Details

analyze261.0ms (6.9%)

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

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample2.1s (55.8%)

Results

1.2s	8256×	body	256	valid
945.0ms	8268×	body	256	invalid

preprocess147.0ms (3.9%)

Algorithm

2×	egg-herbie

Rules

864×	`fma-neg_binary64`
682×	`unsub-neg_binary64`
430×	`distribute-neg-in_binary64`
420×	`sub-neg_binary64`
353×	`distribute-rgt-out_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	18	12
2	22	12
3	37	12
4	76	12
5	152	12
6	359	12
7	756	12
8	2543	12
9	4491	12
10	5836	12
11	6572	12
12	6876	12
13	7073	12
14	7205	12
15	7549	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 11 to 8 computations (27.3% saved)

simplify131.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

864×	`fma-neg_binary64`
682×	`unsub-neg_binary64`
430×	`distribute-neg-in_binary64`
420×	`sub-neg_binary64`
353×	`distribute-rgt-out_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	18	12
2	22	12
3	37	12
4	76	12
5	152	12
6	359	12
7	756	12
8	2543	12
9	4491	12
10	5836	12
11	6572	12
12	6876	12
13	7073	12
14	7205	12
15	7549	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

2 alts after pruning (2 fresh and 0 done)

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

Error

33.2b

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	33.2b	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))

Compiler

Compiled 10 to 7 computations (30% saved)

localize14.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
✓	30.9b	(sqrt.f64 (-.f64 (*.f64 x x) 1))

Compiler

Compiled 34 to 17 computations (50% saved)

series3.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

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

rewrite77.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

821×	`pow1_binary64`
772×	`add-log-exp_binary64`
770×	`log1p-expm1-u_binary64`
770×	`expm1-log1p-u_binary64`
754×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	159	17
2	2275	17

Stop Event

1×	node limit

Counts

2 → 57

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (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 (sqrt.f64 (fma.f64 x x -1)) 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 (+.f64 x 1)) (sqrt.f64 (+.f64 x -1)))))) (#(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 .f64 (pow.f64 (+.f64 x 1) 1/2) (pow.f64 (+.f64 x -1) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (+.f64 (pow.f64 x 6) -1)) (sqrt.f64 (+.f64 (pow.f64 x 4) (fma.f64 x x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (+.f64 (pow.f64 x 4) -1)) (sqrt.f64 (fma.f64 x x 1)))))) (#(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 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 (+.f64 1 (+.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 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 (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 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 exp.f64 (log.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 (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 (cbrt.f64 x) 2) (cbrt.f64 x) (sqrt.f64 (fma.f64 x x -1)))))) (#(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)))))))

Outputs

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

simplify59.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

676×	`associate-/l*_binary64`
635×	`fma-def_binary64`
578×	`unswap-sqr_binary64`
479×	`associate-/r*_binary64`
402×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	69	395
1	200	377
2	515	369
3	1560	366
4	6932	366

Stop Event

1×	node limit

Counts

81 → 99

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

eval33.0ms (0.9%)

Compiler: Compiled 1477 to 1074 computations (27.3% saved)

prune22.0ms (0.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	96	3	99
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	96	4	100

Error

Counts

100 → 4

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.3b	(log.f64 (+.f64 x (+.f64 x (/.f64 -1/2 x))))
▶	0.7b	(log.f64 (+.f64 x x))
✓	33.2b	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
▶	0.3b	(log.f64 (-.f64 (.f64 2 x) (.f64 1/2 (/.f64 1 x))))

Compiler

Compiled 35 to 25 computations (28.6% saved)

localize7.0ms (0.2%)

Compiler: Compiled 9 to 3 computations (66.7% saved)

localize13.0ms (0.3%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 26 to 16 computations (38.5% saved)

series4.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

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

rewrite88.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

547×	`unpow-prod-down_binary64`
424×	`fma-def_binary64`
380×	`log-prod_binary64`
281×	`exp-prod_binary64`
266×	`pow-prod-down_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	7	22
1	166	22
2	2499	18

