Details

analyze7.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	49.7%	50.3%	0
0%	49.7%	50.3%	1
0%	49.7%	50.3%	2
24.8%	24.8%	50.3%	3
37.3%	12.4%	50.3%	4
43.5%	6.2%	50.3%	5
46.6%	3.1%	50.3%	6
48.1%	1.6%	50.3%	7
48.9%	0.8%	50.3%	8
49.3%	0.4%	50.3%	9
49.5%	0.2%	50.3%	10
49.6%	0.1%	50.3%	11
49.6%	0%	50.3%	12

Compiler

Compiled 16 to 12 computations (25% saved)

sample10.9s (68.9%)

Results

8.6s	4099×	body	2048	valid
1.4s	2070×	body	1024	valid
408.0ms	1083×	body	512	valid
337.0ms	221×	body	4096	valid
108.0ms	783×	body	256	valid

preprocess21.0ms (0.1%)

Algorithm

2×	egg-herbie

Rules

39×	`fma-def_binary64`
32×	`fma-neg_binary64`
15×	`cancel-sign-sub-inv_binary64`
12×	`sub-neg_binary64`
10×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	11	12
2	17	12
3	25	12
4	35	12
5	53	12
6	90	12
7	124	12
8	168	12
9	204	12
10	230	12
11	232	12
0	1	1

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0

Outputs
0

Call 2

Inputs
(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))

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

Compiler

Compiled 10 to 8 computations (20% saved)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

39×	`fma-def_binary64`
32×	`fma-neg_binary64`
15×	`cancel-sign-sub-inv_binary64`
12×	`sub-neg_binary64`
10×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	11	12
2	17	12
3	25	12
4	35	12
5	53	12
6	90	12
7	124	12
8	168	12
9	204	12
10	230	12
11	232	12

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

Inputs
(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))

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

eval1.0ms (0%)

Compiler: Compiled 17 to 12 computations (29.4% saved)

prune2.0ms (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

60.1b

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	60.1b	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))

Compiler

Compiled 9 to 7 computations (22.2% saved)

localize12.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	3.7b	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))

Compiler

Compiled 20 to 12 computations (40% saved)

series5.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))
2.0ms	x	@	0	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))
2.0ms	x	@	-inf	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))

rewrite77.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

883×	`pow1_binary64`
823×	`add-log-exp_binary64`
823×	`log1p-expm1-u_binary64`
823×	`expm1-log1p-u_binary64`
805×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	160	12
2	2365	12

Stop Event

1×	node limit

Counts

1 → 43

Calls

Call 1

Inputs
(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))

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

Outputs

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

simplify160.0ms (1%)

Algorithm

1×	egg-herbie

Rules

675×	`sqr-pow_binary64`
624×	`unswap-sqr_binary64`
594×	`cube-prod_binary64`
554×	`fma-def_binary64`
417×	`fabs-mul_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	30	168
1	74	162
2	153	162
3	367	162
4	677	162
5	1437	162
6	2099	162
7	3090	162
8	3307	162
9	3633	162
10	4034	162
11	4566	162
12	5297	162
13	6300	162
14	6946	162
15	7455	162
16	7858	162

Stop Event

1×	node limit

Counts

55 → 54

Calls

Call 1

Inputs
(*.f64 1/3 x)
(+.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3)))
(+.f64 (.f64 1/3 x) (+.f64 (.f64 2/945 (pow.f64 x 5)) (*.f64 1/45 (pow.f64 x 3))))
(+.f64 (.f64 1/3 x) (+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 1/4725 (pow.f64 x 7)))))
(*.f64 -1 (/.f64 (cos.f64 x) (sin.f64 x)))
(+.f64 (*.f64 -1 (/.f64 (cos.f64 x) (sin.f64 x))) (/.f64 1 x))
(+.f64 (*.f64 -1 (/.f64 (cos.f64 x) (sin.f64 x))) (/.f64 1 x))
(+.f64 (*.f64 -1 (/.f64 (cos.f64 x) (sin.f64 x))) (/.f64 1 x))
(*.f64 -1 (/.f64 (cos.f64 x) (sin.f64 x)))
(+.f64 (*.f64 -1 (/.f64 (cos.f64 x) (sin.f64 x))) (/.f64 1 x))
(+.f64 (*.f64 -1 (/.f64 (cos.f64 x) (sin.f64 x))) (/.f64 1 x))
(+.f64 (*.f64 -1 (/.f64 (cos.f64 x) (sin.f64 x))) (/.f64 1 x))

Outputs
(*.f64 1/3 x)
(+.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3)))
(fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))
(.f64 x (fma.f64 x (.f64 x 1/45) 1/3))
(.f64 x (fma.f64 1/45 (.f64 x x) 1/3))
(+.f64 (.f64 1/3 x) (+.f64 (.f64 2/945 (pow.f64 x 5)) (*.f64 1/45 (pow.f64 x 3))))
(fma.f64 1/3 x (fma.f64 2/945 (pow.f64 x 5) (*.f64 1/45 (pow.f64 x 3))))
(fma.f64 1/3 x (fma.f64 1/45 (pow.f64 x 3) (*.f64 2/945 (pow.f64 x 5))))
(fma.f64 x (fma.f64 x (.f64 x 1/45) 1/3) (.f64 2/945 (pow.f64 x 5)))
(fma.f64 x (fma.f64 1/45 (.f64 x x) 1/3) (.f64 2/945 (pow.f64 x 5)))
(+.f64 (.f64 1/3 x) (+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 1/4725 (pow.f64 x 7)))))
(fma.f64 1/3 x (fma.f64 2/945 (pow.f64 x 5) (fma.f64 1/45 (pow.f64 x 3) (*.f64 1/4725 (pow.f64 x 7)))))
(fma.f64 1/45 (pow.f64 x 3) (fma.f64 2/945 (pow.f64 x 5) (fma.f64 1/3 x (*.f64 1/4725 (pow.f64 x 7)))))
(fma.f64 1/3 x (fma.f64 1/45 (pow.f64 x 3) (fma.f64 2/945 (pow.f64 x 5) (*.f64 1/4725 (pow.f64 x 7)))))
(fma.f64 2/945 (pow.f64 x 5) (fma.f64 1/4725 (pow.f64 x 7) (.f64 x (fma.f64 1/45 (.f64 x x) 1/3))))
(*.f64 -1 (/.f64 (cos.f64 x) (sin.f64 x)))
(neg.f64 (/.f64 (cos.f64 x) (sin.f64 x)))
(/.f64 (neg.f64 (cos.f64 x)) (sin.f64 x))
(+.f64 (*.f64 -1 (/.f64 (cos.f64 x) (sin.f64 x))) (/.f64 1 x))
(fma.f64 -1 (/.f64 (cos.f64 x) (sin.f64 x)) (/.f64 1 x))
(-.f64 (/.f64 1 x) (/.f64 (cos.f64 x) (sin.f64 x)))
(+.f64 (*.f64 -1 (/.f64 (cos.f64 x) (sin.f64 x))) (/.f64 1 x))
(fma.f64 -1 (/.f64 (cos.f64 x) (sin.f64 x)) (/.f64 1 x))
(-.f64 (/.f64 1 x) (/.f64 (cos.f64 x) (sin.f64 x)))
(+.f64 (*.f64 -1 (/.f64 (cos.f64 x) (sin.f64 x))) (/.f64 1 x))
(fma.f64 -1 (/.f64 (cos.f64 x) (sin.f64 x)) (/.f64 1 x))
(-.f64 (/.f64 1 x) (/.f64 (cos.f64 x) (sin.f64 x)))
(*.f64 -1 (/.f64 (cos.f64 x) (sin.f64 x)))
(neg.f64 (/.f64 (cos.f64 x) (sin.f64 x)))
(/.f64 (neg.f64 (cos.f64 x)) (sin.f64 x))
(+.f64 (*.f64 -1 (/.f64 (cos.f64 x) (sin.f64 x))) (/.f64 1 x))
(fma.f64 -1 (/.f64 (cos.f64 x) (sin.f64 x)) (/.f64 1 x))
(-.f64 (/.f64 1 x) (/.f64 (cos.f64 x) (sin.f64 x)))
(+.f64 (*.f64 -1 (/.f64 (cos.f64 x) (sin.f64 x))) (/.f64 1 x))
(fma.f64 -1 (/.f64 (cos.f64 x) (sin.f64 x)) (/.f64 1 x))
(-.f64 (/.f64 1 x) (/.f64 (cos.f64 x) (sin.f64 x)))
(+.f64 (*.f64 -1 (/.f64 (cos.f64 x) (sin.f64 x))) (/.f64 1 x))
(fma.f64 -1 (/.f64 (cos.f64 x) (sin.f64 x)) (/.f64 1 x))
(-.f64 (/.f64 1 x) (/.f64 (cos.f64 x) (sin.f64 x)))

eval47.0ms (0.3%)

Compiler: Compiled 777 to 491 computations (36.8% saved)

prune21.0ms (0.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	49	5	54
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	49	6	55

Error

0.3b

Counts

55 → 6

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.6b	(*.f64 1/3 x)
✓	60.1b	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))
▶	60.1b	(/.f64 (/.f64 (-.f64 (tan.f64 x) x) x) (tan.f64 x))
▶	0.4b	(+.f64 (.f64 1/3 x) (+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 1/4725 (pow.f64 x 7)))))
▶	0.4b	(+.f64 (.f64 1/3 x) (+.f64 (.f64 2/945 (pow.f64 x 5)) (*.f64 1/45 (pow.f64 x 3))))
▶	0.4b	(.f64 x (fma.f64 1/45 (.f64 x x) 1/3))

Compiler

Compiled 131 to 97 computations (26% saved)

localize87.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 2/945 (pow.f64 x 5))
✓	0.1b	(*.f64 1/4725 (pow.f64 x 7))
✓	0.1b	(*.f64 1/45 (pow.f64 x 3))
✓	0.4b	(*.f64 1/3 x)

Compiler

Compiled 85 to 68 computations (20% saved)

series14.0ms (0.1%)

Counts

4 → 0

Calls

12 calls:

Time	Variable		Point	Expression
2.0ms	x	@	0	(*.f64 1/45 (pow.f64 x 3))
1.0ms	x	@	0	(*.f64 1/4725 (pow.f64 x 7))
1.0ms	x	@	0	(*.f64 2/945 (pow.f64 x 5))
1.0ms	x	@	inf	(*.f64 1/3 x)
1.0ms	x	@	0	(*.f64 1/3 x)

rewrite93.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

622×	`log-prod_binary64`
378×	`pow2_binary64`
307×	`pow-prod-down_binary64`
266×	`expm1-udef_binary64`
266×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	25
1	344	25
2	3538	25

Stop Event

1×	node limit

Counts

4 → 80

Calls

Call 1

Inputs
(*.f64 1/3 x)
(*.f64 1/45 (pow.f64 x 3))
(*.f64 1/4725 (pow.f64 x 7))
(*.f64 2/945 (pow.f64 x 5))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 1/3 x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (exp.f64 x))) 2)) (log.f64 (cbrt.f64 (cbrt.f64 (exp.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (cbrt.f64 (exp.f64 x)))) (log.f64 (sqrt.f64 (cbrt.f64 (exp.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 1/3 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 1/3 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (.f64 x x) 1/9) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 1/3 x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 1/3 x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 1/3 x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (.f64 (.f64 x x) 1/9))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (cbrt.f64 (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 1/3 x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 1/3 x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 1/3 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 1/3 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 1/3 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 1/3 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 3 (log.f64 (.f64 1/3 x))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 1/3 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 1/3 x))) 2))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 1/45 (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 1/45) (pow.f64 x 3))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 1/45) (pow.f64 x 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 1/45) (pow.f64 x 3)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 1/45) (pow.f64 x 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 1/45 (pow.f64 x 3)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 1/45 (pow.f64 x 3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 1/2025 (pow.f64 x 6)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 x (cbrt.f64 1/45)) 9) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 x (cbrt.f64 1/45)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (sqrt.f64 1/45) (pow.f64 x 3/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (.f64 1/2025 (pow.f64 x 6)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 1/45) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 1/45 (pow.f64 x 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 x (cbrt.f64 1/45)) 9))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 1/45 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 1/45 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 1/45 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 1/45 (pow.f64 x 3))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (pow.f64 (.f64 x (cbrt.f64 1/45)) 9)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 x (cbrt.f64 1/45))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (*.f64 (sqrt.f64 1/45) (pow.f64 x 3/2))) 2))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 1/4725 (pow.f64 x 7)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 1/4725) (pow.f64 x 7))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 1/4725) (pow.f64 x 7)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 1/4725) (pow.f64 x 7)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 1/4725) (pow.f64 x 7)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 1/4725 (pow.f64 x 7)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 1/4725 (pow.f64 x 7)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 1/22325625 (pow.f64 x 14)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 1/4725 (pow.f64 x 7)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 1/4725 (pow.f64 x 7))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (sqrt.f64 1/4725) (pow.f64 x 7/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (.f64 1/22325625 (pow.f64 x 14)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 1/4725) (pow.f64 x 7)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 1/4725 (pow.f64 x 7)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 1/4725 (pow.f64 x 7)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 1/4725 (pow.f64 x 7))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 1/4725 (pow.f64 x 7))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (fma.f64 7 (log.f64 x) (log.f64 1/4725)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (fma.f64 7 (log.f64 x) (log.f64 1/4725)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 3 (fma.f64 7 (log.f64 x) (log.f64 1/4725))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 1/4725 (pow.f64 x 7)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (*.f64 (sqrt.f64 1/4725) (pow.f64 x 7/2))) 2))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 2/945 (pow.f64 x 5)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 2/945) (pow.f64 x 5))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 2/945) (pow.f64 x 5)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 2/945) (pow.f64 x 5)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 2/945) (pow.f64 x 5)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 2/945 (pow.f64 x 5)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 2/945 (pow.f64 x 5)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 x 10) 4/893025) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 2/945 (pow.f64 x 5)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 2/945 (pow.f64 x 5))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (sqrt.f64 2/945) (pow.f64 x 5/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (.f64 (pow.f64 x 10) 4/893025))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 2/945) (pow.f64 x 5)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 2/945 (pow.f64 x 5)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 2/945 (pow.f64 x 5)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 2/945 (pow.f64 x 5))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 2/945 (pow.f64 x 5))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (fma.f64 5 (log.f64 x) (log.f64 2/945)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (fma.f64 5 (log.f64 x) (log.f64 2/945)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 3 (fma.f64 5 (log.f64 x) (log.f64 2/945))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 2/945 (pow.f64 x 5)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (*.f64 (sqrt.f64 2/945) (pow.f64 x 5/2))) 2))))))

simplify15.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

80 → 80

Calls

Call 1

Inputs

Outputs

localize5.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
	0.4b	(*.f64 1/3 x)

Compiler

Compiled 6 to 4 computations (33.3% saved)

localize52.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 1/45 (*.f64 x x) 1/3)
✓	0.3b	(.f64 x (fma.f64 1/45 (.f64 x x) 1/3))

Compiler

Compiled 21 to 11 computations (47.6% saved)

series5.0ms (0%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(.f64 x (fma.f64 1/45 (.f64 x x) 1/3))
1.0ms	x	@	inf	(.f64 x (fma.f64 1/45 (.f64 x x) 1/3))
1.0ms	x	@	-inf	(.f64 x (fma.f64 1/45 (.f64 x x) 1/3))
1.0ms	x	@	0	(fma.f64 1/45 (*.f64 x x) 1/3)
0.0ms	x	@	inf	(fma.f64 1/45 (*.f64 x x) 1/3)

rewrite64.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

612×	`pow1_binary64`
570×	`add-log-exp_binary64`
570×	`log1p-expm1-u_binary64`
570×	`expm1-log1p-u_binary64`
559×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	19
1	142	19
2	1571	19

Stop Event

1×	node limit

Counts

2 → 34

Calls

Call 1

Inputs
(.f64 x (fma.f64 1/45 (.f64 x x) 1/3))
(fma.f64 1/45 (*.f64 x x) 1/3)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 1/45 (*.f64 x x)) x) (*.f64 1/3 x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x (*.f64 1/45 (*.f64 x x))) (*.f64 x 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 x (fma.f64 1/45 (*.f64 x x) 1/3))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (fma.f64 1/45 (*.f64 x x) 1/3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x (fma.f64 1/45 (*.f64 x x) 1/3)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x (fma.f64 1/45 (*.f64 x x) 1/3))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 x (fma.f64 1/45 (*.f64 x x) 1/3))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 x (fma.f64 1/45 (*.f64 x x) 1/3)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (fma.f64 1/45 (*.f64 x x) 1/3)) x))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x (fma.f64 1/45 (*.f64 x x) 1/3)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x (fma.f64 1/45 (*.f64 x x) 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x (fma.f64 1/45 (*.f64 x x) 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x (fma.f64 1/45 (*.f64 x x) 1/3))))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 1/3 (*.f64 1/45 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 1/45 (*.f64 x x)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 1/45 (*.f64 x x)) 1) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (fma.f64 1/45 (*.f64 x x) 1/3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 1/45 (*.f64 x x) 1/3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 1/45 (*.f64 x x) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 1/45 (*.f64 x x) 1/3)) (pow.f64 (cbrt.f64 (fma.f64 1/45 (*.f64 x x) 1/3)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 1/45 (*.f64 x x) 1/3)) 2) (cbrt.f64 (fma.f64 1/45 (*.f64 x x) 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 1/45 (*.f64 x x) 1/3)) (sqrt.f64 (fma.f64 1/45 (*.f64 x x) 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 1/45 (*.f64 x x)) 3) 1/27) (+.f64 (*.f64 (*.f64 1/45 (*.f64 x x)) (*.f64 1/45 (*.f64 x x))) (-.f64 1/9 (*.f64 (*.f64 1/45 (*.f64 x x)) 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 1/45 (*.f64 x x)) (*.f64 1/45 (*.f64 x x))) 1/9) (-.f64 (*.f64 1/45 (*.f64 x x)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 1/45 (*.f64 x x) 1/3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 1/45 (*.f64 x x) 1/3) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 1/45 (*.f64 x x) 1/3)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 1/45 (*.f64 x x) 1/3)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 1/45 (*.f64 x x) 1/3) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 1/45 (*.f64 x x) 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 1/45 (*.f64 x x) 1/3) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 1/45 (*.f64 x x) 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 1/45 (*.f64 x x) 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 1/45 (*.f64 x x) 1/3)))))))

simplify170.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

944×	`sqr-pow_binary64`
564×	`cube-prod_binary64`
536×	`unswap-sqr_binary64`
534×	`fabs-mul_binary64`
502×	`pow-sqr_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	222
1	31	204
2	61	204
3	134	204
4	336	204
5	1386	204
6	2757	204
7	2943	204
8	3194	204
9	3481	204
10	3860	204
11	4370	204
12	4977	204
13	5689	204
14	6160	204
15	6481	204
16	6753	204
17	6921	204
18	7013	204
19	7690	204

