

preprocess99.0ms (1.5%)

Algorithm

2×	egg-herbie

Rules

626×	`associate-*l/_binary64`
457×	`associate-*r/_binary64`
381×	`associate-/l*_binary64`
344×	`distribute-rgt-in_binary64`
324×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	152
1	91	82
2	305	58
3	1481	52
0	1	1

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0

Outputs
0

Call 2

Inputs

(*.f64 (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)))) (+.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (*.f64 (/.f64 1 2) (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))))) (*.f64 (/.f64 3 4) (*.f64 (*.f64 (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))))) (*.f64 (/.f64 15 8) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))))))

Outputs
(.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (.f64 (fabs.f64 x) (fabs.f64 x)))) (+.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (.f64 (/.f64 1 2) (.f64 (.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))))) (.f64 (/.f64 3 4) (.f64 (.f64 (.f64 (.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))))) (.f64 (/.f64 15 8) (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))))))
(.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (.f64 (exp.f64 (.f64 x x)) (+.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (.f64 1/2 (.f64 (/.f64 1 (fabs.f64 x)) (.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x)))))) (.f64 3/4 (.f64 (/.f64 1 (fabs.f64 x)) (.f64 (/.f64 1 (fabs.f64 x)) (.f64 (/.f64 1 (fabs.f64 x)) (.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x)))))))) (.f64 15/8 (.f64 (/.f64 1 (fabs.f64 x)) (.f64 (/.f64 1 (fabs.f64 x)) (.f64 (/.f64 1 (fabs.f64 x)) (.f64 (/.f64 1 (fabs.f64 x)) (.f64 (/.f64 1 (fabs.f64 x)) (.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))))))))))))
(.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (PI.f64))) (fma.f64 15/8 (*.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 3) (/.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 3) (fabs.f64 x))) (fma.f64 3/4 (/.f64 (/.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 3) (fabs.f64 x)) (fabs.f64 x)) (fma.f64 1/2 (pow.f64 (/.f64 1 (fabs.f64 x)) 3) (/.f64 1 (fabs.f64 x))))))
(.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (PI.f64))) (fma.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (/.f64 1 (fabs.f64 x)) (.f64 (/.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 4) (fabs.f64 x)) (+.f64 3/4 (/.f64 15/8 (*.f64 x x))))))
(.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (*.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 (/.f64 15/8 x) x)))))

Compiler

Compiled 104 to 69 computations (33.7% saved)

simplify19.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

626×	`associate-*l/_binary64`
457×	`associate-*r/_binary64`
381×	`associate-/l*_binary64`
344×	`distribute-rgt-in_binary64`
324×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	35	152
1	91	82
2	305	58
3	1481	52

Stop Event

1×	node limit

Counts

1 → 2

Calls

Call 1

Inputs

(*.f64 (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)))) (+.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (*.f64 (/.f64 1 2) (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))))) (*.f64 (/.f64 3 4) (*.f64 (*.f64 (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))))) (*.f64 (/.f64 15 8) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))))))

Outputs
(.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (.f64 (fabs.f64 x) (fabs.f64 x)))) (+.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (.f64 (/.f64 1 2) (.f64 (.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))))) (.f64 (/.f64 3 4) (.f64 (.f64 (.f64 (.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))))) (.f64 (/.f64 15 8) (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))))))
(.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (.f64 (exp.f64 (.f64 x x)) (+.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (.f64 1/2 (.f64 (/.f64 1 (fabs.f64 x)) (.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x)))))) (.f64 3/4 (.f64 (/.f64 1 (fabs.f64 x)) (.f64 (/.f64 1 (fabs.f64 x)) (.f64 (/.f64 1 (fabs.f64 x)) (.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x)))))))) (.f64 15/8 (.f64 (/.f64 1 (fabs.f64 x)) (.f64 (/.f64 1 (fabs.f64 x)) (.f64 (/.f64 1 (fabs.f64 x)) (.f64 (/.f64 1 (fabs.f64 x)) (.f64 (/.f64 1 (fabs.f64 x)) (.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))))))))))))
(.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (PI.f64))) (fma.f64 15/8 (*.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 3) (/.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 3) (fabs.f64 x))) (fma.f64 3/4 (/.f64 (/.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 3) (fabs.f64 x)) (fabs.f64 x)) (fma.f64 1/2 (pow.f64 (/.f64 1 (fabs.f64 x)) 3) (/.f64 1 (fabs.f64 x))))))
(.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (PI.f64))) (fma.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (/.f64 1 (fabs.f64 x)) (.f64 (/.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 4) (fabs.f64 x)) (+.f64 3/4 (/.f64 15/8 (*.f64 x x))))))
(.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (*.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 (/.f64 15/8 x) x)))))

prune14.0ms (0.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

1.4b

Counts

3 → 2

Alt Table

Status

Error

Program

3.0b

(*.f64 (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)))) (+.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (*.f64 (/.f64 1 2) (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))))) (*.f64 (/.f64 3 4) (*.f64 (*.f64 (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))))) (*.f64 (/.f64 15 8) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))))))

▶

1.5b

(*.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (*.f64 x x))) (fabs.f64 x)) (*.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 (/.f64 15/8 x) x)))))

Compiler

Compiled 413 to 278 computations (32.7% saved)

localize23.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (*.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 (/.f64 15/8 x) x)))))
✓	1.0b	(pow.f64 (exp.f64 x) x)
✓	1.0b	(sqrt.f64 (PI.f64))
✓	1.1b	(pow.f64 (/.f64 1 (fabs.f64 x)) 5)

series18.0ms (0.3%)

Counts

4 → 36

Calls

9 calls:

Time	Variable		Point	Expression
5.0ms	x	@	inf	(.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (*.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 (/.f64 15/8 x) x)))))
3.0ms	x	@	-inf	(.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (*.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 (/.f64 15/8 x) x)))))
3.0ms	x	@	0	(.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (*.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 (/.f64 15/8 x) x)))))
2.0ms	x	@	inf	(pow.f64 (/.f64 1 (fabs.f64 x)) 5)
2.0ms	x	@	0	(pow.f64 (/.f64 1 (fabs.f64 x)) 5)

rewrite71.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

289×	`add-sqr-sqrt_binary64`
275×	`pow1_binary64`
274×	`*-un-lft-identity_binary64`
272×	`add-log-exp_binary64`
270×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	71
1	578	71

Stop Event

1×	node limit

Counts

4 → 37

Calls

Call 1

Inputs
(pow.f64 (/.f64 1 (fabs.f64 x)) 5)
(sqrt.f64 (PI.f64))
(pow.f64 (exp.f64 x) x)
(.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (*.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 (/.f64 15/8 x) x)))))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x .f64 1 (pow.f64 (/.f64 1 (fabs.f64 x)) 5))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (cbrt.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5)) (cbrt.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5))) (cbrt.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5)) (sqrt.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5/2) (pow.f64 (/.f64 1 (fabs.f64 x)) 5/2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (*.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (pow.f64 (/.f64 1 (fabs.f64 x)) 5)) (pow.f64 (/.f64 1 (fabs.f64 x)) 5)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5)))))))
((#(struct:change #<rule egg-rr> (2) ((x .f64 1 (sqrt.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) (cbrt.f64 (sqrt.f64 (PI.f64)))) (cbrt.f64 (sqrt.f64 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (sqrt.f64 (sqrt.f64 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (PI.f64) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (PI.f64)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (PI.f64) (sqrt.f64 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (PI.f64))))))))
((#(struct:change #<rule egg-rr> (2) ((x .f64 1 (exp.f64 (.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (cbrt.f64 (exp.f64 (.f64 x x))) (cbrt.f64 (exp.f64 (.f64 x x)))) (cbrt.f64 (exp.f64 (.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (exp.f64 (.f64 x x))) (sqrt.f64 (exp.f64 (.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (exp.f64 x) (/.f64 x 2)) (pow.f64 (exp.f64 x) (/.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (exp.f64 (.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (.f64 (exp.f64 (.f64 x x)) (exp.f64 (.f64 x x))) (exp.f64 (.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (exp.f64 (.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (exp.f64 (.f64 x x))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (PI.f64)))) (.f64 (.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 15/8 (.f64 x x)))) (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (PI.f64))) (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x))) (.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (PI.f64))) (.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 15/8 (.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (exp.f64 (.f64 x x)) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 15/8 (.f64 x x)))))) (sqrt.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (PI.f64))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 15/8 (.f64 x x)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (PI.f64))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 15/8 (.f64 x x))))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (.f64 (.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (PI.f64))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 15/8 (.f64 x x)))))) (.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (PI.f64))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 15/8 (.f64 x x))))))) (.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (PI.f64))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 15/8 (.f64 x x))))))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (PI.f64))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 15/8 (.f64 x x))))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (PI.f64))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 15/8 (.f64 x x))))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (PI.f64))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 15/8 (*.f64 x x))))))))))))

simplify45.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

598×	`fma-def_binary64`
355×	`associate-/l/_binary64`
340×	`associate-+l+_binary64`
325×	`associate-+r+_binary64`
221×	`times-frac_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	99	1346
1	286	1234
2	952	956
3	4474	833