Stop Event

1×	node limit

Counts

2 → 155

Calls

Call 1

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

Outputs
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Outputs

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(cbrt.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 (-.f64 (*.f64 x x) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 2))) (log.f64 (-.f64 x (+.f64 x (/.f64 -1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (log.f64 (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 3))) (log.f64 (fma.f64 (+.f64 x (/.f64 -1/2 x)) (-.f64 (+.f64 x (/.f64 -1/2 x)) x) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (log.f64 (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 3))) (log.f64 (+.f64 (pow.f64 (+.f64 x (/.f64 -1/2 x)) 2) (-.f64 (*.f64 x x) (*.f64 x (+.f64 x (/.f64 -1/2 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (log.f64 (/.f64 (fma.f64 (+.f64 x (/.f64 -1/2 x)) (-.f64 (+.f64 x (/.f64 -1/2 x)) x) (*.f64 x x)) (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (log.f64 (/.f64 (-.f64 x (+.f64 x (/.f64 -1/2 x))) (-.f64 (*.f64 x x) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (log.f64 (neg.f64 (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 3)))) (log.f64 (neg.f64 (fma.f64 (+.f64 x (/.f64 -1/2 x)) (-.f64 (+.f64 x (/.f64 -1/2 x)) x) (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (log.f64 (neg.f64 (-.f64 (*.f64 x x) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 2)))) (log.f64 (neg.f64 (-.f64 x (+.f64 x (/.f64 -1/2 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (log.f64 (+.f64 (*.f64 (pow.f64 x 3) 8) (pow.f64 (/.f64 -1/2 x) 3))) (log.f64 (+.f64 (pow.f64 (+.f64 x x) 2) (-.f64 (*.f64 1/4 (pow.f64 x -2)) (*.f64 (+.f64 x x) (/.f64 -1/2 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (log.f64 (-.f64 (pow.f64 (+.f64 x (/.f64 -1/2 x)) 2) (*.f64 x x))) (log.f64 (-.f64 (+.f64 x (/.f64 -1/2 x)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (log.f64 (-.f64 (pow.f64 (+.f64 x x) 2) (*.f64 1/4 (pow.f64 x -2)))) (log.f64 (-.f64 (+.f64 x x) (/.f64 -1/2 x))))))) (#(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 *.f64 3 (log.f64 (cbrt.f64 (fma.f64 x 2 (/.f64 -1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/3 (*.f64 3 (log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (log.f64 (sqrt.f64 (fma.f64 x 2 (/.f64 -1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (log.f64 (fma.f64 x 2 (/.f64 -1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (pow.f64 (log.f64 (fma.f64 x 2 (/.f64 -1/2 x))) 3)) 1/3) (pow.f64 (sqrt.f64 (pow.f64 (log.f64 (fma.f64 x 2 (/.f64 -1/2 x))) 3)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (*.f64 (log.f64 (fma.f64 x 2 (/.f64 -1/2 x))) (cbrt.f64 (log.f64 (fma.f64 x 2 (/.f64 -1/2 x))))) 2) 1/3) (cbrt.f64 (cbrt.f64 (log.f64 (fma.f64 x 2 (/.f64 -1/2 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (log.f64 (fma.f64 x 2 (/.f64 -1/2 x))) 5/2) 1/3) (cbrt.f64 (sqrt.f64 (log.f64 (fma.f64 x 2 (/.f64 -1/2 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (log.f64 (fma.f64 x 2 (/.f64 -1/2 x))))) 2) 3) (cbrt.f64 (log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (log.f64 (fma.f64 x 2 (/.f64 -1/2 x))))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (log.f64 (fma.f64 x 2 (/.f64 -1/2 x))))) 3))))) (#(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))) 2) 1/2)))) (#(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 pow.f64 (exp.f64 1) (log.f64 (log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (log.f64 (fma.f64 x 2 (/.f64 -1/2 x))))) 2)) (cbrt.f64 (log.f64 (log.f64 (fma.f64 x 2 (/.f64 -1/2 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))))) (sqrt.f64 (log.f64 (log.f64 (fma.f64 x 2 (/.f64 -1/2 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (log.f64 (/.f64 (fma.f64 (+.f64 x (/.f64 -1/2 x)) (-.f64 (+.f64 x (/.f64 -1/2 x)) x) (*.f64 x x)) (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 x (/.f64 -1/2 x)) 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (log.f64 (/.f64 (-.f64 x (+.f64 x (/.f64 -1/2 x))) (-.f64 (*.f64 x x) (pow.f64 (+.f64 x (/.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)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (log.f64 (fma.f64 x 2 (/.f64 -1/2 x))))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (log.f64 (fma.f64 x 2 (/.f64 -1/2 x))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (log.f64 (fma.f64 x 2 (/.f64 -1/2 x))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))) 1) 1))))))