Stop Event

1×	node limit

Counts

58 → 43

Calls

Call 1

Inputs
(*.f64 1/3 x)
(+.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3)))
(+.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3)))
(+.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3)))
(*.f64 1/45 (pow.f64 x 3))
(+.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3)))
(+.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3)))
(+.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3)))
(*.f64 1/45 (pow.f64 x 3))
(+.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3)))
(+.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3)))
(+.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3)))
1/3
(+.f64 1/3 (*.f64 1/45 (pow.f64 x 2)))
(+.f64 1/3 (*.f64 1/45 (pow.f64 x 2)))
(+.f64 1/3 (*.f64 1/45 (pow.f64 x 2)))
(*.f64 1/45 (pow.f64 x 2))
(+.f64 1/3 (*.f64 1/45 (pow.f64 x 2)))
(+.f64 1/3 (*.f64 1/45 (pow.f64 x 2)))
(+.f64 1/3 (*.f64 1/45 (pow.f64 x 2)))
(*.f64 1/45 (pow.f64 x 2))
(+.f64 1/3 (*.f64 1/45 (pow.f64 x 2)))
(+.f64 1/3 (*.f64 1/45 (pow.f64 x 2)))
(+.f64 1/3 (*.f64 1/45 (pow.f64 x 2)))

Outputs
(*.f64 1/3 x)
(+.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3)))
(fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))
(fma.f64 1/45 (pow.f64 x 3) (*.f64 1/3 x))
(.f64 x (fma.f64 1/45 (.f64 x x) 1/3))
(.f64 x (fma.f64 x (.f64 x 1/45) 1/3))
(+.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3)))
(fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))
(fma.f64 1/45 (pow.f64 x 3) (*.f64 1/3 x))
(.f64 x (fma.f64 1/45 (.f64 x x) 1/3))
(.f64 x (fma.f64 x (.f64 x 1/45) 1/3))
(+.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3)))
(fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))
(fma.f64 1/45 (pow.f64 x 3) (*.f64 1/3 x))
(.f64 x (fma.f64 1/45 (.f64 x x) 1/3))
(.f64 x (fma.f64 x (.f64 x 1/45) 1/3))
(*.f64 1/45 (pow.f64 x 3))
(+.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3)))
(fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))
(fma.f64 1/45 (pow.f64 x 3) (*.f64 1/3 x))
(.f64 x (fma.f64 1/45 (.f64 x x) 1/3))
(.f64 x (fma.f64 x (.f64 x 1/45) 1/3))
(+.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3)))
(fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))
(fma.f64 1/45 (pow.f64 x 3) (*.f64 1/3 x))
(.f64 x (fma.f64 1/45 (.f64 x x) 1/3))
(.f64 x (fma.f64 x (.f64 x 1/45) 1/3))
(+.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3)))
(fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))
(fma.f64 1/45 (pow.f64 x 3) (*.f64 1/3 x))
(.f64 x (fma.f64 1/45 (.f64 x x) 1/3))
(.f64 x (fma.f64 x (.f64 x 1/45) 1/3))
(*.f64 1/45 (pow.f64 x 3))
(+.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3)))
(fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))
(fma.f64 1/45 (pow.f64 x 3) (*.f64 1/3 x))
(.f64 x (fma.f64 1/45 (.f64 x x) 1/3))
(.f64 x (fma.f64 x (.f64 x 1/45) 1/3))
(+.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3)))
(fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))
(fma.f64 1/45 (pow.f64 x 3) (*.f64 1/3 x))
(.f64 x (fma.f64 1/45 (.f64 x x) 1/3))
(.f64 x (fma.f64 x (.f64 x 1/45) 1/3))
(+.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3)))
(fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))
(fma.f64 1/45 (pow.f64 x 3) (*.f64 1/3 x))
(.f64 x (fma.f64 1/45 (.f64 x x) 1/3))
(.f64 x (fma.f64 x (.f64 x 1/45) 1/3))
1/3
(+.f64 1/3 (*.f64 1/45 (pow.f64 x 2)))
(+.f64 1/3 (.f64 1/45 (.f64 x x)))
(fma.f64 1/45 (*.f64 x x) 1/3)
(fma.f64 x (*.f64 x 1/45) 1/3)
(+.f64 1/3 (*.f64 1/45 (pow.f64 x 2)))
(+.f64 1/3 (.f64 1/45 (.f64 x x)))
(fma.f64 1/45 (*.f64 x x) 1/3)
(fma.f64 x (*.f64 x 1/45) 1/3)
(+.f64 1/3 (*.f64 1/45 (pow.f64 x 2)))
(+.f64 1/3 (.f64 1/45 (.f64 x x)))
(fma.f64 1/45 (*.f64 x x) 1/3)
(fma.f64 x (*.f64 x 1/45) 1/3)
(*.f64 1/45 (pow.f64 x 2))
(.f64 1/45 (.f64 x x))
(.f64 x (.f64 x 1/45))
(+.f64 1/3 (*.f64 1/45 (pow.f64 x 2)))
(+.f64 1/3 (.f64 1/45 (.f64 x x)))
(fma.f64 1/45 (*.f64 x x) 1/3)
(fma.f64 x (*.f64 x 1/45) 1/3)
(+.f64 1/3 (*.f64 1/45 (pow.f64 x 2)))
(+.f64 1/3 (.f64 1/45 (.f64 x x)))
(fma.f64 1/45 (*.f64 x x) 1/3)
(fma.f64 x (*.f64 x 1/45) 1/3)
(+.f64 1/3 (*.f64 1/45 (pow.f64 x 2)))
(+.f64 1/3 (.f64 1/45 (.f64 x x)))
(fma.f64 1/45 (*.f64 x x) 1/3)
(fma.f64 x (*.f64 x 1/45) 1/3)
(*.f64 1/45 (pow.f64 x 2))
(.f64 1/45 (.f64 x x))
(.f64 x (.f64 x 1/45))
(+.f64 1/3 (*.f64 1/45 (pow.f64 x 2)))
(+.f64 1/3 (.f64 1/45 (.f64 x x)))
(fma.f64 1/45 (*.f64 x x) 1/3)
(fma.f64 x (*.f64 x 1/45) 1/3)
(+.f64 1/3 (*.f64 1/45 (pow.f64 x 2)))
(+.f64 1/3 (.f64 1/45 (.f64 x x)))
(fma.f64 1/45 (*.f64 x x) 1/3)
(fma.f64 x (*.f64 x 1/45) 1/3)
(+.f64 1/3 (*.f64 1/45 (pow.f64 x 2)))
(+.f64 1/3 (.f64 1/45 (.f64 x x)))
(fma.f64 1/45 (*.f64 x x) 1/3)
(fma.f64 x (*.f64 x 1/45) 1/3)

localize7.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 (tan.f64 x) x) x)
✓	0.0b	(/.f64 (/.f64 (-.f64 (tan.f64 x) x) x) (tan.f64 x))
✓	3.7b	(-.f64 (tan.f64 x) x)

Compiler

Compiled 23 to 5 computations (78.3% saved)

series6.0ms (0%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
2.0ms	x	@	0	(/.f64 (/.f64 (-.f64 (tan.f64 x) x) x) (tan.f64 x))
1.0ms	x	@	-inf	(/.f64 (/.f64 (-.f64 (tan.f64 x) x) x) (tan.f64 x))
1.0ms	x	@	inf	(/.f64 (/.f64 (-.f64 (tan.f64 x) x) x) (tan.f64 x))
1.0ms	x	@	0	(-.f64 (tan.f64 x) x)
0.0ms	x	@	0	(/.f64 (-.f64 (tan.f64 x) x) x)

rewrite76.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

496×	`prod-diff_binary64`
436×	`log-prod_binary64`
333×	`exp-prod_binary64`
283×	`pow-prod-down_binary64`
214×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	29
1	148	29
2	2504	29

Stop Event

1×	node limit

Counts

3 → 218

Calls

Call 1

Inputs
(-.f64 (tan.f64 x) x)
(/.f64 (/.f64 (-.f64 (tan.f64 x) x) x) (tan.f64 x))
(/.f64 (-.f64 (tan.f64 x) x) x)

Outputs

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

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

simplify87.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

845×	`fma-def_binary64`
740×	`distribute-lft-out_binary64`
721×	`associate-l_binary64`
698×	`distribute-rgt-out_binary64`
555×	`associate-r_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	66	478
1	167	460
2	391	460
3	1150	460
4	4432	460
5	6918	460
6	7856	460

Stop Event

1×	node limit

Counts

254 → 251

Calls

Call 1

Inputs
(*.f64 1/3 (pow.f64 x 3))
(+.f64 (.f64 1/3 (pow.f64 x 3)) (.f64 2/15 (pow.f64 x 5)))
(+.f64 (.f64 17/315 (pow.f64 x 7)) (+.f64 (.f64 1/3 (pow.f64 x 3)) (*.f64 2/15 (pow.f64 x 5))))
(+.f64 (.f64 17/315 (pow.f64 x 7)) (+.f64 (.f64 1/3 (pow.f64 x 3)) (+.f64 (.f64 62/2835 (pow.f64 x 9)) (.f64 2/15 (pow.f64 x 5)))))
(*.f64 -1 x)
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 -1 x))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 -1 x))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 -1 x))
(*.f64 -1 x)
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 -1 x))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 -1 x))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 -1 x))
(*.f64 1/3 x)
(+.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3)))
(+.f64 (.f64 1/3 x) (+.f64 (.f64 2/945 (pow.f64 x 5)) (*.f64 1/45 (pow.f64 x 3))))
(+.f64 (.f64 1/3 x) (+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 1/4725 (pow.f64 x 7)))))
(*.f64 -1 (/.f64 (cos.f64 x) (sin.f64 x)))
(+.f64 (*.f64 -1 (/.f64 (cos.f64 x) (sin.f64 x))) (/.f64 1 x))
(+.f64 (*.f64 -1 (/.f64 (cos.f64 x) (sin.f64 x))) (/.f64 1 x))
(+.f64 (*.f64 -1 (/.f64 (cos.f64 x) (sin.f64 x))) (/.f64 1 x))
(*.f64 -1 (/.f64 (cos.f64 x) (sin.f64 x)))
(+.f64 (*.f64 -1 (/.f64 (cos.f64 x) (sin.f64 x))) (/.f64 1 x))
(+.f64 (*.f64 -1 (/.f64 (cos.f64 x) (sin.f64 x))) (/.f64 1 x))
(+.f64 (*.f64 -1 (/.f64 (cos.f64 x) (sin.f64 x))) (/.f64 1 x))
(*.f64 1/3 (pow.f64 x 2))
(+.f64 (.f64 1/3 (pow.f64 x 2)) (.f64 2/15 (pow.f64 x 4)))
(+.f64 (.f64 17/315 (pow.f64 x 6)) (+.f64 (.f64 1/3 (pow.f64 x 2)) (*.f64 2/15 (pow.f64 x 4))))
(+.f64 (.f64 17/315 (pow.f64 x 6)) (+.f64 (.f64 62/2835 (pow.f64 x 8)) (+.f64 (.f64 1/3 (pow.f64 x 2)) (.f64 2/15 (pow.f64 x 4)))))
-1
(-.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)) 1)
(-.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)) 1)
(-.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)) 1)
-1
(-.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)) 1)
(-.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)) 1)
(-.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)) 1)

Outputs
(*.f64 1/3 (pow.f64 x 3))
(+.f64 (.f64 1/3 (pow.f64 x 3)) (.f64 2/15 (pow.f64 x 5)))
(fma.f64 1/3 (pow.f64 x 3) (*.f64 2/15 (pow.f64 x 5)))
(+.f64 (.f64 17/315 (pow.f64 x 7)) (+.f64 (.f64 1/3 (pow.f64 x 3)) (*.f64 2/15 (pow.f64 x 5))))
(fma.f64 17/315 (pow.f64 x 7) (fma.f64 1/3 (pow.f64 x 3) (*.f64 2/15 (pow.f64 x 5))))
(fma.f64 1/3 (pow.f64 x 3) (fma.f64 2/15 (pow.f64 x 5) (*.f64 17/315 (pow.f64 x 7))))
(+.f64 (.f64 17/315 (pow.f64 x 7)) (+.f64 (.f64 1/3 (pow.f64 x 3)) (+.f64 (.f64 62/2835 (pow.f64 x 9)) (.f64 2/15 (pow.f64 x 5)))))
(fma.f64 17/315 (pow.f64 x 7) (fma.f64 1/3 (pow.f64 x 3) (fma.f64 62/2835 (pow.f64 x 9) (*.f64 2/15 (pow.f64 x 5)))))
(fma.f64 1/3 (pow.f64 x 3) (fma.f64 17/315 (pow.f64 x 7) (fma.f64 2/15 (pow.f64 x 5) (*.f64 62/2835 (pow.f64 x 9)))))
(fma.f64 1/3 (pow.f64 x 3) (fma.f64 2/15 (pow.f64 x 5) (fma.f64 17/315 (pow.f64 x 7) (*.f64 62/2835 (pow.f64 x 9)))))
(*.f64 -1 x)
(neg.f64 x)
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 -1 x))
(+.f64 (neg.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)))
(-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) x)
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 -1 x))
(+.f64 (neg.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)))
(-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) x)
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 -1 x))
(+.f64 (neg.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)))
(-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) x)
(*.f64 -1 x)
(neg.f64 x)
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 -1 x))
(+.f64 (neg.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)))
(-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) x)
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 -1 x))
(+.f64 (neg.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)))
(-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) x)
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 -1 x))
(+.f64 (neg.f64 x) (/.f64 (sin.f64 x) (cos.f64 x)))
(-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) x)
(*.f64 1/3 x)
(+.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3)))
(fma.f64 1/3 x (*.f64 (pow.f64 x 3) 1/45))
(fma.f64 (pow.f64 x 3) 1/45 (*.f64 1/3 x))
(.f64 x (fma.f64 x (.f64 x 1/45) 1/3))
(+.f64 (.f64 1/3 x) (+.f64 (.f64 2/945 (pow.f64 x 5)) (*.f64 1/45 (pow.f64 x 3))))
(fma.f64 1/3 x (fma.f64 2/945 (pow.f64 x 5) (*.f64 (pow.f64 x 3) 1/45)))
(fma.f64 1/3 x (fma.f64 (pow.f64 x 3) 1/45 (*.f64 (pow.f64 x 5) 2/945)))
(+.f64 (.f64 1/3 x) (+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 1/4725 (pow.f64 x 7)))))
(fma.f64 1/3 x (fma.f64 2/945 (pow.f64 x 5) (fma.f64 1/45 (pow.f64 x 3) (*.f64 (pow.f64 x 7) 1/4725))))
(fma.f64 1/3 x (fma.f64 (pow.f64 x 5) 2/945 (fma.f64 (pow.f64 x 3) 1/45 (*.f64 (pow.f64 x 7) 1/4725))))
(*.f64 -1 (/.f64 (cos.f64 x) (sin.f64 x)))
(neg.f64 (/.f64 (cos.f64 x) (sin.f64 x)))
(/.f64 (neg.f64 (cos.f64 x)) (sin.f64 x))
(+.f64 (*.f64 -1 (/.f64 (cos.f64 x) (sin.f64 x))) (/.f64 1 x))
(fma.f64 -1 (/.f64 (cos.f64 x) (sin.f64 x)) (/.f64 1 x))
(-.f64 (/.f64 1 x) (/.f64 (cos.f64 x) (sin.f64 x)))
(+.f64 (*.f64 -1 (/.f64 (cos.f64 x) (sin.f64 x))) (/.f64 1 x))
(fma.f64 -1 (/.f64 (cos.f64 x) (sin.f64 x)) (/.f64 1 x))
(-.f64 (/.f64 1 x) (/.f64 (cos.f64 x) (sin.f64 x)))
(+.f64 (*.f64 -1 (/.f64 (cos.f64 x) (sin.f64 x))) (/.f64 1 x))
(fma.f64 -1 (/.f64 (cos.f64 x) (sin.f64 x)) (/.f64 1 x))
(-.f64 (/.f64 1 x) (/.f64 (cos.f64 x) (sin.f64 x)))
(*.f64 -1 (/.f64 (cos.f64 x) (sin.f64 x)))
(neg.f64 (/.f64 (cos.f64 x) (sin.f64 x)))
(/.f64 (neg.f64 (cos.f64 x)) (sin.f64 x))
(+.f64 (*.f64 -1 (/.f64 (cos.f64 x) (sin.f64 x))) (/.f64 1 x))
(fma.f64 -1 (/.f64 (cos.f64 x) (sin.f64 x)) (/.f64 1 x))
(-.f64 (/.f64 1 x) (/.f64 (cos.f64 x) (sin.f64 x)))
(+.f64 (*.f64 -1 (/.f64 (cos.f64 x) (sin.f64 x))) (/.f64 1 x))
(fma.f64 -1 (/.f64 (cos.f64 x) (sin.f64 x)) (/.f64 1 x))
(-.f64 (/.f64 1 x) (/.f64 (cos.f64 x) (sin.f64 x)))
(+.f64 (*.f64 -1 (/.f64 (cos.f64 x) (sin.f64 x))) (/.f64 1 x))
(fma.f64 -1 (/.f64 (cos.f64 x) (sin.f64 x)) (/.f64 1 x))
(-.f64 (/.f64 1 x) (/.f64 (cos.f64 x) (sin.f64 x)))
(*.f64 1/3 (pow.f64 x 2))
(.f64 1/3 (.f64 x x))
(+.f64 (.f64 1/3 (pow.f64 x 2)) (.f64 2/15 (pow.f64 x 4)))
(fma.f64 1/3 (.f64 x x) (.f64 2/15 (pow.f64 x 4)))
(+.f64 (.f64 17/315 (pow.f64 x 6)) (+.f64 (.f64 1/3 (pow.f64 x 2)) (*.f64 2/15 (pow.f64 x 4))))
(fma.f64 17/315 (pow.f64 x 6) (fma.f64 1/3 (.f64 x x) (.f64 2/15 (pow.f64 x 4))))
(fma.f64 1/3 (.f64 x x) (fma.f64 2/15 (pow.f64 x 4) (.f64 17/315 (pow.f64 x 6))))
(+.f64 (.f64 17/315 (pow.f64 x 6)) (+.f64 (.f64 62/2835 (pow.f64 x 8)) (+.f64 (.f64 1/3 (pow.f64 x 2)) (.f64 2/15 (pow.f64 x 4)))))
(fma.f64 17/315 (pow.f64 x 6) (fma.f64 62/2835 (pow.f64 x 8) (fma.f64 1/3 (.f64 x x) (.f64 2/15 (pow.f64 x 4)))))
(fma.f64 17/315 (pow.f64 x 6) (fma.f64 2/15 (pow.f64 x 4) (fma.f64 1/3 (.f64 x x) (.f64 62/2835 (pow.f64 x 8)))))
(fma.f64 2/15 (pow.f64 x 4) (fma.f64 x (.f64 1/3 x) (fma.f64 62/2835 (pow.f64 x 8) (.f64 17/315 (pow.f64 x 6)))))
-1
(-.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)) 1)
(+.f64 (/.f64 (sin.f64 x) (*.f64 x (cos.f64 x))) -1)
(+.f64 -1 (/.f64 (sin.f64 x) (*.f64 x (cos.f64 x))))
(-.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)) 1)
(+.f64 (/.f64 (sin.f64 x) (*.f64 x (cos.f64 x))) -1)
(+.f64 -1 (/.f64 (sin.f64 x) (*.f64 x (cos.f64 x))))
(-.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)) 1)
(+.f64 (/.f64 (sin.f64 x) (*.f64 x (cos.f64 x))) -1)
(+.f64 -1 (/.f64 (sin.f64 x) (*.f64 x (cos.f64 x))))
-1
(-.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)) 1)
(+.f64 (/.f64 (sin.f64 x) (*.f64 x (cos.f64 x))) -1)
(+.f64 -1 (/.f64 (sin.f64 x) (*.f64 x (cos.f64 x))))
(-.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)) 1)
(+.f64 (/.f64 (sin.f64 x) (*.f64 x (cos.f64 x))) -1)
(+.f64 -1 (/.f64 (sin.f64 x) (*.f64 x (cos.f64 x))))
(-.f64 (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) x)) 1)
(+.f64 (/.f64 (sin.f64 x) (*.f64 x (cos.f64 x))) -1)
(+.f64 -1 (/.f64 (sin.f64 x) (*.f64 x (cos.f64 x))))