Stop Event

1×	node limit

Counts

73 → 61

Calls

Call 1

Inputs
(/.f64 1 (pow.f64 (fabs.f64 x) 5))
(/.f64 1 (pow.f64 (fabs.f64 x) 5))
(/.f64 1 (pow.f64 (fabs.f64 x) 5))
(/.f64 1 (pow.f64 (fabs.f64 x) 5))
(/.f64 1 (pow.f64 (fabs.f64 x) 5))
(/.f64 1 (pow.f64 (fabs.f64 x) 5))
(/.f64 1 (pow.f64 (fabs.f64 x) 5))
(/.f64 1 (pow.f64 (fabs.f64 x) 5))
(/.f64 1 (pow.f64 (fabs.f64 x) 5))
(/.f64 1 (pow.f64 (fabs.f64 x) 5))
(/.f64 1 (pow.f64 (fabs.f64 x) 5))
(/.f64 1 (pow.f64 (fabs.f64 x) 5))
1
(+.f64 1 (pow.f64 x 2))
(+.f64 (*.f64 1/2 (pow.f64 x 4)) (+.f64 1 (pow.f64 x 2)))
(+.f64 (.f64 1/2 (pow.f64 x 4)) (+.f64 1 (+.f64 (.f64 1/6 (pow.f64 x 6)) (pow.f64 x 2))))
(exp.f64 (pow.f64 x 2))
(exp.f64 (pow.f64 x 2))
(exp.f64 (pow.f64 x 2))
(exp.f64 (pow.f64 x 2))
(exp.f64 (pow.f64 x 2))
(exp.f64 (pow.f64 x 2))
(exp.f64 (pow.f64 x 2))
(exp.f64 (pow.f64 x 2))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (/.f64 (+.f64 (.f64 1/2 (/.f64 1 (fabs.f64 x))) (*.f64 15/8 (/.f64 1 (pow.f64 (fabs.f64 x) 5)))) (pow.f64 x 2)))
(+.f64 (.f64 3/2 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (/.f64 1 (fabs.f64 x)))) (+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (/.f64 1 (.f64 (fabs.f64 x) (pow.f64 x 2))))) (+.f64 (.f64 21/8 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (/.f64 1 (pow.f64 (fabs.f64 x) 5)))) (.f64 15/8 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (/.f64 1 (.f64 (pow.f64 (fabs.f64 x) 5) (pow.f64 x 2))))))))
(+.f64 (.f64 3/2 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (/.f64 1 (fabs.f64 x)))) (+.f64 (.f64 27/16 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (/.f64 (pow.f64 x 2) (pow.f64 (fabs.f64 x) 5)))) (+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (/.f64 1 (.f64 (fabs.f64 x) (pow.f64 x 2))))) (+.f64 (.f64 21/8 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (/.f64 1 (pow.f64 (fabs.f64 x) 5)))) (+.f64 (.f64 5/4 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (/.f64 (pow.f64 x 2) (fabs.f64 x)))) (.f64 15/8 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (/.f64 1 (.f64 (pow.f64 (fabs.f64 x) 5) (pow.f64 x 2))))))))))
(+.f64 (.f64 3/2 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (/.f64 1 (fabs.f64 x)))) (+.f64 (.f64 27/16 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (/.f64 (pow.f64 x 2) (pow.f64 (fabs.f64 x) 5)))) (+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (/.f64 1 (.f64 (fabs.f64 x) (pow.f64 x 2))))) (+.f64 (.f64 21/8 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (/.f64 1 (pow.f64 (fabs.f64 x) 5)))) (+.f64 (.f64 7/12 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (/.f64 (pow.f64 x 4) (fabs.f64 x)))) (+.f64 (.f64 11/16 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (/.f64 (pow.f64 x 4) (pow.f64 (fabs.f64 x) 5)))) (+.f64 (.f64 5/4 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (/.f64 (pow.f64 x 2) (fabs.f64 x)))) (.f64 15/8 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (/.f64 1 (.f64 (pow.f64 (fabs.f64 x) 5) (pow.f64 x 2))))))))))))
(.f64 (.f64 (exp.f64 (pow.f64 x 2)) (+.f64 (/.f64 1 (fabs.f64 x)) (*.f64 3/4 (/.f64 1 (pow.f64 (fabs.f64 x) 5))))) (sqrt.f64 (/.f64 1 (PI.f64))))
(+.f64 (.f64 3/4 (.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 (fabs.f64 x) 5)) (sqrt.f64 (/.f64 1 (PI.f64))))) (+.f64 (.f64 15/8 (.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (.f64 (pow.f64 (fabs.f64 x) 5) (pow.f64 x 2))) (sqrt.f64 (/.f64 1 (PI.f64))))) (+.f64 (.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (fabs.f64 x)) (sqrt.f64 (/.f64 1 (PI.f64)))) (.f64 1/2 (.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (*.f64 (fabs.f64 x) (pow.f64 x 2))) (sqrt.f64 (/.f64 1 (PI.f64))))))))
(+.f64 (.f64 3/4 (.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 (fabs.f64 x) 5)) (sqrt.f64 (/.f64 1 (PI.f64))))) (+.f64 (.f64 15/8 (.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (.f64 (pow.f64 (fabs.f64 x) 5) (pow.f64 x 2))) (sqrt.f64 (/.f64 1 (PI.f64))))) (+.f64 (.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (fabs.f64 x)) (sqrt.f64 (/.f64 1 (PI.f64)))) (.f64 1/2 (.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (*.f64 (fabs.f64 x) (pow.f64 x 2))) (sqrt.f64 (/.f64 1 (PI.f64))))))))
(+.f64 (.f64 3/4 (.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 (fabs.f64 x) 5)) (sqrt.f64 (/.f64 1 (PI.f64))))) (+.f64 (.f64 15/8 (.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (.f64 (pow.f64 (fabs.f64 x) 5) (pow.f64 x 2))) (sqrt.f64 (/.f64 1 (PI.f64))))) (+.f64 (.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (fabs.f64 x)) (sqrt.f64 (/.f64 1 (PI.f64)))) (.f64 1/2 (.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (*.f64 (fabs.f64 x) (pow.f64 x 2))) (sqrt.f64 (/.f64 1 (PI.f64))))))))
(.f64 (.f64 (exp.f64 (pow.f64 x 2)) (+.f64 (*.f64 3/4 (/.f64 1 (pow.f64 (fabs.f64 x) 5))) (/.f64 1 (fabs.f64 x)))) (sqrt.f64 (/.f64 1 (PI.f64))))
(+.f64 (.f64 3/4 (.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 (fabs.f64 x) 5)) (sqrt.f64 (/.f64 1 (PI.f64))))) (+.f64 (.f64 15/8 (.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (.f64 (pow.f64 (fabs.f64 x) 5) (pow.f64 x 2))) (sqrt.f64 (/.f64 1 (PI.f64))))) (+.f64 (.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (fabs.f64 x)) (sqrt.f64 (/.f64 1 (PI.f64)))) (.f64 1/2 (.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (*.f64 (fabs.f64 x) (pow.f64 x 2))) (sqrt.f64 (/.f64 1 (PI.f64))))))))
(+.f64 (.f64 3/4 (.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 (fabs.f64 x) 5)) (sqrt.f64 (/.f64 1 (PI.f64))))) (+.f64 (.f64 15/8 (.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (.f64 (pow.f64 (fabs.f64 x) 5) (pow.f64 x 2))) (sqrt.f64 (/.f64 1 (PI.f64))))) (+.f64 (.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (fabs.f64 x)) (sqrt.f64 (/.f64 1 (PI.f64)))) (.f64 1/2 (.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (*.f64 (fabs.f64 x) (pow.f64 x 2))) (sqrt.f64 (/.f64 1 (PI.f64))))))))
(+.f64 (.f64 3/4 (.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 (fabs.f64 x) 5)) (sqrt.f64 (/.f64 1 (PI.f64))))) (+.f64 (.f64 15/8 (.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (.f64 (pow.f64 (fabs.f64 x) 5) (pow.f64 x 2))) (sqrt.f64 (/.f64 1 (PI.f64))))) (+.f64 (.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (fabs.f64 x)) (sqrt.f64 (/.f64 1 (PI.f64)))) (.f64 1/2 (.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (*.f64 (fabs.f64 x) (pow.f64 x 2))) (sqrt.f64 (/.f64 1 (PI.f64))))))))

Outputs
(/.f64 1 (pow.f64 (fabs.f64 x) 5))
(/.f64 1 (pow.f64 x 5))
(/.f64 1 (pow.f64 (fabs.f64 x) 5))
(/.f64 1 (pow.f64 x 5))
(/.f64 1 (pow.f64 (fabs.f64 x) 5))
(/.f64 1 (pow.f64 x 5))
(/.f64 1 (pow.f64 (fabs.f64 x) 5))
(/.f64 1 (pow.f64 x 5))
(/.f64 1 (pow.f64 (fabs.f64 x) 5))
(/.f64 1 (pow.f64 x 5))
(/.f64 1 (pow.f64 (fabs.f64 x) 5))
(/.f64 1 (pow.f64 x 5))
(/.f64 1 (pow.f64 (fabs.f64 x) 5))
(/.f64 1 (pow.f64 x 5))
(/.f64 1 (pow.f64 (fabs.f64 x) 5))
(/.f64 1 (pow.f64 x 5))
(/.f64 1 (pow.f64 (fabs.f64 x) 5))
(/.f64 1 (pow.f64 x 5))
(/.f64 1 (pow.f64 (fabs.f64 x) 5))
(/.f64 1 (pow.f64 x 5))
(/.f64 1 (pow.f64 (fabs.f64 x) 5))
(/.f64 1 (pow.f64 x 5))
(/.f64 1 (pow.f64 (fabs.f64 x) 5))
(/.f64 1 (pow.f64 x 5))
1
(+.f64 1 (pow.f64 x 2))
(+.f64 1 (*.f64 x x))
(fma.f64 x x 1)
(+.f64 (*.f64 1/2 (pow.f64 x 4)) (+.f64 1 (pow.f64 x 2)))
(fma.f64 1/2 (pow.f64 x 4) (+.f64 1 (*.f64 x x)))
(fma.f64 1/2 (pow.f64 x 4) (fma.f64 x x 1))
(fma.f64 x x (fma.f64 1/2 (pow.f64 x 4) 1))
(+.f64 (.f64 1/2 (pow.f64 x 4)) (+.f64 1 (+.f64 (.f64 1/6 (pow.f64 x 6)) (pow.f64 x 2))))
(fma.f64 1/2 (pow.f64 x 4) (+.f64 1 (fma.f64 1/6 (pow.f64 x 6) (*.f64 x x))))
(+.f64 (fma.f64 x x (*.f64 1/6 (pow.f64 x 6))) (fma.f64 1/2 (pow.f64 x 4) 1))
(fma.f64 1/2 (pow.f64 x 4) (fma.f64 x x (fma.f64 1/6 (pow.f64 x 6) 1)))
(fma.f64 1/2 (pow.f64 x 4) (fma.f64 1/6 (pow.f64 x 6) (fma.f64 x x 1)))
(exp.f64 (pow.f64 x 2))
(exp.f64 (*.f64 x x))
(pow.f64 (exp.f64 x) x)
(exp.f64 (pow.f64 x 2))
(exp.f64 (*.f64 x x))
(pow.f64 (exp.f64 x) x)
(exp.f64 (pow.f64 x 2))
(exp.f64 (*.f64 x x))
(pow.f64 (exp.f64 x) x)
(exp.f64 (pow.f64 x 2))
(exp.f64 (*.f64 x x))
(pow.f64 (exp.f64 x) x)
(exp.f64 (pow.f64 x 2))
(exp.f64 (*.f64 x x))
(pow.f64 (exp.f64 x) x)
(exp.f64 (pow.f64 x 2))
(exp.f64 (*.f64 x x))
(pow.f64 (exp.f64 x) x)
(exp.f64 (pow.f64 x 2))
(exp.f64 (*.f64 x x))
(pow.f64 (exp.f64 x) x)
(exp.f64 (pow.f64 x 2))
(exp.f64 (*.f64 x x))
(pow.f64 (exp.f64 x) x)
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (/.f64 (+.f64 (.f64 1/2 (/.f64 1 (fabs.f64 x))) (*.f64 15/8 (/.f64 1 (pow.f64 (fabs.f64 x) 5)))) (pow.f64 x 2)))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (/.f64 (+.f64 (/.f64 1/2 (fabs.f64 x)) (/.f64 15/8 (pow.f64 (fabs.f64 x) 5))) (.f64 x x)))
(*.f64 (/.f64 (sqrt.f64 (/.f64 1 (PI.f64))) x) (/.f64 (+.f64 (/.f64 1/2 (fabs.f64 x)) (/.f64 15/8 (pow.f64 (fabs.f64 x) 5))) x))
(.f64 (/.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (.f64 x x)) (+.f64 (/.f64 15/8 (pow.f64 x 5)) (/.f64 1/2 x)))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (/.f64 1/2 (pow.f64 x 3)) (/.f64 15/8 (.f64 x (pow.f64 x 6)))))
(+.f64 (.f64 3/2 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (/.f64 1 (fabs.f64 x)))) (+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (/.f64 1 (.f64 (fabs.f64 x) (pow.f64 x 2))))) (+.f64 (.f64 21/8 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (/.f64 1 (pow.f64 (fabs.f64 x) 5)))) (.f64 15/8 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (/.f64 1 (.f64 (pow.f64 (fabs.f64 x) 5) (pow.f64 x 2))))))))
(fma.f64 3/2 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (/.f64 1 (fabs.f64 x))) (fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (/.f64 1 (.f64 (fabs.f64 x) (.f64 x x)))) (fma.f64 21/8 (.f64 (/.f64 1 (pow.f64 (fabs.f64 x) 5)) (sqrt.f64 (/.f64 1 (PI.f64)))) (.f64 15/8 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (/.f64 1 (.f64 (pow.f64 (fabs.f64 x) 5) (*.f64 x x))))))))
(fma.f64 3/2 (/.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fabs.f64 x)) (fma.f64 1/2 (/.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (.f64 (fabs.f64 x) (.f64 x x))) (fma.f64 15/8 (/.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (.f64 (pow.f64 (fabs.f64 x) 5) (.f64 x x))) (*.f64 21/8 (/.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (pow.f64 (fabs.f64 x) 5))))))
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(+.f64 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (/.f64 (exp.f64 (.f64 x x)) (fabs.f64 x)) (/.f64 (.f64 1/2 (exp.f64 (.f64 x x))) (.f64 (fabs.f64 x) (.f64 x x))))) (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (exp.f64 (.f64 x x)) (/.f64 3/4 (pow.f64 (fabs.f64 x) 5))) (.f64 15/8 (/.f64 (exp.f64 (.f64 x x)) (.f64 (pow.f64 (fabs.f64 x) 5) (*.f64 x x)))))))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (fma.f64 1/2 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 3)) (/.f64 (pow.f64 (exp.f64 x) x) x)) (fma.f64 (pow.f64 (exp.f64 x) x) (/.f64 3/4 (pow.f64 x 5)) (.f64 15/8 (/.f64 (pow.f64 (exp.f64 x) x) (.f64 (pow.f64 x 5) (.f64 x x)))))))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (+.f64 (/.f64 1/2 (.f64 x x)) 1) (/.f64 (pow.f64 (exp.f64 x) x) x)) (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (*.f64 x x))))))
(+.f64 (.f64 3/4 (.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 (fabs.f64 x) 5)) (sqrt.f64 (/.f64 1 (PI.f64))))) (+.f64 (.f64 15/8 (.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (.f64 (pow.f64 (fabs.f64 x) 5) (pow.f64 x 2))) (sqrt.f64 (/.f64 1 (PI.f64))))) (+.f64 (.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (fabs.f64 x)) (sqrt.f64 (/.f64 1 (PI.f64)))) (.f64 1/2 (.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (*.f64 (fabs.f64 x) (pow.f64 x 2))) (sqrt.f64 (/.f64 1 (PI.f64))))))))
(fma.f64 3/4 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (/.f64 (exp.f64 (.f64 x x)) (pow.f64 (fabs.f64 x) 5))) (fma.f64 15/8 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (/.f64 (exp.f64 (.f64 x x)) (.f64 (pow.f64 (fabs.f64 x) 5) (.f64 x x)))) (fma.f64 (/.f64 (exp.f64 (.f64 x x)) (fabs.f64 x)) (sqrt.f64 (/.f64 1 (PI.f64))) (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (/.f64 (exp.f64 (.f64 x x)) (.f64 (fabs.f64 x) (.f64 x x))))))))
(+.f64 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (/.f64 (exp.f64 (.f64 x x)) (fabs.f64 x)) (/.f64 (.f64 1/2 (exp.f64 (.f64 x x))) (.f64 (fabs.f64 x) (.f64 x x))))) (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (exp.f64 (.f64 x x)) (/.f64 3/4 (pow.f64 (fabs.f64 x) 5))) (.f64 15/8 (/.f64 (exp.f64 (.f64 x x)) (.f64 (pow.f64 (fabs.f64 x) 5) (*.f64 x x)))))))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (fma.f64 1/2 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 3)) (/.f64 (pow.f64 (exp.f64 x) x) x)) (fma.f64 (pow.f64 (exp.f64 x) x) (/.f64 3/4 (pow.f64 x 5)) (.f64 15/8 (/.f64 (pow.f64 (exp.f64 x) x) (.f64 (pow.f64 x 5) (.f64 x x)))))))
(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (+.f64 (/.f64 1/2 (.f64 x x)) 1) (/.f64 (pow.f64 (exp.f64 x) x) x)) (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (*.f64 x x))))))

