Details

analyze392.0ms (12.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
12.5%	62.5%	25%	4
18.7%	43.7%	37.5%	5
21.9%	34.4%	43.8%	6
23.4%	29.7%	46.9%	7
24.2%	27.3%	48.5%	8
24.6%	26.2%	49.2%	9
24.8%	25.6%	49.6%	10
24.9%	25.3%	49.8%	11
24.9%	25.1%	49.9%	12
25%	25.1%	50%	13
25%	25%	50%	14

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample1.8s (57.5%)

Results

1.0s	8256×	body	128	valid
802.0ms	8211×	body	128	invalid

preprocess36.0ms (1.1%)

Algorithm

2×	egg-herbie

Rules

868×	`fma-neg_binary64`
396×	`unsub-neg_binary64`
348×	`distribute-neg-in_binary64`
330×	`fma-def_binary64`
262×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	18	12
2	22	12
3	37	12
4	78	12
5	154	12
6	360	12
7	751	12
8	2365	12
9	4284	12
0	1	1

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0

Outputs
0

Call 2

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

Outputs
(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))

Compiler

Compiled 10 to 7 computations (30% saved)

simplify26.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

868×	`fma-neg_binary64`
396×	`unsub-neg_binary64`
348×	`distribute-neg-in_binary64`
330×	`fma-def_binary64`
262×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	18	12
2	22	12
3	37	12
4	78	12
5	154	12
6	360	12
7	751	12
8	2365	12
9	4284	12

Stop Event

1×	node limit

Counts

1 → 2

Calls

Call 1

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

Outputs
(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))

eval1.0ms (0%)

Compiler: Compiled 18 to 12 computations (33.3% saved)

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

34.8b

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	34.8b	(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))

Compiler

Compiled 18 to 12 computations (33.3% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (sqrt.f64 (fma.f64 x x -1)))
✓	0.2b	(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))
✓	32.2b	(sqrt.f64 (fma.f64 x x -1))

series8.0ms (0.3%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
3.0ms	x	@	-inf	(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))
1.0ms	x	@	0	(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))
1.0ms	x	@	0	(sqrt.f64 (fma.f64 x x -1))
1.0ms	x	@	inf	(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))
1.0ms	x	@	inf	(sqrt.f64 (fma.f64 x x -1))

rewrite45.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

722×	`pow1_binary64`
671×	`add-log-exp_binary64`
671×	`log1p-expm1-u_binary64`
671×	`expm1-log1p-u_binary64`
72×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	29
1	142	29
2	1836	29

Stop Event

1×	node limit

Counts

3 → 78

Calls

Call 1

Inputs
(sqrt.f64 (fma.f64 x x -1))
(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))
(+.f64 x (sqrt.f64 (fma.f64 x x -1)))

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

Outputs

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

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

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

simplify36.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

478×	`associate-*l/_binary64`
286×	`sub-neg_binary64`
260×	`fma-def_binary64`
247×	`associate-/l/_binary64`
243×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	111	680
1	313	648
2	902	636
3	2998	636

Stop Event

1×	node limit

Counts

114 → 142

Calls

Call 1

Inputs
(sqrt.f64 -1)
(+.f64 (sqrt.f64 -1) (*.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3))) (+.f64 (sqrt.f64 -1) (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1)))))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3))) (+.f64 (sqrt.f64 -1) (+.f64 (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))) (*.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 (sqrt.f64 -1) 5))))))
x
(-.f64 x (*.f64 1/2 (/.f64 1 x)))
(-.f64 x (+.f64 (.f64 1/2 (/.f64 1 x)) (.f64 1/8 (/.f64 1 (pow.f64 x 3)))))
(-.f64 x (+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 5))) (*.f64 1/8 (/.f64 1 (pow.f64 x 3))))))
(*.f64 -1 x)
(+.f64 (.f64 -1 x) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (*.f64 -1 x)))
(+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 5))) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (.f64 -1 x))))
(log.f64 (sqrt.f64 -1))
(+.f64 (/.f64 x (sqrt.f64 -1)) (log.f64 (sqrt.f64 -1)))
(+.f64 (*.f64 -1/6 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 -1) 3))) (+.f64 (/.f64 x (sqrt.f64 -1)) (log.f64 (sqrt.f64 -1))))
(+.f64 (.f64 3/40 (/.f64 (pow.f64 x 5) (pow.f64 (sqrt.f64 -1) 5))) (+.f64 (.f64 -1/6 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 -1) 3))) (+.f64 (/.f64 x (sqrt.f64 -1)) (log.f64 (sqrt.f64 -1)))))
(+.f64 (log.f64 2) (*.f64 -1 (log.f64 (/.f64 1 x))))
(-.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 2)) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 2)) (+.f64 (.f64 3/32 (/.f64 1 (pow.f64 x 4))) (*.f64 1/4 (/.f64 1 (pow.f64 x 2)))))
(-.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 2)) (+.f64 (.f64 3/32 (/.f64 1 (pow.f64 x 4))) (+.f64 (.f64 5/96 (/.f64 1 (pow.f64 x 6))) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))))
(+.f64 (log.f64 -1/2) (log.f64 (/.f64 -1 x)))
(+.f64 (log.f64 (/.f64 -1 x)) (+.f64 (log.f64 -1/2) (*.f64 1/4 (/.f64 1 (pow.f64 x 2)))))
(+.f64 (log.f64 (/.f64 -1 x)) (+.f64 (log.f64 -1/2) (+.f64 (.f64 3/32 (/.f64 1 (pow.f64 x 4))) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))))
(+.f64 (log.f64 (/.f64 -1 x)) (+.f64 (log.f64 -1/2) (+.f64 (.f64 3/32 (/.f64 1 (pow.f64 x 4))) (+.f64 (.f64 5/96 (/.f64 1 (pow.f64 x 6))) (*.f64 1/4 (/.f64 1 (pow.f64 x 2)))))))
(sqrt.f64 -1)
(+.f64 (sqrt.f64 -1) x)
(+.f64 (sqrt.f64 -1) (+.f64 (*.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))) x))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3))) (+.f64 (sqrt.f64 -1) (+.f64 (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))) x)))
(*.f64 2 x)
(-.f64 (.f64 2 x) (.f64 1/2 (/.f64 1 x)))
(-.f64 (.f64 2 x) (+.f64 (.f64 1/2 (/.f64 1 x)) (*.f64 1/8 (/.f64 1 (pow.f64 x 3)))))
(-.f64 (.f64 2 x) (+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 5))) (.f64 1/8 (/.f64 1 (pow.f64 x 3))))))
(/.f64 1/2 x)
(+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 5))) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (*.f64 1/2 (/.f64 1 x))))
(+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 5))) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 1 x)) (.f64 5/128 (/.f64 1 (pow.f64 x 7))))))