localize25.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.1b	(*.f64 2/945 (pow.f64 x 5))
	0.1b	(*.f64 1/45 (pow.f64 x 3))
	0.4b	(*.f64 1/3 x)

Compiler

Compiled 52 to 41 computations (21.2% saved)

eval150.0ms (0.9%)

Compiler: Compiled 7729 to 4498 computations (41.8% saved)

prune66.0ms (0.4%)

Pruning

14 alts after pruning (9 fresh and 5 done)

	Pruned	Kept	Total
New	445	9	454
Fresh	0	0	0
Picked	0	1	1
Done	1	4	5
Total	446	14	460

Error

0.2b

Counts

460 → 14

Alt Table

Click to see full alt table

Status	Error	Program
▶	28.7b	(/.f64 (.f64 1/3 (.f64 x x)) (tan.f64 x))
✓	60.1b	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))
	1.8b	(pow.f64 (cbrt.f64 (*.f64 1/3 x)) 3)
✓	0.4b	(+.f64 (.f64 1/3 x) (+.f64 (.f64 2/945 (pow.f64 x 5)) (*.f64 1/45 (pow.f64 x 3))))
▶	0.4b	(.f64 x (+.f64 (.f64 1/45 (*.f64 x x)) 1/3))
▶	31.6b	(pow.f64 (sqrt.f64 (*.f64 1/3 x)) 2)
	42.4b	(sqrt.f64 (.f64 (.f64 x x) 1/9))
✓	0.6b	(*.f64 1/3 x)
▶	38.2b	(cbrt.f64 (pow.f64 (*.f64 1/3 x) 3))
✓	60.1b	(/.f64 (/.f64 (-.f64 (tan.f64 x) x) x) (tan.f64 x))
▶	0.4b	(.f64 x (/.f64 (+.f64 (pow.f64 (.f64 1/45 (.f64 x x)) 3) 1/27) (+.f64 (.f64 (.f64 1/45 (.f64 x x)) (.f64 1/45 (.f64 x x))) (-.f64 1/9 (.f64 (.f64 1/45 (*.f64 x x)) 1/3)))))
	34.1b	(exp.f64 (log.f64 (*.f64 1/3 x)))
	38.1b	(/.f64 (/.f64 (*.f64 1/3 (pow.f64 x 3)) x) (tan.f64 x))
✓	0.4b	(+.f64 (.f64 1/3 x) (+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 1/4725 (pow.f64 x 7)))))

Compiler

Compiled 257 to 188 computations (26.8% saved)

localize55.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(pow.f64 (.f64 1/45 (.f64 x x)) 3)
✓	0.1b	(.f64 1/45 (.f64 x x))
✓	0.2b	(.f64 (.f64 1/45 (*.f64 x x)) 1/3)
✓	0.3b	(.f64 x (/.f64 (+.f64 (pow.f64 (.f64 1/45 (.f64 x x)) 3) 1/27) (+.f64 (.f64 (.f64 1/45 (.f64 x x)) (.f64 1/45 (.f64 x x))) (-.f64 1/9 (.f64 (.f64 1/45 (*.f64 x x)) 1/3)))))

Compiler

Compiled 143 to 85 computations (40.6% saved)

series6.0ms (0%)

Counts

4 → 48

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(.f64 x (/.f64 (+.f64 (pow.f64 (.f64 1/45 (.f64 x x)) 3) 1/27) (+.f64 (.f64 (.f64 1/45 (.f64 x x)) (.f64 1/45 (.f64 x x))) (-.f64 1/9 (.f64 (.f64 1/45 (*.f64 x x)) 1/3)))))
1.0ms	x	@	0	(.f64 x (/.f64 (+.f64 (pow.f64 (.f64 1/45 (.f64 x x)) 3) 1/27) (+.f64 (.f64 (.f64 1/45 (.f64 x x)) (.f64 1/45 (.f64 x x))) (-.f64 1/9 (.f64 (.f64 1/45 (*.f64 x x)) 1/3)))))
0.0ms	x	@	0	(pow.f64 (.f64 1/45 (.f64 x x)) 3)
0.0ms	x	@	inf	(.f64 (.f64 1/45 (*.f64 x x)) 1/3)
0.0ms	x	@	-inf	(.f64 x (/.f64 (+.f64 (pow.f64 (.f64 1/45 (.f64 x x)) 3) 1/27) (+.f64 (.f64 (.f64 1/45 (.f64 x x)) (.f64 1/45 (.f64 x x))) (-.f64 1/9 (.f64 (.f64 1/45 (*.f64 x x)) 1/3)))))

rewrite88.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

652×	`fma-def_binary64`
384×	`fma-neg_binary64`
319×	`expm1-udef_binary64`
319×	`log1p-udef_binary64`
252×	`log-pow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	70
1	400	51
2	5359	51

Stop Event

1×	node limit

Counts

4 → 87

Calls

Call 1

Inputs
(.f64 x (/.f64 (+.f64 (pow.f64 (.f64 1/45 (.f64 x x)) 3) 1/27) (+.f64 (.f64 (.f64 1/45 (.f64 x x)) (.f64 1/45 (.f64 x x))) (-.f64 1/9 (.f64 (.f64 1/45 (*.f64 x x)) 1/3)))))
(.f64 (.f64 1/45 (*.f64 x x)) 1/3)
(.f64 1/45 (.f64 x x))
(pow.f64 (.f64 1/45 (.f64 x x)) 3)

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 x (/.f64 (-.f64 (fma.f64 1/2025 (pow.f64 x 4) 1/9) (.f64 (.f64 x x) 1/135)) (fma.f64 1/91125 (pow.f64 x 6) 1/27))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 x (/.f64 (-.f64 (fma.f64 1/2025 (pow.f64 x 4) 1/9) (.f64 (.f64 x x) 1/135)) (fma.f64 1/91125 (pow.f64 x 6) 1/27)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (fma.f64 1/2025 (pow.f64 x 4) 1/9) (.f64 (.f64 x x) 1/135)) (.f64 x (fma.f64 1/91125 (pow.f64 x 6) 1/27))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 x (fma.f64 1/91125 (pow.f64 x 6) 1/27)) (-.f64 (fma.f64 1/2025 (pow.f64 x 4) 1/9) (.f64 (.f64 x x) 1/135)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (.f64 x (fma.f64 1/91125 (pow.f64 x 6) 1/27))) (neg.f64 (-.f64 (fma.f64 1/2025 (pow.f64 x 4) 1/9) (.f64 (.f64 x x) 1/135))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (.f64 x (fma.f64 1/91125 (pow.f64 x 6) 1/27)) 1) (-.f64 (fma.f64 1/2025 (pow.f64 x 4) 1/9) (.f64 (.f64 x x) 1/135)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (.f64 x (fma.f64 1/91125 (pow.f64 x 6) 1/27)) (pow.f64 (cbrt.f64 (-.f64 (fma.f64 1/2025 (pow.f64 x 4) 1/9) (.f64 (.f64 x x) 1/135))) 2)) (cbrt.f64 (-.f64 (fma.f64 1/2025 (pow.f64 x 4) 1/9) (.f64 (.f64 x x) 1/135))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (.f64 x (fma.f64 1/91125 (pow.f64 x 6) 1/27)) (sqrt.f64 (-.f64 (fma.f64 1/2025 (pow.f64 x 4) 1/9) (.f64 (.f64 x x) 1/135)))) (sqrt.f64 (-.f64 (fma.f64 1/2025 (pow.f64 x 4) 1/9) (.f64 (.f64 x x) 1/135))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (neg.f64 (fma.f64 1/91125 (pow.f64 x 6) 1/27)) x) (neg.f64 (-.f64 (fma.f64 1/2025 (pow.f64 x 4) 1/9) (.f64 (.f64 x x) 1/135))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 x (neg.f64 (fma.f64 1/91125 (pow.f64 x 6) 1/27))) (neg.f64 (-.f64 (fma.f64 1/2025 (pow.f64 x 4) 1/9) (.f64 (.f64 x x) 1/135))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 x (/.f64 (-.f64 (fma.f64 1/2025 (pow.f64 x 4) 1/9) (.f64 (.f64 x x) 1/135)) (fma.f64 1/91125 (pow.f64 x 6) 1/27))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 x (/.f64 (-.f64 (fma.f64 1/2025 (pow.f64 x 4) 1/9) (.f64 (.f64 x x) 1/135)) (fma.f64 1/91125 (pow.f64 x 6) 1/27))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 x (/.f64 (-.f64 (fma.f64 1/2025 (pow.f64 x 4) 1/9) (.f64 (.f64 x x) 1/135)) (fma.f64 1/91125 (pow.f64 x 6) 1/27)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 x (/.f64 (-.f64 (fma.f64 1/2025 (pow.f64 x 4) 1/9) (.f64 (.f64 x x) 1/135)) (fma.f64 1/91125 (pow.f64 x 6) 1/27)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 x (/.f64 (-.f64 (fma.f64 1/2025 (pow.f64 x 4) 1/9) (.f64 (.f64 x x) 1/135)) (fma.f64 1/91125 (pow.f64 x 6) 1/27))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 x) (/.f64 (fma.f64 1/91125 (pow.f64 x 6) 1/27) (-.f64 (fma.f64 1/2025 (pow.f64 x 4) 1/9) (.f64 (.f64 x x) 1/135)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 x (/.f64 (-.f64 (fma.f64 1/2025 (pow.f64 x 4) 1/9) (.f64 (.f64 x x) 1/135)) (fma.f64 1/91125 (pow.f64 x 6) 1/27))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 x (/.f64 (-.f64 (fma.f64 1/2025 (pow.f64 x 4) 1/9) (.f64 (.f64 x x) 1/135)) (fma.f64 1/91125 (pow.f64 x 6) 1/27))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 x 3) (pow.f64 (/.f64 (fma.f64 1/91125 (pow.f64 x 6) 1/27) (-.f64 (fma.f64 1/2025 (pow.f64 x 4) 1/9) (.f64 (.f64 x x) 1/135))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (/.f64 (fma.f64 1/91125 (pow.f64 x 6) 1/27) (-.f64 (fma.f64 1/2025 (pow.f64 x 4) 1/9) (.f64 (.f64 x x) 1/135))) 3) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 x (/.f64 (-.f64 (fma.f64 1/2025 (pow.f64 x 4) 1/9) (.f64 (.f64 x x) 1/135)) (fma.f64 1/91125 (pow.f64 x 6) 1/27)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 x (/.f64 (-.f64 (fma.f64 1/2025 (pow.f64 x 4) 1/9) (.f64 (.f64 x x) 1/135)) (fma.f64 1/91125 (pow.f64 x 6) 1/27)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 x (/.f64 (-.f64 (fma.f64 1/2025 (pow.f64 x 4) 1/9) (.f64 (.f64 x x) 1/135)) (fma.f64 1/91125 (pow.f64 x 6) 1/27)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (/.f64 x (/.f64 (-.f64 (fma.f64 1/2025 (pow.f64 x 4) 1/9) (.f64 (*.f64 x x) 1/135)) (fma.f64 1/91125 (pow.f64 x 6) 1/27)))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 (.f64 x x) 1/135))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (.f64 x x) 1/135) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 (.f64 x x) 1/135)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 (.f64 x x) 1/135)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (.f64 1/91125 (pow.f64 x 6)) 1/27) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (.f64 (.f64 1/2025 (pow.f64 x 4)) 1/9))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (.f64 (.f64 x x) 1/135)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 (.f64 x x) 1/135))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (.f64 1/91125 (pow.f64 x 6)) 1/27))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 (.f64 x x) 1/135)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 (.f64 x x) 1/135)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 (.f64 x x) 1/135)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 (*.f64 x x) 1/135)) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 x (.f64 x 1/45)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 x (.f64 x 1/45)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 1/91125 (pow.f64 x 6)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 1/2025 (pow.f64 x 4)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 x (.f64 x 1/45))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 x (sqrt.f64 1/45)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (.f64 1/2025 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (.f64 x (.f64 x 1/45)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 1/45) (.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 x (.f64 x 1/45)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 1/91125 (pow.f64 x 6)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 x (.f64 x 1/45))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 x (.f64 x 1/45))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 x (.f64 x 1/45))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 x (*.f64 x 1/45))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 1/91125 (pow.f64 x 6)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/45 (.f64 (.f64 x x) (.f64 1/2025 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/45 (.f64 (.f64 (pow.f64 x 4) 1/45) (.f64 x (.f64 x 1/45))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 x x) (.f64 1/45 (.f64 1/2025 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 x (.f64 x 1/45)) (.f64 1/2025 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 1/91125 (pow.f64 x 6)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 1/2025 (pow.f64 x 4)) (.f64 x (.f64 x 1/45)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (.f64 1/91125 (pow.f64 x 6)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/2025 (.f64 (pow.f64 x 4) (.f64 x (.f64 x 1/45))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/91125 (pow.f64 x 6))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (.f64 1/2025 (pow.f64 x 4))) (.f64 (cbrt.f64 (.f64 x (.f64 x 1/45))) (.f64 1/2025 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (.f64 1/2025 (pow.f64 x 4))) 2) (.f64 (cbrt.f64 (.f64 1/2025 (pow.f64 x 4))) (.f64 x (.f64 x 1/45))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 x (sqrt.f64 1/45)) (.f64 (.f64 x (sqrt.f64 1/45)) (.f64 1/2025 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 x 6) 1/91125)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (.f64 1/91125 (pow.f64 x 6))) (sqrt.f64 (.f64 1/91125 (pow.f64 x 6))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 x 1/45) (.f64 x (.f64 1/2025 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (.f64 x x) 1/2025) (.f64 (pow.f64 x 4) 1/45))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 x (sqrt.f64 1/45)) 3) (pow.f64 (.f64 x (sqrt.f64 1/45)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 x 1/45) 3) (pow.f64 x 3))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (.f64 1/2025 (pow.f64 x 4)) 1/45) (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (.f64 x (.f64 x 1/45)) 1/2025) (pow.f64 x 4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (.f64 x (.f64 x 1/45)) (pow.f64 (cbrt.f64 (.f64 1/2025 (pow.f64 x 4))) 2)) (cbrt.f64 (.f64 1/2025 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (.f64 x (.f64 x 1/45)) (.f64 (.f64 x x) 1/2025)) (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (.f64 1/2025 (pow.f64 x 4)) (.f64 x x)) 1/45)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (.f64 1/2025 (pow.f64 x 4)) (cbrt.f64 (.f64 1/2025 (pow.f64 x 4)))) (cbrt.f64 (.f64 x (.f64 x 1/45))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (.f64 1/2025 (pow.f64 x 4)) (.f64 x (sqrt.f64 1/45))) (.f64 x (sqrt.f64 1/45)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (.f64 1/2025 (pow.f64 x 4)) (.f64 x 1/45)) x)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (.f64 x (.f64 x 1/45)) 6))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 1/91125) (pow.f64 x 6)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 1/91125 (pow.f64 x 6)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 1/756680642578125 (pow.f64 (pow.f64 x 6) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 1/91125 (pow.f64 x 6))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 1/91125 (pow.f64 x 6))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 1/91125 (pow.f64 x 6))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 1/91125 (pow.f64 x 6))) 1))))))

simplify153.0ms (1%)