prune97.0ms (1.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	50	11	61
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	51	12	63

Error

0.7b

Counts

63 → 12

Alt Table

Status	Error	Program
	3.1b	(expm1.f64 (log1p.f64 (.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (PI.f64))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 15/8 (*.f64 x x))))))))
	53.9b	(.f64 (/.f64 (fma.f64 1/2 (pow.f64 x 4) (fma.f64 1/6 (pow.f64 x 6) (fma.f64 x x 1))) (sqrt.f64 (PI.f64))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (*.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 (/.f64 15/8 x) x)))))
	1.5b	(.f64 (/.f64 (pow.f64 (exp.f64 x) x) (.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (sqrt.f64 (sqrt.f64 (PI.f64))))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 (/.f64 15/8 x) x)))))
	3.0b	(.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (.f64 (fabs.f64 x) (fabs.f64 x)))) (+.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (.f64 (/.f64 1 2) (.f64 (.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))))) (.f64 (/.f64 3 4) (.f64 (.f64 (.f64 (.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))))) (.f64 (/.f64 15 8) (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))))))
	1.6b	(.f64 (/.f64 (pow.f64 (exp.f64 x) x) (expm1.f64 (log1p.f64 (sqrt.f64 (PI.f64))))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (*.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 (/.f64 15/8 x) x)))))
	2.8b	(+.f64 (.f64 3/4 (.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 (fabs.f64 x) 5)) (sqrt.f64 (/.f64 1 (PI.f64))))) (+.f64 (.f64 15/8 (.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (.f64 (pow.f64 (fabs.f64 x) 5) (pow.f64 x 2))) (sqrt.f64 (/.f64 1 (PI.f64))))) (+.f64 (.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (fabs.f64 x)) (sqrt.f64 (/.f64 1 (PI.f64)))) (.f64 1/2 (.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (*.f64 (fabs.f64 x) (pow.f64 x 2))) (sqrt.f64 (/.f64 1 (PI.f64))))))))
	3.2b	(exp.f64 (log.f64 (.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (PI.f64))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 15/8 (*.f64 x x))))))))
	8.8b	(cbrt.f64 (.f64 (.f64 (.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (PI.f64))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 15/8 (.f64 x x)))))) (.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (PI.f64))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 15/8 (.f64 x x))))))) (.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 (PI.f64))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 15/8 (*.f64 x x))))))))
	2.4b	(.f64 (/.f64 (pow.f64 (exp.f64 x) x) (.f64 (.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) (cbrt.f64 (sqrt.f64 (PI.f64)))) (cbrt.f64 (sqrt.f64 (PI.f64))))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (*.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 (/.f64 15/8 x) x)))))
	1.7b	(.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (*.f64 (log.f64 (exp.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5))) (+.f64 3/4 (/.f64 (/.f64 15/8 x) x)))))
	1.5b	(.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (.f64 (.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5/2) (pow.f64 (/.f64 1 (fabs.f64 x)) 5/2)) (+.f64 3/4 (/.f64 (/.f64 15/8 x) x)))))
▶	1.4b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (+.f64 (/.f64 1/2 (.f64 x x)) 1) (/.f64 (pow.f64 (exp.f64 x) x) x)) (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (*.f64 x x))))))

Compiler

Compiled 3729 to 2349 computations (37% saved)

localize22.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(.f64 (+.f64 (/.f64 1/2 (.f64 x x)) 1) (/.f64 (pow.f64 (exp.f64 x) x) x))
✓	0.4b	(/.f64 (pow.f64 (exp.f64 x) x) x)
✓	0.6b	(/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5))
	1.0b	(pow.f64 (exp.f64 x) x)

series119.0ms (1.7%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
114.0ms	x	@	inf	(.f64 (+.f64 (/.f64 1/2 (.f64 x x)) 1) (/.f64 (pow.f64 (exp.f64 x) x) x))
1.0ms	x	@	inf	(/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5))
1.0ms	x	@	0	(/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5))
1.0ms	x	@	-inf	(.f64 (+.f64 (/.f64 1/2 (.f64 x x)) 1) (/.f64 (pow.f64 (exp.f64 x) x) x))
1.0ms	x	@	-inf	(/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5))

rewrite61.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

308×	`prod-diff_binary64`
257×	`log1p-udef_binary64`
153×	`add-sqr-sqrt_binary64`
145×	`add-log-exp_binary64`
145×	`pow1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	42
1	310	40
2	4092	40

Stop Event

1×	node limit

Counts

3 → 110

Calls

Call 1

Inputs
(/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5))
(/.f64 (pow.f64 (exp.f64 x) x) x)
(.f64 (+.f64 (/.f64 1/2 (.f64 x x)) 1) (/.f64 (pow.f64 (exp.f64 x) x) x))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 (exp.f64 (.f64 x x)) (pow.f64 x -5)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (exp.f64 (.f64 x x)) (pow.f64 x -5))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (exp.f64 (.f64 x x)) (pow.f64 x -5)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (.f64 (exp.f64 (.f64 x x)) (pow.f64 x -5)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (.f64 (exp.f64 (.f64 x x)) (pow.f64 x -5))) (pow.f64 (cbrt.f64 (.f64 (exp.f64 (.f64 x x)) (pow.f64 x -5))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (.f64 (exp.f64 (.f64 x x)) (pow.f64 x -5))) 2) (cbrt.f64 (.f64 (exp.f64 (.f64 x x)) (pow.f64 x -5))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (exp.f64 (.f64 x x))) 2) (.f64 (cbrt.f64 (exp.f64 (.f64 x x))) (pow.f64 x -5)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (exp.f64 (.f64 x x))) (pow.f64 x 5/2)) (/.f64 (sqrt.f64 (exp.f64 (.f64 x x))) (pow.f64 x 5/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (neg.f64 (exp.f64 (.f64 x x))) (/.f64 1 (neg.f64 (pow.f64 x 5))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 x -5) (exp.f64 (.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (exp.f64 (.f64 x x))) (.f64 (sqrt.f64 (exp.f64 (.f64 x x))) (pow.f64 x -5)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 (exp.f64 (.f64 x x))) 2) 1) (/.f64 (cbrt.f64 (exp.f64 (.f64 x x))) (pow.f64 x 5)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (exp.f64 (.f64 x x))) 1) (/.f64 (sqrt.f64 (exp.f64 (.f64 x x))) (pow.f64 x 5)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (cbrt.f64 (pow.f64 x 10))) (/.f64 (exp.f64 (.f64 x x)) (cbrt.f64 (pow.f64 x 5))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 (exp.f64 (.f64 x x))) 2) (cbrt.f64 (pow.f64 x 10))) (cbrt.f64 (.f64 (exp.f64 (.f64 x x)) (pow.f64 x -5))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (exp.f64 (.f64 x x))) (cbrt.f64 (pow.f64 x 10))) (/.f64 (sqrt.f64 (exp.f64 (.f64 x x))) (cbrt.f64 (pow.f64 x 5))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (pow.f64 x 5/2)) (/.f64 (exp.f64 (.f64 x x)) (pow.f64 x 5/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 (exp.f64 (.f64 x x))) 2) (pow.f64 x 5/2)) (/.f64 (cbrt.f64 (exp.f64 (.f64 x x))) (pow.f64 x 5/2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (exp.f64 (.f64 x x)) (pow.f64 x -5)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 (exp.f64 (.f64 x x)) (pow.f64 x -5)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 (exp.f64 (.f64 x x)) (pow.f64 x -5))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 (exp.f64 (.f64 x x))) (pow.f64 x 5/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 x 5) (exp.f64 (.f64 x x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (exp.f64 (.f64 x x)) (neg.f64 (pow.f64 x 5))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (pow.f64 (exp.f64 x) (+.f64 x x)) (pow.f64 x 10)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (exp.f64 (.f64 x x))) (pow.f64 x -5)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 (exp.f64 (.f64 x x)) (pow.f64 x -5)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 (exp.f64 (.f64 x x)) (pow.f64 x -5)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (exp.f64 (.f64 x x)) 3) (pow.f64 (pow.f64 x 5) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 (exp.f64 (.f64 x x)) (pow.f64 x -5))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (.f64 x x) (log.f64 (pow.f64 x -5))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (+.f64 (.f64 x x) (log.f64 (pow.f64 x -5))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 (exp.f64 (*.f64 x x)) (pow.f64 x -5))))))))
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Outputs