Outputs
(sqrt.f64 -1)
(+.f64 (sqrt.f64 -1) (*.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))))
(+.f64 (sqrt.f64 -1) (.f64 1/2 (/.f64 (.f64 x x) (sqrt.f64 -1))))
(fma.f64 1/2 (/.f64 x (/.f64 (sqrt.f64 -1) x)) (sqrt.f64 -1))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3))) (+.f64 (sqrt.f64 -1) (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1)))))
(fma.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3)) (+.f64 (sqrt.f64 -1) (.f64 1/2 (/.f64 (.f64 x x) (sqrt.f64 -1)))))
(+.f64 (fma.f64 1/2 (/.f64 x (/.f64 (sqrt.f64 -1) x)) (sqrt.f64 -1)) (*.f64 1/8 (/.f64 (pow.f64 x 4) (sqrt.f64 -1))))
(fma.f64 1/8 (/.f64 (pow.f64 x 4) (sqrt.f64 -1)) (fma.f64 1/2 (/.f64 x (/.f64 (sqrt.f64 -1) x)) (sqrt.f64 -1)))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3))) (+.f64 (sqrt.f64 -1) (+.f64 (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))) (*.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 (sqrt.f64 -1) 5))))))
(fma.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3)) (+.f64 (sqrt.f64 -1) (fma.f64 1/2 (/.f64 (.f64 x x) (sqrt.f64 -1)) (/.f64 (.f64 1/16 (pow.f64 x 6)) (pow.f64 (sqrt.f64 -1) 5)))))
(+.f64 (+.f64 (fma.f64 1/2 (/.f64 x (/.f64 (sqrt.f64 -1) x)) (sqrt.f64 -1)) (.f64 1/8 (/.f64 (pow.f64 x 4) (sqrt.f64 -1)))) (.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 (sqrt.f64 -1) 5))))
(fma.f64 1/8 (/.f64 (pow.f64 x 4) (sqrt.f64 -1)) (fma.f64 1/2 (/.f64 x (/.f64 (sqrt.f64 -1) x)) (fma.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 (sqrt.f64 -1) 5)) (sqrt.f64 -1))))
x
(-.f64 x (*.f64 1/2 (/.f64 1 x)))
(-.f64 x (/.f64 1/2 x))
(+.f64 x (/.f64 -1/2 x))
(-.f64 x (+.f64 (.f64 1/2 (/.f64 1 x)) (.f64 1/8 (/.f64 1 (pow.f64 x 3)))))
(-.f64 (-.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))
(+.f64 x (-.f64 (/.f64 -1/2 x) (/.f64 1/8 (pow.f64 x 3))))
(+.f64 x (+.f64 (/.f64 -1/2 x) (/.f64 -1/8 (pow.f64 x 3))))
(+.f64 (+.f64 x (/.f64 -1/2 x)) (/.f64 -1/8 (pow.f64 x 3)))
(-.f64 x (+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 5))) (*.f64 1/8 (/.f64 1 (pow.f64 x 3))))))
(-.f64 (-.f64 x (/.f64 1/2 x)) (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/16 (pow.f64 x 5))))
(-.f64 (-.f64 x (/.f64 1/16 (pow.f64 x 5))) (+.f64 (/.f64 1/2 x) (/.f64 1/8 (pow.f64 x 3))))
(+.f64 x (+.f64 (/.f64 -1/2 x) (+.f64 (/.f64 -1/8 (pow.f64 x 3)) (/.f64 -1/16 (pow.f64 x 5)))))
(+.f64 x (+.f64 (/.f64 -1/2 x) (-.f64 (/.f64 -1/8 (pow.f64 x 3)) (/.f64 1/16 (pow.f64 x 5)))))
(*.f64 -1 x)
(neg.f64 x)
(+.f64 (.f64 -1 x) (.f64 1/2 (/.f64 1 x)))
(fma.f64 -1 x (/.f64 1/2 x))
(-.f64 (/.f64 1/2 x) x)
(+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (*.f64 -1 x)))
(+.f64 (/.f64 1/2 x) (+.f64 (/.f64 1/8 (pow.f64 x 3)) (neg.f64 x)))
(+.f64 (/.f64 1/2 x) (-.f64 (/.f64 1/8 (pow.f64 x 3)) x))
(-.f64 (/.f64 1/2 x) (+.f64 x (/.f64 -1/8 (pow.f64 x 3))))
(+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 5))) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (.f64 -1 x))))
(+.f64 (/.f64 1/2 x) (+.f64 (/.f64 1/16 (pow.f64 x 5)) (+.f64 (/.f64 1/8 (pow.f64 x 3)) (neg.f64 x))))
(+.f64 (/.f64 1/2 x) (+.f64 (/.f64 1/16 (pow.f64 x 5)) (-.f64 (/.f64 1/8 (pow.f64 x 3)) x)))
(log.f64 (sqrt.f64 -1))
(+.f64 (/.f64 x (sqrt.f64 -1)) (log.f64 (sqrt.f64 -1)))
(+.f64 (log.f64 (sqrt.f64 -1)) (/.f64 x (sqrt.f64 -1)))
(+.f64 (*.f64 -1/6 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 -1) 3))) (+.f64 (/.f64 x (sqrt.f64 -1)) (log.f64 (sqrt.f64 -1))))
(fma.f64 -1/6 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 -1) 3)) (+.f64 (log.f64 (sqrt.f64 -1)) (/.f64 x (sqrt.f64 -1))))
(+.f64 (+.f64 (log.f64 (sqrt.f64 -1)) (/.f64 x (sqrt.f64 -1))) (*.f64 1/6 (/.f64 (pow.f64 x 3) (sqrt.f64 -1))))
(+.f64 (log.f64 (sqrt.f64 -1)) (fma.f64 1/6 (/.f64 (pow.f64 x 3) (sqrt.f64 -1)) (/.f64 x (sqrt.f64 -1))))
(fma.f64 1/6 (/.f64 (pow.f64 x 3) (sqrt.f64 -1)) (+.f64 (log.f64 (sqrt.f64 -1)) (/.f64 x (sqrt.f64 -1))))
(+.f64 (.f64 3/40 (/.f64 (pow.f64 x 5) (pow.f64 (sqrt.f64 -1) 5))) (+.f64 (.f64 -1/6 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 -1) 3))) (+.f64 (/.f64 x (sqrt.f64 -1)) (log.f64 (sqrt.f64 -1)))))
(fma.f64 3/40 (/.f64 (pow.f64 x 5) (pow.f64 (sqrt.f64 -1) 5)) (fma.f64 -1/6 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 -1) 3)) (+.f64 (log.f64 (sqrt.f64 -1)) (/.f64 x (sqrt.f64 -1)))))
(+.f64 (+.f64 (log.f64 (sqrt.f64 -1)) (/.f64 x (sqrt.f64 -1))) (fma.f64 3/40 (/.f64 (pow.f64 x 5) (pow.f64 (sqrt.f64 -1) 5)) (*.f64 1/6 (/.f64 (pow.f64 x 3) (sqrt.f64 -1)))))
(fma.f64 3/40 (/.f64 (pow.f64 x 5) (pow.f64 (sqrt.f64 -1) 5)) (+.f64 (log.f64 (sqrt.f64 -1)) (fma.f64 1/6 (/.f64 (pow.f64 x 3) (sqrt.f64 -1)) (/.f64 x (sqrt.f64 -1)))))
(fma.f64 3/40 (/.f64 (pow.f64 x 5) (pow.f64 (sqrt.f64 -1) 5)) (fma.f64 1/6 (/.f64 (pow.f64 x 3) (sqrt.f64 -1)) (+.f64 (log.f64 (sqrt.f64 -1)) (/.f64 x (sqrt.f64 -1)))))
(+.f64 (log.f64 2) (*.f64 -1 (log.f64 (/.f64 1 x))))
(fma.f64 -1 (neg.f64 (log.f64 x)) (log.f64 2))
(+.f64 (log.f64 2) (log.f64 x))
(-.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 2)) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (fma.f64 -1 (neg.f64 (log.f64 x)) (log.f64 2)) (/.f64 1/4 (*.f64 x x)))
(+.f64 (log.f64 2) (-.f64 (log.f64 x) (/.f64 1/4 (*.f64 x x))))
(+.f64 (log.f64 2) (+.f64 (log.f64 x) (/.f64 (/.f64 -1/4 x) x)))
(-.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 2)) (+.f64 (.f64 3/32 (/.f64 1 (pow.f64 x 4))) (*.f64 1/4 (/.f64 1 (pow.f64 x 2)))))
(-.f64 (-.f64 (fma.f64 -1 (neg.f64 (log.f64 x)) (log.f64 2)) (/.f64 3/32 (pow.f64 x 4))) (/.f64 1/4 (*.f64 x x)))
(+.f64 (log.f64 2) (-.f64 (log.f64 x) (+.f64 (/.f64 1/4 (*.f64 x x)) (/.f64 3/32 (pow.f64 x 4)))))
(+.f64 (+.f64 (log.f64 2) (log.f64 x)) (-.f64 (/.f64 -3/32 (pow.f64 x 4)) (/.f64 1/4 (*.f64 x x))))
(+.f64 (+.f64 (log.f64 2) (/.f64 (/.f64 -1/4 x) x)) (+.f64 (log.f64 x) (/.f64 -3/32 (pow.f64 x 4))))
(-.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 2)) (+.f64 (.f64 3/32 (/.f64 1 (pow.f64 x 4))) (+.f64 (.f64 5/96 (/.f64 1 (pow.f64 x 6))) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))))
(-.f64 (fma.f64 -1 (neg.f64 (log.f64 x)) (log.f64 2)) (+.f64 (/.f64 3/32 (pow.f64 x 4)) (+.f64 (/.f64 1/4 (*.f64 x x)) (/.f64 5/96 (pow.f64 x 6)))))
(-.f64 (+.f64 (log.f64 2) (-.f64 (log.f64 x) (/.f64 3/32 (pow.f64 x 4)))) (+.f64 (/.f64 1/4 (*.f64 x x)) (/.f64 5/96 (pow.f64 x 6))))
(-.f64 (+.f64 (+.f64 (log.f64 2) (log.f64 x)) (-.f64 (/.f64 -3/32 (pow.f64 x 4)) (/.f64 1/4 (*.f64 x x)))) (/.f64 5/96 (pow.f64 x 6)))
(+.f64 (+.f64 (+.f64 (log.f64 2) (/.f64 (/.f64 -1/4 x) x)) (+.f64 (log.f64 x) (/.f64 -3/32 (pow.f64 x 4)))) (/.f64 -5/96 (pow.f64 x 6)))
(+.f64 (log.f64 -1/2) (log.f64 (/.f64 -1 x)))
(+.f64 (log.f64 (/.f64 -1 x)) (+.f64 (log.f64 -1/2) (*.f64 1/4 (/.f64 1 (pow.f64 x 2)))))
(+.f64 (log.f64 (/.f64 -1 x)) (+.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 -1/2)))
(+.f64 (log.f64 -1/2) (+.f64 (log.f64 (/.f64 -1 x)) (/.f64 1/4 (*.f64 x x))))
(+.f64 (/.f64 1/4 (*.f64 x x)) (+.f64 (log.f64 -1/2) (log.f64 (/.f64 -1 x))))
(+.f64 (log.f64 (/.f64 -1 x)) (+.f64 (log.f64 -1/2) (+.f64 (.f64 3/32 (/.f64 1 (pow.f64 x 4))) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))))
(+.f64 (log.f64 (/.f64 -1 x)) (+.f64 (+.f64 (log.f64 -1/2) (/.f64 3/32 (pow.f64 x 4))) (/.f64 1/4 (*.f64 x x))))
(+.f64 (+.f64 (/.f64 1/4 (*.f64 x x)) (/.f64 3/32 (pow.f64 x 4))) (+.f64 (log.f64 -1/2) (log.f64 (/.f64 -1 x))))
(+.f64 (log.f64 (/.f64 -1 x)) (+.f64 (/.f64 1/4 (*.f64 x x)) (+.f64 (/.f64 3/32 (pow.f64 x 4)) (log.f64 -1/2))))
(+.f64 (/.f64 1/4 (*.f64 x x)) (+.f64 (log.f64 (/.f64 -1 x)) (+.f64 (/.f64 3/32 (pow.f64 x 4)) (log.f64 -1/2))))
(+.f64 (log.f64 (/.f64 -1 x)) (+.f64 (log.f64 -1/2) (+.f64 (.f64 3/32 (/.f64 1 (pow.f64 x 4))) (+.f64 (.f64 5/96 (/.f64 1 (pow.f64 x 6))) (*.f64 1/4 (/.f64 1 (pow.f64 x 2)))))))
(+.f64 (log.f64 (/.f64 -1 x)) (+.f64 (+.f64 (/.f64 3/32 (pow.f64 x 4)) (+.f64 (/.f64 1/4 (*.f64 x x)) (/.f64 5/96 (pow.f64 x 6)))) (log.f64 -1/2)))
(+.f64 (+.f64 (/.f64 3/32 (pow.f64 x 4)) (log.f64 -1/2)) (+.f64 (+.f64 (/.f64 1/4 (*.f64 x x)) (/.f64 5/96 (pow.f64 x 6))) (log.f64 (/.f64 -1 x))))
(+.f64 (+.f64 (/.f64 1/4 (*.f64 x x)) (/.f64 3/32 (pow.f64 x 4))) (+.f64 (/.f64 5/96 (pow.f64 x 6)) (+.f64 (log.f64 -1/2) (log.f64 (/.f64 -1 x)))))
(+.f64 (/.f64 3/32 (pow.f64 x 4)) (+.f64 (+.f64 (/.f64 1/4 (*.f64 x x)) (+.f64 (/.f64 5/96 (pow.f64 x 6)) (log.f64 -1/2))) (log.f64 (/.f64 -1 x))))
(sqrt.f64 -1)
(+.f64 (sqrt.f64 -1) x)
(+.f64 (sqrt.f64 -1) (+.f64 (*.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))) x))
(+.f64 (sqrt.f64 -1) (fma.f64 1/2 (/.f64 (*.f64 x x) (sqrt.f64 -1)) x))
(+.f64 (sqrt.f64 -1) (fma.f64 1/2 (/.f64 x (/.f64 (sqrt.f64 -1) x)) x))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3))) (+.f64 (sqrt.f64 -1) (+.f64 (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))) x)))
(fma.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3)) (+.f64 (sqrt.f64 -1) (fma.f64 1/2 (/.f64 (*.f64 x x) (sqrt.f64 -1)) x)))
(+.f64 (*.f64 1/8 (/.f64 (pow.f64 x 4) (sqrt.f64 -1))) (+.f64 (sqrt.f64 -1) (fma.f64 1/2 (/.f64 x (/.f64 (sqrt.f64 -1) x)) x)))
(+.f64 x (fma.f64 1/8 (/.f64 (pow.f64 x 4) (sqrt.f64 -1)) (fma.f64 1/2 (/.f64 x (/.f64 (sqrt.f64 -1) x)) (sqrt.f64 -1))))
(*.f64 2 x)
(*.f64 x 2)
(-.f64 (.f64 2 x) (.f64 1/2 (/.f64 1 x)))
(-.f64 (*.f64 x 2) (/.f64 1/2 x))
(fma.f64 x 2 (/.f64 -1/2 x))
(-.f64 (.f64 2 x) (+.f64 (.f64 1/2 (/.f64 1 x)) (*.f64 1/8 (/.f64 1 (pow.f64 x 3)))))
(-.f64 (*.f64 x 2) (+.f64 (/.f64 1/2 x) (/.f64 1/8 (pow.f64 x 3))))
(-.f64 (fma.f64 x 2 (/.f64 -1/2 x)) (/.f64 1/8 (pow.f64 x 3)))
(+.f64 (fma.f64 x 2 (/.f64 -1/2 x)) (/.f64 -1/8 (pow.f64 x 3)))
(-.f64 (.f64 2 x) (+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 5))) (.f64 1/8 (/.f64 1 (pow.f64 x 3))))))
(-.f64 (*.f64 x 2) (+.f64 (/.f64 1/2 x) (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/16 (pow.f64 x 5)))))
(-.f64 (-.f64 (fma.f64 x 2 (/.f64 -1/2 x)) (/.f64 1/16 (pow.f64 x 5))) (/.f64 1/8 (pow.f64 x 3)))
(+.f64 (fma.f64 x 2 (/.f64 -1/2 x)) (+.f64 (/.f64 -1/8 (pow.f64 x 3)) (/.f64 -1/16 (pow.f64 x 5))))
(+.f64 (/.f64 -1/2 x) (-.f64 (fma.f64 x 2 (/.f64 -1/8 (pow.f64 x 3))) (/.f64 1/16 (pow.f64 x 5))))
(/.f64 1/2 x)
(+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/2 x) (/.f64 1/8 (pow.f64 x 3)))
(+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 5))) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (*.f64 1/2 (/.f64 1 x))))
(+.f64 (/.f64 1/2 x) (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/16 (pow.f64 x 5))))
(+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 5))) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 1 x)) (.f64 5/128 (/.f64 1 (pow.f64 x 7))))))
(+.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/16 (pow.f64 x 5))) (+.f64 (/.f64 1/2 x) (/.f64 5/128 (pow.f64 x 7))))
(+.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/16 (pow.f64 x 5)) (+.f64 (/.f64 1/2 x) (/.f64 5/128 (pow.f64 x 7)))))
(+.f64 (/.f64 1/2 x) (+.f64 (/.f64 1/16 (pow.f64 x 5)) (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 5/128 (pow.f64 x 7)))))