Algorithm

1×	egg-herbie

Rules

810×	`sqr-pow_binary64`
793×	`cube-prod_binary64`
598×	`fabs-mul_binary64`
467×	`unswap-sqr_binary64`
415×	`unpow3_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	369
1	39	369
2	91	369
3	275	369
4	1244	369
5	2325	369
6	2492	369
7	2757	369
8	3021	369
9	3367	369
10	3826	369
11	4352	369
12	4992	369
13	5758	369
14	6201	369
15	6699	369
16	7207	369
17	7753	369

Stop Event

1×	node limit

Counts

135 → 95

Calls

Call 1

Inputs
(*.f64 1/3 x)
(+.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3)))
(+.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3)))
(+.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3)))
(*.f64 1/45 (pow.f64 x 3))
(+.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3)))
(+.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3)))
(+.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3)))
(*.f64 1/45 (pow.f64 x 3))
(+.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3)))
(+.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3)))
(+.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3)))
(*.f64 1/135 (pow.f64 x 2))
(*.f64 1/135 (pow.f64 x 2))
(*.f64 1/135 (pow.f64 x 2))
(*.f64 1/135 (pow.f64 x 2))
(*.f64 1/135 (pow.f64 x 2))
(*.f64 1/135 (pow.f64 x 2))
(*.f64 1/135 (pow.f64 x 2))
(*.f64 1/135 (pow.f64 x 2))
(*.f64 1/135 (pow.f64 x 2))
(*.f64 1/135 (pow.f64 x 2))
(*.f64 1/135 (pow.f64 x 2))
(*.f64 1/135 (pow.f64 x 2))
(*.f64 1/45 (pow.f64 x 2))
(*.f64 1/45 (pow.f64 x 2))
(*.f64 1/45 (pow.f64 x 2))
(*.f64 1/45 (pow.f64 x 2))
(*.f64 1/45 (pow.f64 x 2))
(*.f64 1/45 (pow.f64 x 2))
(*.f64 1/45 (pow.f64 x 2))
(*.f64 1/45 (pow.f64 x 2))
(*.f64 1/45 (pow.f64 x 2))
(*.f64 1/45 (pow.f64 x 2))
(*.f64 1/45 (pow.f64 x 2))
(*.f64 1/45 (pow.f64 x 2))
(*.f64 1/91125 (pow.f64 x 6))
(*.f64 1/91125 (pow.f64 x 6))
(*.f64 1/91125 (pow.f64 x 6))
(*.f64 1/91125 (pow.f64 x 6))
(*.f64 1/91125 (pow.f64 x 6))
(*.f64 1/91125 (pow.f64 x 6))
(*.f64 1/91125 (pow.f64 x 6))
(*.f64 1/91125 (pow.f64 x 6))
(*.f64 1/91125 (pow.f64 x 6))
(*.f64 1/91125 (pow.f64 x 6))
(*.f64 1/91125 (pow.f64 x 6))
(*.f64 1/91125 (pow.f64 x 6))

Outputs
(*.f64 1/3 x)
(+.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3)))
(fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))
(fma.f64 1/45 (pow.f64 x 3) (*.f64 1/3 x))
(.f64 x (fma.f64 x (.f64 x 1/45) 1/3))
(+.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3)))
(fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))
(fma.f64 1/45 (pow.f64 x 3) (*.f64 1/3 x))
(.f64 x (fma.f64 x (.f64 x 1/45) 1/3))
(+.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3)))
(fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))
(fma.f64 1/45 (pow.f64 x 3) (*.f64 1/3 x))
(.f64 x (fma.f64 x (.f64 x 1/45) 1/3))
(*.f64 1/45 (pow.f64 x 3))
(+.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3)))
(fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))
(fma.f64 1/45 (pow.f64 x 3) (*.f64 1/3 x))
(.f64 x (fma.f64 x (.f64 x 1/45) 1/3))
(+.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3)))
(fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))
(fma.f64 1/45 (pow.f64 x 3) (*.f64 1/3 x))
(.f64 x (fma.f64 x (.f64 x 1/45) 1/3))
(+.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3)))
(fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))
(fma.f64 1/45 (pow.f64 x 3) (*.f64 1/3 x))
(.f64 x (fma.f64 x (.f64 x 1/45) 1/3))
(*.f64 1/45 (pow.f64 x 3))
(+.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3)))
(fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))
(fma.f64 1/45 (pow.f64 x 3) (*.f64 1/3 x))
(.f64 x (fma.f64 x (.f64 x 1/45) 1/3))
(+.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3)))
(fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))
(fma.f64 1/45 (pow.f64 x 3) (*.f64 1/3 x))
(.f64 x (fma.f64 x (.f64 x 1/45) 1/3))
(+.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3)))
(fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))
(fma.f64 1/45 (pow.f64 x 3) (*.f64 1/3 x))
(.f64 x (fma.f64 x (.f64 x 1/45) 1/3))
(*.f64 1/135 (pow.f64 x 2))
(.f64 1/135 (.f64 x x))
(.f64 x (.f64 x 1/135))
(*.f64 1/135 (pow.f64 x 2))
(.f64 1/135 (.f64 x x))
(.f64 x (.f64 x 1/135))
(*.f64 1/135 (pow.f64 x 2))
(.f64 1/135 (.f64 x x))
(.f64 x (.f64 x 1/135))
(*.f64 1/135 (pow.f64 x 2))
(.f64 1/135 (.f64 x x))
(.f64 x (.f64 x 1/135))
(*.f64 1/135 (pow.f64 x 2))
(.f64 1/135 (.f64 x x))
(.f64 x (.f64 x 1/135))
(*.f64 1/135 (pow.f64 x 2))
(.f64 1/135 (.f64 x x))
(.f64 x (.f64 x 1/135))
(*.f64 1/135 (pow.f64 x 2))
(.f64 1/135 (.f64 x x))
(.f64 x (.f64 x 1/135))
(*.f64 1/135 (pow.f64 x 2))
(.f64 1/135 (.f64 x x))
(.f64 x (.f64 x 1/135))
(*.f64 1/135 (pow.f64 x 2))
(.f64 1/135 (.f64 x x))
(.f64 x (.f64 x 1/135))
(*.f64 1/135 (pow.f64 x 2))
(.f64 1/135 (.f64 x x))
(.f64 x (.f64 x 1/135))
(*.f64 1/135 (pow.f64 x 2))
(.f64 1/135 (.f64 x x))
(.f64 x (.f64 x 1/135))
(*.f64 1/135 (pow.f64 x 2))
(.f64 1/135 (.f64 x x))
(.f64 x (.f64 x 1/135))
(*.f64 1/45 (pow.f64 x 2))
(.f64 1/45 (.f64 x x))
(.f64 x (.f64 x 1/45))
(*.f64 1/45 (pow.f64 x 2))
(.f64 1/45 (.f64 x x))
(.f64 x (.f64 x 1/45))
(*.f64 1/45 (pow.f64 x 2))
(.f64 1/45 (.f64 x x))
(.f64 x (.f64 x 1/45))
(*.f64 1/45 (pow.f64 x 2))
(.f64 1/45 (.f64 x x))
(.f64 x (.f64 x 1/45))
(*.f64 1/45 (pow.f64 x 2))
(.f64 1/45 (.f64 x x))
(.f64 x (.f64 x 1/45))
(*.f64 1/45 (pow.f64 x 2))
(.f64 1/45 (.f64 x x))
(.f64 x (.f64 x 1/45))
(*.f64 1/45 (pow.f64 x 2))
(.f64 1/45 (.f64 x x))
(.f64 x (.f64 x 1/45))
(*.f64 1/45 (pow.f64 x 2))
(.f64 1/45 (.f64 x x))
(.f64 x (.f64 x 1/45))
(*.f64 1/45 (pow.f64 x 2))
(.f64 1/45 (.f64 x x))
(.f64 x (.f64 x 1/45))
(*.f64 1/45 (pow.f64 x 2))
(.f64 1/45 (.f64 x x))
(.f64 x (.f64 x 1/45))
(*.f64 1/45 (pow.f64 x 2))
(.f64 1/45 (.f64 x x))
(.f64 x (.f64 x 1/45))
(*.f64 1/45 (pow.f64 x 2))
(.f64 1/45 (.f64 x x))
(.f64 x (.f64 x 1/45))
(*.f64 1/91125 (pow.f64 x 6))
(*.f64 1/91125 (pow.f64 x 6))
(*.f64 1/91125 (pow.f64 x 6))
(*.f64 1/91125 (pow.f64 x 6))
(*.f64 1/91125 (pow.f64 x 6))
(*.f64 1/91125 (pow.f64 x 6))
(*.f64 1/91125 (pow.f64 x 6))
(*.f64 1/91125 (pow.f64 x 6))
(*.f64 1/91125 (pow.f64 x 6))
(*.f64 1/91125 (pow.f64 x 6))
(*.f64 1/91125 (pow.f64 x 6))
(*.f64 1/91125 (pow.f64 x 6))

localize42.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 1/45 (.f64 x x)) 1/3)
	0.1b	(.f64 1/45 (.f64 x x))
✓	0.3b	(.f64 x (+.f64 (.f64 1/45 (*.f64 x x)) 1/3))

Compiler

Compiled 28 to 15 computations (46.4% saved)

series2.0ms (0%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(.f64 x (+.f64 (.f64 1/45 (*.f64 x x)) 1/3))
0.0ms	x	@	inf	(.f64 x (+.f64 (.f64 1/45 (*.f64 x x)) 1/3))
0.0ms	x	@	-inf	(.f64 x (+.f64 (.f64 1/45 (*.f64 x x)) 1/3))
0.0ms	x	@	inf	(+.f64 (.f64 1/45 (.f64 x x)) 1/3)
0.0ms	x	@	-inf	(+.f64 (.f64 1/45 (.f64 x x)) 1/3)

rewrite61.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

894×	`pow1_binary64`
840×	`add-log-exp_binary64`
840×	`log1p-expm1-u_binary64`
840×	`expm1-log1p-u_binary64`
824×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	181	19
2	2330	19

Stop Event

1×	node limit

Counts

2 → 57

Calls

Call 1

Inputs
(.f64 x (+.f64 (.f64 1/45 (*.f64 x x)) 1/3))
(+.f64 (.f64 1/45 (.f64 x x)) 1/3)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 1/45 (pow.f64 x 3)) (*.f64 x 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x 1/3) (*.f64 1/45 (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 1/45 (pow.f64 x 3)) 1) (*.f64 (*.f64 x 1/3) 1))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 x (fma.f64 (*.f64 x 1/45) x 1/3))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 1/45 (pow.f64 x 3)) 3) (pow.f64 (*.f64 x 1/3) 3)) (+.f64 (*.f64 (*.f64 1/45 (pow.f64 x 3)) (*.f64 1/45 (pow.f64 x 3))) (-.f64 (*.f64 (*.f64 x 1/3) (*.f64 x 1/3)) (*.f64 (*.f64 1/45 (pow.f64 x 3)) (*.f64 x 1/3)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 1/45 (pow.f64 x 3)) (*.f64 1/45 (pow.f64 x 3))) (*.f64 (*.f64 x 1/3) (*.f64 x 1/3))) (-.f64 (*.f64 1/45 (pow.f64 x 3)) (*.f64 x 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 1/27 (pow.f64 (*.f64 x (*.f64 x 1/45)) 3)) x) (+.f64 (*.f64 1/2025 (pow.f64 x 4)) (-.f64 1/9 (*.f64 (*.f64 x x) 1/135))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (*.f64 1/2025 (pow.f64 x 4)) -1/9) x) (fma.f64 1/45 (*.f64 x x) -1/3))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 x (+.f64 1/27 (pow.f64 (*.f64 x (*.f64 x 1/45)) 3))) (+.f64 (*.f64 1/2025 (pow.f64 x 4)) (-.f64 1/9 (*.f64 (*.f64 x x) 1/135))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 x (+.f64 (*.f64 1/2025 (pow.f64 x 4)) -1/9)) (fma.f64 1/45 (*.f64 x x) -1/3))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (fma.f64 (*.f64 x 1/45) x 1/3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x (fma.f64 (*.f64 x 1/45) x 1/3)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x (fma.f64 (*.f64 x 1/45) x 1/3))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 x (fma.f64 (*.f64 x 1/45) x 1/3))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 x (fma.f64 (*.f64 x 1/45) x 1/3)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 x) (fma.f64 (*.f64 x 1/45) x 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x (fma.f64 (*.f64 x 1/45) x 1/3)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 x 3) (pow.f64 (fma.f64 (*.f64 x 1/45) x 1/3) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (fma.f64 (*.f64 x 1/45) x 1/3) 3) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x (fma.f64 (*.f64 x 1/45) x 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x (fma.f64 (*.f64 x 1/45) x 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x (fma.f64 (*.f64 x 1/45) x 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x (*.f64 x (*.f64 x 1/45)) (*.f64 x 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x (*.f64 x 1/45)) x (*.f64 x 1/3))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (fma.f64 (*.f64 x 1/45) x 1/3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (*.f64 1/2025 (pow.f64 x 4)) (fma.f64 1/45 (*.f64 x x) -1/3)) (/.f64 1/9 (fma.f64 1/45 (*.f64 x x) -1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 (*.f64 x 1/45) x 1/3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 (*.f64 x 1/45) x 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 (*.f64 x 1/45) x 1/3)) (pow.f64 (cbrt.f64 (fma.f64 (*.f64 x 1/45) x 1/3)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 (*.f64 x 1/45) x 1/3)) 2) (cbrt.f64 (fma.f64 (*.f64 x 1/45) x 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 (*.f64 x 1/45) x 1/3)) (sqrt.f64 (fma.f64 (*.f64 x 1/45) x 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1/27 (pow.f64 (*.f64 x (*.f64 x 1/45)) 3)) (/.f64 1 (+.f64 (*.f64 1/2025 (pow.f64 x 4)) (-.f64 1/9 (*.f64 (*.f64 x x) 1/135)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (*.f64 1/2025 (pow.f64 x 4)) -1/9) (/.f64 1 (fma.f64 1/45 (*.f64 x x) -1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (*.f64 1/2025 (pow.f64 x 4)) (-.f64 1/9 (*.f64 (*.f64 x x) 1/135))) (+.f64 1/27 (pow.f64 (*.f64 x (*.f64 x 1/45)) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 1/45 (*.f64 x x) -1/3) (+.f64 (*.f64 1/2025 (pow.f64 x 4)) -1/9)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1/27 (pow.f64 (*.f64 x (*.f64 x 1/45)) 3)) (+.f64 (*.f64 1/2025 (pow.f64 x 4)) (-.f64 1/9 (*.f64 (*.f64 x x) 1/135))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1/27 (pow.f64 (*.f64 x (*.f64 x 1/45)) 3)) (+.f64 1/9 (-.f64 (*.f64 1/2025 (pow.f64 x 4)) (*.f64 (*.f64 x x) 1/135))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 1/2025 (pow.f64 x 4)) -1/9) (fma.f64 1/45 (*.f64 x x) -1/3))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 1/27 (pow.f64 (*.f64 x (*.f64 x 1/45)) 3))) (neg.f64 (+.f64 (*.f64 1/2025 (pow.f64 x 4)) (-.f64 1/9 (*.f64 (*.f64 x x) 1/135)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (*.f64 1/2025 (pow.f64 x 4)) -1/9)) (neg.f64 (fma.f64 1/45 (*.f64 x x) -1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1/9 (*.f64 1/2025 (pow.f64 x 4))) (-.f64 1/3 (*.f64 x (*.f64 x 1/45))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 (*.f64 x 1/45) x 1/3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 (*.f64 x 1/45) x 1/3) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 (*.f64 x 1/45) x 1/3)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 (*.f64 x 1/45) x 1/3)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 (*.f64 x 1/45) x 1/3) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 (*.f64 x 1/45) x 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 (*.f64 x 1/45) x 1/3) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 (*.f64 x 1/45) x 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 (*.f64 x 1/45) x 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 (*.f64 x 1/45) x 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/45 (*.f64 x x) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x x) 1/45 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 x (*.f64 x 1/45)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 1/2025 (pow.f64 x 4))) (cbrt.f64 (*.f64 x (*.f64 x 1/45))) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x (sqrt.f64 1/45)) (*.f64 x (sqrt.f64 1/45)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x 1/45) x 1/3)))))

simplify169.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

944×	`sqr-pow_binary64`
564×	`cube-prod_binary64`
536×	`unswap-sqr_binary64`
534×	`fabs-mul_binary64`
502×	`pow-sqr_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	222
1	31	204
2	61	204
3	134	204
4	336	204
5	1386	204
6	2757	204
7	2943	204
8	3194	204
9	3481	204
10	3860	204
11	4370	204
12	4977	204
13	5689	204
14	6160	204
15	6481	204
16	6753	204
17	6921	204
18	7013	204
19	7690	204

Stop Event

1×	node limit

Counts

81 → 66

Calls

Call 1

Inputs
(*.f64 1/3 x)
(+.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3)))
(+.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3)))
(+.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3)))
(*.f64 1/45 (pow.f64 x 3))
(+.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3)))
(+.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3)))
(+.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3)))
(*.f64 1/45 (pow.f64 x 3))
(+.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3)))
(+.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3)))
(+.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3)))
1/3
(+.f64 1/3 (*.f64 1/45 (pow.f64 x 2)))
(+.f64 1/3 (*.f64 1/45 (pow.f64 x 2)))
(+.f64 1/3 (*.f64 1/45 (pow.f64 x 2)))
(*.f64 1/45 (pow.f64 x 2))
(+.f64 1/3 (*.f64 1/45 (pow.f64 x 2)))
(+.f64 1/3 (*.f64 1/45 (pow.f64 x 2)))
(+.f64 1/3 (*.f64 1/45 (pow.f64 x 2)))
(*.f64 1/45 (pow.f64 x 2))
(+.f64 1/3 (*.f64 1/45 (pow.f64 x 2)))
(+.f64 1/3 (*.f64 1/45 (pow.f64 x 2)))
(+.f64 1/3 (*.f64 1/45 (pow.f64 x 2)))