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((#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (exp.f64 (*.f64 x x)) x) (*.f64 (/.f64 1/2 (*.f64 x x)) (/.f64 (exp.f64 (*.f64 x x)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (exp.f64 (*.f64 x x)) x) (*.f64 (/.f64 (exp.f64 (*.f64 x x)) x) (/.f64 1/2 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (/.f64 1/2 (*.f64 x x)) (/.f64 (exp.f64 (*.f64 x x)) x)) (/.f64 (exp.f64 (*.f64 x x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (/.f64 (exp.f64 (*.f64 x x)) x) (/.f64 1/2 (*.f64 x x))) (/.f64 (exp.f64 (*.f64 x x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (/.f64 (exp.f64 (*.f64 x x)) x) (fma.f64 1/2 (pow.f64 x -2) 1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 x (*.f64 (exp.f64 (*.f64 x x)) (fma.f64 1/2 (pow.f64 x -2) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 1/2 (pow.f64 x -2) 1) (/.f64 x (exp.f64 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> 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simplify30.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

740×	`fma-def_binary64`
632×	`associate-/r*_binary64`
526×	`associate-/l*_binary64`
503×	`associate-/l/_binary64`
392×	`associate-*l/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	48	518
1	117	510
2	285	490
3	737	490
4	1990	490

Stop Event

1×	node limit

Counts

146 → 136

Calls

Call 1

Inputs
(/.f64 1 (pow.f64 x 5))
(+.f64 (/.f64 1 (pow.f64 x 5)) (/.f64 1 (pow.f64 x 3)))
(+.f64 (/.f64 1 (pow.f64 x 5)) (+.f64 (*.f64 1/2 (/.f64 1 x)) (/.f64 1 (pow.f64 x 3))))
(+.f64 (/.f64 1 (pow.f64 x 5)) (+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (/.f64 1 (pow.f64 x 3)) (.f64 1/6 x))))
(/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 5))
(/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 5))
(/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 5))
(/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 5))
(/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 5))
(/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 5))
(/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 5))
(/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 5))
(/.f64 1 x)
(+.f64 (/.f64 1 x) x)
(+.f64 (/.f64 1 x) (+.f64 x (*.f64 1/2 (pow.f64 x 3))))
(+.f64 (.f64 1/6 (pow.f64 x 5)) (+.f64 (/.f64 1 x) (+.f64 x (.f64 1/2 (pow.f64 x 3)))))
(/.f64 (exp.f64 (pow.f64 x 2)) x)
(/.f64 (exp.f64 (pow.f64 x 2)) x)
(/.f64 (exp.f64 (pow.f64 x 2)) x)
(/.f64 (exp.f64 (pow.f64 x 2)) x)
(/.f64 (exp.f64 (pow.f64 x 2)) x)
(/.f64 (exp.f64 (pow.f64 x 2)) x)
(/.f64 (exp.f64 (pow.f64 x 2)) x)
(/.f64 (exp.f64 (pow.f64 x 2)) x)
(/.f64 1/2 (pow.f64 x 3))
(+.f64 (.f64 3/2 (/.f64 1 x)) (.f64 1/2 (/.f64 1 (pow.f64 x 3))))
(+.f64 (.f64 3/2 (/.f64 1 x)) (+.f64 (.f64 1/2 (/.f64 1 (pow.f64 x 3))) (*.f64 5/4 x)))
(+.f64 (.f64 3/2 (/.f64 1 x)) (+.f64 (.f64 1/2 (/.f64 1 (pow.f64 x 3))) (+.f64 (.f64 7/12 (pow.f64 x 3)) (.f64 5/4 x))))
(/.f64 (exp.f64 (pow.f64 x 2)) x)
(+.f64 (*.f64 1/2 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 3))) (/.f64 (exp.f64 (pow.f64 x 2)) x))
(+.f64 (*.f64 1/2 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 3))) (/.f64 (exp.f64 (pow.f64 x 2)) x))
(+.f64 (*.f64 1/2 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 3))) (/.f64 (exp.f64 (pow.f64 x 2)) x))
(/.f64 (exp.f64 (pow.f64 x 2)) x)
(+.f64 (*.f64 1/2 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 3))) (/.f64 (exp.f64 (pow.f64 x 2)) x))
(+.f64 (*.f64 1/2 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 3))) (/.f64 (exp.f64 (pow.f64 x 2)) x))
(+.f64 (*.f64 1/2 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 3))) (/.f64 (exp.f64 (pow.f64 x 2)) x))

Outputs
(/.f64 1 (pow.f64 x 5))
(+.f64 (/.f64 1 (pow.f64 x 5)) (/.f64 1 (pow.f64 x 3)))
(+.f64 (/.f64 1 (pow.f64 x 5)) (+.f64 (*.f64 1/2 (/.f64 1 x)) (/.f64 1 (pow.f64 x 3))))
(+.f64 (+.f64 (/.f64 1 (pow.f64 x 5)) (/.f64 1/2 x)) (/.f64 1 (pow.f64 x 3)))
(+.f64 (/.f64 1 (pow.f64 x 5)) (+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 1/2 x)))
(+.f64 (/.f64 1 (pow.f64 x 5)) (+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (/.f64 1 (pow.f64 x 3)) (.f64 1/6 x))))
(+.f64 (/.f64 1 (pow.f64 x 5)) (+.f64 (/.f64 1/2 x) (+.f64 (/.f64 1 (pow.f64 x 3)) (*.f64 x 1/6))))
(+.f64 (/.f64 1 (pow.f64 x 5)) (+.f64 (/.f64 1/2 x) (fma.f64 x 1/6 (/.f64 1 (pow.f64 x 3)))))
(+.f64 (/.f64 1 (pow.f64 x 3)) (+.f64 (/.f64 1 (pow.f64 x 5)) (fma.f64 x 1/6 (/.f64 1/2 x))))
(+.f64 (/.f64 1 (pow.f64 x 5)) (+.f64 (/.f64 1 (pow.f64 x 3)) (fma.f64 x 1/6 (/.f64 1/2 x))))
(/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 5))
(/.f64 (exp.f64 (*.f64 x x)) (pow.f64 x 5))
(/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5))
(/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 5))
(/.f64 (exp.f64 (*.f64 x x)) (pow.f64 x 5))
(/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5))
(/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 5))
(/.f64 (exp.f64 (*.f64 x x)) (pow.f64 x 5))
(/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5))
(/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 5))
(/.f64 (exp.f64 (*.f64 x x)) (pow.f64 x 5))
(/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5))
(/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 5))
(/.f64 (exp.f64 (*.f64 x x)) (pow.f64 x 5))
(/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5))
(/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 5))
(/.f64 (exp.f64 (*.f64 x x)) (pow.f64 x 5))
(/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5))
(/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 5))
(/.f64 (exp.f64 (*.f64 x x)) (pow.f64 x 5))
(/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5))
(/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 5))
(/.f64 (exp.f64 (*.f64 x x)) (pow.f64 x 5))
(/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5))
(/.f64 1 x)
(+.f64 (/.f64 1 x) x)
(+.f64 x (/.f64 1 x))
(+.f64 (/.f64 1 x) (+.f64 x (*.f64 1/2 (pow.f64 x 3))))
(+.f64 (/.f64 1 x) (+.f64 x (*.f64 (pow.f64 x 3) 1/2)))
(+.f64 (/.f64 1 x) (fma.f64 (pow.f64 x 3) 1/2 x))
(+.f64 x (fma.f64 (pow.f64 x 3) 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/6 (pow.f64 x 5)) (+.f64 (/.f64 1 x) (+.f64 x (.f64 1/2 (pow.f64 x 3)))))
(fma.f64 1/6 (pow.f64 x 5) (+.f64 (/.f64 1 x) (+.f64 x (*.f64 (pow.f64 x 3) 1/2))))
(fma.f64 (pow.f64 x 5) 1/6 (+.f64 (/.f64 1 x) (fma.f64 (pow.f64 x 3) 1/2 x)))
(+.f64 (/.f64 1 x) (fma.f64 (pow.f64 x 5) 1/6 (fma.f64 (pow.f64 x 3) 1/2 x)))
(/.f64 (exp.f64 (pow.f64 x 2)) x)
(/.f64 (exp.f64 (*.f64 x x)) x)
(/.f64 (pow.f64 (exp.f64 x) x) x)
(/.f64 (exp.f64 (pow.f64 x 2)) x)
(/.f64 (exp.f64 (*.f64 x x)) x)
(/.f64 (pow.f64 (exp.f64 x) x) x)
(/.f64 (exp.f64 (pow.f64 x 2)) x)
(/.f64 (exp.f64 (*.f64 x x)) x)
(/.f64 (pow.f64 (exp.f64 x) x) x)
(/.f64 (exp.f64 (pow.f64 x 2)) x)
(/.f64 (exp.f64 (*.f64 x x)) x)
(/.f64 (pow.f64 (exp.f64 x) x) x)
(/.f64 (exp.f64 (pow.f64 x 2)) x)
(/.f64 (exp.f64 (*.f64 x x)) x)
(/.f64 (pow.f64 (exp.f64 x) x) x)
(/.f64 (exp.f64 (pow.f64 x 2)) x)
(/.f64 (exp.f64 (*.f64 x x)) x)
(/.f64 (pow.f64 (exp.f64 x) x) x)
(/.f64 (exp.f64 (pow.f64 x 2)) x)
(/.f64 (exp.f64 (*.f64 x x)) x)
(/.f64 (pow.f64 (exp.f64 x) x) x)
(/.f64 (exp.f64 (pow.f64 x 2)) x)
(/.f64 (exp.f64 (*.f64 x x)) x)
(/.f64 (pow.f64 (exp.f64 x) x) x)
(/.f64 1/2 (pow.f64 x 3))
(+.f64 (.f64 3/2 (/.f64 1 x)) (.f64 1/2 (/.f64 1 (pow.f64 x 3))))
(+.f64 (/.f64 3/2 x) (/.f64 1/2 (pow.f64 x 3)))
(+.f64 (.f64 3/2 (/.f64 1 x)) (+.f64 (.f64 1/2 (/.f64 1 (pow.f64 x 3))) (*.f64 5/4 x)))
(+.f64 (/.f64 3/2 x) (+.f64 (/.f64 1/2 (pow.f64 x 3)) (*.f64 x 5/4)))
(+.f64 (/.f64 3/2 x) (fma.f64 x 5/4 (/.f64 1/2 (pow.f64 x 3))))
(+.f64 (.f64 3/2 (/.f64 1 x)) (+.f64 (.f64 1/2 (/.f64 1 (pow.f64 x 3))) (+.f64 (.f64 7/12 (pow.f64 x 3)) (.f64 5/4 x))))
(+.f64 (/.f64 3/2 x) (+.f64 (/.f64 1/2 (pow.f64 x 3)) (fma.f64 7/12 (pow.f64 x 3) (*.f64 x 5/4))))
(+.f64 (/.f64 1/2 (pow.f64 x 3)) (+.f64 (/.f64 3/2 x) (fma.f64 x 5/4 (*.f64 (pow.f64 x 3) 7/12))))
(+.f64 (/.f64 3/2 x) (fma.f64 x 5/4 (fma.f64 (pow.f64 x 3) 7/12 (/.f64 1/2 (pow.f64 x 3)))))
(+.f64 (/.f64 1/2 (pow.f64 x 3)) (fma.f64 x 5/4 (fma.f64 (pow.f64 x 3) 7/12 (/.f64 3/2 x))))
(/.f64 (exp.f64 (pow.f64 x 2)) x)
(/.f64 (exp.f64 (*.f64 x x)) x)
(/.f64 (pow.f64 (exp.f64 x) x) x)
(+.f64 (*.f64 1/2 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 3))) (/.f64 (exp.f64 (pow.f64 x 2)) x))
(fma.f64 1/2 (/.f64 (exp.f64 (.f64 x x)) (pow.f64 x 3)) (/.f64 (exp.f64 (.f64 x x)) x))
(.f64 (+.f64 (/.f64 1/2 (.f64 x x)) 1) (/.f64 (pow.f64 (exp.f64 x) x) x))
(.f64 (/.f64 (pow.f64 (exp.f64 x) x) x) (+.f64 1 (/.f64 1/2 (.f64 x x))))
(.f64 (/.f64 (exp.f64 (.f64 x x)) x) (+.f64 1 (/.f64 1/2 (*.f64 x x))))
(+.f64 (*.f64 1/2 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 3))) (/.f64 (exp.f64 (pow.f64 x 2)) x))
(fma.f64 1/2 (/.f64 (exp.f64 (.f64 x x)) (pow.f64 x 3)) (/.f64 (exp.f64 (.f64 x x)) x))
(.f64 (+.f64 (/.f64 1/2 (.f64 x x)) 1) (/.f64 (pow.f64 (exp.f64 x) x) x))
(.f64 (/.f64 (pow.f64 (exp.f64 x) x) x) (+.f64 1 (/.f64 1/2 (.f64 x x))))
(.f64 (/.f64 (exp.f64 (.f64 x x)) x) (+.f64 1 (/.f64 1/2 (*.f64 x x))))
(+.f64 (*.f64 1/2 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 3))) (/.f64 (exp.f64 (pow.f64 x 2)) x))
(fma.f64 1/2 (/.f64 (exp.f64 (.f64 x x)) (pow.f64 x 3)) (/.f64 (exp.f64 (.f64 x x)) x))
(.f64 (+.f64 (/.f64 1/2 (.f64 x x)) 1) (/.f64 (pow.f64 (exp.f64 x) x) x))
(.f64 (/.f64 (pow.f64 (exp.f64 x) x) x) (+.f64 1 (/.f64 1/2 (.f64 x x))))
(.f64 (/.f64 (exp.f64 (.f64 x x)) x) (+.f64 1 (/.f64 1/2 (*.f64 x x))))
(/.f64 (exp.f64 (pow.f64 x 2)) x)
(/.f64 (exp.f64 (*.f64 x x)) x)
(/.f64 (pow.f64 (exp.f64 x) x) x)
(+.f64 (*.f64 1/2 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 3))) (/.f64 (exp.f64 (pow.f64 x 2)) x))
(fma.f64 1/2 (/.f64 (exp.f64 (.f64 x x)) (pow.f64 x 3)) (/.f64 (exp.f64 (.f64 x x)) x))
(.f64 (+.f64 (/.f64 1/2 (.f64 x x)) 1) (/.f64 (pow.f64 (exp.f64 x) x) x))
(.f64 (/.f64 (pow.f64 (exp.f64 x) x) x) (+.f64 1 (/.f64 1/2 (.f64 x x))))
(.f64 (/.f64 (exp.f64 (.f64 x x)) x) (+.f64 1 (/.f64 1/2 (*.f64 x x))))
(+.f64 (*.f64 1/2 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 3))) (/.f64 (exp.f64 (pow.f64 x 2)) x))
(fma.f64 1/2 (/.f64 (exp.f64 (.f64 x x)) (pow.f64 x 3)) (/.f64 (exp.f64 (.f64 x x)) x))
(.f64 (+.f64 (/.f64 1/2 (.f64 x x)) 1) (/.f64 (pow.f64 (exp.f64 x) x) x))
(.f64 (/.f64 (pow.f64 (exp.f64 x) x) x) (+.f64 1 (/.f64 1/2 (.f64 x x))))
(.f64 (/.f64 (exp.f64 (.f64 x x)) x) (+.f64 1 (/.f64 1/2 (*.f64 x x))))
(+.f64 (*.f64 1/2 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 3))) (/.f64 (exp.f64 (pow.f64 x 2)) x))
(fma.f64 1/2 (/.f64 (exp.f64 (.f64 x x)) (pow.f64 x 3)) (/.f64 (exp.f64 (.f64 x x)) x))
(.f64 (+.f64 (/.f64 1/2 (.f64 x x)) 1) (/.f64 (pow.f64 (exp.f64 x) x) x))
(.f64 (/.f64 (pow.f64 (exp.f64 x) x) x) (+.f64 1 (/.f64 1/2 (.f64 x x))))
(.f64 (/.f64 (exp.f64 (.f64 x x)) x) (+.f64 1 (/.f64 1/2 (*.f64 x x))))