eval48.0ms (1.5%)

Compiler: Compiled 2168 to 1615 computations (25.5% saved)

prune59.0ms (1.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	140	2	142
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	141	2	143

Error

0.0b

Counts

143 → 2

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.2b	(+.f64 (log.f64 2) (+.f64 (log.f64 x) (/.f64 (/.f64 -1/4 x) x)))
	0.2b	(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))

Compiler

Compiled 40 to 30 computations (25% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (/.f64 -1/4 x) x)
✓	0.2b	(+.f64 (log.f64 2) (+.f64 (log.f64 x) (/.f64 (/.f64 -1/4 x) x)))

series21.0ms (0.7%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
9.0ms	x	@	-inf	(+.f64 (log.f64 2) (+.f64 (log.f64 x) (/.f64 (/.f64 -1/4 x) x)))
6.0ms	x	@	0	(+.f64 (log.f64 2) (+.f64 (log.f64 x) (/.f64 (/.f64 -1/4 x) x)))
5.0ms	x	@	inf	(+.f64 (log.f64 2) (+.f64 (log.f64 x) (/.f64 (/.f64 -1/4 x) x)))
1.0ms	x	@	0	(/.f64 (/.f64 -1/4 x) x)
0.0ms	x	@	inf	(/.f64 (/.f64 -1/4 x) x)

rewrite58.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

448×	`fma-def_binary64`
243×	`fma-neg_binary64`
204×	`expm1-udef_binary64`
203×	`log1p-udef_binary64`
117×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	24
1	230	22
2	3342	22

Stop Event

1×	node limit

Counts

2 → 120

Calls

Call 1

Inputs
(+.f64 (log.f64 2) (+.f64 (log.f64 x) (/.f64 (/.f64 -1/4 x) x)))
(/.f64 (/.f64 -1/4 x) x)

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

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(log.f64 (*.f64 2 x)))) (cbrt.f64 (log.f64 (*.f64 2 x))) (/.f64 -1/4 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (log.f64 (*.f64 2 x))) (sqrt.f64 (log.f64 (*.f64 2 x))) (/.f64 -1/4 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (cbrt.f64 (/.f64 1/16 (*.f64 x x))) 1) (/.f64 (cbrt.f64 (/.f64 -1/4 x)) x) (log.f64 (*.f64 2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (sqrt.f64 (/.f64 -1/4 x)) 1) (/.f64 (sqrt.f64 (/.f64 -1/4 x)) x) (log.f64 (*.f64 2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 -1/4 (pow.f64 (cbrt.f64 x) 2)) (/.f64 (/.f64 1 x) (cbrt.f64 x)) (log.f64 (*.f64 2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (pow.f64 (cbrt.f64 x) 2)) (/.f64 (/.f64 -1/4 x) (cbrt.f64 x)) (log.f64 (*.f64 2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (cbrt.f64 (/.f64 1/16 (*.f64 x x))) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 (/.f64 -1/4 (*.f64 x x))) (log.f64 (*.f64 2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (sqrt.f64 (/.f64 -1/4 x)) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (sqrt.f64 (/.f64 -1/4 x)) (cbrt.f64 x)) (log.f64 (*.f64 2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 -1/4 (sqrt.f64 x)) (/.f64 (/.f64 1 x) (sqrt.f64 x)) (log.f64 (*.f64 2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (/.f64 -1/4 x) (sqrt.f64 x)) (log.f64 (*.f64 2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (cbrt.f64 (/.f64 1/16 (*.f64 x x))) (sqrt.f64 x)) (/.f64 (cbrt.f64 (/.f64 -1/4 x)) (sqrt.f64 x)) (log.f64 (*.f64 2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 (/.f64 -1/4 (*.f64 x x)) (log.f64 (*.f64 2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (+.f64 (/.f64 -1/4 (*.f64 x x)) (log.f64 (*.f64 2 x)))) 1))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 -1/4 (*.f64 x x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1/4 (*.f64 (/.f64 1 x) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1/4 (/.f64 (/.f64 1 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1/4 (/.f64 1 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 -1/4 x) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 -1/4 (*.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 -1/4 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 -1/4 (*.f64 x x))) (cbrt.f64 (pow.f64 (/.f64 -1/4 (*.f64 x x)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (/.f64 -1/4 (*.f64 x x)) 2)) (cbrt.f64 (/.f64 -1/4 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 1/16 (*.f64 x x))) (*.f64 (cbrt.f64 (/.f64 -1/4 x)) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 -1/4) x) (/.f64 (sqrt.f64 -1/4) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 -1/4 x)) (*.f64 (sqrt.f64 (/.f64 -1/4 x)) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1/4 x) (/.f64 1 (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 x) (/.f64 -1/4 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (/.f64 1/16 (*.f64 x x))) 1) (/.f64 (cbrt.f64 (/.f64 -1/4 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (/.f64 -1/4 x)) 1) (/.f64 (sqrt.f64 (/.f64 -1/4 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 -1/4 (pow.f64 (cbrt.f64 x) 2)) (/.f64 (/.f64 1 x) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 x) 2)) (/.f64 (/.f64 -1/4 x) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (/.f64 1/16 (*.f64 x x))) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 (/.f64 -1/4 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (/.f64 -1/4 x)) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (sqrt.f64 (/.f64 -1/4 x)) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 -1/4 (sqrt.f64 x)) (/.f64 (/.f64 1 x) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (/.f64 -1/4 x) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (/.f64 1/16 (*.f64 x x))) (sqrt.f64 x)) (/.f64 (cbrt.f64 (/.f64 -1/4 x)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 -1/4 (*.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 -1/4 (*.f64 x x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 -1/4) x) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 -1/64 (pow.f64 (*.f64 x x) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (*.f64 x -4)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (/.f64 -1/4 x) (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 -1/4 (*.f64 x x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 -1/4 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 -1/4 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 -1/64 (pow.f64 (*.f64 x x) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 -1/4 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 -1/4 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 -1/4 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 -1/4 (*.f64 x x))) 1))))))

simplify31.0ms (1%)

Algorithm

1×	egg-herbie

Rules

773×	`times-frac_binary64`
325×	`sub-neg_binary64`
276×	`fma-def_binary64`
202×	`associate--r+_binary64`
180×	`distribute-neg-frac_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	28	266
1	67	260
2	138	260
3	354	260
4	1054	260
5	3378	260

Stop Event

1×	node limit

Counts

144 → 129

Calls

Call 1

Inputs
(/.f64 -1/4 (pow.f64 x 2))
(-.f64 (+.f64 (log.f64 2) (log.f64 x)) (*.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (log.f64 2) (log.f64 x)) (*.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (log.f64 2) (log.f64 x)) (*.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(+.f64 (log.f64 2) (*.f64 -1 (log.f64 (/.f64 1 x))))
(-.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 2)) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 2)) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 2)) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (+.f64 (log.f64 2) (log.f64 -1)))
(-.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (+.f64 (log.f64 2) (log.f64 -1))) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (+.f64 (log.f64 2) (log.f64 -1))) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (+.f64 (log.f64 2) (log.f64 -1))) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(/.f64 -1/4 (pow.f64 x 2))
(/.f64 -1/4 (pow.f64 x 2))
(/.f64 -1/4 (pow.f64 x 2))
(/.f64 -1/4 (pow.f64 x 2))
(/.f64 -1/4 (pow.f64 x 2))
(/.f64 -1/4 (pow.f64 x 2))
(/.f64 -1/4 (pow.f64 x 2))
(/.f64 -1/4 (pow.f64 x 2))
(/.f64 -1/4 (pow.f64 x 2))
(/.f64 -1/4 (pow.f64 x 2))
(/.f64 -1/4 (pow.f64 x 2))
(/.f64 -1/4 (pow.f64 x 2))