Outputs
(*.f64 1/3 x)
(+.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3)))
(fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))
(fma.f64 1/45 (pow.f64 x 3) (*.f64 1/3 x))
(.f64 x (fma.f64 1/45 (.f64 x x) 1/3))
(.f64 x (fma.f64 x (.f64 x 1/45) 1/3))
(+.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3)))
(fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))
(fma.f64 1/45 (pow.f64 x 3) (*.f64 1/3 x))
(.f64 x (fma.f64 1/45 (.f64 x x) 1/3))
(.f64 x (fma.f64 x (.f64 x 1/45) 1/3))
(+.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3)))
(fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))
(fma.f64 1/45 (pow.f64 x 3) (*.f64 1/3 x))
(.f64 x (fma.f64 1/45 (.f64 x x) 1/3))
(.f64 x (fma.f64 x (.f64 x 1/45) 1/3))
(*.f64 1/45 (pow.f64 x 3))
(+.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3)))
(fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))
(fma.f64 1/45 (pow.f64 x 3) (*.f64 1/3 x))
(.f64 x (fma.f64 1/45 (.f64 x x) 1/3))
(.f64 x (fma.f64 x (.f64 x 1/45) 1/3))
(+.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3)))
(fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))
(fma.f64 1/45 (pow.f64 x 3) (*.f64 1/3 x))
(.f64 x (fma.f64 1/45 (.f64 x x) 1/3))
(.f64 x (fma.f64 x (.f64 x 1/45) 1/3))
(+.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3)))
(fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))
(fma.f64 1/45 (pow.f64 x 3) (*.f64 1/3 x))
(.f64 x (fma.f64 1/45 (.f64 x x) 1/3))
(.f64 x (fma.f64 x (.f64 x 1/45) 1/3))
(*.f64 1/45 (pow.f64 x 3))
(+.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3)))
(fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))
(fma.f64 1/45 (pow.f64 x 3) (*.f64 1/3 x))
(.f64 x (fma.f64 1/45 (.f64 x x) 1/3))
(.f64 x (fma.f64 x (.f64 x 1/45) 1/3))
(+.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3)))
(fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))
(fma.f64 1/45 (pow.f64 x 3) (*.f64 1/3 x))
(.f64 x (fma.f64 1/45 (.f64 x x) 1/3))
(.f64 x (fma.f64 x (.f64 x 1/45) 1/3))
(+.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3)))
(fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))
(fma.f64 1/45 (pow.f64 x 3) (*.f64 1/3 x))
(.f64 x (fma.f64 1/45 (.f64 x x) 1/3))
(.f64 x (fma.f64 x (.f64 x 1/45) 1/3))
1/3
(+.f64 1/3 (*.f64 1/45 (pow.f64 x 2)))
(+.f64 1/3 (.f64 1/45 (.f64 x x)))
(fma.f64 1/45 (*.f64 x x) 1/3)
(fma.f64 x (*.f64 x 1/45) 1/3)
(+.f64 1/3 (*.f64 1/45 (pow.f64 x 2)))
(+.f64 1/3 (.f64 1/45 (.f64 x x)))
(fma.f64 1/45 (*.f64 x x) 1/3)
(fma.f64 x (*.f64 x 1/45) 1/3)
(+.f64 1/3 (*.f64 1/45 (pow.f64 x 2)))
(+.f64 1/3 (.f64 1/45 (.f64 x x)))
(fma.f64 1/45 (*.f64 x x) 1/3)
(fma.f64 x (*.f64 x 1/45) 1/3)
(*.f64 1/45 (pow.f64 x 2))
(.f64 1/45 (.f64 x x))
(.f64 x (.f64 x 1/45))
(+.f64 1/3 (*.f64 1/45 (pow.f64 x 2)))
(+.f64 1/3 (.f64 1/45 (.f64 x x)))
(fma.f64 1/45 (*.f64 x x) 1/3)
(fma.f64 x (*.f64 x 1/45) 1/3)
(+.f64 1/3 (*.f64 1/45 (pow.f64 x 2)))
(+.f64 1/3 (.f64 1/45 (.f64 x x)))
(fma.f64 1/45 (*.f64 x x) 1/3)
(fma.f64 x (*.f64 x 1/45) 1/3)
(+.f64 1/3 (*.f64 1/45 (pow.f64 x 2)))
(+.f64 1/3 (.f64 1/45 (.f64 x x)))
(fma.f64 1/45 (*.f64 x x) 1/3)
(fma.f64 x (*.f64 x 1/45) 1/3)
(*.f64 1/45 (pow.f64 x 2))
(.f64 1/45 (.f64 x x))
(.f64 x (.f64 x 1/45))
(+.f64 1/3 (*.f64 1/45 (pow.f64 x 2)))
(+.f64 1/3 (.f64 1/45 (.f64 x x)))
(fma.f64 1/45 (*.f64 x x) 1/3)
(fma.f64 x (*.f64 x 1/45) 1/3)
(+.f64 1/3 (*.f64 1/45 (pow.f64 x 2)))
(+.f64 1/3 (.f64 1/45 (.f64 x x)))
(fma.f64 1/45 (*.f64 x x) 1/3)
(fma.f64 x (*.f64 x 1/45) 1/3)
(+.f64 1/3 (*.f64 1/45 (pow.f64 x 2)))
(+.f64 1/3 (.f64 1/45 (.f64 x x)))
(fma.f64 1/45 (*.f64 x x) 1/3)
(fma.f64 x (*.f64 x 1/45) 1/3)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 1/3 (.f64 x x))
✓	28.3b	(/.f64 (.f64 1/3 (.f64 x x)) (tan.f64 x))

Compiler

Compiled 21 to 9 computations (57.1% saved)

series4.0ms (0%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(/.f64 (.f64 1/3 (.f64 x x)) (tan.f64 x))
1.0ms	x	@	-inf	(/.f64 (.f64 1/3 (.f64 x x)) (tan.f64 x))
1.0ms	x	@	0	(/.f64 (.f64 1/3 (.f64 x x)) (tan.f64 x))
0.0ms	x	@	inf	(.f64 1/3 (.f64 x x))
0.0ms	x	@	0	(.f64 1/3 (.f64 x x))

rewrite60.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

816×	`pow1_binary64`
762×	`add-log-exp_binary64`
762×	`log1p-expm1-u_binary64`
762×	`expm1-log1p-u_binary64`
746×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	19
1	152	19
2	2041	19

Stop Event

1×	node limit

Counts

2 → 57

Calls

Call 1

Inputs
(/.f64 (.f64 1/3 (.f64 x x)) (tan.f64 x))
(.f64 1/3 (.f64 x x))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 (/.f64 1/3 (tan.f64 x)) (*.f64 x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/3 (/.f64 (*.f64 x x) (tan.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/3 (/.f64 1 (/.f64 (tan.f64 x) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/3 (*.f64 (*.f64 x x) (/.f64 1 (tan.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x x) (*.f64 1/3 (/.f64 1 (tan.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 1/3 (*.f64 x x)) (/.f64 1 (tan.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 1/3 (tan.f64 x)) (*.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 (/.f64 1/3 (tan.f64 x)) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 1/9 (pow.f64 x 4))) (*.f64 (cbrt.f64 (*.f64 1/3 (*.f64 x x))) (/.f64 1 (tan.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (/.f64 1/3 (tan.f64 x)) (*.f64 x x))) (pow.f64 (cbrt.f64 (*.f64 (/.f64 1/3 (tan.f64 x)) (*.f64 x x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 (/.f64 1/3 (tan.f64 x)) (*.f64 x x))) 2) (cbrt.f64 (*.f64 (/.f64 1/3 (tan.f64 x)) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x (sqrt.f64 1/3)) (*.f64 (*.f64 x (sqrt.f64 1/3)) (/.f64 1 (tan.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 x (sqrt.f64 1/3)) (sqrt.f64 (tan.f64 x))) (/.f64 (*.f64 x (sqrt.f64 1/3)) (sqrt.f64 (tan.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (*.f64 x x) -1/3) (/.f64 1 (neg.f64 (tan.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (tan.f64 x)) (*.f64 1/3 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 1/3 x) (*.f64 x (/.f64 1 (tan.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 x x) 1) (/.f64 1/3 (tan.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1/3 (tan.f64 x)) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (*.f64 1/9 (pow.f64 x 4))) 1) (/.f64 (cbrt.f64 (*.f64 1/3 (*.f64 x x))) (tan.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 x (sqrt.f64 1/3)) 1) (/.f64 (*.f64 x (sqrt.f64 1/3)) (tan.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 1/3 x) 1) (/.f64 x (tan.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1/3 (pow.f64 (cbrt.f64 (tan.f64 x)) 2)) (/.f64 (*.f64 x x) (cbrt.f64 (tan.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 x x) (pow.f64 (cbrt.f64 (tan.f64 x)) 2)) (/.f64 1/3 (cbrt.f64 (tan.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 (tan.f64 x)) 2)) (/.f64 (*.f64 1/3 (*.f64 x x)) (cbrt.f64 (tan.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (*.f64 1/9 (pow.f64 x 4))) (pow.f64 (cbrt.f64 (tan.f64 x)) 2)) (cbrt.f64 (*.f64 (/.f64 1/3 (tan.f64 x)) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 x (sqrt.f64 1/3)) (pow.f64 (cbrt.f64 (tan.f64 x)) 2)) (/.f64 (*.f64 x (sqrt.f64 1/3)) (cbrt.f64 (tan.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 1/3 x) (pow.f64 (cbrt.f64 (tan.f64 x)) 2)) (/.f64 x (cbrt.f64 (tan.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1/3 (sqrt.f64 (tan.f64 x))) (/.f64 (*.f64 x x) (sqrt.f64 (tan.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 x x) (sqrt.f64 (tan.f64 x))) (/.f64 1/3 (sqrt.f64 (tan.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 (tan.f64 x))) (/.f64 (*.f64 1/3 (*.f64 x x)) (sqrt.f64 (tan.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (*.f64 1/9 (pow.f64 x 4))) (sqrt.f64 (tan.f64 x))) (/.f64 (cbrt.f64 (*.f64 1/3 (*.f64 x x))) (sqrt.f64 (tan.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 1/3 x) (sqrt.f64 (tan.f64 x))) (/.f64 x (sqrt.f64 (tan.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 1/3 (*.f64 x x)) (sin.f64 x)) (cos.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 1/3 (tan.f64 x)) (*.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (/.f64 1/3 (tan.f64 x)) (*.f64 x x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (/.f64 1/3 (tan.f64 x)) (*.f64 x x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (*.f64 x (sqrt.f64 1/3)) (sqrt.f64 (tan.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 3 (/.f64 (tan.f64 x) (*.f64 x x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (*.f64 1/3 (*.f64 x x)) (neg.f64 (tan.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (*.f64 1/9 (pow.f64 x 4)) (pow.f64 (tan.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (*.f64 (/.f64 1/3 (tan.f64 x)) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (/.f64 1/3 (tan.f64 x)) (*.f64 x x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (*.f64 1/3 (*.f64 x x)) 3) (pow.f64 (tan.f64 x) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (/.f64 1/3 (tan.f64 x)) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (/.f64 1/3 (tan.f64 x)) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (/.f64 1/3 (tan.f64 x)) (*.f64 x x))))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 1/3 (*.f64 x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 1/3 (*.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 1/3 (*.f64 x x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 1/3 (*.f64 x x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (sqrt.f64 1/3)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 1/9 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 1/3) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 1/3 (*.f64 x x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 1/3 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 1/3 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 1/3 (*.f64 x x))))))))

simplify104.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

613×	`associate-/l/_binary64`
596×	`associate-/r/_binary64`
586×	`associate-*r/_binary64`
439×	`unswap-sqr_binary64`
424×	`fma-def_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	278
1	77	278
2	178	278
3	477	278
4	1259	278
5	2378	278
6	5520	278
7	6078	278
8	6641	278
9	7088	278
10	7522	278

Stop Event

1×	node limit

Counts

81 → 68

Calls

Call 1

Inputs
(*.f64 1/3 x)
(+.f64 (.f64 -1/9 (pow.f64 x 3)) (.f64 1/3 x))
(+.f64 (.f64 -1/9 (pow.f64 x 3)) (+.f64 (.f64 -1/135 (pow.f64 x 5)) (*.f64 1/3 x)))
(+.f64 (.f64 -1/9 (pow.f64 x 3)) (+.f64 (.f64 -1/135 (pow.f64 x 5)) (+.f64 (.f64 1/3 x) (.f64 -2/2835 (pow.f64 x 7)))))
(.f64 1/3 (/.f64 (.f64 (cos.f64 x) (pow.f64 x 2)) (sin.f64 x)))
(.f64 1/3 (/.f64 (.f64 (cos.f64 x) (pow.f64 x 2)) (sin.f64 x)))
(.f64 1/3 (/.f64 (.f64 (cos.f64 x) (pow.f64 x 2)) (sin.f64 x)))
(.f64 1/3 (/.f64 (.f64 (cos.f64 x) (pow.f64 x 2)) (sin.f64 x)))
(.f64 1/3 (/.f64 (.f64 (cos.f64 x) (pow.f64 x 2)) (sin.f64 x)))
(.f64 1/3 (/.f64 (.f64 (cos.f64 x) (pow.f64 x 2)) (sin.f64 x)))
(.f64 1/3 (/.f64 (.f64 (cos.f64 x) (pow.f64 x 2)) (sin.f64 x)))
(.f64 1/3 (/.f64 (.f64 (cos.f64 x) (pow.f64 x 2)) (sin.f64 x)))
(*.f64 1/3 (pow.f64 x 2))
(*.f64 1/3 (pow.f64 x 2))
(*.f64 1/3 (pow.f64 x 2))
(*.f64 1/3 (pow.f64 x 2))
(*.f64 1/3 (pow.f64 x 2))
(*.f64 1/3 (pow.f64 x 2))
(*.f64 1/3 (pow.f64 x 2))
(*.f64 1/3 (pow.f64 x 2))
(*.f64 1/3 (pow.f64 x 2))
(*.f64 1/3 (pow.f64 x 2))
(*.f64 1/3 (pow.f64 x 2))
(*.f64 1/3 (pow.f64 x 2))