prune244.0ms (3.6%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	162	10	172
Fresh	3	8	11
Picked	1	0	1
Done	0	0	0
Total	166	18	184

Error

0.6b

Counts

184 → 18

Alt Table

Status	Error	Program
	3.0b	(.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (.f64 (fabs.f64 x) (fabs.f64 x)))) (+.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (.f64 (/.f64 1 2) (.f64 (.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))))) (.f64 (/.f64 3 4) (.f64 (.f64 (.f64 (.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))))) (.f64 (/.f64 15 8) (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))))))
	8.6b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (cbrt.f64 (.f64 (pow.f64 (/.f64 (exp.f64 (.f64 x x)) x) 3) (pow.f64 (fma.f64 1/2 (pow.f64 x -2) 1) 3))) (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (*.f64 x x))))))
	1.5b	(.f64 (/.f64 (pow.f64 (exp.f64 x) x) (.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (sqrt.f64 (sqrt.f64 (PI.f64))))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 (/.f64 15/8 x) x)))))
	2.9b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (+.f64 (/.f64 1/2 (.f64 x x)) 1) (exp.f64 (-.f64 (.f64 x x) (log.f64 x)))) (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (.f64 x x))))))
	3.0b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (+.f64 (/.f64 1/2 (.f64 x x)) 1) (/.f64 (.f64 (.f64 (cbrt.f64 (exp.f64 (.f64 x x))) (cbrt.f64 (exp.f64 (.f64 x x)))) (cbrt.f64 (exp.f64 (.f64 x x)))) x)) (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (.f64 x x))))))
	2.8b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (+.f64 (/.f64 1/2 (.f64 x x)) 1) (.f64 (sqrt.f64 (exp.f64 (.f64 x x))) (.f64 (sqrt.f64 (exp.f64 (.f64 x x))) (/.f64 1 x)))) (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (*.f64 x x))))))
▶	1.4b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (+.f64 (/.f64 1/2 (.f64 x x)) 1) (/.f64 (.f64 (pow.f64 (exp.f64 x) (/.f64 x 2)) (pow.f64 (exp.f64 x) (/.f64 x 2))) x)) (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (.f64 x x))))))
	7.2b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (+.f64 (/.f64 1/2 (.f64 x x)) 1) (/.f64 (pow.f64 (exp.f64 x) x) x)) (.f64 (pow.f64 (pow.f64 (.f64 (exp.f64 (.f64 x x)) (pow.f64 x -5)) 3) 1/3) (+.f64 3/4 (/.f64 15/8 (*.f64 x x))))))
	1.6b	(.f64 (/.f64 (pow.f64 (exp.f64 x) x) (expm1.f64 (log1p.f64 (sqrt.f64 (PI.f64))))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (*.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 (/.f64 15/8 x) x)))))
	2.8b	(+.f64 (.f64 3/4 (.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 (fabs.f64 x) 5)) (sqrt.f64 (/.f64 1 (PI.f64))))) (+.f64 (.f64 15/8 (.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (.f64 (pow.f64 (fabs.f64 x) 5) (pow.f64 x 2))) (sqrt.f64 (/.f64 1 (PI.f64))))) (+.f64 (.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (fabs.f64 x)) (sqrt.f64 (/.f64 1 (PI.f64)))) (.f64 1/2 (.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (*.f64 (fabs.f64 x) (pow.f64 x 2))) (sqrt.f64 (/.f64 1 (PI.f64))))))))
	9.0b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (+.f64 (/.f64 1/2 (.f64 x x)) 1) (pow.f64 (pow.f64 (/.f64 (exp.f64 (.f64 x x)) x) 3) 1/3)) (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (.f64 x x))))))
	53.9b	(.f64 (/.f64 (fma.f64 1/2 (pow.f64 x 4) (fma.f64 1/6 (pow.f64 x 6) (fma.f64 x x 1))) (sqrt.f64 (PI.f64))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (*.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 (/.f64 15/8 x) x)))))
	3.1b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (exp.f64 (+.f64 (-.f64 (.f64 x x) (log.f64 x)) (log1p.f64 (/.f64 1/2 (.f64 x x))))) (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (*.f64 x x))))))
	3.1b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (expm1.f64 (log1p.f64 (.f64 (/.f64 (exp.f64 (.f64 x x)) x) (fma.f64 1/2 (pow.f64 x -2) 1)))) (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (*.f64 x x))))))
	2.4b	(.f64 (/.f64 (pow.f64 (exp.f64 x) x) (.f64 (.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) (cbrt.f64 (sqrt.f64 (PI.f64)))) (cbrt.f64 (sqrt.f64 (PI.f64))))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (*.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 (/.f64 15/8 x) x)))))
	3.0b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (pow.f64 (cbrt.f64 (.f64 (/.f64 (exp.f64 (.f64 x x)) x) (fma.f64 1/2 (pow.f64 x -2) 1))) 3) (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (*.f64 x x))))))
	1.7b	(.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (*.f64 (log.f64 (exp.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5))) (+.f64 3/4 (/.f64 (/.f64 15/8 x) x)))))
	1.5b	(.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (.f64 (.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5/2) (pow.f64 (/.f64 1 (fabs.f64 x)) 5/2)) (+.f64 3/4 (/.f64 (/.f64 15/8 x) x)))))

Compiler

Compiled 8699 to 5042 computations (42% saved)

localize28.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (pow.f64 (exp.f64 x) (/.f64 x 2)) (pow.f64 (exp.f64 x) (/.f64 x 2)))
	0.6b	(/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5))
✓	0.6b	(pow.f64 (exp.f64 x) (/.f64 x 2))
	1.0b	(pow.f64 (exp.f64 x) x)

series3.0ms (0%)

Counts

2 → 24

Calls

6 calls:

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

rewrite38.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

674×	`pow1_binary64`
630×	`add-log-exp_binary64`
630×	`log1p-expm1-u_binary64`
630×	`expm1-log1p-u_binary64`
74×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	21
1	152	14
2	1914	14