simplify62.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

672×	`fma-def_binary64`
624×	`times-frac_binary64`
412×	`associate-+l-_binary64`
299×	`sub-neg_binary64`
287×	`fma-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	65	384
1	179	348
2	513	346
3	1718	342
4	6384	342

Stop Event

1×	node limit

Counts

179 → 183

Calls

Call 1

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

localize18.0ms (0.5%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 35 to 27 computations (22.9% saved)

series3.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

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

rewrite67.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

461×	`log-prod_binary64`
362×	`fma-def_binary64`
351×	`exp-prod_binary64`
282×	`prod-exp_binary64`
257×	`pow-prod-down_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	223	14
2	2741	14

Stop Event

1×	node limit

Counts

2 → 78

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (fma.f64 2 x (/.f64 -1/2 x))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (log.f64 (fma.f64 2 x (/.f64 -1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (-.f64 (*.f64 4 (*.f64 x x)) (*.f64 1/4 (pow.f64 x -2)))) (log.f64 (/.f64 1 (fma.f64 2 x (/.f64 1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (cbrt.f64 (fma.f64 2 x (/.f64 -1/2 x)))) (*.f64 2 (log.f64 (cbrt.f64 (fma.f64 2 x (/.f64 -1/2 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (fma.f64 2 x (/.f64 -1/2 x)))) (log.f64 (sqrt.f64 (fma.f64 2 x (/.f64 -1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 2 (log.f64 (cbrt.f64 (fma.f64 2 x (/.f64 -1/2 x))))) (log.f64 (cbrt.f64 (fma.f64 2 x (/.f64 -1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (-.f64 (*.f64 8 (pow.f64 x 3)) (*.f64 1/8 (pow.f64 x -3)))) (log.f64 (/.f64 1 (fma.f64 (/.f64 1/2 x) (fma.f64 2 x (/.f64 1/2 x)) (*.f64 4 (*.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 (/.f64 1/2 x)))) (log.f64 (-.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 (/.f64 1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (log.f64 (/.f64 (fma.f64 (/.f64 1/2 x) (fma.f64 2 x (/.f64 1/2 x)) (*.f64 4 (*.f64 x x))) (-.f64 (*.f64 8 (pow.f64 x 3)) (*.f64 1/8 (pow.f64 x -3))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (log.f64 (/.f64 (fma.f64 2 x (/.f64 1/2 x)) (-.f64 (*.f64 4 (*.f64 x x)) (*.f64 1/4 (pow.f64 x -2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (log.f64 (fma.f64 2 x (/.f64 -1/2 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (log.f64 (-.f64 (*.f64 4 (*.f64 x x)) (*.f64 1/4 (pow.f64 x -2)))) (log.f64 (fma.f64 2 x (/.f64 1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (log.f64 (-.f64 (*.f64 8 (pow.f64 x 3)) (*.f64 1/8 (pow.f64 x -3)))) (log.f64 (fma.f64 (/.f64 1/2 x) (fma.f64 2 x (/.f64 1/2 x)) (*.f64 4 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (log.f64 (neg.f64 (-.f64 (*.f64 8 (pow.f64 x 3)) (*.f64 1/8 (pow.f64 x -3))))) (log.f64 (neg.f64 (fma.f64 (/.f64 1/2 x) (fma.f64 2 x (/.f64 1/2 x)) (*.f64 4 (*.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (log.f64 (neg.f64 (-.f64 (*.f64 4 (*.f64 x x)) (*.f64 1/4 (pow.f64 x -2))))) (log.f64 (neg.f64 (fma.f64 2 x (/.f64 1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (log.f64 (fma.f64 8 (pow.f64 x 3) (pow.f64 (/.f64 -1/2 x) 3))) (log.f64 (fma.f64 4 (*.f64 x x) (-.f64 (pow.f64 (/.f64 -1/2 x) 2) (*.f64 (+.f64 x x) (/.f64 -1/2 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (log.f64 (+.f64 (pow.f64 (fma.f64 2 x (/.f64 -1/2 x)) 3) (pow.f64 (+.f64 (/.f64 -1/2 x) (/.f64 1/2 x)) 3))) (log.f64 (+.f64 (pow.f64 (fma.f64 2 x (/.f64 -1/2 x)) 2) (-.f64 (pow.f64 (+.f64 (/.f64 -1/2 x) (/.f64 1/2 x)) 2) (*.f64 (fma.f64 2 x (/.f64 -1/2 x)) (+.f64 (/.f64 -1/2 x) (/.f64 1/2 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (log.f64 (-.f64 (*.f64 4 (*.f64 x x)) (pow.f64 (/.f64 -1/2 x) 2))) (log.f64 (-.f64 (+.f64 x x) (/.f64 -1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (log.f64 (-.f64 (pow.f64 (fma.f64 2 x (/.f64 -1/2 x)) 2) (pow.f64 (+.f64 (/.f64 -1/2 x) (/.f64 1/2 x)) 2))) (log.f64 (-.f64 (fma.f64 2 x (/.f64 -1/2 x)) (+.f64 (/.f64 -1/2 x) (/.f64 1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (log.f64 (sqrt.f64 (fma.f64 2 x (/.f64 -1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (log.f64 (fma.f64 2 x (/.f64 -1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (log.f64 (fma.f64 2 