Outputs
(*.f64 1/3 x)
(+.f64 (.f64 -1/9 (pow.f64 x 3)) (.f64 1/3 x))
(fma.f64 -1/9 (pow.f64 x 3) (*.f64 1/3 x))
(fma.f64 1/3 x (*.f64 -1/9 (pow.f64 x 3)))
(.f64 x (fma.f64 x (.f64 x -1/9) 1/3))
(+.f64 (.f64 -1/9 (pow.f64 x 3)) (+.f64 (.f64 -1/135 (pow.f64 x 5)) (*.f64 1/3 x)))
(fma.f64 -1/9 (pow.f64 x 3) (fma.f64 -1/135 (pow.f64 x 5) (*.f64 1/3 x)))
(fma.f64 -1/9 (pow.f64 x 3) (fma.f64 1/3 x (*.f64 -1/135 (pow.f64 x 5))))
(fma.f64 x (fma.f64 x (.f64 x -1/9) 1/3) (.f64 -1/135 (pow.f64 x 5)))
(fma.f64 1/3 x (fma.f64 -1/9 (pow.f64 x 3) (*.f64 -1/135 (pow.f64 x 5))))
(+.f64 (.f64 -1/9 (pow.f64 x 3)) (+.f64 (.f64 -1/135 (pow.f64 x 5)) (+.f64 (.f64 1/3 x) (.f64 -2/2835 (pow.f64 x 7)))))
(fma.f64 -1/9 (pow.f64 x 3) (fma.f64 -1/135 (pow.f64 x 5) (fma.f64 1/3 x (*.f64 -2/2835 (pow.f64 x 7)))))
(fma.f64 -1/9 (pow.f64 x 3) (fma.f64 -1/135 (pow.f64 x 5) (fma.f64 -2/2835 (pow.f64 x 7) (*.f64 1/3 x))))
(fma.f64 x (fma.f64 x (.f64 x -1/9) 1/3) (fma.f64 -1/135 (pow.f64 x 5) (.f64 -2/2835 (pow.f64 x 7))))
(fma.f64 1/3 x (fma.f64 -1/9 (pow.f64 x 3) (fma.f64 -1/135 (pow.f64 x 5) (*.f64 -2/2835 (pow.f64 x 7)))))
(.f64 1/3 (/.f64 (.f64 (cos.f64 x) (pow.f64 x 2)) (sin.f64 x)))
(.f64 1/3 (/.f64 (cos.f64 x) (/.f64 (sin.f64 x) (.f64 x x))))
(.f64 1/3 (/.f64 (.f64 (cos.f64 x) (*.f64 x x)) (sin.f64 x)))
(/.f64 (.f64 x (.f64 1/3 x)) (/.f64 (sin.f64 x) (cos.f64 x)))
(.f64 1/3 (/.f64 (.f64 x x) (/.f64 (sin.f64 x) (cos.f64 x))))
(.f64 (cos.f64 x) (/.f64 (.f64 1/3 (*.f64 x x)) (sin.f64 x)))
(.f64 1/3 (.f64 (cos.f64 x) (/.f64 (*.f64 x x) (sin.f64 x))))
(.f64 (.f64 x (*.f64 x (cos.f64 x))) (/.f64 1/3 (sin.f64 x)))
(.f64 1/3 (/.f64 (.f64 (cos.f64 x) (pow.f64 x 2)) (sin.f64 x)))
(.f64 1/3 (/.f64 (cos.f64 x) (/.f64 (sin.f64 x) (.f64 x x))))
(.f64 1/3 (/.f64 (.f64 (cos.f64 x) (*.f64 x x)) (sin.f64 x)))
(/.f64 (.f64 x (.f64 1/3 x)) (/.f64 (sin.f64 x) (cos.f64 x)))
(.f64 1/3 (/.f64 (.f64 x x) (/.f64 (sin.f64 x) (cos.f64 x))))
(.f64 (cos.f64 x) (/.f64 (.f64 1/3 (*.f64 x x)) (sin.f64 x)))
(.f64 1/3 (.f64 (cos.f64 x) (/.f64 (*.f64 x x) (sin.f64 x))))
(.f64 (.f64 x (*.f64 x (cos.f64 x))) (/.f64 1/3 (sin.f64 x)))
(.f64 1/3 (/.f64 (.f64 (cos.f64 x) (pow.f64 x 2)) (sin.f64 x)))
(.f64 1/3 (/.f64 (cos.f64 x) (/.f64 (sin.f64 x) (.f64 x x))))
(.f64 1/3 (/.f64 (.f64 (cos.f64 x) (*.f64 x x)) (sin.f64 x)))
(/.f64 (.f64 x (.f64 1/3 x)) (/.f64 (sin.f64 x) (cos.f64 x)))
(.f64 1/3 (/.f64 (.f64 x x) (/.f64 (sin.f64 x) (cos.f64 x))))
(.f64 (cos.f64 x) (/.f64 (.f64 1/3 (*.f64 x x)) (sin.f64 x)))
(.f64 1/3 (.f64 (cos.f64 x) (/.f64 (*.f64 x x) (sin.f64 x))))
(.f64 (.f64 x (*.f64 x (cos.f64 x))) (/.f64 1/3 (sin.f64 x)))
(.f64 1/3 (/.f64 (.f64 (cos.f64 x) (pow.f64 x 2)) (sin.f64 x)))
(.f64 1/3 (/.f64 (cos.f64 x) (/.f64 (sin.f64 x) (.f64 x x))))
(.f64 1/3 (/.f64 (.f64 (cos.f64 x) (*.f64 x x)) (sin.f64 x)))
(/.f64 (.f64 x (.f64 1/3 x)) (/.f64 (sin.f64 x) (cos.f64 x)))
(.f64 1/3 (/.f64 (.f64 x x) (/.f64 (sin.f64 x) (cos.f64 x))))
(.f64 (cos.f64 x) (/.f64 (.f64 1/3 (*.f64 x x)) (sin.f64 x)))
(.f64 1/3 (.f64 (cos.f64 x) (/.f64 (*.f64 x x) (sin.f64 x))))
(.f64 (.f64 x (*.f64 x (cos.f64 x))) (/.f64 1/3 (sin.f64 x)))
(.f64 1/3 (/.f64 (.f64 (cos.f64 x) (pow.f64 x 2)) (sin.f64 x)))
(.f64 1/3 (/.f64 (cos.f64 x) (/.f64 (sin.f64 x) (.f64 x x))))
(.f64 1/3 (/.f64 (.f64 (cos.f64 x) (*.f64 x x)) (sin.f64 x)))
(/.f64 (.f64 x (.f64 1/3 x)) (/.f64 (sin.f64 x) (cos.f64 x)))
(.f64 1/3 (/.f64 (.f64 x x) (/.f64 (sin.f64 x) (cos.f64 x))))
(.f64 (cos.f64 x) (/.f64 (.f64 1/3 (*.f64 x x)) (sin.f64 x)))
(.f64 1/3 (.f64 (cos.f64 x) (/.f64 (*.f64 x x) (sin.f64 x))))
(.f64 (.f64 x (*.f64 x (cos.f64 x))) (/.f64 1/3 (sin.f64 x)))
(.f64 1/3 (/.f64 (.f64 (cos.f64 x) (pow.f64 x 2)) (sin.f64 x)))
(.f64 1/3 (/.f64 (cos.f64 x) (/.f64 (sin.f64 x) (.f64 x x))))
(.f64 1/3 (/.f64 (.f64 (cos.f64 x) (*.f64 x x)) (sin.f64 x)))
(/.f64 (.f64 x (.f64 1/3 x)) (/.f64 (sin.f64 x) (cos.f64 x)))
(.f64 1/3 (/.f64 (.f64 x x) (/.f64 (sin.f64 x) (cos.f64 x))))
(.f64 (cos.f64 x) (/.f64 (.f64 1/3 (*.f64 x x)) (sin.f64 x)))
(.f64 1/3 (.f64 (cos.f64 x) (/.f64 (*.f64 x x) (sin.f64 x))))
(.f64 (.f64 x (*.f64 x (cos.f64 x))) (/.f64 1/3 (sin.f64 x)))
(.f64 1/3 (/.f64 (.f64 (cos.f64 x) (pow.f64 x 2)) (sin.f64 x)))
(.f64 1/3 (/.f64 (cos.f64 x) (/.f64 (sin.f64 x) (.f64 x x))))
(.f64 1/3 (/.f64 (.f64 (cos.f64 x) (*.f64 x x)) (sin.f64 x)))
(/.f64 (.f64 x (.f64 1/3 x)) (/.f64 (sin.f64 x) (cos.f64 x)))
(.f64 1/3 (/.f64 (.f64 x x) (/.f64 (sin.f64 x) (cos.f64 x))))
(.f64 (cos.f64 x) (/.f64 (.f64 1/3 (*.f64 x x)) (sin.f64 x)))
(.f64 1/3 (.f64 (cos.f64 x) (/.f64 (*.f64 x x) (sin.f64 x))))
(.f64 (.f64 x (*.f64 x (cos.f64 x))) (/.f64 1/3 (sin.f64 x)))
(.f64 1/3 (/.f64 (.f64 (cos.f64 x) (pow.f64 x 2)) (sin.f64 x)))
(.f64 1/3 (/.f64 (cos.f64 x) (/.f64 (sin.f64 x) (.f64 x x))))
(.f64 1/3 (/.f64 (.f64 (cos.f64 x) (*.f64 x x)) (sin.f64 x)))
(/.f64 (.f64 x (.f64 1/3 x)) (/.f64 (sin.f64 x) (cos.f64 x)))
(.f64 1/3 (/.f64 (.f64 x x) (/.f64 (sin.f64 x) (cos.f64 x))))
(.f64 (cos.f64 x) (/.f64 (.f64 1/3 (*.f64 x x)) (sin.f64 x)))
(.f64 1/3 (.f64 (cos.f64 x) (/.f64 (*.f64 x x) (sin.f64 x))))
(.f64 (.f64 x (*.f64 x (cos.f64 x))) (/.f64 1/3 (sin.f64 x)))
(*.f64 1/3 (pow.f64 x 2))
(.f64 1/3 (.f64 x x))
(.f64 x (.f64 1/3 x))
(*.f64 1/3 (pow.f64 x 2))
(.f64 1/3 (.f64 x x))
(.f64 x (.f64 1/3 x))
(*.f64 1/3 (pow.f64 x 2))
(.f64 1/3 (.f64 x x))
(.f64 x (.f64 1/3 x))
(*.f64 1/3 (pow.f64 x 2))
(.f64 1/3 (.f64 x x))
(.f64 x (.f64 1/3 x))
(*.f64 1/3 (pow.f64 x 2))
(.f64 1/3 (.f64 x x))
(.f64 x (.f64 1/3 x))
(*.f64 1/3 (pow.f64 x 2))
(.f64 1/3 (.f64 x x))
(.f64 x (.f64 1/3 x))
(*.f64 1/3 (pow.f64 x 2))
(.f64 1/3 (.f64 x x))
(.f64 x (.f64 1/3 x))
(*.f64 1/3 (pow.f64 x 2))
(.f64 1/3 (.f64 x x))
(.f64 x (.f64 1/3 x))
(*.f64 1/3 (pow.f64 x 2))
(.f64 1/3 (.f64 x x))
(.f64 x (.f64 1/3 x))
(*.f64 1/3 (pow.f64 x 2))
(.f64 1/3 (.f64 x x))
(.f64 x (.f64 1/3 x))
(*.f64 1/3 (pow.f64 x 2))
(.f64 1/3 (.f64 x x))
(.f64 x (.f64 1/3 x))
(*.f64 1/3 (pow.f64 x 2))
(.f64 1/3 (.f64 x x))
(.f64 x (.f64 1/3 x))

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (*.f64 1/3 x) 3)
	0.4b	(*.f64 1/3 x)
✓	37.9b	(cbrt.f64 (pow.f64 (*.f64 1/3 x) 3))

Compiler

Compiled 18 to 14 computations (22.2% saved)

series10.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
6.0ms	x	@	0	(pow.f64 (*.f64 1/3 x) 3)
2.0ms	x	@	-inf	(cbrt.f64 (pow.f64 (*.f64 1/3 x) 3))
1.0ms	x	@	-inf	(pow.f64 (*.f64 1/3 x) 3)
1.0ms	x	@	inf	(pow.f64 (*.f64 1/3 x) 3)
0.0ms	x	@	0	(cbrt.f64 (pow.f64 (*.f64 1/3 x) 3))

rewrite49.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

520×	`pow1_binary64`
512×	`add-sqr-sqrt_binary64`
492×	`add-log-exp_binary64`
492×	`log1p-expm1-u_binary64`
492×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	150	11
2	1410	11

Stop Event

1×	node limit

Counts

2 → 51

Calls

Call 1

Inputs
(cbrt.f64 (pow.f64 (*.f64 1/3 x) 3))
(pow.f64 (*.f64 1/3 x) 3)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 1/3 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/3 x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 1/3 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 1/3 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 1/3 x)) (pow.f64 (cbrt.f64 (*.f64 1/3 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 1/3 x)) (pow.f64 (pow.f64 (*.f64 1/3 x) 2) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 1/3 x)) 2) (cbrt.f64 (*.f64 1/3 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 1/3 x)) (sqrt.f64 (*.f64 1/3 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (*.f64 1/3 x) 2) 1/3) (cbrt.f64 (*.f64 1/3 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (*.f64 1/3 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1/27 1/3) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (*.f64 1/3 x) 3/2) 1/3) (pow.f64 (pow.f64 (*.f64 1/3 x) 3/2) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 1/3 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 1/3 (sqrt.f64 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 1/3 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 1/27 (pow.f64 x 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 1/3 x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 1/3 x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 1/3 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 1/3) x))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 1/3 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 1/3 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 1/3 x)))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 1/27 (pow.f64 x 3))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/3 (*.f64 x (pow.f64 (*.f64 1/3 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (*.f64 1/3 (pow.f64 (*.f64 1/3 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 1/3 x) (pow.f64 (*.f64 1/3 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 1/27 (pow.f64 x 3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 1/27 (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/27 (pow.f64 x 3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 1/3 x) 2) (*.f64 1/3 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 1/3 x)) 2) (*.f64 (cbrt.f64 (*.f64 1/3 x)) (pow.f64 (*.f64 1/3 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 1/3 x)) (*.f64 (sqrt.f64 (*.f64 1/3 x)) (pow.f64 (*.f64 1/3 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x 3) 1/27)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 1/3 x) 3/2) (pow.f64 (*.f64 1/3 x) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 1/3 x)) 2) 3) (*.f64 1/3 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (*.f64 1/3 x)) 3) (pow.f64 (sqrt.f64 (*.f64 1/3 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (*.f64 1/3 x) 2) 1/3) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (*.f64 1/3 x) 2) x) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (*.f64 1/3 x) 2) 1) (*.f64 1/3 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (*.f64 1/3 x) 2) (pow.f64 (cbrt.f64 (*.f64 1/3 x)) 2)) (cbrt.f64 (*.f64 1/3 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (*.f64 1/3 x) 2) (sqrt.f64 (*.f64 1/3 x))) (sqrt.f64 (*.f64 1/3 x)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 1/3 x) 6))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 1/27) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 1/27 (pow.f64 x 3)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 1/27 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 1/27 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 3 (log.f64 (*.f64 1/3 x))))))))

simplify173.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

1274×	`sqr-pow_binary64`
666×	`pow-sqr_binary64`
529×	`cube-prod_binary64`
475×	`fabs-mul_binary64`
444×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	148
1	28	148
2	58	148
3	86	148
4	148	148
5	385	148
6	1266	148
7	1961	148
8	2079	148
9	2467	148
10	2625	148
11	2869	148
12	3191	148
13	3613	148
14	4113	148
15	4714	148
16	5438	148
17	5761	148
18	6047	148
19	6269	148
20	6447	148
21	6531	148
22	7471	148

Stop Event

1×	node limit

Counts

75 → 53

Calls

Call 1

Inputs
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(.f64 -1 (.f64 (cbrt.f64 -1/27) x))
(.f64 -1 (.f64 (cbrt.f64 -1/27) x))
(.f64 -1 (.f64 (cbrt.f64 -1/27) x))
(.f64 -1 (.f64 (cbrt.f64 -1/27) x))
(*.f64 1/27 (pow.f64 x 3))
(*.f64 1/27 (pow.f64 x 3))
(*.f64 1/27 (pow.f64 x 3))
(*.f64 1/27 (pow.f64 x 3))
(*.f64 1/27 (pow.f64 x 3))
(*.f64 1/27 (pow.f64 x 3))
(*.f64 1/27 (pow.f64 x 3))
(*.f64 1/27 (pow.f64 x 3))
(*.f64 1/27 (pow.f64 x 3))
(*.f64 1/27 (pow.f64 x 3))
(*.f64 1/27 (pow.f64 x 3))
(*.f64 1/27 (pow.f64 x 3))

Outputs
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(.f64 -1 (.f64 (cbrt.f64 -1/27) x))
(neg.f64 (*.f64 x (cbrt.f64 -1/27)))
(*.f64 x (neg.f64 (cbrt.f64 -1/27)))
(*.f64 (cbrt.f64 -1/27) (neg.f64 x))
(.f64 -1 (.f64 (cbrt.f64 -1/27) x))
(neg.f64 (*.f64 x (cbrt.f64 -1/27)))
(*.f64 x (neg.f64 (cbrt.f64 -1/27)))
(*.f64 (cbrt.f64 -1/27) (neg.f64 x))
(.f64 -1 (.f64 (cbrt.f64 -1/27) x))
(neg.f64 (*.f64 x (cbrt.f64 -1/27)))
(*.f64 x (neg.f64 (cbrt.f64 -1/27)))
(*.f64 (cbrt.f64 -1/27) (neg.f64 x))
(.f64 -1 (.f64 (cbrt.f64 -1/27) x))
(neg.f64 (*.f64 x (cbrt.f64 -1/27)))
(*.f64 x (neg.f64 (cbrt.f64 -1/27)))
(*.f64 (cbrt.f64 -1/27) (neg.f64 x))
(*.f64 1/27 (pow.f64 x 3))
(*.f64 1/27 (pow.f64 x 3))
(*.f64 1/27 (pow.f64 x 3))
(*.f64 1/27 (pow.f64 x 3))
(*.f64 1/27 (pow.f64 x 3))
(*.f64 1/27 (pow.f64 x 3))
(*.f64 1/27 (pow.f64 x 3))
(*.f64 1/27 (pow.f64 x 3))
(*.f64 1/27 (pow.f64 x 3))
(*.f64 1/27 (pow.f64 x 3))
(*.f64 1/27 (pow.f64 x 3))
(*.f64 1/27 (pow.f64 x 3))

localize49.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (*.f64 1/3 x))
✓	0.2b	(pow.f64 (sqrt.f64 (*.f64 1/3 x)) 2)
	0.4b	(*.f64 1/3 x)

Compiler

Compiled 17 to 13 computations (23.5% saved)

series5.0ms (0%)

Counts

2 → 0

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	x	@	0	(pow.f64 (sqrt.f64 (*.f64 1/3 x)) 2)
1.0ms	x	@	-inf	(pow.f64 (sqrt.f64 (*.f64 1/3 x)) 2)
1.0ms	x	@	inf	(pow.f64 (sqrt.f64 (*.f64 1/3 x)) 2)
1.0ms	x	@	0	(sqrt.f64 (*.f64 1/3 x))
0.0ms	x	@	-inf	(sqrt.f64 (*.f64 1/3 x))

rewrite71.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

497×	`pow1_binary64`
486×	`add-sqr-sqrt_binary64`
464×	`add-log-exp_binary64`
464×	`log1p-expm1-u_binary64`
464×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	146	10
2	1318	10

Stop Event

1×	node limit

Counts

2 → 47

Calls

Call 1

Inputs
(pow.f64 (sqrt.f64 (*.f64 1/3 x)) 2)
(sqrt.f64 (*.f64 1/3 x))

Outputs

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

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

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

47 → 47

Calls

Call 1

Inputs

Outputs

eval240.0ms (1.5%)

Compiler: Compiled 7987 to 5488 computations (31.3% saved)

prune96.0ms (0.6%)

Pruning

19 alts after pruning (11 fresh and 8 done)

	Pruned	Kept	Total
New	427	10	437
Fresh	3	1	4
Picked	0	1	1
Done	2	7	9
Total	432	19	451