Stop Event

1×	node limit

Counts

2 → 35

Calls

Call 1

Inputs
(pow.f64 (exp.f64 x) (/.f64 x 2))
(*.f64 (pow.f64 (exp.f64 x) (/.f64 x 2)) (pow.f64 (exp.f64 x) (/.f64 x 2)))

Outputs

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

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

simplify34.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

421×	`unswap-sqr_binary64`
386×	`fma-def_binary64`
379×	`distribute-rgt-out_binary64`
358×	`*-commutative_binary64`
322×	`distribute-lft-out_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	30	263
1	78	255
2	187	219
3	537	195
4	2081	195
5	4866	195

Stop Event

1×	node limit

Counts

59 → 51

Calls

Call 1

Inputs
1
(+.f64 1 (*.f64 1/2 (pow.f64 x 2)))
(+.f64 (.f64 1/8 (pow.f64 x 4)) (+.f64 1 (.f64 1/2 (pow.f64 x 2))))
(+.f64 (.f64 1/8 (pow.f64 x 4)) (+.f64 1 (+.f64 (.f64 1/48 (pow.f64 x 6)) (*.f64 1/2 (pow.f64 x 2)))))
(exp.f64 (*.f64 1/2 (pow.f64 x 2)))
(exp.f64 (*.f64 1/2 (pow.f64 x 2)))
(exp.f64 (*.f64 1/2 (pow.f64 x 2)))
(exp.f64 (*.f64 1/2 (pow.f64 x 2)))
(exp.f64 (*.f64 1/2 (pow.f64 x 2)))
(exp.f64 (*.f64 1/2 (pow.f64 x 2)))
(exp.f64 (*.f64 1/2 (pow.f64 x 2)))
(exp.f64 (*.f64 1/2 (pow.f64 x 2)))
1
(+.f64 1 (pow.f64 x 2))
(+.f64 (*.f64 1/2 (pow.f64 x 4)) (+.f64 1 (pow.f64 x 2)))
(+.f64 (.f64 1/2 (pow.f64 x 4)) (+.f64 1 (+.f64 (.f64 1/6 (pow.f64 x 6)) (pow.f64 x 2))))
(pow.f64 (exp.f64 (*.f64 1/2 (pow.f64 x 2))) 2)
(pow.f64 (exp.f64 (*.f64 1/2 (pow.f64 x 2))) 2)
(pow.f64 (exp.f64 (*.f64 1/2 (pow.f64 x 2))) 2)
(pow.f64 (exp.f64 (*.f64 1/2 (pow.f64 x 2))) 2)
(pow.f64 (exp.f64 (*.f64 1/2 (pow.f64 x 2))) 2)
(pow.f64 (exp.f64 (*.f64 1/2 (pow.f64 x 2))) 2)
(pow.f64 (exp.f64 (*.f64 1/2 (pow.f64 x 2))) 2)
(pow.f64 (exp.f64 (*.f64 1/2 (pow.f64 x 2))) 2)

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 (.f64 1/8 (pow.f64 x 4)) (+.f64 1 (.f64 1/2 (pow.f64 x 2))))
(fma.f64 1/8 (pow.f64 x 4) (+.f64 1 (.f64 1/2 (.f64 x x))))
(fma.f64 1/8 (pow.f64 x 4) (fma.f64 1/2 (*.f64 x x) 1))
(fma.f64 1/2 (*.f64 x x) (fma.f64 1/8 (pow.f64 x 4) 1))
(+.f64 (.f64 1/8 (pow.f64 x 4)) (+.f64 1 (+.f64 (.f64 1/48 (pow.f64 x 6)) (*.f64 1/2 (pow.f64 x 2)))))
(fma.f64 1/8 (pow.f64 x 4) (+.f64 1 (fma.f64 1/48 (pow.f64 x 6) (.f64 1/2 (.f64 x x)))))
(+.f64 (fma.f64 1/8 (pow.f64 x 4) (fma.f64 1/2 (.f64 x x) 1)) (.f64 1/48 (pow.f64 x 6)))
(fma.f64 1/8 (pow.f64 x 4) (fma.f64 1/2 (*.f64 x x) (fma.f64 1/48 (pow.f64 x 6) 1)))
(fma.f64 1/2 (*.f64 x x) (fma.f64 1/8 (pow.f64 x 4) (fma.f64 1/48 (pow.f64 x 6) 1)))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x 1/8) 1/2) (fma.f64 1/48 (pow.f64 x 6) 1))
(exp.f64 (*.f64 1/2 (pow.f64 x 2)))
(pow.f64 (exp.f64 1/2) (*.f64 x x))
(sqrt.f64 (pow.f64 (exp.f64 x) x))
(pow.f64 (sqrt.f64 (exp.f64 x)) x)
(exp.f64 (*.f64 1/2 (pow.f64 x 2)))
(pow.f64 (exp.f64 1/2) (*.f64 x x))
(sqrt.f64 (pow.f64 (exp.f64 x) x))
(pow.f64 (sqrt.f64 (exp.f64 x)) x)
(exp.f64 (*.f64 1/2 (pow.f64 x 2)))
(pow.f64 (exp.f64 1/2) (*.f64 x x))
(sqrt.f64 (pow.f64 (exp.f64 x) x))
(pow.f64 (sqrt.f64 (exp.f64 x)) x)
(exp.f64 (*.f64 1/2 (pow.f64 x 2)))
(pow.f64 (exp.f64 1/2) (*.f64 x x))
(sqrt.f64 (pow.f64 (exp.f64 x) x))
(pow.f64 (sqrt.f64 (exp.f64 x)) x)
(exp.f64 (*.f64 1/2 (pow.f64 x 2)))
(pow.f64 (exp.f64 1/2) (*.f64 x x))
(sqrt.f64 (pow.f64 (exp.f64 x) x))
(pow.f64 (sqrt.f64 (exp.f64 x)) x)
(exp.f64 (*.f64 1/2 (pow.f64 x 2)))
(pow.f64 (exp.f64 1/2) (*.f64 x x))
(sqrt.f64 (pow.f64 (exp.f64 x) x))
(pow.f64 (sqrt.f64 (exp.f64 x)) x)
(exp.f64 (*.f64 1/2 (pow.f64 x 2)))
(pow.f64 (exp.f64 1/2) (*.f64 x x))
(sqrt.f64 (pow.f64 (exp.f64 x) x))
(pow.f64 (sqrt.f64 (exp.f64 x)) x)
(exp.f64 (*.f64 1/2 (pow.f64 x 2)))
(pow.f64 (exp.f64 1/2) (*.f64 x x))
(sqrt.f64 (pow.f64 (exp.f64 x) x))
(pow.f64 (sqrt.f64 (exp.f64 x)) x)
1
(+.f64 1 (pow.f64 x 2))
(+.f64 1 (*.f64 x x))
(fma.f64 x x 1)
(+.f64 (*.f64 1/2 (pow.f64 x 4)) (+.f64 1 (pow.f64 x 2)))
(fma.f64 1/2 (pow.f64 x 4) (+.f64 1 (*.f64 x x)))
(fma.f64 1/2 (pow.f64 x 4) (fma.f64 x x 1))
(fma.f64 x x (fma.f64 1/2 (pow.f64 x 4) 1))
(+.f64 (.f64 1/2 (pow.f64 x 4)) (+.f64 1 (+.f64 (.f64 1/6 (pow.f64 x 6)) (pow.f64 x 2))))
(fma.f64 1/2 (pow.f64 x 4) (+.f64 1 (fma.f64 1/6 (pow.f64 x 6) (*.f64 x x))))
(+.f64 (fma.f64 x x (*.f64 (pow.f64 x 6) 1/6)) (fma.f64 1/2 (pow.f64 x 4) 1))
(fma.f64 1/2 (pow.f64 x 4) (fma.f64 x x (fma.f64 (pow.f64 x 6) 1/6 1)))
(fma.f64 1/2 (pow.f64 x 4) (fma.f64 (pow.f64 x 6) 1/6 (fma.f64 x x 1)))
(fma.f64 (pow.f64 x 6) 1/6 (fma.f64 1/2 (pow.f64 x 4) (fma.f64 x x 1)))
(pow.f64 (exp.f64 (*.f64 1/2 (pow.f64 x 2))) 2)
(pow.f64 (pow.f64 (exp.f64 1/2) (*.f64 x x)) 2)
(pow.f64 (pow.f64 (exp.f64 x) x) 1)
(pow.f64 (exp.f64 x) x)
(pow.f64 (exp.f64 (*.f64 1/2 (pow.f64 x 2))) 2)
(pow.f64 (pow.f64 (exp.f64 1/2) (*.f64 x x)) 2)
(pow.f64 (pow.f64 (exp.f64 x) x) 1)
(pow.f64 (exp.f64 x) x)
(pow.f64 (exp.f64 (*.f64 1/2 (pow.f64 x 2))) 2)
(pow.f64 (pow.f64 (exp.f64 1/2) (*.f64 x x)) 2)
(pow.f64 (pow.f64 (exp.f64 x) x) 1)
(pow.f64 (exp.f64 x) x)
(pow.f64 (exp.f64 (*.f64 1/2 (pow.f64 x 2))) 2)
(pow.f64 (pow.f64 (exp.f64 1/2) (*.f64 x x)) 2)
(pow.f64 (pow.f64 (exp.f64 x) x) 1)
(pow.f64 (exp.f64 x) x)
(pow.f64 (exp.f64 (*.f64 1/2 (pow.f64 x 2))) 2)
(pow.f64 (pow.f64 (exp.f64 1/2) (*.f64 x x)) 2)
(pow.f64 (pow.f64 (exp.f64 x) x) 1)
(pow.f64 (exp.f64 x) x)
(pow.f64 (exp.f64 (*.f64 1/2 (pow.f64 x 2))) 2)
(pow.f64 (pow.f64 (exp.f64 1/2) (*.f64 x x)) 2)
(pow.f64 (pow.f64 (exp.f64 x) x) 1)
(pow.f64 (exp.f64 x) x)
(pow.f64 (exp.f64 (*.f64 1/2 (pow.f64 x 2))) 2)
(pow.f64 (pow.f64 (exp.f64 1/2) (*.f64 x x)) 2)
(pow.f64 (pow.f64 (exp.f64 x) x) 1)
(pow.f64 (exp.f64 x) x)
(pow.f64 (exp.f64 (*.f64 1/2 (pow.f64 x 2))) 2)
(pow.f64 (pow.f64 (exp.f64 1/2) (*.f64 x x)) 2)
(pow.f64 (pow.f64 (exp.f64 x) x) 1)
(pow.f64 (exp.f64 x) x)

prune266.0ms (3.9%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	127	10	137
Fresh	5	12	17
Picked	1	0	1
Done	0	0	0
Total	133	22	155