Outputs
(/.f64 -1/4 (pow.f64 x 2))
(/.f64 -1/4 (*.f64 x x))
(-.f64 (+.f64 (log.f64 2) (log.f64 x)) (*.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(+.f64 (log.f64 2) (-.f64 (log.f64 x) (/.f64 1/4 (*.f64 x x))))
(+.f64 (log.f64 2) (+.f64 (log.f64 x) (/.f64 -1/4 (*.f64 x x))))
(-.f64 (log.f64 x) (-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 2)))
(-.f64 (+.f64 (log.f64 2) (log.f64 x)) (*.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(+.f64 (log.f64 2) (-.f64 (log.f64 x) (/.f64 1/4 (*.f64 x x))))
(+.f64 (log.f64 2) (+.f64 (log.f64 x) (/.f64 -1/4 (*.f64 x x))))
(-.f64 (log.f64 x) (-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 2)))
(-.f64 (+.f64 (log.f64 2) (log.f64 x)) (*.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(+.f64 (log.f64 2) (-.f64 (log.f64 x) (/.f64 1/4 (*.f64 x x))))
(+.f64 (log.f64 2) (+.f64 (log.f64 x) (/.f64 -1/4 (*.f64 x x))))
(-.f64 (log.f64 x) (-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 2)))
(+.f64 (log.f64 2) (*.f64 -1 (log.f64 (/.f64 1 x))))
(fma.f64 -1 (neg.f64 (log.f64 x)) (log.f64 2))
(+.f64 (log.f64 2) (log.f64 x))
(-.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 2)) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(+.f64 (log.f64 2) (-.f64 (log.f64 x) (/.f64 1/4 (*.f64 x x))))
(+.f64 (log.f64 2) (+.f64 (log.f64 x) (/.f64 -1/4 (*.f64 x x))))
(-.f64 (log.f64 x) (-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 2)))
(-.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 2)) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(+.f64 (log.f64 2) (-.f64 (log.f64 x) (/.f64 1/4 (*.f64 x x))))
(+.f64 (log.f64 2) (+.f64 (log.f64 x) (/.f64 -1/4 (*.f64 x x))))
(-.f64 (log.f64 x) (-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 2)))
(-.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 2)) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(+.f64 (log.f64 2) (-.f64 (log.f64 x) (/.f64 1/4 (*.f64 x x))))
(+.f64 (log.f64 2) (+.f64 (log.f64 x) (/.f64 -1/4 (*.f64 x x))))
(-.f64 (log.f64 x) (-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 2)))
(+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (+.f64 (log.f64 2) (log.f64 -1)))
(fma.f64 -1 (neg.f64 (log.f64 x)) (log.f64 2))
(+.f64 (log.f64 2) (log.f64 x))
(-.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (+.f64 (log.f64 2) (log.f64 -1))) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(+.f64 (log.f64 2) (-.f64 (log.f64 x) (/.f64 1/4 (*.f64 x x))))
(+.f64 (log.f64 2) (+.f64 (log.f64 x) (/.f64 -1/4 (*.f64 x x))))
(-.f64 (log.f64 x) (-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 2)))
(-.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (+.f64 (log.f64 2) (log.f64 -1))) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(+.f64 (log.f64 2) (-.f64 (log.f64 x) (/.f64 1/4 (*.f64 x x))))
(+.f64 (log.f64 2) (+.f64 (log.f64 x) (/.f64 -1/4 (*.f64 x x))))
(-.f64 (log.f64 x) (-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 2)))
(-.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (+.f64 (log.f64 2) (log.f64 -1))) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(+.f64 (log.f64 2) (-.f64 (log.f64 x) (/.f64 1/4 (*.f64 x x))))
(+.f64 (log.f64 2) (+.f64 (log.f64 x) (/.f64 -1/4 (*.f64 x x))))
(-.f64 (log.f64 x) (-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 2)))
(/.f64 -1/4 (pow.f64 x 2))
(/.f64 -1/4 (*.f64 x x))
(/.f64 -1/4 (pow.f64 x 2))
(/.f64 -1/4 (*.f64 x x))
(/.f64 -1/4 (pow.f64 x 2))
(/.f64 -1/4 (*.f64 x x))
(/.f64 -1/4 (pow.f64 x 2))
(/.f64 -1/4 (*.f64 x x))
(/.f64 -1/4 (pow.f64 x 2))
(/.f64 -1/4 (*.f64 x x))
(/.f64 -1/4 (pow.f64 x 2))
(/.f64 -1/4 (*.f64 x x))
(/.f64 -1/4 (pow.f64 x 2))
(/.f64 -1/4 (*.f64 x x))
(/.f64 -1/4 (pow.f64 x 2))
(/.f64 -1/4 (*.f64 x x))
(/.f64 -1/4 (pow.f64 x 2))
(/.f64 -1/4 (*.f64 x x))
(/.f64 -1/4 (pow.f64 x 2))
(/.f64 -1/4 (*.f64 x x))
(/.f64 -1/4 (pow.f64 x 2))
(/.f64 -1/4 (*.f64 x x))
(/.f64 -1/4 (pow.f64 x 2))
(/.f64 -1/4 (*.f64 x x))

eval46.0ms (1.4%)

Compiler: Compiled 2219 to 1472 computations (33.7% saved)

prune46.0ms (1.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	128	1	129
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	129	2	131

Error

Counts

131 → 2

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.2b	(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))
	0.4b	(fma.f64 (-.f64 (pow.f64 (log.f64 x) 2) (pow.f64 (/.f64 -1/4 (.f64 x x)) 2)) (/.f64 1 (-.f64 (log.f64 x) (/.f64 -1/4 (.f64 x x)))) (log1p.f64 1))

Compiler

Compiled 68 to 48 computations (29.4% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))

series2.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))
1.0ms	x	@	-inf	(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))
1.0ms	x	@	inf	(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))

rewrite33.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

652×	`pow1_binary64`
607×	`add-log-exp_binary64`
606×	`log1p-expm1-u_binary64`
606×	`expm1-log1p-u_binary64`
71×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	146	10
2	1642	10

Stop Event

1×	node limit

Counts

1 → 18

Calls

Call 1

Inputs
(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))

Outputs

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

simplify25.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

660×	`fma-def_binary64`
297×	`sub-neg_binary64`
281×	`fma-neg_binary64`
270×	`associate--l+_binary64`
268×	`associate--r+_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	60	282
1	165	264
2	476	262
3	1661	258

Stop Event

1×	node limit

Counts

30 → 42

Calls

Call 1

Inputs
(+.f64 (log.f64 -1/2) (*.f64 -1 (log.f64 x)))
(+.f64 (log.f64 -1/2) (+.f64 (.f64 -4 (pow.f64 x 2)) (.f64 -1 (log.f64 x))))
(+.f64 (log.f64 -1/2) (+.f64 (.f64 -4 (pow.f64 x 2)) (+.f64 (.f64 -8 (pow.f64 x 4)) (*.f64 -1 (log.f64 x)))))
(+.f64 (log.f64 -1/2) (+.f64 (.f64 -4 (pow.f64 x 2)) (+.f64 (.f64 -8 (pow.f64 x 4)) (+.f64 (.f64 -64/3 (pow.f64 x 6)) (.f64 -1 (log.f64 x))))))
(+.f64 (log.f64 2) (*.f64 -1 (log.f64 (/.f64 1 x))))
(-.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 2)) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 2)) (+.f64 (.f64 1/32 (/.f64 1 (pow.f64 x 4))) (*.f64 1/4 (/.f64 1 (pow.f64 x 2)))))
(-.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 2)) (+.f64 (.f64 1/32 (/.f64 1 (pow.f64 x 4))) (+.f64 (.f64 1/192 (/.f64 1 (pow.f64 x 6))) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))))
(+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -2))
(-.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -2)) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -2)) (+.f64 (.f64 1/32 (/.f64 1 (pow.f64 x 4))) (*.f64 1/4 (/.f64 1 (pow.f64 x 2)))))
(-.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -2)) (+.f64 (.f64 1/32 (/.f64 1 (pow.f64 x 4))) (+.f64 (.f64 1/192 (/.f64 1 (pow.f64 x 6))) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))))