x (/.f64 -1/2 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (log.f64 (fma.f64 2 x (/.f64 -1/2 x)))) (pow.f64 (cbrt.f64 (log.f64 (fma.f64 2 x (/.f64 -1/2 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (log.f64 (fma.f64 2 x (/.f64 -1/2 x)))) 2) (cbrt.f64 (log.f64 (fma.f64 2 x (/.f64 -1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (log.f64 (fma.f64 2 x (/.f64 -1/2 x)))) (sqrt.f64 (log.f64 (fma.f64 2 x (/.f64 -1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 3 (log.f64 (cbrt.f64 (fma.f64 2 x (/.f64 -1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/3 (*.f64 3 (log.f64 (fma.f64 2 x (/.f64 -1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (log.f64 (fma.f64 2 x (/.f64 -1/2 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (log.f64 (log.f64 (fma.f64 2 x (/.f64 -1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (log.f64 (fma.f64 2 x (/.f64 -1/2 x))) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (log.f64 (fma.f64 2 x (/.f64 -1/2 x))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (log.f64 (fma.f64 2 x (/.f64 -1/2 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (log.f64 (fma.f64 2 x (/.f64 -1/2 x)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (log.f64 (fma.f64 2 x (/.f64 -1/2 x))))) 2)) (cbrt.f64 (log.f64 (log.f64 (fma.f64 2 x (/.f64 -1/2 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (log.f64 (fma.f64 2 x (/.f64 -1/2 x)))))) (sqrt.f64 (log.f64 (log.f64 (fma.f64 2 x (/.f64 -1/2 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (log.f64 (/.f64 (fma.f64 (/.f64 1/2 x) (fma.f64 2 x (/.f64 1/2 x)) (*.f64 4 (*.f64 x x))) (-.f64 (*.f64 8 (pow.f64 x 3)) (*.f64 1/8 (pow.f64 x -3))))))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (log.f64 (/.f64 (fma.f64 2 x (/.f64 1/2 x)) (-.f64 (*.f64 4 (*.f64 x x)) (*.f64 1/4 (pow.f64 x -2))))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (log.f64 (fma.f64 2 x (/.f64 -1/2 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (log.f64 (fma.f64 2 x (/.f64 -1/2 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (log.f64 (fma.f64 2 x (/.f64 -1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (-.f64 (fma.f64 2 x (/.f64 -1/2 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (log.f64 (fma.f64 2 x (/.f64 -1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (log.f64 (fma.f64 2 x (/.f64 -1/2 x)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (log.f64 (fma.f64 2 x (/.f64 -1/2 x))))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (log.f64 (fma.f64 2 x (/.f64 -1/2 x))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (log.f64 (fma.f64 2 x (/.f64 -1/2 x))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (log.f64 (fma.f64 2 x (/.f64 -1/2 x)))) 1) 1))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 1/2 x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 1/2 x))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 1/2 x)))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 1/2 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1/2 x)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -1/2 (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 1/2 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 1/2 (sqrt.f64 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1/2 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (log.f64 (/.f64 1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 1/4 (pow.f64 x -2)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 1/2 x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 1/2 x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 1/8 (pow.f64 x -3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 x 1/2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (/.f64 1/2 x))) 2)) (cbrt.f64 (log.f64 (/.f64 1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (/.f64 1/2 x)))) (sqrt.f64 (log.f64 (/.f64 1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 1/4 (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 1/8 (pow.f64 x -3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 1/2 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (/.f64 1/2 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 1/2 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 1/8 (pow.f64 x -3))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (/.f64 1/2 x)) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (/.f64 1/2 x)) 3) 1/3))))))