Error

0.4b

Counts

155 → 22

Alt Table

Status	Error	Program
	1.4b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (+.f64 (/.f64 1/2 (.f64 x x)) 1) (/.f64 (.f64 (pow.f64 (exp.f64 x) (/.f64 x 2)) (pow.f64 (exp.f64 x) (/.f64 x 2))) x)) (.f64 (/.f64 (exp.f64 (.f64 x x)) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (*.f64 x x))))))
	4.8b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (+.f64 (/.f64 1/2 (.f64 x x)) 1) (/.f64 (.f64 (pow.f64 (exp.f64 x) (/.f64 x 2)) (cbrt.f64 (pow.f64 (sqrt.f64 (pow.f64 (exp.f64 x) x)) 3))) x)) (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (.f64 x x))))))
	3.1b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (expm1.f64 (log1p.f64 (.f64 (/.f64 (exp.f64 (.f64 x x)) x) (fma.f64 1/2 (pow.f64 x -2) 1)))) (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (*.f64 x x))))))
	1.5b	(.f64 (/.f64 (pow.f64 (exp.f64 x) x) (.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (sqrt.f64 (sqrt.f64 (PI.f64))))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 (/.f64 15/8 x) x)))))
	8.6b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (cbrt.f64 (.f64 (pow.f64 (/.f64 (exp.f64 (.f64 x x)) x) 3) (pow.f64 (fma.f64 1/2 (pow.f64 x -2) 1) 3))) (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (*.f64 x x))))))
	2.9b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (+.f64 (/.f64 1/2 (.f64 x x)) 1) (exp.f64 (-.f64 (.f64 x x) (log.f64 x)))) (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (.f64 x x))))))
	2.2b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (+.f64 (/.f64 1/2 (.f64 x x)) 1) (/.f64 (.f64 (pow.f64 (exp.f64 x) (/.f64 x 2)) (.f64 (pow.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (.f64 x 1/2)) (pow.f64 (cbrt.f64 (exp.f64 x)) (.f64 x 1/2)))) x)) (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (*.f64 x x))))))
	3.0b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (pow.f64 (cbrt.f64 (.f64 (/.f64 (exp.f64 (.f64 x x)) x) (fma.f64 1/2 (pow.f64 x -2) 1))) 3) (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (*.f64 x x))))))
	1.5b	(.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (.f64 (.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5/2) (pow.f64 (/.f64 1 (fabs.f64 x)) 5/2)) (+.f64 3/4 (/.f64 (/.f64 15/8 x) x)))))
	1.7b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (+.f64 (/.f64 1/2 (.f64 x x)) 1) (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) x)) 3) x)) (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (*.f64 x x))))))
▶	1.1b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (+.f64 (/.f64 1/2 (.f64 x x)) 1) (/.f64 (pow.f64 (exp.f64 (+.f64 x x)) (.f64 x 1/2)) x)) (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (.f64 x x))))))
	1.5b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (+.f64 (/.f64 1/2 (.f64 x x)) 1) (/.f64 (.f64 (pow.f64 (exp.f64 x) (/.f64 x 2)) (.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (exp.f64 x) x))) (cbrt.f64 (pow.f64 (exp.f64 x) x)))) x)) (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (*.f64 x x))))))
	1.6b	(.f64 (/.f64 (pow.f64 (exp.f64 x) x) (expm1.f64 (log1p.f64 (sqrt.f64 (PI.f64))))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (*.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 (/.f64 15/8 x) x)))))
	2.8b	(+.f64 (.f64 3/4 (.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 (fabs.f64 x) 5)) (sqrt.f64 (/.f64 1 (PI.f64))))) (+.f64 (.f64 15/8 (.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (.f64 (pow.f64 (fabs.f64 x) 5) (pow.f64 x 2))) (sqrt.f64 (/.f64 1 (PI.f64))))) (+.f64 (.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (fabs.f64 x)) (sqrt.f64 (/.f64 1 (PI.f64)))) (.f64 1/2 (.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (*.f64 (fabs.f64 x) (pow.f64 x 2))) (sqrt.f64 (/.f64 1 (PI.f64))))))))
	53.9b	(.f64 (/.f64 (fma.f64 1/2 (pow.f64 x 4) (fma.f64 1/6 (pow.f64 x 6) (fma.f64 x x 1))) (sqrt.f64 (PI.f64))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (*.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 (/.f64 15/8 x) x)))))
	2.3b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (+.f64 (/.f64 1/2 (.f64 x x)) 1) (/.f64 (.f64 (pow.f64 (exp.f64 x) (/.f64 x 2)) (expm1.f64 (log1p.f64 (sqrt.f64 (pow.f64 (exp.f64 x) x))))) x)) (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (.f64 x x))))))
	2.4b	(.f64 (/.f64 (pow.f64 (exp.f64 x) x) (.f64 (.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) (cbrt.f64 (sqrt.f64 (PI.f64)))) (cbrt.f64 (sqrt.f64 (PI.f64))))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (*.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 (/.f64 15/8 x) x)))))
	7.7b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (+.f64 (/.f64 1/2 (.f64 x x)) 1) (/.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 x) x) 3)) x)) (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (*.f64 x x))))))
	1.6b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (+.f64 (/.f64 1/2 (.f64 x x)) 1) (/.f64 (.f64 (pow.f64 (exp.f64 x) (/.f64 x 2)) (.f64 (pow.f64 (sqrt.f64 (exp.f64 x)) (.f64 x 1/2)) (pow.f64 (sqrt.f64 (exp.f64 x)) (.f64 x 1/2)))) x)) (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (*.f64 x x))))))
	1.7b	(.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (*.f64 (log.f64 (exp.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5))) (+.f64 3/4 (/.f64 (/.f64 15/8 x) x)))))
	7.2b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (+.f64 (/.f64 1/2 (.f64 x x)) 1) (/.f64 (pow.f64 (exp.f64 x) x) x)) (.f64 (pow.f64 (pow.f64 (.f64 (exp.f64 (.f64 x x)) (pow.f64 x -5)) 3) 1/3) (+.f64 3/4 (/.f64 15/8 (*.f64 x x))))))
	1.4b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (+.f64 (/.f64 1/2 (.f64 x x)) 1) (/.f64 (.f64 (pow.f64 (exp.f64 x) (/.f64 x 2)) (.f64 (pow.f64 (exp.f64 x) (/.f64 x 4)) (pow.f64 (exp.f64 x) (/.f64 x 4)))) x)) (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (*.f64 x x))))))

Compiler

Compiled 8512 to 5187 computations (39.1% saved)

localize31.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(/.f64 (pow.f64 (exp.f64 (+.f64 x x)) (*.f64 x 1/2)) x)
	0.6b	(/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5))
✓	0.7b	(pow.f64 (exp.f64 (+.f64 x x)) (*.f64 x 1/2))
	1.0b	(pow.f64 (exp.f64 x) x)

series3.0ms (0%)

Counts

2 → 24

Calls

6 calls:

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

rewrite42.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

816×	`log1p-expm1-u_binary64`
816×	`expm1-log1p-u_binary64`
91×	`add-sqr-sqrt_binary64`
88×	`pow1_binary64`
87×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	27
1	178	15
2	2462	15

Stop Event

1×	node limit

Counts

2 → 51

Calls

Call 1

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

Outputs

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

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

simplify30.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

614×	`distribute-lft-out_binary64`
492×	`unswap-sqr_binary64`
378×	`fma-def_binary64`
343×	`associate-l_binary64`
301×	`*-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	31	213
1	77	205
2	191	203
3	534	203
4	1921	203
5	4025	203

Stop Event

1×	node limit

Counts

75 → 69

Calls

Call 1

Inputs
1
(+.f64 1 (pow.f64 x 2))
(+.f64 (*.f64 1/2 (pow.f64 x 4)) (+.f64 1 (pow.f64 x 2)))
(+.f64 (.f64 1/2 (pow.f64 x 4)) (+.f64 1 (+.f64 (.f64 1/6 (pow.f64 x 6)) (pow.f64 x 2))))
(exp.f64 (pow.f64 x 2))
(exp.f64 (pow.f64 x 2))
(exp.f64 (pow.f64 x 2))
(exp.f64 (pow.f64 x 2))
(exp.f64 (pow.f64 x 2))
(exp.f64 (pow.f64 x 2))
(exp.f64 (pow.f64 x 2))
(exp.f64 (pow.f64 x 2))
(/.f64 1 x)
(+.f64 (/.f64 1 x) x)
(+.f64 (/.f64 1 x) (+.f64 x (*.f64 1/2 (pow.f64 x 3))))
(+.f64 (.f64 1/6 (pow.f64 x 5)) (+.f64 (/.f64 1 x) (+.f64 x (.f64 1/2 (pow.f64 x 3)))))
(/.f64 (exp.f64 (pow.f64 x 2)) x)
(/.f64 (exp.f64 (pow.f64 x 2)) x)
(/.f64 (exp.f64 (pow.f64 x 2)) x)
(/.f64 (exp.f64 (pow.f64 x 2)) x)
(/.f64 (exp.f64 (pow.f64 x 2)) x)
(/.f64 (exp.f64 (pow.f64 x 2)) x)
(/.f64 (exp.f64 (pow.f64 x 2)) x)
(/.f64 (exp.f64 (pow.f64 x 2)) x)

Outputs
1
(+.f64 1 (pow.f64 x 2))
(+.f64 1 (*.f64 x x))
(fma.f64 x x 1)
(+.f64 (*.f64 1/2 (pow.f64 x 4)) (+.f64 1 (pow.f64 x 2)))
(fma.f64 1/2 (pow.f64 x 4) (+.f64 1 (*.f64 x x)))
(fma.f64 1/2 (pow.f64 x 4) (fma.f64 x x 1))
(fma.f64 x x (fma.f64 1/2 (pow.f64 x 4) 1))
(+.f64 (.f64 1/2 (pow.f64 x 4)) (+.f64 1 (+.f64 (.f64 1/6 (pow.f64 x 6)) (pow.f64 x 2))))
(fma.f64 1/2 (pow.f64 x 4) (+.f64 1 (fma.f64 1/6 (pow.f64 x 6) (*.f64 x x))))
(+.f64 (fma.f64 x x (*.f64 1/6 (pow.f64 x 6))) (fma.f64 1/2 (pow.f64 x 4) 1))
(fma.f64 1/2 (pow.f64 x 4) (fma.f64 x x (fma.f64 1/6 (pow.f64 x 6) 1)))
(fma.f64 x x (fma.f64 1/2 (pow.f64 x 4) (fma.f64 1/6 (pow.f64 x 6) 1)))
(fma.f64 1/6 (pow.f64 x 6) (fma.f64 1/2 (pow.f64 x 4) (fma.f64 x x 1)))
(exp.f64 (pow.f64 x 2))
(exp.f64 (*.f64 x x))
(pow.f64 (exp.f64 x) x)
(exp.f64 (pow.f64 x 2))
(exp.f64 (*.f64 x x))
(pow.f64 (exp.f64 x) x)
(exp.f64 (pow.f64 x 2))
(exp.f64 (*.f64 x x))
(pow.f64 (exp.f64 x) x)
(exp.f64 (pow.f64 x 2))
(exp.f64 (*.f64 x x))
(pow.f64 (exp.f64 x) x)
(exp.f64 (pow.f64 x 2))
(exp.f64 (*.f64 x x))
(pow.f64 (exp.f64 x) x)
(exp.f64 (pow.f64 x 2))
(exp.f64 (*.f64 x x))
(pow.f64 (exp.f64 x) x)
(exp.f64 (pow.f64 x 2))
(exp.f64 (*.f64 x x))
(pow.f64 (exp.f64 x) x)
(exp.f64 (pow.f64 x 2))
(exp.f64 (*.f64 x x))
(pow.f64 (exp.f64 x) x)
(/.f64 1 x)
(+.f64 (/.f64 1 x) x)
(+.f64 x (/.f64 1 x))
(+.f64 (/.f64 1 x) (+.f64 x (*.f64 1/2 (pow.f64 x 3))))
(+.f64 (/.f64 1 x) (fma.f64 1/2 (pow.f64 x 3) x))
(+.f64 x (fma.f64 1/2 (pow.f64 x 3) (/.f64 1 x)))
(+.f64 (.f64 1/6 (pow.f64 x 5)) (+.f64 (/.f64 1 x) (+.f64 x (.f64 1/2 (pow.f64 x 3)))))
(fma.f64 1/6 (pow.f64 x 5) (+.f64 (/.f64 1 x) (+.f64 x (*.f64 1/2 (pow.f64 x 3)))))
(+.f64 (fma.f64 1/2 (pow.f64 x 3) x) (fma.f64 1/6 (pow.f64 x 5) (/.f64 1 x)))
(+.f64 x (fma.f64 1/2 (pow.f64 x 3) (fma.f64 1/6 (pow.f64 x 5) (/.f64 1 x))))
(/.f64 (exp.f64 (pow.f64 x 2)) x)
(/.f64 (exp.f64 (*.f64 x x)) x)
(/.f64 (pow.f64 (exp.f64 x) x) x)
(/.f64 (exp.f64 (pow.f64 x 2)) x)
(/.f64 (exp.f64 (*.f64 x x)) x)
(/.f64 (pow.f64 (exp.f64 x) x) x)
(/.f64 (exp.f64 (pow.f64 x 2)) x)
(/.f64 (exp.f64 (*.f64 x x)) x)
(/.f64 (pow.f64 (exp.f64 x) x) x)
(/.f64 (exp.f64 (pow.f64 x 2)) x)
(/.f64 (exp.f64 (*.f64 x x)) x)
(/.f64 (pow.f64 (exp.f64 x) x) x)
(/.f64 (exp.f64 (pow.f64 x 2)) x)
(/.f64 (exp.f64 (*.f64 x x)) x)
(/.f64 (pow.f64 (exp.f64 x) x) x)
(/.f64 (exp.f64 (pow.f64 x 2)) x)
(/.f64 (exp.f64 (*.f64 x x)) x)
(/.f64 (pow.f64 (exp.f64 x) x) x)
(/.f64 (exp.f64 (pow.f64 x 2)) x)
(/.f64 (exp.f64 (*.f64 x x)) x)
(/.f64 (pow.f64 (exp.f64 x) x) x)
(/.f64 (exp.f64 (pow.f64 x 2)) x)
(/.f64 (exp.f64 (*.f64 x x)) x)
(/.f64 (pow.f64 (exp.f64 x) x) x)