Error

Counts

451 → 19

Alt Table

Click to see full alt table

Status	Error	Program
	0.4b	(/.f64 (.f64 (+.f64 (.f64 1/2025 (pow.f64 x 4)) -1/9) x) (fma.f64 1/45 (*.f64 x x) -1/3))
✓	0.6b	(*.f64 1/3 x)
	38.2b	(cbrt.f64 (.f64 (.f64 (pow.f64 (*.f64 1/3 x) 2) 1/3) x))
▶	1.0b	(*.f64 (pow.f64 1/27 1/3) x)
▶	0.3b	(/.f64 (.f64 (+.f64 1/27 (pow.f64 (.f64 x (.f64 x 1/45)) 3)) x) (+.f64 (.f64 1/2025 (pow.f64 x 4)) (-.f64 1/9 (.f64 (.f64 x x) 1/135))))
✓	28.7b	(/.f64 (.f64 1/3 (.f64 x x)) (tan.f64 x))
✓	60.1b	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))
	31.6b	(.f64 (.f64 1/3 (sqrt.f64 x)) (sqrt.f64 x))
▶	28.7b	(.f64 (.f64 x x) (*.f64 1/3 (/.f64 1 (tan.f64 x))))
▶	59.2b	(-.f64 (+.f64 1 (*.f64 1/3 x)) 1)
▶	1.8b	(pow.f64 (cbrt.f64 (*.f64 1/3 x)) 3)
	0.4b	(.f64 x (/.f64 (+.f64 (.f64 (.f64 (.f64 x (.f64 x 1/45)) (.f64 (.f64 x x) 1/2025)) (.f64 x x)) 1/27) (+.f64 (.f64 (.f64 1/45 (.f64 x x)) (.f64 1/45 (.f64 x x))) (-.f64 1/9 (.f64 (.f64 1/45 (.f64 x x)) 1/3)))))
✓	0.4b	(+.f64 (.f64 1/3 x) (+.f64 (.f64 2/945 (pow.f64 x 5)) (*.f64 1/45 (pow.f64 x 3))))
✓	0.4b	(.f64 x (+.f64 (.f64 1/45 (*.f64 x x)) 1/3))
✓	31.6b	(pow.f64 (sqrt.f64 (*.f64 1/3 x)) 2)
	42.4b	(sqrt.f64 (.f64 (.f64 x x) 1/9))
✓	60.1b	(/.f64 (/.f64 (-.f64 (tan.f64 x) x) x) (tan.f64 x))
	38.2b	(cbrt.f64 (*.f64 (pow.f64 x 3) 1/27))
✓	0.4b	(+.f64 (.f64 1/3 x) (+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 1/4725 (pow.f64 x 7)))))

Compiler

Compiled 387 to 283 computations (26.9% saved)

localize68.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 x (.f64 x 1/45))
✓	0.3b	(*.f64 x 1/45)
✓	0.4b	(.f64 (+.f64 1/27 (pow.f64 (.f64 x (*.f64 x 1/45)) 3)) x)
✓	0.4b	(/.f64 (.f64 (+.f64 1/27 (pow.f64 (.f64 x (.f64 x 1/45)) 3)) x) (+.f64 (.f64 1/2025 (pow.f64 x 4)) (-.f64 1/9 (.f64 (.f64 x x) 1/135))))

Compiler

Compiled 105 to 73 computations (30.5% saved)

series5.0ms (0%)

Counts

4 → 48

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(.f64 (+.f64 1/27 (pow.f64 (.f64 x (*.f64 x 1/45)) 3)) x)
0.0ms	x	@	inf	(.f64 (+.f64 1/27 (pow.f64 (.f64 x (*.f64 x 1/45)) 3)) x)
0.0ms	x	@	0	(*.f64 x 1/45)
0.0ms	x	@	-inf	(*.f64 x 1/45)
0.0ms	x	@	0	(/.f64 (.f64 (+.f64 1/27 (pow.f64 (.f64 x (.f64 x 1/45)) 3)) x) (+.f64 (.f64 1/2025 (pow.f64 x 4)) (-.f64 1/9 (.f64 (.f64 x x) 1/135))))

rewrite254.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

620×	`fma-def_binary64`
373×	`expm1-udef_binary64`
373×	`log1p-udef_binary64`
334×	`fma-neg_binary64`
226×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	21	62
1	485	56
2	6221	50

Stop Event

1×	node limit

Counts

4 → 100

Calls

Call 1

Inputs
(/.f64 (.f64 (+.f64 1/27 (pow.f64 (.f64 x (.f64 x 1/45)) 3)) x) (+.f64 (.f64 1/2025 (pow.f64 x 4)) (-.f64 1/9 (.f64 (.f64 x x) 1/135))))
(.f64 (+.f64 1/27 (pow.f64 (.f64 x (*.f64 x 1/45)) 3)) x)
(*.f64 x 1/45)
(.f64 x (.f64 x 1/45))

Outputs
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((#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 1/27 x) (.f64 (.f64 (pow.f64 x 6) 1/91125) x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (.f64 (pow.f64 x 6) 1/91125) x) (.f64 1/27 x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 x 1/27) (.f64 x (.f64 (pow.f64 x 6) 1/91125)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 x (.f64 (pow.f64 x 6) 1/91125)) (.f64 x 1/27))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 x (fma.f64 (pow.f64 x 6) 1/91125 1/27)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (+.f64 1/19683 (pow.f64 (.f64 (pow.f64 x 6) 1/91125) 3)) x) (fma.f64 (.f64 (pow.f64 x 6) 1/91125) (fma.f64 (pow.f64 x 6) 1/91125 -1/27) 1/729))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (-.f64 1/729 (pow.f64 (.f64 (pow.f64 x 6) 1/91125) 2)) x) (-.f64 1/27 (.f64 (pow.f64 x 6) 1/91125)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 x (+.f64 1/19683 (pow.f64 (.f64 (pow.f64 x 6) 1/91125) 3))) (fma.f64 (.f64 (pow.f64 x 6) 1/91125) (fma.f64 (pow.f64 x 6) 1/91125 -1/27) 1/729))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 x (-.f64 1/729 (pow.f64 (.f64 (pow.f64 x 6) 1/91125) 2))) (-.f64 1/27 (.f64 (pow.f64 x 6) 1/91125)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 x (fma.f64 (pow.f64 x 6) 1/91125 1/27)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 x (fma.f64 (pow.f64 x 6) 1/91125 1/27)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 x (fma.f64 (pow.f64 x 6) 1/91125 1/27))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 x (fma.f64 (pow.f64 x 6) 1/91125 1/27))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (.f64 x (fma.f64 (pow.f64 x 6) 1/91125 1/27)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (fma.f64 (pow.f64 x 6) 1/91125 1/27)) x))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 x (fma.f64 (pow.f64 x 6) 1/91125 1/27)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 x (fma.f64 (pow.f64 x 6) 1/91125 1/27)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 x 3) (pow.f64 (fma.f64 (pow.f64 x 6) 1/91125 1/27) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (fma.f64 (pow.f64 x 6) 1/91125 1/27) 3) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 x (fma.f64 (pow.f64 x 6) 1/91125 1/27))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 x (fma.f64 (pow.f64 x 6) 1/91125 1/27))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 x (fma.f64 (pow.f64 x 6) 1/91125 1/27))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 x (fma.f64 (pow.f64 x 6) 1/91125 1/27))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/27 x (.f64 (.f64 (pow.f64 x 6) 1/91125) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x 1/27 (.f64 x (.f64 (pow.f64 x 6) 1/91125)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x (.f64 (pow.f64 x 6) 1/91125) (.f64 x 1/27))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (pow.f64 x 6) 1/91125) x (*.f64 1/27 x))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 x 1/45))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 x 1/45) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 x 1/45)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 x 1/45)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 1/91125 (pow.f64 x 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (.f64 1/2025 (.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 1/45) x))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 x 1/45))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 1/91125 (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 x 1/45)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 x 1/45)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 x 1/45)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 x 1/45)) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 1/45 (.f64 x x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 1/45 (.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 x 6) 1/91125) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 1/2025 (pow.f64 x 4)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 1/45 (.f64 x x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 x (sqrt.f64 1/45)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (.f64 1/2025 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (.f64 1/45 (.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 x) (.f64 x 1/45)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 1/45 (.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 x 6) 1/91125))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 1/45 (.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 1/45 (.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 1/45 (.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 1/45 (*.f64 x x))) 1))))))

simplify207.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

798×	`fma-def_binary64`
602×	`unswap-sqr_binary64`
525×	`associate-l_binary64`
508×	`distribute-lft-in_binary64`
508×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	366
1	46	366
2	84	366
3	177	366
4	488	366
5	1785	366
6	3134	366
7	3391	366
8	3845	366
9	4623	366
10	5914	366
11	7790	366

Stop Event

1×	node limit

Counts

148 → 113

Calls

Call 1

Inputs
(*.f64 1/3 x)
(+.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3)))
(+.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3)))
(+.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3)))
(*.f64 1/45 (pow.f64 x 3))
(+.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3)))
(+.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3)))
(+.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3)))
(*.f64 1/45 (pow.f64 x 3))
(+.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3)))
(+.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3)))
(+.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3)))
(*.f64 1/27 x)
(+.f64 (.f64 1/91125 (pow.f64 x 7)) (.f64 1/27 x))
(+.f64 (.f64 1/91125 (pow.f64 x 7)) (.f64 1/27 x))
(+.f64 (.f64 1/91125 (pow.f64 x 7)) (.f64 1/27 x))
(*.f64 1/91125 (pow.f64 x 7))
(+.f64 (.f64 1/91125 (pow.f64 x 7)) (.f64 1/27 x))
(+.f64 (.f64 1/91125 (pow.f64 x 7)) (.f64 1/27 x))
(+.f64 (.f64 1/91125 (pow.f64 x 7)) (.f64 1/27 x))
(*.f64 1/91125 (pow.f64 x 7))
(+.f64 (.f64 1/91125 (pow.f64 x 7)) (.f64 1/27 x))
(+.f64 (.f64 1/91125 (pow.f64 x 7)) (.f64 1/27 x))
(+.f64 (.f64 1/91125 (pow.f64 x 7)) (.f64 1/27 x))
(*.f64 1/45 x)
(*.f64 1/45 x)
(*.f64 1/45 x)
(*.f64 1/45 x)
(*.f64 1/45 x)
(*.f64 1/45 x)
(*.f64 1/45 x)
(*.f64 1/45 x)
(*.f64 1/45 x)
(*.f64 1/45 x)
(*.f64 1/45 x)
(*.f64 1/45 x)
(*.f64 1/45 (pow.f64 x 2))
(*.f64 1/45 (pow.f64 x 2))
(*.f64 1/45 (pow.f64 x 2))
(*.f64 1/45 (pow.f64 x 2))
(*.f64 1/45 (pow.f64 x 2))
(*.f64 1/45 (pow.f64 x 2))
(*.f64 1/45 (pow.f64 x 2))
(*.f64 1/45 (pow.f64 x 2))
(*.f64 1/45 (pow.f64 x 2))
(*.f64 1/45 (pow.f64 x 2))
(*.f64 1/45 (pow.f64 x 2))
(*.f64 1/45 (pow.f64 x 2))

Outputs
(*.f64 1/3 x)
(+.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3)))
(fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))
(.f64 x (fma.f64 1/45 (.f64 x x) 1/3))
(fma.f64 1/45 (pow.f64 x 3) (*.f64 1/3 x))
(+.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3)))
(fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))
(.f64 x (fma.f64 1/45 (.f64 x x) 1/3))
(fma.f64 1/45 (pow.f64 x 3) (*.f64 1/3 x))
(+.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3)))
(fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))
(.f64 x (fma.f64 1/45 (.f64 x x) 1/3))
(fma.f64 1/45 (pow.f64 x 3) (*.f64 1/3 x))
(*.f64 1/45 (pow.f64 x 3))
(+.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3)))
(fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))
(.f64 x (fma.f64 1/45 (.f64 x x) 1/3))
(fma.f64 1/45 (pow.f64 x 3) (*.f64 1/3 x))
(+.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3)))
(fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))
(.f64 x (fma.f64 1/45 (.f64 x x) 1/3))
(fma.f64 1/45 (pow.f64 x 3) (*.f64 1/3 x))
(+.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3)))
(fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))
(.f64 x (fma.f64 1/45 (.f64 x x) 1/3))
(fma.f64 1/45 (pow.f64 x 3) (*.f64 1/3 x))
(*.f64 1/45 (pow.f64 x 3))
(+.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3)))
(fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))
(.f64 x (fma.f64 1/45 (.f64 x x) 1/3))
(fma.f64 1/45 (pow.f64 x 3) (*.f64 1/3 x))
(+.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3)))
(fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))
(.f64 x (fma.f64 1/45 (.f64 x x) 1/3))
(fma.f64 1/45 (pow.f64 x 3) (*.f64 1/3 x))
(+.f64 (.f64 1/3 x) (.f64 1/45 (pow.f64 x 3)))
(fma.f64 1/3 x (*.f64 1/45 (pow.f64 x 3)))
(.f64 x (fma.f64 1/45 (.f64 x x) 1/3))
(fma.f64 1/45 (pow.f64 x 3) (*.f64 1/3 x))
(*.f64 1/27 x)
(*.f64 x 1/27)
(+.f64 (.f64 1/91125 (pow.f64 x 7)) (.f64 1/27 x))
(fma.f64 1/91125 (pow.f64 x 7) (*.f64 x 1/27))
(fma.f64 x 1/27 (*.f64 1/91125 (pow.f64 x 7)))
(+.f64 (.f64 1/91125 (pow.f64 x 7)) (.f64 1/27 x))
(fma.f64 1/91125 (pow.f64 x 7) (*.f64 x 1/27))
(fma.f64 x 1/27 (*.f64 1/91125 (pow.f64 x 7)))
(+.f64 (.f64 1/91125 (pow.f64 x 7)) (.f64 1/27 x))
(fma.f64 1/91125 (pow.f64 x 7) (*.f64 x 1/27))
(fma.f64 x 1/27 (*.f64 1/91125 (pow.f64 x 7)))
(*.f64 1/91125 (pow.f64 x 7))
(+.f64 (.f64 1/91125 (pow.f64 x 7)) (.f64 1/27 x))
(fma.f64 1/91125 (pow.f64 x 7) (*.f64 x 1/27))
(fma.f64 x 1/27 (*.f64 1/91125 (pow.f64 x 7)))
(+.f64 (.f64 1/91125 (pow.f64 x 7)) (.f64 1/27 x))
(fma.f64 1/91125 (pow.f64 x 7) (*.f64 x 1/27))
(fma.f64 x 1/27 (*.f64 1/91125 (pow.f64 x 7)))
(+.f64 (.f64 1/91125 (pow.f64 x 7)) (.f64 1/27 x))
(fma.f64 1/91125 (pow.f64 x 7) (*.f64 x 1/27))
(fma.f64 x 1/27 (*.f64 1/91125 (pow.f64 x 7)))
(*.f64 1/91125 (pow.f64 x 7))
(+.f64 (.f64 1/91125 (pow.f64 x 7)) (.f64 1/27 x))
(fma.f64 1/91125 (pow.f64 x 7) (*.f64 x 1/27))
(fma.f64 x 1/27 (*.f64 1/91125 (pow.f64 x 7)))
(+.f64 (.f64 1/91125 (pow.f64 x 7)) (.f64 1/27 x))
(fma.f64 1/91125 (pow.f64 x 7) (*.f64 x 1/27))
(fma.f64 x 1/27 (*.f64 1/91125 (pow.f64 x 7)))
(+.f64 (.f64 1/91125 (pow.f64 x 7)) (.f64 1/27 x))
(fma.f64 1/91125 (pow.f64 x 7) (*.f64 x 1/27))
(fma.f64 x 1/27 (*.f64 1/91125 (pow.f64 x 7)))
(*.f64 1/45 x)
(*.f64 x 1/45)
(*.f64 1/45 x)
(*.f64 x 1/45)
(*.f64 1/45 x)
(*.f64 x 1/45)
(*.f64 1/45 x)
(*.f64 x 1/45)
(*.f64 1/45 x)
(*.f64 x 1/45)
(*.f64 1/45 x)
(*.f64 x 1/45)
(*.f64 1/45 x)
(*.f64 x 1/45)
(*.f64 1/45 x)
(*.f64 x 1/45)
(*.f64 1/45 x)
(*.f64 x 1/45)
(*.f64 1/45 x)
(*.f64 x 1/45)
(*.f64 1/45 x)
(*.f64 x 1/45)
(*.f64 1/45 x)
(*.f64 x 1/45)
(*.f64 1/45 (pow.f64 x 2))
(.f64 1/45 (.f64 x x))
(*.f64 1/45 (pow.f64 x 2))
(.f64 1/45 (.f64 x x))
(*.f64 1/45 (pow.f64 x 2))
(.f64 1/45 (.f64 x x))
(*.f64 1/45 (pow.f64 x 2))
(.f64 1/45 (.f64 x x))
(*.f64 1/45 (pow.f64 x 2))
(.f64 1/45 (.f64 x x))
(*.f64 1/45 (pow.f64 x 2))
(.f64 1/45 (.f64 x x))
(*.f64 1/45 (pow.f64 x 2))
(.f64 1/45 (.f64 x x))
(*.f64 1/45 (pow.f64 x 2))
(.f64 1/45 (.f64 x x))
(*.f64 1/45 (pow.f64 x 2))
(.f64 1/45 (.f64 x x))
(*.f64 1/45 (pow.f64 x 2))
(.f64 1/45 (.f64 x x))
(*.f64 1/45 (pow.f64 x 2))
(.f64 1/45 (.f64 x x))
(*.f64 1/45 (pow.f64 x 2))
(.f64 1/45 (.f64 x x))

localize16.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.4b	(*.f64 1/3 x)
✓	6.2b	(-.f64 (+.f64 1 (*.f64 1/3 x)) 1)

Compiler

Compiled 19 to 15 computations (21.1% saved)

series2.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(-.f64 (+.f64 1 (*.f64 1/3 x)) 1)
1.0ms	x	@	inf	(-.f64 (+.f64 1 (*.f64 1/3 x)) 1)
0.0ms	x	@	0	(-.f64 (+.f64 1 (*.f64 1/3 x)) 1)

rewrite134.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

726×	`pow1_binary64`
683×	`add-log-exp_binary64`
683×	`log1p-expm1-u_binary64`
683×	`expm1-log1p-u_binary64`
673×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	156	4
2	2108	4