simplify55.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

660×	`fma-def_binary64`
585×	`times-frac_binary64`
412×	`associate-+l-_binary64`
293×	`sub-neg_binary64`
285×	`unswap-sqr_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	62	330
1	167	312
2	488	310
3	1674	306
4	6271	306

Stop Event

1×	node limit

Counts

102 → 102

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))))))
(/.f64 1/2 x)
(/.f64 1/2 x)
(/.f64 1/2 x)
(/.f64 1/2 x)
(/.f64 1/2 x)
(/.f64 1/2 x)
(/.f64 1/2 x)
(/.f64 1/2 x)
(/.f64 1/2 x)
(/.f64 1/2 x)
(/.f64 1/2 x)
(/.f64 1/2 x)

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

eval109.0ms (2.9%)

Compiler: Compiled 4747 to 3559 computations (25% saved)

prune47.0ms (1.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	284	1	285
Fresh	0	0	0
Picked	1	0	1
Done	1	2	3
Total	286	3	289

Error

Counts

289 → 3

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.7b	(log.f64 (+.f64 x x))
▶	0.3b	(log.f64 (-.f64 (*.f64 2 x) (/.f64 1/2 x)))
✓	33.2b	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))

Compiler

Compiled 24 to 17 computations (29.2% saved)

localize30.0ms (0.8%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 25 to 18 computations (28% saved)

series2.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

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

rewrite64.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

893×	`pow1_binary64`
835×	`add-log-exp_binary64`
834×	`log1p-expm1-u_binary64`
834×	`expm1-log1p-u_binary64`
820×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	178	10
2	2335	10