prune379.0ms (5.5%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	119	9	128
Fresh	7	14	21
Picked	1	0	1
Done	0	0	0
Total	127	23	150

Error

0.4b

Counts

150 → 23

Alt Table

Status	Error	Program
	1.7b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (+.f64 (/.f64 1/2 (.f64 x x)) 1) (.f64 (/.f64 (sqrt.f64 (pow.f64 (exp.f64 x) x)) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (sqrt.f64 (pow.f64 (exp.f64 x) x)) (cbrt.f64 x)))) (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (.f64 x x))))))
	1.7b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (+.f64 (/.f64 1/2 (.f64 x x)) 1) (/.f64 (.f64 (cbrt.f64 (pow.f64 (exp.f64 x) x)) (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) x)) 2)) x)) (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (.f64 x x))))))
	2.3b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (+.f64 (/.f64 1/2 (.f64 x x)) 1) (/.f64 (.f64 (pow.f64 (exp.f64 x) (/.f64 x 2)) (expm1.f64 (log1p.f64 (sqrt.f64 (pow.f64 (exp.f64 x) x))))) x)) (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (.f64 x x))))))
	1.1b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (+.f64 (/.f64 1/2 (.f64 x x)) 1) (/.f64 (pow.f64 (exp.f64 (+.f64 x x)) (.f64 x 1/2)) x)) (.f64 (.f64 (sqrt.f64 (exp.f64 (.f64 x x))) (.f64 (sqrt.f64 (exp.f64 (.f64 x x))) (pow.f64 x -5))) (+.f64 3/4 (/.f64 15/8 (.f64 x x))))))
	1.6b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (+.f64 (/.f64 1/2 (.f64 x x)) 1) (.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) x)) 2) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 (/.f64 (pow.f64 (exp.f64 x) x) x)))) (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (.f64 x x))))))
	3.1b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (expm1.f64 (log1p.f64 (.f64 (/.f64 (exp.f64 (.f64 x x)) x) (fma.f64 1/2 (pow.f64 x -2) 1)))) (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (*.f64 x x))))))
	1.7b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (+.f64 (/.f64 1/2 (.f64 x x)) 1) (.f64 (/.f64 1 (pow.f64 (cbrt.f64 x) 2)) (/.f64 (pow.f64 (exp.f64 x) x) (cbrt.f64 x)))) (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (.f64 x x))))))
	1.5b	(.f64 (/.f64 (pow.f64 (exp.f64 x) x) (.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (sqrt.f64 (sqrt.f64 (PI.f64))))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 (/.f64 15/8 x) x)))))
	8.6b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (cbrt.f64 (.f64 (pow.f64 (/.f64 (exp.f64 (.f64 x x)) x) 3) (pow.f64 (fma.f64 1/2 (pow.f64 x -2) 1) 3))) (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (*.f64 x x))))))
	7.7b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (+.f64 (/.f64 1/2 (.f64 x x)) 1) (cbrt.f64 (pow.f64 (/.f64 (pow.f64 (exp.f64 x) x) x) 3))) (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (*.f64 x x))))))
	1.6b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (+.f64 (/.f64 1/2 (.f64 x x)) 1) (/.f64 (.f64 (pow.f64 (exp.f64 x) (/.f64 x 2)) (.f64 (pow.f64 (sqrt.f64 (exp.f64 x)) (.f64 x 1/2)) (pow.f64 (sqrt.f64 (exp.f64 x)) (.f64 x 1/2)))) x)) (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (*.f64 x x))))))
	1.6b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (+.f64 (/.f64 1/2 (.f64 x x)) 1) (.f64 (cbrt.f64 (/.f64 (pow.f64 (exp.f64 x) x) x)) (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (exp.f64 x) x) x)) 2))) (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (.f64 x x))))))
	1.7b	(.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (*.f64 (log.f64 (exp.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5))) (+.f64 3/4 (/.f64 (/.f64 15/8 x) x)))))
	1.6b	(.f64 (/.f64 (pow.f64 (exp.f64 x) x) (expm1.f64 (log1p.f64 (sqrt.f64 (PI.f64))))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (*.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 (/.f64 15/8 x) x)))))
	2.8b	(+.f64 (.f64 3/4 (.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 (fabs.f64 x) 5)) (sqrt.f64 (/.f64 1 (PI.f64))))) (+.f64 (.f64 15/8 (.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (.f64 (pow.f64 (fabs.f64 x) 5) (pow.f64 x 2))) (sqrt.f64 (/.f64 1 (PI.f64))))) (+.f64 (.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (fabs.f64 x)) (sqrt.f64 (/.f64 1 (PI.f64)))) (.f64 1/2 (.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (*.f64 (fabs.f64 x) (pow.f64 x 2))) (sqrt.f64 (/.f64 1 (PI.f64))))))))
	2.3b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (+.f64 (/.f64 1/2 (.f64 x x)) 1) (/.f64 (.f64 (pow.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) 2)) 2) (.f64 x 1/2)) (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) 2)) (.f64 x 1/2))) x)) (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (.f64 x x))))))
	53.9b	(.f64 (/.f64 (fma.f64 1/2 (pow.f64 x 4) (fma.f64 1/6 (pow.f64 x 6) (fma.f64 x x 1))) (sqrt.f64 (PI.f64))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (*.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 (/.f64 15/8 x) x)))))
	2.4b	(.f64 (/.f64 (pow.f64 (exp.f64 x) x) (.f64 (.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) (cbrt.f64 (sqrt.f64 (PI.f64)))) (cbrt.f64 (sqrt.f64 (PI.f64))))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (*.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 (/.f64 15/8 x) x)))))
	2.7b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (+.f64 (/.f64 1/2 (.f64 x x)) 1) (exp.f64 (log.f64 (/.f64 (pow.f64 (exp.f64 x) x) x)))) (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (*.f64 x x))))))
	3.0b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (pow.f64 (cbrt.f64 (.f64 (/.f64 (exp.f64 (.f64 x x)) x) (fma.f64 1/2 (pow.f64 x -2) 1))) 3) (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (*.f64 x x))))))
	1.5b	(.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (PI.f64))) (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (.f64 x x))) (fabs.f64 x)) (.f64 (.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5/2) (pow.f64 (/.f64 1 (fabs.f64 x)) 5/2)) (+.f64 3/4 (/.f64 (/.f64 15/8 x) x)))))
	7.2b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (+.f64 (/.f64 1/2 (.f64 x x)) 1) (/.f64 (pow.f64 (exp.f64 x) x) x)) (.f64 (pow.f64 (pow.f64 (.f64 (exp.f64 (.f64 x x)) (pow.f64 x -5)) 3) 1/3) (+.f64 3/4 (/.f64 15/8 (*.f64 x x))))))
	1.5b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (.f64 (+.f64 (/.f64 1/2 (.f64 x x)) 1) (/.f64 (.f64 (pow.f64 (exp.f64 x) (/.f64 x 2)) (.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (exp.f64 x) x))) (cbrt.f64 (pow.f64 (exp.f64 x) x)))) x)) (.f64 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (*.f64 x x))))))

Compiler

Compiled 6522 to 3818 computations (41.5% saved)

regimes778.0ms (11.4%)

Accuracy

Total 0.6b remaining (70.5%)

Threshold costs 0.6b (70.5%)

Counts

265 → 1

Compiler

Compiled 11405 to 6244 computations (45.3% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
3×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	62
1	38	62

Stop Event

1×

saturated

Calls

Call 1

Inputs

(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (*.f64 (+.f64 (/.f64 1/2 (*.f64 x x)) 1) (/.f64 (pow.f64 (exp.f64 (+.f64 x x)) (*.f64 x 1/2)) x)) (*.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (*.f64 x x))))))

Outputs

(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (*.f64 (+.f64 (/.f64 1/2 (*.f64 x x)) 1) (/.f64 (pow.f64 (exp.f64 (+.f64 x x)) (*.f64 x 1/2)) x)) (*.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (*.f64 x x))))))

(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (*.f64 (+.f64 1 (/.f64 1/2 (*.f64 x x))) (/.f64 (pow.f64 (exp.f64 (+.f64 x x)) (*.f64 1/2 x)) x)) (*.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 5)) (+.f64 3/4 (/.f64 15/8 (*.f64 x x))))))

end657.0ms (9.6%)

Stop Event

1×

fuel

Compiler

Compiled 1125 to 773 computations (31.3% saved)

Details

analyze17.0ms (0.2%)

sample3.7s (53.8%)

preprocess99.0ms (1.5%)

simplify19.0ms (0.3%)

prune14.0ms (0.2%)

localize23.0ms (0.3%)

series18.0ms (0.3%)

rewrite71.0ms (1%)

simplify45.0ms (0.7%)

prune97.0ms (1.4%)

localize22.0ms (0.3%)

series119.0ms (1.7%)

rewrite61.0ms (0.9%)

simplify30.0ms (0.4%)

prune244.0ms (3.6%)

localize28.0ms (0.4%)

series3.0ms (0%)

rewrite38.0ms (0.6%)

simplify34.0ms (0.5%)

prune266.0ms (3.9%)

localize31.0ms (0.5%)

series3.0ms (0%)

rewrite42.0ms (0.6%)

simplify30.0ms (0.4%)

prune379.0ms (5.5%)

regimes778.0ms (11.4%)

simplify2.0ms (0%)

end657.0ms (9.6%)

Profiling