Outputs
(+.f64 (log.f64 -1/2) (*.f64 -1 (log.f64 x)))
(+.f64 (log.f64 -1/2) (neg.f64 (log.f64 x)))
(-.f64 (log.f64 -1/2) (log.f64 x))
(+.f64 (log.f64 -1/2) (+.f64 (.f64 -4 (pow.f64 x 2)) (.f64 -1 (log.f64 x))))
(+.f64 (log.f64 -1/2) (fma.f64 -4 (*.f64 x x) (neg.f64 (log.f64 x))))
(-.f64 (+.f64 (log.f64 -1/2) (.f64 -4 (.f64 x x))) (log.f64 x))
(-.f64 (fma.f64 x (*.f64 x -4) (log.f64 -1/2)) (log.f64 x))
(+.f64 (log.f64 -1/2) (+.f64 (.f64 -4 (pow.f64 x 2)) (+.f64 (.f64 -8 (pow.f64 x 4)) (*.f64 -1 (log.f64 x)))))
(+.f64 (log.f64 -1/2) (fma.f64 -4 (*.f64 x x) (fma.f64 -8 (pow.f64 x 4) (neg.f64 (log.f64 x)))))
(+.f64 (log.f64 -1/2) (-.f64 (fma.f64 -4 (.f64 x x) (.f64 -8 (pow.f64 x 4))) (log.f64 x)))
(-.f64 (fma.f64 -4 (.f64 x x) (.f64 -8 (pow.f64 x 4))) (-.f64 (log.f64 x) (log.f64 -1/2)))
(-.f64 (fma.f64 (.f64 x x) (fma.f64 (.f64 -8 x) x -4) (log.f64 -1/2)) (log.f64 x))
(+.f64 (log.f64 -1/2) (+.f64 (.f64 -4 (pow.f64 x 2)) (+.f64 (.f64 -8 (pow.f64 x 4)) (+.f64 (.f64 -64/3 (pow.f64 x 6)) (.f64 -1 (log.f64 x))))))
(+.f64 (log.f64 -1/2) (fma.f64 -4 (*.f64 x x) (fma.f64 -8 (pow.f64 x 4) (fma.f64 -64/3 (pow.f64 x 6) (neg.f64 (log.f64 x))))))
(+.f64 (log.f64 -1/2) (fma.f64 x (.f64 x -4) (-.f64 (fma.f64 -8 (pow.f64 x 4) (.f64 -64/3 (pow.f64 x 6))) (log.f64 x))))
(fma.f64 x (*.f64 x -4) (fma.f64 -8 (pow.f64 x 4) (fma.f64 -64/3 (pow.f64 x 6) (-.f64 (log.f64 -1/2) (log.f64 x)))))
(+.f64 (log.f64 2) (*.f64 -1 (log.f64 (/.f64 1 x))))
(fma.f64 -1 (neg.f64 (log.f64 x)) (log.f64 2))
(+.f64 (log.f64 x) (log.f64 2))
(-.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 2)) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (fma.f64 -1 (neg.f64 (log.f64 x)) (log.f64 2)) (/.f64 1/4 (*.f64 x x)))
(+.f64 (log.f64 x) (+.f64 (log.f64 2) (/.f64 -1/4 (*.f64 x x))))
(+.f64 (log.f64 x) (+.f64 (log.f64 2) (/.f64 (/.f64 -1/4 x) x)))
(-.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 2)) (+.f64 (.f64 1/32 (/.f64 1 (pow.f64 x 4))) (*.f64 1/4 (/.f64 1 (pow.f64 x 2)))))
(-.f64 (-.f64 (fma.f64 -1 (neg.f64 (log.f64 x)) (log.f64 2)) (/.f64 1/32 (pow.f64 x 4))) (/.f64 1/4 (*.f64 x x)))
(+.f64 (log.f64 x) (-.f64 (log.f64 2) (+.f64 (/.f64 1/4 (*.f64 x x)) (/.f64 1/32 (pow.f64 x 4)))))
(+.f64 (+.f64 (log.f64 2) (/.f64 -1/4 (*.f64 x x))) (+.f64 (log.f64 x) (/.f64 -1/32 (pow.f64 x 4))))
(+.f64 (log.f64 x) (+.f64 (log.f64 2) (+.f64 (/.f64 (/.f64 -1/4 x) x) (/.f64 -1/32 (pow.f64 x 4)))))
(-.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 2)) (+.f64 (.f64 1/32 (/.f64 1 (pow.f64 x 4))) (+.f64 (.f64 1/192 (/.f64 1 (pow.f64 x 6))) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))))
(-.f64 (fma.f64 -1 (neg.f64 (log.f64 x)) (log.f64 2)) (+.f64 (/.f64 1/32 (pow.f64 x 4)) (+.f64 (/.f64 1/4 (*.f64 x x)) (/.f64 1/192 (pow.f64 x 6)))))
(+.f64 (log.f64 x) (-.f64 (log.f64 2) (+.f64 (+.f64 (/.f64 1/4 (*.f64 x x)) (/.f64 1/32 (pow.f64 x 4))) (/.f64 1/192 (pow.f64 x 6)))))
(+.f64 (log.f64 x) (+.f64 (log.f64 2) (-.f64 (/.f64 -1/32 (pow.f64 x 4)) (+.f64 (/.f64 1/4 (*.f64 x x)) (/.f64 1/192 (pow.f64 x 6))))))
(+.f64 (log.f64 2) (+.f64 (/.f64 (/.f64 -1/4 x) x) (-.f64 (log.f64 x) (+.f64 (/.f64 1/32 (pow.f64 x 4)) (/.f64 1/192 (pow.f64 x 6))))))
(+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -2))
(fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -2))
(-.f64 (log.f64 -2) (log.f64 (/.f64 -1 x)))
(-.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -2)) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -2)) (/.f64 1/4 (*.f64 x x)))
(+.f64 (-.f64 (log.f64 -2) (log.f64 (/.f64 -1 x))) (/.f64 -1/4 (*.f64 x x)))
(+.f64 (log.f64 -2) (-.f64 (/.f64 (/.f64 -1/4 x) x) (log.f64 (/.f64 -1 x))))
(-.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -2)) (+.f64 (.f64 1/32 (/.f64 1 (pow.f64 x 4))) (*.f64 1/4 (/.f64 1 (pow.f64 x 2)))))
(-.f64 (-.f64 (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -2)) (/.f64 1/32 (pow.f64 x 4))) (/.f64 1/4 (*.f64 x x)))
(+.f64 (-.f64 (-.f64 (log.f64 -2) (log.f64 (/.f64 -1 x))) (/.f64 1/32 (pow.f64 x 4))) (/.f64 -1/4 (*.f64 x x)))
(+.f64 (-.f64 (log.f64 -2) (log.f64 (/.f64 -1 x))) (+.f64 (/.f64 -1/4 (*.f64 x x)) (/.f64 -1/32 (pow.f64 x 4))))
(+.f64 (log.f64 -2) (+.f64 (-.f64 (/.f64 (/.f64 -1/4 x) x) (log.f64 (/.f64 -1 x))) (/.f64 -1/32 (pow.f64 x 4))))
(-.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -2)) (+.f64 (.f64 1/32 (/.f64 1 (pow.f64 x 4))) (+.f64 (.f64 1/192 (/.f64 1 (pow.f64 x 6))) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))))
(-.f64 (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -2)) (+.f64 (/.f64 1/32 (pow.f64 x 4)) (+.f64 (/.f64 1/4 (*.f64 x x)) (/.f64 1/192 (pow.f64 x 6)))))
(-.f64 (-.f64 (log.f64 -2) (log.f64 (/.f64 -1 x))) (+.f64 (+.f64 (/.f64 1/4 (*.f64 x x)) (/.f64 1/32 (pow.f64 x 4))) (/.f64 1/192 (pow.f64 x 6))))
(+.f64 (-.f64 (log.f64 -2) (log.f64 (/.f64 -1 x))) (-.f64 (/.f64 -1/32 (pow.f64 x 4)) (+.f64 (/.f64 1/4 (*.f64 x x)) (/.f64 1/192 (pow.f64 x 6)))))
(+.f64 (/.f64 (/.f64 -1/4 x) x) (-.f64 (log.f64 -2) (+.f64 (log.f64 (/.f64 -1 x)) (+.f64 (/.f64 1/32 (pow.f64 x 4)) (/.f64 1/192 (pow.f64 x 6))))))

eval14.0ms (0.4%)

Compiler: Compiled 619 to 492 computations (20.5% saved)

prune11.0ms (0.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	42	0	42
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	42	2	44

Error

Counts

44 → 2

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.2b	(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))
▶	0.4b	(fma.f64 (-.f64 (pow.f64 (log.f64 x) 2) (pow.f64 (/.f64 -1/4 (.f64 x x)) 2)) (/.f64 1 (-.f64 (log.f64 x) (/.f64 -1/4 (.f64 x x)))) (log1p.f64 1))

Compiler

Compiled 60 to 42 computations (30% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1 (-.f64 (log.f64 x) (/.f64 -1/4 (*.f64 x x))))
✓	0.4b	(fma.f64 (-.f64 (pow.f64 (log.f64 x) 2) (pow.f64 (/.f64 -1/4 (.f64 x x)) 2)) (/.f64 1 (-.f64 (log.f64 x) (/.f64 -1/4 (.f64 x x)))) (log1p.f64 1))
✓	0.5b	(pow.f64 (log.f64 x) 2)
✓	0.6b	(/.f64 -1/4 (*.f64 x x))

series50.0ms (1.6%)

Counts

4 → 44

Calls

12 calls:

Time	Variable		Point	Expression
22.0ms	x	@	0	(pow.f64 (log.f64 x) 2)
12.0ms	x	@	-inf	(pow.f64 (log.f64 x) 2)
5.0ms	x	@	inf	(pow.f64 (log.f64 x) 2)
4.0ms	x	@	inf	(fma.f64 (-.f64 (pow.f64 (log.f64 x) 2) (pow.f64 (/.f64 -1/4 (.f64 x x)) 2)) (/.f64 1 (-.f64 (log.f64 x) (/.f64 -1/4 (.f64 x x)))) (log1p.f64 1))
2.0ms	x	@	-inf	(fma.f64 (-.f64 (pow.f64 (log.f64 x) 2) (pow.f64 (/.f64 -1/4 (.f64 x x)) 2)) (/.f64 1 (-.f64 (log.f64 x) (/.f64 -1/4 (.f64 x x)))) (log1p.f64 1))

rewrite61.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

990×	`prod-diff_binary64`
159×	`add-sqr-sqrt_binary64`
154×	`pow1_binary64`
152×	`*-un-lft-identity_binary64`
152×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	66
1	330	45
2	4227	45