Stop Event

1×	node limit

Counts

1 → 20

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (fma.f64 2 x (/.f64 -1/2 x))) 2)) (log.f64 (cbrt.f64 (fma.f64 2 x (/.f64 -1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (log.f64 (fma.f64 2 x (/.f64 -1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (fma.f64 2 x (/.f64 -1/2 x)))) (log.f64 (sqrt.f64 (fma.f64 2 x (/.f64 -1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (log.f64 (fma.f64 2 x (/.f64 -1/2 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (log.f64 (-.f64 (pow.f64 (*.f64 2 x) 3) (/.f64 1/8 (pow.f64 x 3)))) (log.f64 (+.f64 (pow.f64 (*.f64 2 x) 2) (*.f64 (/.f64 1/2 x) (fma.f64 2 x (/.f64 1/2 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (log.f64 (-.f64 (pow.f64 (*.f64 2 x) 2) (/.f64 1/4 (*.f64 x x)))) (log.f64 (fma.f64 2 x (/.f64 1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (log.f64 (fma.f64 2 x (/.f64 -1/2 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (log.f64 (fma.f64 2 x (/.f64 -1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (log.f64 (fma.f64 2 x (/.f64 -1/2 x)))) (pow.f64 (cbrt.f64 (log.f64 (fma.f64 2 x (/.f64 -1/2 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (log.f64 (fma.f64 2 x (/.f64 -1/2 x)))) 2) (cbrt.f64 (log.f64 (fma.f64 2 x (/.f64 -1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (log.f64 (fma.f64 2 x (/.f64 -1/2 x)))) (sqrt.f64 (log.f64 (fma.f64 2 x (/.f64 -1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (log.f64 (fma.f64 2 x (/.f64 -1/2 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (log.f64 (fma.f64 2 x (/.f64 -1/2 x))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (log.f64 (fma.f64 2 x (/.f64 -1/2 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (log.f64 (fma.f64 2 x (/.f64 -1/2 x)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (log.f64 (fma.f64 2 x (/.f64 -1/2 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (log.f64 (fma.f64 2 x (/.f64 -1/2 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (log.f64 (fma.f64 2 x (/.f64 -1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (-.f64 (fma.f64 2 x (/.f64 -1/2 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (log.f64 (fma.f64 2 x (/.f64 -1/2 x)))))))))

simplify161.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

660×	`fma-def_binary64`
585×	`times-frac_binary64`
411×	`associate-+l-_binary64`
293×	`sub-neg_binary64`
285×	`unswap-sqr_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	60	282
1	165	264
2	487	262
3	1672	258
4	6271	258

Stop Event

1×	node limit

Counts

32 → 44

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

eval134.0ms (3.5%)

Compiler: Compiled 669 to 528 computations (21.1% saved)

prune6.0ms (0.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	44	0	44
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	44	3	47

Error

Counts

47 → 3

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.7b	(log.f64 (+.f64 x x))
✓	0.3b	(log.f64 (-.f64 (*.f64 2 x) (/.f64 1/2 x)))
✓	33.2b	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))

Compiler

Compiled 24 to 17 computations (29.2% saved)

regimes18.0ms (0.5%)

Accuracy

Total -33.6b remaining (-9801.5%)

Threshold costs -33.6b (-9801.5%)

Counts

5 → 1

Calls

Call 1

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

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

Calls

3 calls:

8.0ms	x
4.0ms	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
4.0ms	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))

Results

Error	Segments	Branch
0.3b	1	`x`
0.3b	1	`(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))`
0.3b	1	`(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))`

Compiler

Compiled 61 to 42 computations (31.1% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`distribute-neg-frac_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	18
1	13	18
2	21	18
3	23	18
4	24	18

Stop Event

1×	done
1×	saturated

Calls

Call 1

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

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

Compiler

Compiled 14 to 10 computations (28.6% saved)

soundness0.0ms (0%)

end36.0ms (0.9%)

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

Details

analyze261.0ms (6.9%)

sample2.1s (55.8%)

preprocess147.0ms (3.9%)

simplify131.0ms (3.5%)

eval1.0ms (0%)

prune1.0ms (0%)

localize14.0ms (0.4%)

series3.0ms (0.1%)

rewrite77.0ms (2%)

simplify59.0ms (1.6%)

eval33.0ms (0.9%)

prune22.0ms (0.6%)

localize7.0ms (0.2%)

localize13.0ms (0.3%)

series4.0ms (0.1%)

rewrite88.0ms (2.3%)

simplify62.0ms (1.6%)

localize18.0ms (0.5%)

series3.0ms (0.1%)

rewrite67.0ms (1.8%)

simplify55.0ms (1.4%)

eval109.0ms (2.9%)

prune47.0ms (1.2%)

localize30.0ms (0.8%)

series2.0ms (0.1%)

rewrite64.0ms (1.7%)

simplify161.0ms (4.2%)

eval134.0ms (3.5%)

prune6.0ms (0.2%)

regimes18.0ms (0.5%)

simplify6.0ms (0.2%)

soundness0.0ms (0%)

end36.0ms (0.9%)

Profiling