Details

analyze505.0ms (19.1%)

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 (69.5%)

Results

937.0ms	8256×	body	128	valid
872.0ms	8371×	body	128	invalid

preprocess37.0ms (1.4%)

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)

simplify30.0ms (1.2%)

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)

prune2.0ms (0.1%)

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

34.5b

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	34.5b	(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 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (sqrt.f64 (fma.f64 x x -1)))
✓	32.1b	(sqrt.f64 (fma.f64 x x -1))

series4.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(sqrt.f64 (fma.f64 x x -1))
1.0ms	x	@	inf	(sqrt.f64 (fma.f64 x x -1))
1.0ms	x	@	-inf	(+.f64 x (sqrt.f64 (fma.f64 x x -1)))
1.0ms	x	@	-inf	(sqrt.f64 (fma.f64 x x -1))
0.0ms	x	@	0	(+.f64 x (sqrt.f64 (fma.f64 x x -1)))

rewrite43.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

654×	`pow1_binary64`
610×	`add-log-exp_binary64`
610×	`log1p-expm1-u_binary64`
610×	`expm1-log1p-u_binary64`
64×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	17
1	125	17
2	1657	17

Stop Event

1×	node limit

Counts

2 → 55

Calls

Call 1

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

simplify28.0ms (1%)

Algorithm

1×	egg-herbie

Rules

676×	`associate-/l*_binary64`
634×	`fma-def_binary64`
474×	`associate-/r*_binary64`
379×	`associate-l_binary64`
221×	`associate-*l/_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	69	395
1	200	377
2	511	369
3	1543	366

Stop Event

1×	node limit

Counts

79 → 97

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))))
(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))
(fma.f64 1/2 (*.f64 (/.f64 x (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 1/2 (*.f64 (/.f64 x (sqrt.f64 -1)) x) (fma.f64 1/8 (/.f64 (pow.f64 x 4) (sqrt.f64 -1)) (sqrt.f64 -1)))
(+.f64 (sqrt.f64 -1) (.f64 (.f64 (/.f64 x (sqrt.f64 -1)) x) (+.f64 1/2 (/.f64 (*.f64 x x) 8))))
(+.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 1/16 (/.f64 (pow.f64 x 6) (pow.f64 (sqrt.f64 -1) 5))))))
(+.f64 (fma.f64 1/2 (/.f64 x (/.f64 (sqrt.f64 -1) x)) (sqrt.f64 -1)) (+.f64 (/.f64 (.f64 1/16 (pow.f64 x 6)) (pow.f64 (sqrt.f64 -1) 5)) (.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 1/16 (/.f64 (pow.f64 x 6) (pow.f64 (sqrt.f64 -1) 5)) (fma.f64 1/2 (*.f64 (/.f64 x (sqrt.f64 -1)) x) (sqrt.f64 -1))))
(+.f64 (fma.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 (sqrt.f64 -1) 5)) (sqrt.f64 -1)) (.f64 (.f64 (/.f64 x (sqrt.f64 -1)) x) (+.f64 1/2 (/.f64 (*.f64 x x) 8))))
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 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 x (+.f64 (/.f64 1/2 x) (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/16 (pow.f64 x 5)))))
(-.f64 (+.f64 x (/.f64 -1/2 x)) (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/16 (pow.f64 x 5))))
(+.f64 x (+.f64 (+.f64 (/.f64 -1/2 x) (/.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 (/.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)))
(+.f64 (/.f64 1/16 (pow.f64 x 5)) (+.f64 (/.f64 1/2 x) (-.f64 (/.f64 1/8 (pow.f64 x 3)) 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 x (fma.f64 1/2 (/.f64 x (/.f64 (sqrt.f64 -1) x)) (sqrt.f64 -1)))
(+.f64 (sqrt.f64 -1) (fma.f64 1/2 (*.f64 (/.f64 x (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 x (fma.f64 1/2 (/.f64 x (/.f64 (sqrt.f64 -1) x)) (sqrt.f64 -1))))
(+.f64 (sqrt.f64 -1) (fma.f64 1/8 (/.f64 (pow.f64 x 4) (sqrt.f64 -1)) (fma.f64 1/2 (*.f64 (/.f64 x (sqrt.f64 -1)) x) x)))
(+.f64 (sqrt.f64 -1) (+.f64 x (.f64 (.f64 (/.f64 x (sqrt.f64 -1)) x) (+.f64 1/2 (/.f64 (*.f64 x x) 8)))))
(*.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 (*.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 (fma.f64 x 2 (/.f64 -1/2 x)) (/.f64 -1/8 (pow.f64 x 3)))
(+.f64 (/.f64 -1/2 x) (fma.f64 x 2 (/.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 (*.f64 x 2) (/.f64 1/2 x)) (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/16 (pow.f64 x 5))))
(-.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 (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 (/.f64 -1/2 x) (/.f64 -1/8 (pow.f64 x 3))) (fma.f64 x 2 (/.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 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.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 1/16 (pow.f64 x 5)) (+.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 5/128 (pow.f64 x 7)))))
(+.f64 (/.f64 1/16 (pow.f64 x 5)) (+.f64 (/.f64 1/2 x) (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.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)))))

eval37.0ms (1.4%)

Compiler: Compiled 1441 to 1047 computations (27.3% saved)

prune77.0ms (2.9%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	96	1	97
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	97	1	98

Error

Counts

98 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	0b	(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))

Compiler

Compiled 16 to 12 computations (25% saved)

localize5.0ms (0.2%)

eval0.0ms (0%)

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

prune1.0ms (0%)

Pruning

1 alts after pruning (0 fresh and 1 done)

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

Error

Counts

1 → 1

Alt Table

Click to see full alt table

Status	Error	Program
✓	0b	(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))

Compiler

Compiled 8 to 6 computations (25% saved)

regimes13.0ms (0.5%)

Accuracy

Total -34.5b remaining (-∞%)

Threshold costs -34.5b (-∞%)

Counts

3 → 1

Calls

Call 1

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

Results

Time	Error	Segments	Branch
3.0ms	0b	1	`x`
5.0ms	0b	1	`(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))`
3.0ms	0b	1	`(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))`

Compiler

Compiled 46 to 31 computations (32.6% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10

Stop Event

1×

saturated

Calls

Call 1

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

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

end17.0ms (0.6%)

Stop Event

1×

done

Compiler

Compiled 16 to 12 computations (25% saved)

Details

analyze505.0ms (19.1%)

sample1.8s (69.5%)

preprocess37.0ms (1.4%)

simplify30.0ms (1.2%)

eval1.0ms (0%)

prune2.0ms (0.1%)

localize6.0ms (0.2%)

series4.0ms (0.1%)

rewrite43.0ms (1.6%)

simplify28.0ms (1%)

eval37.0ms (1.4%)

prune77.0ms (2.9%)

localize5.0ms (0.2%)

eval0.0ms (0%)

prune1.0ms (0%)

regimes13.0ms (0.5%)

simplify2.0ms (0.1%)

end17.0ms (0.6%)

Profiling