Stop Event

1×	node limit

Counts

4 → 92

Calls

Call 1

Inputs
(/.f64 -1/4 (*.f64 x x))
(pow.f64 (log.f64 x) 2)
(fma.f64 (-.f64 (pow.f64 (log.f64 x) 2) (pow.f64 (/.f64 -1/4 (.f64 x x)) 2)) (/.f64 1 (-.f64 (log.f64 x) (/.f64 -1/4 (.f64 x x)))) (log1p.f64 1))
(/.f64 1 (-.f64 (log.f64 x) (/.f64 -1/4 (*.f64 x x))))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 -1/4 (pow.f64 x -2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -1/4 (pow.f64 x -2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 -1/4 (pow.f64 x -2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (.f64 -1/4 (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 1/16 (pow.f64 x 4))) (cbrt.f64 (.f64 -1/4 (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (.f64 -1/4 (pow.f64 x -2))) (cbrt.f64 (/.f64 1/16 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 -1/4) x) (/.f64 (sqrt.f64 -1/4) x))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/4 (/.f64 1 (.f64 x (neg.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 x -2) -1/4)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 -1/4 x) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (pow.f64 (cbrt.f64 (/.f64 1/16 (pow.f64 x 4))) 2)) (sqrt.f64 (cbrt.f64 (/.f64 1/16 (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 -1/4 (pow.f64 x -2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1/16 (pow.f64 x 4)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 -1/4 (pow.f64 x -2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 -1/4) x) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 -1/64 (pow.f64 (pow.f64 x -2) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (.f64 x x) -4) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 1/16 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (.f64 -1/4 (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 -1/4) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 -1/4 (pow.f64 x -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 -1/64 (pow.f64 (pow.f64 x -2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 -1/4 (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 -1/4 (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 -1/4 (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (*.f64 -1/4 (pow.f64 x -2))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (log.f64 x) 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (log.f64 x) (log.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (log.f64 x) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (pow.f64 (log.f64 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (log.f64 x)) 2) (cbrt.f64 (pow.f64 (log.f64 x) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (log.f64 x)) 2) (.f64 (cbrt.f64 (log.f64 x)) (log.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (log.f64 x) 4)) (pow.f64 (cbrt.f64 (log.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (log.f64 x)) (.f64 (sqrt.f64 (log.f64 x)) (log.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (log.f64 x) (sqrt.f64 (log.f64 x))) (sqrt.f64 (log.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (log.f64 x) (pow.f64 (cbrt.f64 (log.f64 x)) 2)) (cbrt.f64 (log.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (log.f64 x) 4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 x (log.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (log.f64 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (log.f64 x) 6))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (log.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (log.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 2 (log.f64 (log.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 2 (log.f64 (log.f64 x))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 2) (+.f64 (.f64 -1/4 (pow.f64 x -2)) (log.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (.f64 -1/4 (pow.f64 x -2)) (log.f64 x)) (log.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (+.f64 (.f64 -1/4 (pow.f64 x -2)) (log.f64 x)) 1) (log.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 (log.f64 2) (+.f64 (.f64 -1/4 (pow.f64 x -2)) (log.f64 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (+.f64 (log.f64 2) (+.f64 (.f64 -1/4 (pow.f64 x -2)) (log.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 (log.f64 2) (+.f64 (.f64 -1/4 (pow.f64 x -2)) (log.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (+.f64 (log.f64 2) (+.f64 (.f64 -1/4 (pow.f64 x -2)) (log.f64 x)))) (pow.f64 (cbrt.f64 (+.f64 (log.f64 2) (+.f64 (.f64 -1/4 (pow.f64 x -2)) (log.f64 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (+.f64 (log.f64 2) (+.f64 (.f64 -1/4 (pow.f64 x -2)) (log.f64 x)))) 2) (cbrt.f64 (+.f64 (log.f64 2) (+.f64 (.f64 -1/4 (pow.f64 x -2)) (log.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (+.f64 (log.f64 2) (+.f64 (.f64 -1/4 (pow.f64 x -2)) (log.f64 x)))) (sqrt.f64 (+.f64 (log.f64 2) (+.f64 (.f64 -1/4 (pow.f64 x -2)) (log.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 (.f64 -1/4 (pow.f64 x -2)) (log.f64 x)) 3) (pow.f64 (log.f64 2) 3)) (+.f64 (.f64 (+.f64 (.f64 -1/4 (pow.f64 x -2)) (log.f64 x)) (+.f64 (.f64 -1/4 (pow.f64 x -2)) (log.f64 x))) (-.f64 (pow.f64 (log.f64 2) 2) (.f64 (+.f64 (.f64 -1/4 (pow.f64 x -2)) (log.f64 x)) (log.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 (+.f64 (.f64 -1/4 (pow.f64 x -2)) (log.f64 x)) (+.f64 (.f64 -1/4 (pow.f64 x -2)) (log.f64 x))) (pow.f64 (log.f64 2) 2)) (-.f64 (+.f64 (.f64 -1/4 (pow.f64 x -2)) (log.f64 x)) (log.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (log.f64 2) (+.f64 (.f64 -1/4 (pow.f64 x -2)) (log.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (log.f64 2) (+.f64 (.f64 -1/4 (pow.f64 x -2)) (log.f64 x))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 (log.f64 2) (+.f64 (.f64 -1/4 (pow.f64 x -2)) (log.f64 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 (log.f64 2) (+.f64 (.f64 -1/4 (pow.f64 x -2)) (log.f64 x)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 (log.f64 2) (+.f64 (.f64 -1/4 (pow.f64 x -2)) (log.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (exp.f64 (+.f64 (.f64 -1/4 (pow.f64 x -2)) (log.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 (log.f64 2) (+.f64 (.f64 -1/4 (pow.f64 x -2)) (log.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 (log.f64 2) (+.f64 (.f64 -1/4 (pow.f64 x -2)) (log.f64 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 (log.f64 2) (+.f64 (.f64 -1/4 (pow.f64 x -2)) (log.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 (log.f64 2) (+.f64 (.f64 -1/4 (pow.f64 x -2)) (log.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 (log.f64 2) (+.f64 (.f64 -1/4 (pow.f64 x -2)) (log.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (+.f64 (log.f64 2) (+.f64 (.f64 -1/4 (pow.f64 x -2)) (log.f64 x)))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 1 (+.f64 (log.f64 x) (.f64 1/4 (pow.f64 x -2)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (/.f64 1 (+.f64 (log.f64 x) (.f64 1/4 (pow.f64 x -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (+.f64 (log.f64 x) (.f64 1/4 (pow.f64 x -2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (cbrt.f64 (+.f64 (log.f64 x) (.f64 1/4 (pow.f64 x -2))))) (cbrt.f64 (pow.f64 (+.f64 (log.f64 x) (.f64 1/4 (pow.f64 x -2))) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (+.f64 (log.f64 x) (.f64 1/4 (pow.f64 x -2))) -2)) (/.f64 1 (cbrt.f64 (+.f64 (log.f64 x) (.f64 1/4 (pow.f64 x -2))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (+.f64 (log.f64 x) (.f64 1/4 (pow.f64 x -2))) -1/2) (pow.f64 (+.f64 (log.f64 x) (.f64 1/4 (pow.f64 x -2))) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -1 (/.f64 1 (neg.f64 (+.f64 (log.f64 x) (.f64 1/4 (pow.f64 x -2))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 (log.f64 x) (.f64 1/4 (pow.f64 x -2)))) 2) -1) (pow.f64 (cbrt.f64 (+.f64 (log.f64 x) (.f64 1/4 (pow.f64 x -2)))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (sqrt.f64 (+.f64 (log.f64 x) (.f64 1/4 (pow.f64 x -2)))) -1) (pow.f64 (sqrt.f64 (+.f64 (log.f64 x) (.f64 1/4 (pow.f64 x -2)))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (-.f64 (pow.f64 (log.f64 x) 2) (/.f64 1/16 (pow.f64 x 4)))) (+.f64 (.f64 -1/4 (pow.f64 x -2)) (log.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (-.f64 (pow.f64 (log.f64 x) 3) (.f64 -1/64 (pow.f64 (pow.f64 x -2) 3)))) (+.f64 (pow.f64 (log.f64 x) 2) (+.f64 (/.f64 1/16 (pow.f64 x 4)) (/.f64 (log.f64 x) (.f64 (.f64 x x) -4)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (log.f64 x) (.f64 1/4 (pow.f64 x -2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (+.f64 (log.f64 x) (.f64 1/4 (pow.f64 x -2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 1 (+.f64 (log.f64 x) (.f64 1/4 (pow.f64 x -2)))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (cbrt.f64 (+.f64 (log.f64 x) (.f64 1/4 (pow.f64 x -2))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (log.f64 x) (.f64 1/4 (pow.f64 x -2))) -1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 (log.f64 x) (.f64 1/4 (pow.f64 x -2))) -2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1 (+.f64 (log.f64 x) (.f64 1/4 (pow.f64 x -2))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 1 (+.f64 (log.f64 x) (.f64 1/4 (pow.f64 x -2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 1 (+.f64 (log.f64 x) (.f64 1/4 (pow.f64 x -2)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1 (+.f64 (log.f64 x) (.f64 1/4 (pow.f64 x -2))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1 (+.f64 (log.f64 x) (.f64 1/4 (pow.f64 x -2))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (neg.f64 (log.f64 (+.f64 (log.f64 x) (.f64 1/4 (pow.f64 x -2))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (+.f64 (log.f64 x) (.f64 1/4 (pow.f64 x -2)))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (neg.f64 (log.f64 (+.f64 (log.f64 x) (.f64 1/4 (pow.f64 x -2))))) 1))))))

simplify31.0ms (1%)

Algorithm

1×	egg-herbie

Rules

462×	`associate-l_binary64`
457×	`associate-r_binary64`
377×	`fma-def_binary64`
279×	`associate-/r*_binary64`
155×	`*-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	111	868
1	324	827
2	1054	815

Stop Event

1×	node limit

Counts

136 → 133

Calls

Call 1

Inputs
(/.f64 -1/4 (pow.f64 x 2))
(/.f64 -1/4 (pow.f64 x 2))
(/.f64 -1/4 (pow.f64 x 2))
(/.f64 -1/4 (pow.f64 x 2))
(/.f64 -1/4 (pow.f64 x 2))
(/.f64 -1/4 (pow.f64 x 2))
(/.f64 -1/4 (pow.f64 x 2))
(/.f64 -1/4 (pow.f64 x 2))
(/.f64 -1/4 (pow.f64 x 2))
(/.f64 -1/4 (pow.f64 x 2))
(/.f64 -1/4 (pow.f64 x 2))
(/.f64 -1/4 (pow.f64 x 2))
(pow.f64 (log.f64 (/.f64 1 x)) 2)
(pow.f64 (log.f64 (/.f64 1 x)) 2)
(pow.f64 (log.f64 (/.f64 1 x)) 2)
(pow.f64 (log.f64 (/.f64 1 x)) 2)
(pow.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)) 2)
(pow.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)) 2)
(pow.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)) 2)
(pow.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)) 2)
(/.f64 -1/4 (pow.f64 x 2))
(-.f64 (+.f64 (log.f64 2) (log.f64 x)) (*.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (log.f64 2) (+.f64 (.f64 (pow.f64 x 2) (+.f64 (.f64 -4 (pow.f64 (log.f64 x) 2)) (.f64 4 (pow.f64 (log.f64 x) 2)))) (log.f64 x))) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (log.f64 2) (+.f64 (.f64 (+.f64 (.f64 16 (pow.f64 (log.f64 x) 3)) (.f64 -16 (pow.f64 (log.f64 x) 3))) (pow.f64 x 4)) (+.f64 (.f64 (pow.f64 x 2) (+.f64 (.f64 -4 (pow.f64 (log.f64 x) 2)) (.f64 4 (pow.f64 (log.f64 x) 2)))) (log.f64 x)))) (*.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(+.f64 (log.f64 2) (*.f64 -1 (log.f64 (/.f64 1 x))))
(-.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 2)) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 2)) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 2)) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (+.f64 (log.f64 2) (log.f64 -1)))
(-.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (+.f64 (log.f64 2) (log.f64 -1))) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (+.f64 (log.f64 2) (log.f64 -1))) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (+.f64 (log.f64 2) (log.f64 -1))) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(*.f64 4 (pow.f64 x 2))
(+.f64 (.f64 4 (pow.f64 x 2)) (.f64 -16 (*.f64 (pow.f64 x 4) (log.f64 x))))
(+.f64 (.f64 4 (pow.f64 x 2)) (+.f64 (.f64 -16 (.f64 (pow.f64 x 4) (log.f64 x))) (.f64 64 (*.f64 (pow.f64 x 6) (pow.f64 (log.f64 x) 2)))))
(+.f64 (.f64 -256 (.f64 (pow.f64 x 8) (pow.f64 (log.f64 x) 3))) (+.f64 (.f64 4 (pow.f64 x 2)) (+.f64 (.f64 -16 (.f64 (pow.f64 x 4) (log.f64 x))) (.f64 64 (*.f64 (pow.f64 x 6) (pow.f64 (log.f64 x) 2))))))
(/.f64 -1 (log.f64 (/.f64 1 x)))
(neg.f64 (+.f64 (/.f64 1 (log.f64 (/.f64 1 x))) (.f64 1/4 (/.f64 1 (.f64 (pow.f64 (log.f64 (/.f64 1 x)) 2) (pow.f64 x 2))))))
(neg.f64 (+.f64 (/.f64 1 (log.f64 (/.f64 1 x))) (+.f64 (.f64 1/4 (/.f64 1 (.f64 (pow.f64 (log.f64 (/.f64 1 x)) 2) (pow.f64 x 2)))) (.f64 1/16 (/.f64 1 (.f64 (pow.f64 (log.f64 (/.f64 1 x)) 3) (pow.f64 x 4)))))))
(neg.f64 (+.f64 (/.f64 1 (log.f64 (/.f64 1 x))) (+.f64 (.f64 1/4 (/.f64 1 (.f64 (pow.f64 (log.f64 (/.f64 1 x)) 2) (pow.f64 x 2)))) (+.f64 (.f64 1/16 (/.f64 1 (.f64 (pow.f64 (log.f64 (/.f64 1 x)) 3) (pow.f64 x 4)))) (.f64 1/64 (/.f64 1 (.f64 (pow.f64 (log.f64 (/.f64 1 x)) 4) (pow.f64 x 6))))))))
(/.f64 1 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))
(-.f64 (/.f64 1 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))) (.f64 1/4 (/.f64 1 (.f64 (pow.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)) 2) (pow.f64 x 2)))))
(-.f64 (+.f64 (.f64 1/16 (/.f64 1 (.f64 (pow.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)) 3) (pow.f64 x 4)))) (/.f64 1 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (.f64 1/4 (/.f64 1 (.f64 (pow.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)) 2) (pow.f64 x 2)))))
(-.f64 (+.f64 (.f64 1/16 (/.f64 1 (.f64 (pow.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)) 3) (pow.f64 x 4)))) (/.f64 1 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (+.f64 (.f64 1/4 (/.f64 1 (.f64 (pow.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)) 2) (pow.f64 x 2)))) (.f64 1/64 (/.f64 1 (.f64 (pow.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)) 4) (pow.f64 x 6))))))

Outputs
(/.f64 -1/4 (pow.f64 x 2))
(/.f64 -1/4 (*.f64 x x))
(/.f64 (/.f64 -1/4 x) x)
(/.f64 -1/4 (pow.f64 x 2))
(/.f64 -1/4 (*.f64 x x))
(/.f64 (/.f64 -1/4 x) x)
(/.f64 -1/4 (pow.f64 x 2))
(/.f64 -1/4 (*.f64 x x))
(/.f64 (/.f64 -1/4 x) x)
(/.f64 -1/4 (pow.f64 x 2))
(/.f64 -1/4 (*.f64 x x))
(/.f64 (/.f64 -1/4 x) x)
(/.f64 -1/4 (pow.f64 x 2))
(/.f64 -1/4 (*.f64 x x))
(/.f64 (/.f64 -1/4 x) x)
(/.f64 -1/4 (pow.f64 x 2))
(/.f64 -1/4 (*.f64 x x))
(/.f64 (/.f64 -1/4 x) x)
(/.f64 -1/4 (pow.f64 x 2))
(/.f64 -1/4 (*.f64 x x))
(/.f64 (/.f64 -1/4 x) x)
(/.f64 -1/4 (pow.f64 x 2))
(/.f64 -1/4 (*.f64 x x))
(/.f64 (/.f64 -1/4 x) x)
(/.f64 -1/4 (pow.f64 x 2))
(/.f64 -1/4 (*.f64 x x))
(/.f64 (/.f64 -1/4 x) x)
(/.f64 -1/4 (pow.f64 x 2))
(/.f64 -1/4 (*.f64 x x))
(/.f64 (/.f64 -1/4 x) x)
(/.f64 -1/4 (pow.f64 x 2))
(/.f64 -1/4 (*.f64 x x))
(/.f64 (/.f64 -1/4 x) x)
(/.f64 -1/4 (pow.f64 x 2))
(/.f64 -1/4 (*.f64 x x))
(/.f64 (/.f64 -1/4 x) x)
(pow.f64 (log.f64 (/.f64 1 x)) 2)
(pow.f64 (neg.f64 (log.f64 x)) 2)
(pow.f64 (log.f64 x) 2)
(pow.f64 (log.f64 (/.f64 1 x)) 2)
(pow.f64 (neg.f64 (log.f64 x)) 2)
(pow.f64 (log.f64 x) 2)
(pow.f64 (log.f64 (/.f64 1 x)) 2)
(pow.f64 (neg.f64 (log.f64 x)) 2)
(pow.f64 (log.f64 x) 2)
(pow.f64 (log.f64 (/.f64 1 x)) 2)
(pow.f64 (neg.f64 (log.f64 x)) 2)
(pow.f64 (log.f64 x) 2)
(pow.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)) 2)
(pow.f64 (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)) 2)
(pow.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))) 2)
(pow.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)) 2)
(pow.f64 (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)) 2)
(pow.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))) 2)
(pow.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)) 2)
(pow.f64 (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)) 2)
(pow.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))) 2)
(pow.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)) 2)
(pow.f64 (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)) 2)
(pow.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))) 2)
(/.f64 -1/4 (pow.f64 x 2))
(/.f64 -1/4 (*.f64 x x))
(/.f64 (/.f64 -1/4 x) x)
(-.f64 (+.f64 (log.f64 2) (log.f64 x)) (*.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (log.f64 2) (log.f64 x)) (/.f64 1/4 (*.f64 x x)))
(+.f64 (log.f64 2) (+.f64 (log.f64 x) (/.f64 (/.f64 -1/4 x) x)))
(-.f64 (+.f64 (log.f64 2) (+.f64 (.f64 (pow.f64 x 2) (+.f64 (.f64 -4 (pow.f64 (log.f64 x) 2)) (.f64 4 (pow.f64 (log.f64 x) 2)))) (log.f64 x))) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (log.f64 2) (log.f64 x)) (/.f64 1/4 (*.f64 x x)))
(+.f64 (log.f64 2) (+.f64 (log.f64 x) (/.f64 (/.f64 -1/4 x) x)))
(-.f64 (+.f64 (log.f64 2) (+.f64 (.f64 (+.f64 (.f64 16 (pow.f64 (log.f64 x) 3)) (.f64 -16 (pow.f64 (log.f64 x) 3))) (pow.f64 x 4)) (+.f64 (.f64 (pow.f64 x 2) (+.f64 (.f64 -4 (pow.f64 (log.f64 x) 2)) (.f64 4 (pow.f64 (log.f64 x) 2)))) (log.f64 x)))) (*.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (log.f64 2) (log.f64 x)) (/.f64 1/4 (*.f64 x x)))
(+.f64 (log.f64 2) (+.f64 (log.f64 x) (/.f64 (/.f64 -1/4 x) x)))
(+.f64 (log.f64 2) (*.f64 -1 (log.f64 (/.f64 1 x))))
(fma.f64 -1 (neg.f64 (log.f64 x)) (log.f64 2))
(+.f64 (log.f64 2) (log.f64 x))
(-.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 2)) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (log.f64 2) (log.f64 x)) (/.f64 1/4 (*.f64 x x)))
(+.f64 (log.f64 2) (+.f64 (log.f64 x) (/.f64 (/.f64 -1/4 x) x)))
(-.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 2)) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (log.f64 2) (log.f64 x)) (/.f64 1/4 (*.f64 x x)))
(+.f64 (log.f64 2) (+.f64 (log.f64 x) (/.f64 (/.f64 -1/4 x) x)))
(-.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 2)) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (log.f64 2) (log.f64 x)) (/.f64 1/4 (*.f64 x x)))
(+.f64 (log.f64 2) (+.f64 (log.f64 x) (/.f64 (/.f64 -1/4 x) x)))
(+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (+.f64 (log.f64 2) (log.f64 -1)))
(fma.f64 -1 (log.f64 (/.f64 -1 x)) (+.f64 (log.f64 -1) (log.f64 2)))
(-.f64 (+.f64 (log.f64 -1) (log.f64 2)) (log.f64 (/.f64 -1 x)))
(-.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (+.f64 (log.f64 2) (log.f64 -1))) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (fma.f64 -1 (log.f64 (/.f64 -1 x)) (+.f64 (log.f64 -1) (log.f64 2))) (/.f64 1/4 (*.f64 x x)))
(+.f64 (-.f64 (+.f64 (log.f64 -1) (log.f64 2)) (log.f64 (/.f64 -1 x))) (/.f64 (/.f64 -1/4 x) x))
(+.f64 (log.f64 -1) (+.f64 (-.f64 (log.f64 2) (log.f64 (/.f64 -1 x))) (/.f64 (/.f64 -1/4 x) x)))
(-.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (+.f64 (log.f64 2) (log.f64 -1))) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (fma.f64 -1 (log.f64 (/.f64 -1 x)) (+.f64 (log.f64 -1) (log.f64 2))) (/.f64 1/4 (*.f64 x x)))
(+.f64 (-.f64 (+.f64 (log.f64 -1) (log.f64 2)) (log.f64 (/.f64 -1 x))) (/.f64 (/.f64 -1/4 x) x))
(+.f64 (log.f64 -1) (+.f64 (-.f64 (log.f64 2) (log.f64 (/.f64 -1 x))) (/.f64 (/.f64 -1/4 x) x)))
(-.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (+.f64 (log.f64 2) (log.f64 -1))) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (fma.f64 -1 (log.f64 (/.f64 -1 x)) (+.f64 (log.f64 -1) (log.f64 2))) (/.f64 1/4 (*.f64 x x)))
(+.f64 (-.f64 (+.f64 (log.f64 -1) (log.f64 2)) (log.f64 (/.f64 -1 x))) (/.f64 (/.f64 -1/4 x) x))
(+.f64 (log.f64 -1) (+.f64 (-.f64 (log.f64 2) (log.f64 (/.f64 -1 x))) (/.f64 (/.f64 -1/4 x) x)))
(*.f64 4 (pow.f64 x 2))
(.f64 (.f64 x x) 4)
(.f64 x (.f64 x 4))
(+.f64 (.f64 4 (pow.f64 x 2)) (.f64 -16 (*.f64 (pow.f64 x 4) (log.f64 x))))
(fma.f64 4 (.f64 x x) (.f64 -16 (*.f64 (log.f64 x) (pow.f64 x 4))))
(fma.f64 (.f64 x x) 4 (.f64 (log.f64 x) (*.f64 -16 (pow.f64 x 4))))
(fma.f64 x (.f64 x 4) (.f64 -16 (*.f64 (log.f64 x) (pow.f64 x 4))))
(+.f64 (.f64 4 (pow.f64 x 2)) (+.f64 (.f64 -16 (.f64 (pow.f64 x 4) (log.f64 x))) (.f64 64 (*.f64 (pow.f64 x 6) (pow.f64 (log.f64 x) 2)))))
(fma.f64 4 (.f64 x x) (fma.f64 -16 (.f64 (log.f64 x) (pow.f64 x 4)) (.f64 64 (.f64 (pow.f64 (log.f64 x) 2) (pow.f64 x 6)))))
(fma.f64 (.f64 x x) 4 (fma.f64 -16 (.f64 (log.f64 x) (pow.f64 x 4)) (.f64 64 (.f64 (pow.f64 (log.f64 x) 2) (pow.f64 x 6)))))
(fma.f64 x (.f64 x 4) (.f64 (log.f64 x) (+.f64 (.f64 -16 (pow.f64 x 4)) (.f64 (pow.f64 x 6) (*.f64 64 (log.f64 x))))))
(+.f64 (.f64 -256 (.f64 (pow.f64 x 8) (pow.f64 (log.f64 x) 3))) (+.f64 (.f64 4 (pow.f64 x 2)) (+.f64 (.f64 -16 (.f64 (pow.f64 x 4) (log.f64 x))) (.f64 64 (*.f64 (pow.f64 x 6) (pow.f64 (log.f64 x) 2))))))
(fma.f64 -256 (.f64 (pow.f64 (log.f64 x) 3) (pow.f64 x 8)) (fma.f64 4 (.f64 x x) (fma.f64 -16 (.f64 (log.f64 x) (pow.f64 x 4)) (.f64 64 (*.f64 (pow.f64 (log.f64 x) 2) (pow.f64 x 6))))))
(fma.f64 -256 (.f64 (pow.f64 (log.f64 x) 3) (pow.f64 x 8)) (fma.f64 (.f64 x x) 4 (fma.f64 -16 (.f64 (log.f64 x) (pow.f64 x 4)) (.f64 64 (*.f64 (pow.f64 (log.f64 x) 2) (pow.f64 x 6))))))
(fma.f64 (pow.f64 (log.f64 x) 3) (.f64 -256 (pow.f64 x 8)) (fma.f64 x (.f64 x 4) (.f64 (log.f64 x) (+.f64 (.f64 -16 (pow.f64 x 4)) (.f64 (pow.f64 x 6) (.f64 64 (log.f64 x)))))))
(/.f64 -1 (log.f64 (/.f64 1 x)))
(/.f64 -1 (neg.f64 (log.f64 x)))
(/.f64 1 (log.f64 x))
(neg.f64 (+.f64 (/.f64 1 (log.f64 (/.f64 1 x))) (.f64 1/4 (/.f64 1 (.f64 (pow.f64 (log.f64 (/.f64 1 x)) 2) (pow.f64 x 2))))))
(neg.f64 (+.f64 (/.f64 1 (neg.f64 (log.f64 x))) (/.f64 1/4 (.f64 (.f64 x x) (pow.f64 (neg.f64 (log.f64 x)) 2)))))
(-.f64 (/.f64 -1 (neg.f64 (log.f64 x))) (/.f64 (/.f64 1/4 (*.f64 x x)) (pow.f64 (log.f64 x) 2)))
(-.f64 (/.f64 (/.f64 (/.f64 -1/4 x) x) (pow.f64 (log.f64 x) 2)) (/.f64 -1 (log.f64 x)))
(neg.f64 (+.f64 (/.f64 1 (log.f64 (/.f64 1 x))) (+.f64 (.f64 1/4 (/.f64 1 (.f64 (pow.f64 (log.f64 (/.f64 1 x)) 2) (pow.f64 x 2)))) (.f64 1/16 (/.f64 1 (.f64 (pow.f64 (log.f64 (/.f64 1 x)) 3) (pow.f64 x 4)))))))
(neg.f64 (+.f64 (/.f64 1 (neg.f64 (log.f64 x))) (+.f64 (/.f64 1/4 (.f64 (.f64 x x) (pow.f64 (neg.f64 (log.f64 x)) 2))) (/.f64 1/16 (*.f64 (pow.f64 x 4) (pow.f64 (neg.f64 (log.f64 x)) 3))))))
(-.f64 (/.f64 -1 (neg.f64 (log.f64 x))) (+.f64 (/.f64 (/.f64 1/4 (.f64 x x)) (pow.f64 (log.f64 x) 2)) (/.f64 1/16 (.f64 (pow.f64 x 4) (pow.f64 (neg.f64 (log.f64 x)) 3)))))
(+.f64 (/.f64 (/.f64 (/.f64 -1/4 x) x) (pow.f64 (log.f64 x) 2)) (-.f64 (/.f64 -1/16 (*.f64 (pow.f64 x 4) (pow.f64 (neg.f64 (log.f64 x)) 3))) (/.f64 -1 (log.f64 x))))
(neg.f64 (+.f64 (/.f64 1 (log.f64 (/.f64 1 x))) (+.f64 (.f64 1/4 (/.f64 1 (.f64 (pow.f64 (log.f64 (/.f64 1 x)) 2) (pow.f64 x 2)))) (+.f64 (.f64 1/16 (/.f64 1 (.f64 (pow.f64 (log.f64 (/.f64 1 x)) 3) (pow.f64 x 4)))) (.f64 1/64 (/.f64 1 (.f64 (pow.f64 (log.f64 (/.f64 1 x)) 4) (pow.f64 x 6))))))))
(neg.f64 (+.f64 (/.f64 1 (neg.f64 (log.f64 x))) (+.f64 (/.f64 1/4 (.f64 (.f64 x x) (pow.f64 (neg.f64 (log.f64 x)) 2))) (+.f64 (/.f64 1/16 (.f64 (pow.f64 x 4) (pow.f64 (neg.f64 (log.f64 x)) 3))) (/.f64 1/64 (.f64 (pow.f64 x 6) (pow.f64 (neg.f64 (log.f64 x)) 4)))))))
(-.f64 (/.f64 -1 (neg.f64 (log.f64 x))) (+.f64 (/.f64 (/.f64 1/4 (.f64 x x)) (pow.f64 (log.f64 x) 2)) (+.f64 (/.f64 1/16 (.f64 (pow.f64 x 4) (pow.f64 (neg.f64 (log.f64 x)) 3))) (/.f64 1/64 (*.f64 (pow.f64 x 6) (pow.f64 (neg.f64 (log.f64 x)) 4))))))
(+.f64 (/.f64 (/.f64 (/.f64 -1/4 x) x) (pow.f64 (log.f64 x) 2)) (-.f64 (+.f64 (/.f64 -1/16 (.f64 (pow.f64 x 4) (pow.f64 (neg.f64 (log.f64 x)) 3))) (/.f64 -1/64 (.f64 (pow.f64 x 6) (pow.f64 (log.f64 x) 4)))) (/.f64 -1 (log.f64 x))))
(/.f64 1 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))
(/.f64 1 (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)))
(/.f64 1 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))
(-.f64 (/.f64 1 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))) (.f64 1/4 (/.f64 1 (.f64 (pow.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)) 2) (pow.f64 x 2)))))
(-.f64 (/.f64 1 (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (/.f64 1/4 (.f64 (.f64 x x) (pow.f64 (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)) 2))))
(+.f64 (/.f64 1 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (/.f64 -1/4 (.f64 (.f64 x x) (pow.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))) 2))))
(-.f64 (/.f64 1 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (/.f64 (/.f64 1/4 (*.f64 x x)) (pow.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))) 2)))
(-.f64 (+.f64 (.f64 1/16 (/.f64 1 (.f64 (pow.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)) 3) (pow.f64 x 4)))) (/.f64 1 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (.f64 1/4 (/.f64 1 (.f64 (pow.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)) 2) (pow.f64 x 2)))))
(+.f64 (/.f64 1/16 (.f64 (pow.f64 x 4) (pow.f64 (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)) 3))) (-.f64 (/.f64 1 (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (/.f64 1/4 (.f64 (*.f64 x x) (pow.f64 (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)) 2)))))
(+.f64 (/.f64 1 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (-.f64 (/.f64 1/16 (.f64 (pow.f64 x 4) (pow.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))) 3))) (/.f64 1/4 (.f64 (*.f64 x x) (pow.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))) 2)))))
(+.f64 (/.f64 1 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (+.f64 (/.f64 1/16 (.f64 (pow.f64 x 4) (pow.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))) 3))) (/.f64 -1/4 (.f64 x (*.f64 x (pow.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))) 2))))))
(-.f64 (+.f64 (.f64 1/16 (/.f64 1 (.f64 (pow.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)) 3) (pow.f64 x 4)))) (/.f64 1 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (+.f64 (.f64 1/4 (/.f64 1 (.f64 (pow.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)) 2) (pow.f64 x 2)))) (.f64 1/64 (/.f64 1 (.f64 (pow.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)) 4) (pow.f64 x 6))))))
(-.f64 (+.f64 (/.f64 1 (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (/.f64 1/16 (.f64 (pow.f64 x 4) (pow.f64 (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)) 3)))) (+.f64 (/.f64 1/4 (.f64 (.f64 x x) (pow.f64 (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)) 2))) (/.f64 1/64 (.f64 (pow.f64 x 6) (pow.f64 (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)) 4)))))
(+.f64 (/.f64 1 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (-.f64 (/.f64 1/16 (.f64 (pow.f64 x 4) (pow.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))) 3))) (+.f64 (/.f64 1/4 (.f64 (.f64 x x) (pow.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))) 2))) (/.f64 1/64 (.f64 (pow.f64 x 6) (pow.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))) 4))))))
(+.f64 (/.f64 1 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (+.f64 (/.f64 1/16 (.f64 (pow.f64 x 4) (pow.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))) 3))) (+.f64 (/.f64 -1/4 (.f64 x (.f64 x (pow.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))) 2)))) (/.f64 -1/64 (.f64 (pow.f64 x 6) (pow.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))) 4))))))

eval132.0ms (4.1%)

Compiler: Compiled 4566 to 3242 computations (29% saved)

prune69.0ms (2.2%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	161	0	161
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	161	2	163

Error

Counts

163 → 2

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.2b	(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))
✓	0.4b	(fma.f64 (-.f64 (pow.f64 (log.f64 x) 2) (pow.f64 (/.f64 -1/4 (.f64 x x)) 2)) (/.f64 1 (-.f64 (log.f64 x) (/.f64 -1/4 (.f64 x x)))) (log1p.f64 1))

Compiler

Compiled 34 to 24 computations (29.4% saved)

regimes21.0ms (0.6%)

Accuracy

Total -34.6b remaining (-15030.5%)

Threshold costs -34.6b (-15030.5%)

Counts

5 → 1

Calls

Call 1

Inputs
(fma.f64 (-.f64 (pow.f64 (log.f64 x) 2) (pow.f64 (/.f64 -1/4 (.f64 x x)) 2)) (/.f64 1 (-.f64 (log.f64 x) (/.f64 -1/4 (.f64 x x)))) (log1p.f64 1))
(+.f64 (log.f64 2) (+.f64 (log.f64 x) (/.f64 (/.f64 -1/4 x) x)))
(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))
(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))
(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))

Outputs
(+.f64 (log.f64 2) (+.f64 (log.f64 x) (/.f64 (/.f64 -1/4 x) x)))

Results

Time	Error	Segments	Branch
11.0ms	0.2b	1	`x`
4.0ms	0.2b	1	`(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))`
4.0ms	0.2b	1	`(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))`

Compiler

Compiled 82 to 54 computations (34.1% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	12	17

Stop Event

1×

saturated

Calls

Call 1

Inputs
(+.f64 (log.f64 2) (+.f64 (log.f64 x) (/.f64 (/.f64 -1/4 x) x)))

Outputs
(+.f64 (log.f64 2) (+.f64 (log.f64 x) (/.f64 (/.f64 -1/4 x) x)))

end17.0ms (0.5%)

Stop Event

1×

done

Compiler

Compiled 24 to 18 computations (25% saved)

Details

analyze392.0ms (12.3%)

sample1.8s (57.5%)

preprocess36.0ms (1.1%)

simplify26.0ms (0.8%)

eval1.0ms (0%)

prune1.0ms (0%)

localize6.0ms (0.2%)

series8.0ms (0.3%)

rewrite45.0ms (1.4%)

simplify36.0ms (1.1%)

eval48.0ms (1.5%)

prune59.0ms (1.8%)

localize8.0ms (0.2%)

series21.0ms (0.7%)

rewrite58.0ms (1.8%)

simplify31.0ms (1%)

eval46.0ms (1.4%)

prune46.0ms (1.4%)

localize5.0ms (0.2%)

series2.0ms (0.1%)

rewrite33.0ms (1%)

simplify25.0ms (0.8%)

eval14.0ms (0.4%)

prune11.0ms (0.3%)

localize13.0ms (0.4%)

series50.0ms (1.6%)

rewrite61.0ms (1.9%)

simplify31.0ms (1%)

eval132.0ms (4.1%)

prune69.0ms (2.2%)

regimes21.0ms (0.6%)

simplify2.0ms (0.1%)

end17.0ms (0.5%)

Profiling