Stop Event

1×	node limit

Counts

1 → 43

Calls

Call 1

Inputs
(-.f64 (+.f64 1 (*.f64 1/3 x)) 1)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (fma.f64 1/3 x -1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 (fma.f64 1/3 x -1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 1/3 x) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 1/3 x 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (fma.f64 1/3 x 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 1/3 x -1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 1/3 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/3 x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 1/3 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 1/3 x)) (pow.f64 (cbrt.f64 (*.f64 1/3 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 1/3 x)) 2) (cbrt.f64 (*.f64 1/3 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 1/3 x)) (sqrt.f64 (*.f64 1/3 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (fma.f64 1/3 x 1) 3) -1) (/.f64 1 (+.f64 (pow.f64 (fma.f64 1/3 x 1) 2) (+.f64 (*.f64 1/3 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (fma.f64 1/3 x 1) 2) -1) (/.f64 1 (+.f64 (*.f64 1/3 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (sqrt.f64 (fma.f64 1/3 x 1)) 1) (-.f64 (sqrt.f64 (fma.f64 1/3 x 1)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 1/3 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 1/3 (sqrt.f64 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (fma.f64 1/3 x 1) 2) (+.f64 (*.f64 1/3 x) 2)) (+.f64 (pow.f64 (fma.f64 1/3 x 1) 3) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (*.f64 1/3 x) 2) (+.f64 (pow.f64 (fma.f64 1/3 x 1) 2) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (fma.f64 1/3 x 1) 3) -1) (+.f64 (pow.f64 (fma.f64 1/3 x 1) 2) (+.f64 (*.f64 1/3 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (fma.f64 1/3 x 1) 3) -1) (+.f64 (pow.f64 (fma.f64 1/3 x 1) 2) (-.f64 1 (*.f64 (fma.f64 1/3 x 1) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (fma.f64 1/3 x 1) 2) -1) (+.f64 (*.f64 1/3 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (fma.f64 1/3 x 1) 2) -1) (-.f64 (fma.f64 1/3 x 1) -1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (fma.f64 1/3 x 1) 3) -1)) (neg.f64 (+.f64 (pow.f64 (fma.f64 1/3 x 1) 2) (+.f64 (*.f64 1/3 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (fma.f64 1/3 x 1) 2) -1)) (neg.f64 (+.f64 (*.f64 1/3 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (fma.f64 1/3 x -1) 3)) (+.f64 1 (-.f64 (*.f64 (fma.f64 1/3 x -1) (fma.f64 1/3 x -1)) (fma.f64 1/3 x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (*.f64 (fma.f64 1/3 x -1) (fma.f64 1/3 x -1))) (-.f64 1 (fma.f64 1/3 x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 1/3 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 1/3 x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 1/3 x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 1/27 (pow.f64 x 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 1/3 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 1/3) x))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 1/27 (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 1/3 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 1/3 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 1/3 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 1/3 x 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (fma.f64 1/3 x 1)) 2) (cbrt.f64 (fma.f64 1/3 x 1)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (fma.f64 1/3 x 1)) (sqrt.f64 (fma.f64 1/3 x 1)) -1)))))

simplify13.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	48
1	5	48

Stop Event

1×

saturated

Counts

55 → 43

Calls

Call 1

Inputs
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)

Outputs
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)

localize25.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.4b	(*.f64 (pow.f64 1/27 1/3) x)
✓	1.0b	(pow.f64 1/27 1/3)

Compiler

Compiled 12 to 10 computations (16.7% saved)

series7.0ms (0%)

Counts

2 → 12

Calls

3 calls:

Time	Variable		Point	Expression
5.0ms	x	@	0	(*.f64 (pow.f64 1/27 1/3) x)
1.0ms	x	@	-inf	(*.f64 (pow.f64 1/27 1/3) x)
1.0ms	x	@	inf	(*.f64 (pow.f64 1/27 1/3) x)

rewrite178.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

421×	`pow1_binary64`
416×	`add-sqr-sqrt_binary64`
402×	`*-un-lft-identity_binary64`
397×	`add-log-exp_binary64`
397×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	5
1	126	5
2	1087	5

Stop Event

1×	node limit

Counts

2 → 15

Calls

Call 1

Inputs
(pow.f64 1/27 1/3)
(*.f64 (pow.f64 1/27 1/3) x)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x . 1/3)))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 1/3 x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (exp.f64 x))) 2)) (log.f64 (cbrt.f64 (cbrt.f64 (exp.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (cbrt.f64 (exp.f64 x)))) (log.f64 (sqrt.f64 (cbrt.f64 (exp.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 1/3 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 1/3 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 1/3 x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 1/3 x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 1/3 x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 1/9 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (cbrt.f64 (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 1/3 x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 1/3 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 1/3 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 1/3 x)))))))

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	48
1	5	48

Stop Event

1×

saturated

Counts

27 → 16

Calls

Call 1

Inputs
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)

Outputs
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)

localize17.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.4b	(*.f64 1/3 (/.f64 1 (tan.f64 x)))
✓	28.3b	(.f64 (.f64 x x) (*.f64 1/3 (/.f64 1 (tan.f64 x))))

Compiler

Compiled 29 to 16 computations (44.8% saved)

series3.0ms (0%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(*.f64 1/3 (/.f64 1 (tan.f64 x)))
0.0ms	x	@	-inf	(*.f64 1/3 (/.f64 1 (tan.f64 x)))
0.0ms	x	@	0	(.f64 (.f64 x x) (*.f64 1/3 (/.f64 1 (tan.f64 x))))
0.0ms	x	@	0	(*.f64 1/3 (/.f64 1 (tan.f64 x)))
0.0ms	x	@	-inf	(.f64 (.f64 x x) (*.f64 1/3 (/.f64 1 (tan.f64 x))))

rewrite92.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

824×	`pow1_binary64`
763×	`add-log-exp_binary64`
762×	`log1p-expm1-u_binary64`
762×	`expm1-log1p-u_binary64`
746×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	18
1	187	18
2	2184	18

Stop Event

1×	node limit

Counts

2 → 32

Calls

Call 1

Inputs
(.f64 (.f64 x x) (*.f64 1/3 (/.f64 1 (tan.f64 x))))
(*.f64 1/3 (/.f64 1 (tan.f64 x)))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 x (*.f64 x (/.f64 1/3 (tan.f64 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 x (*.f64 x 1/3)) (tan.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 x (*.f64 x 1/3)) 1) (tan.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 x (*.f64 x 1/3)) -1) (neg.f64 (tan.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (*.f64 x (/.f64 1/3 (tan.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x (*.f64 x (/.f64 1/3 (tan.f64 x)))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x (*.f64 x (/.f64 1/3 (tan.f64 x))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (sqrt.f64 (/.f64 1/3 (tan.f64 x)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (*.f64 (pow.f64 (tan.f64 x) -2) 1/9) (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 x) (*.f64 x (/.f64 1/3 (tan.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x (*.f64 x (/.f64 1/3 (tan.f64 x)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (*.f64 x x) 3) (pow.f64 (/.f64 1/3 (tan.f64 x)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (/.f64 1/3 (tan.f64 x)) 3) (pow.f64 (*.f64 x x) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x (*.f64 x (/.f64 1/3 (tan.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x (*.f64 x (/.f64 1/3 (tan.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x (*.f64 x (/.f64 1/3 (tan.f64 x))))))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 1/3 (tan.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1/3 (tan.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (tan.f64 x) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -1/3 (neg.f64 (tan.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 1/3 (pow.f64 (cbrt.f64 (tan.f64 x)) 2)) (cbrt.f64 (tan.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 1/3 (sqrt.f64 (tan.f64 x))) (sqrt.f64 (tan.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1/3 (tan.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 1/3 (tan.f64 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 1/3 (tan.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 1/3 (tan.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 (tan.f64 x) -2) 1/9))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1/3 (tan.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 1/3 (tan.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1/3 (tan.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1/3 (tan.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 1/3 (tan.f64 x))))))))

simplify83.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

993×	`fma-def_binary64`
623×	`associate-/l/_binary64`
590×	`associate-/r/_binary64`
439×	`unswap-sqr_binary64`
428×	`associate-/r*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	42	337
1	108	335
2	252	331
3	688	331
4	1752	331
5	3159	331
6	6479	331
7	7277	331

Stop Event

1×	node limit

Counts

56 → 50

Calls

Call 1

Inputs
(*.f64 1/3 x)
(+.f64 (.f64 -1/9 (pow.f64 x 3)) (.f64 1/3 x))
(+.f64 (.f64 -1/9 (pow.f64 x 3)) (+.f64 (.f64 -1/135 (pow.f64 x 5)) (*.f64 1/3 x)))
(+.f64 (.f64 -1/9 (pow.f64 x 3)) (+.f64 (.f64 -1/135 (pow.f64 x 5)) (+.f64 (.f64 1/3 x) (.f64 -2/2835 (pow.f64 x 7)))))
(.f64 1/3 (/.f64 (.f64 (cos.f64 x) (pow.f64 x 2)) (sin.f64 x)))
(.f64 1/3 (/.f64 (.f64 (cos.f64 x) (pow.f64 x 2)) (sin.f64 x)))
(.f64 1/3 (/.f64 (.f64 (cos.f64 x) (pow.f64 x 2)) (sin.f64 x)))
(.f64 1/3 (/.f64 (.f64 (cos.f64 x) (pow.f64 x 2)) (sin.f64 x)))
(.f64 1/3 (/.f64 (.f64 (cos.f64 x) (pow.f64 x 2)) (sin.f64 x)))
(.f64 1/3 (/.f64 (.f64 (cos.f64 x) (pow.f64 x 2)) (sin.f64 x)))
(.f64 1/3 (/.f64 (.f64 (cos.f64 x) (pow.f64 x 2)) (sin.f64 x)))
(.f64 1/3 (/.f64 (.f64 (cos.f64 x) (pow.f64 x 2)) (sin.f64 x)))
(/.f64 1/3 x)
(+.f64 (.f64 1/3 (/.f64 1 x)) (.f64 -1/9 x))
(+.f64 (.f64 1/3 (/.f64 1 x)) (+.f64 (.f64 -1/9 x) (*.f64 -1/135 (pow.f64 x 3))))
(+.f64 (.f64 -2/2835 (pow.f64 x 5)) (+.f64 (.f64 1/3 (/.f64 1 x)) (+.f64 (.f64 -1/9 x) (.f64 -1/135 (pow.f64 x 3)))))
(*.f64 1/3 (/.f64 (cos.f64 x) (sin.f64 x)))
(*.f64 1/3 (/.f64 (cos.f64 x) (sin.f64 x)))
(*.f64 1/3 (/.f64 (cos.f64 x) (sin.f64 x)))
(*.f64 1/3 (/.f64 (cos.f64 x) (sin.f64 x)))
(*.f64 1/3 (/.f64 (cos.f64 x) (sin.f64 x)))
(*.f64 1/3 (/.f64 (cos.f64 x) (sin.f64 x)))
(*.f64 1/3 (/.f64 (cos.f64 x) (sin.f64 x)))
(*.f64 1/3 (/.f64 (cos.f64 x) (sin.f64 x)))

Outputs
(*.f64 1/3 x)
(+.f64 (.f64 -1/9 (pow.f64 x 3)) (.f64 1/3 x))
(fma.f64 -1/9 (pow.f64 x 3) (*.f64 1/3 x))
(fma.f64 1/3 x (*.f64 -1/9 (pow.f64 x 3)))
(.f64 x (fma.f64 -1/9 (.f64 x x) 1/3))
(.f64 x (fma.f64 x (.f64 x -1/9) 1/3))
(+.f64 (.f64 -1/9 (pow.f64 x 3)) (+.f64 (.f64 -1/135 (pow.f64 x 5)) (*.f64 1/3 x)))
(fma.f64 -1/9 (pow.f64 x 3) (fma.f64 -1/135 (pow.f64 x 5) (*.f64 1/3 x)))
(fma.f64 -1/9 (pow.f64 x 3) (fma.f64 1/3 x (*.f64 -1/135 (pow.f64 x 5))))
(fma.f64 x (fma.f64 x (.f64 x -1/9) 1/3) (.f64 -1/135 (pow.f64 x 5)))
(fma.f64 1/3 x (fma.f64 -1/135 (pow.f64 x 5) (*.f64 -1/9 (pow.f64 x 3))))
(+.f64 (.f64 -1/9 (pow.f64 x 3)) (+.f64 (.f64 -1/135 (pow.f64 x 5)) (+.f64 (.f64 1/3 x) (.f64 -2/2835 (pow.f64 x 7)))))
(fma.f64 -1/9 (pow.f64 x 3) (fma.f64 -1/135 (pow.f64 x 5) (fma.f64 1/3 x (*.f64 -2/2835 (pow.f64 x 7)))))
(fma.f64 -1/9 (pow.f64 x 3) (fma.f64 -1/135 (pow.f64 x 5) (fma.f64 -2/2835 (pow.f64 x 7) (*.f64 1/3 x))))
(fma.f64 x (fma.f64 x (.f64 x -1/9) 1/3) (fma.f64 -1/135 (pow.f64 x 5) (.f64 -2/2835 (pow.f64 x 7))))
(fma.f64 1/3 x (fma.f64 -2/2835 (pow.f64 x 7) (fma.f64 -1/135 (pow.f64 x 5) (*.f64 -1/9 (pow.f64 x 3)))))
(fma.f64 1/3 x (fma.f64 -1/9 (pow.f64 x 3) (fma.f64 -1/135 (pow.f64 x 5) (*.f64 -2/2835 (pow.f64 x 7)))))
(.f64 1/3 (/.f64 (.f64 (cos.f64 x) (pow.f64 x 2)) (sin.f64 x)))
(.f64 1/3 (/.f64 (.f64 (cos.f64 x) (*.f64 x x)) (sin.f64 x)))
(.f64 (/.f64 (cos.f64 x) (sin.f64 x)) (.f64 1/3 (*.f64 x x)))
(.f64 1/3 (.f64 (cos.f64 x) (/.f64 (*.f64 x x) (sin.f64 x))))
(/.f64 (.f64 (.f64 x x) (*.f64 1/3 (cos.f64 x))) (sin.f64 x))
(.f64 1/3 (/.f64 (.f64 (cos.f64 x) (pow.f64 x 2)) (sin.f64 x)))
(.f64 1/3 (/.f64 (.f64 (cos.f64 x) (*.f64 x x)) (sin.f64 x)))
(.f64 (/.f64 (cos.f64 x) (sin.f64 x)) (.f64 1/3 (*.f64 x x)))
(.f64 1/3 (.f64 (cos.f64 x) (/.f64 (*.f64 x x) (sin.f64 x))))
(/.f64 (.f64 (.f64 x x) (*.f64 1/3 (cos.f64 x))) (sin.f64 x))
(.f64 1/3 (/.f64 (.f64 (cos.f64 x) (pow.f64 x 2)) (sin.f64 x)))
(.f64 1/3 (/.f64 (.f64 (cos.f64 x) (*.f64 x x)) (sin.f64 x)))
(.f64 (/.f64 (cos.f64 x) (sin.f64 x)) (.f64 1/3 (*.f64 x x)))
(.f64 1/3 (.f64 (cos.f64 x) (/.f64 (*.f64 x x) (sin.f64 x))))
(/.f64 (.f64 (.f64 x x) (*.f64 1/3 (cos.f64 x))) (sin.f64 x))
(.f64 1/3 (/.f64 (.f64 (cos.f64 x) (pow.f64 x 2)) (sin.f64 x)))
(.f64 1/3 (/.f64 (.f64 (cos.f64 x) (*.f64 x x)) (sin.f64 x)))
(.f64 (/.f64 (cos.f64 x) (sin.f64 x)) (.f64 1/3 (*.f64 x x)))
(.f64 1/3 (.f64 (cos.f64 x) (/.f64 (*.f64 x x) (sin.f64 x))))
(/.f64 (.f64 (.f64 x x) (*.f64 1/3 (cos.f64 x))) (sin.f64 x))
(.f64 1/3 (/.f64 (.f64 (cos.f64 x) (pow.f64 x 2)) (sin.f64 x)))
(.f64 1/3 (/.f64 (.f64 (cos.f64 x) (*.f64 x x)) (sin.f64 x)))
(.f64 (/.f64 (cos.f64 x) (sin.f64 x)) (.f64 1/3 (*.f64 x x)))
(.f64 1/3 (.f64 (cos.f64 x) (/.f64 (*.f64 x x) (sin.f64 x))))
(/.f64 (.f64 (.f64 x x) (*.f64 1/3 (cos.f64 x))) (sin.f64 x))
(.f64 1/3 (/.f64 (.f64 (cos.f64 x) (pow.f64 x 2)) (sin.f64 x)))
(.f64 1/3 (/.f64 (.f64 (cos.f64 x) (*.f64 x x)) (sin.f64 x)))
(.f64 (/.f64 (cos.f64 x) (sin.f64 x)) (.f64 1/3 (*.f64 x x)))
(.f64 1/3 (.f64 (cos.f64 x) (/.f64 (*.f64 x x) (sin.f64 x))))
(/.f64 (.f64 (.f64 x x) (*.f64 1/3 (cos.f64 x))) (sin.f64 x))
(.f64 1/3 (/.f64 (.f64 (cos.f64 x) (pow.f64 x 2)) (sin.f64 x)))
(.f64 1/3 (/.f64 (.f64 (cos.f64 x) (*.f64 x x)) (sin.f64 x)))
(.f64 (/.f64 (cos.f64 x) (sin.f64 x)) (.f64 1/3 (*.f64 x x)))
(.f64 1/3 (.f64 (cos.f64 x) (/.f64 (*.f64 x x) (sin.f64 x))))
(/.f64 (.f64 (.f64 x x) (*.f64 1/3 (cos.f64 x))) (sin.f64 x))
(.f64 1/3 (/.f64 (.f64 (cos.f64 x) (pow.f64 x 2)) (sin.f64 x)))
(.f64 1/3 (/.f64 (.f64 (cos.f64 x) (*.f64 x x)) (sin.f64 x)))
(.f64 (/.f64 (cos.f64 x) (sin.f64 x)) (.f64 1/3 (*.f64 x x)))
(.f64 1/3 (.f64 (cos.f64 x) (/.f64 (*.f64 x x) (sin.f64 x))))
(/.f64 (.f64 (.f64 x x) (*.f64 1/3 (cos.f64 x))) (sin.f64 x))
(/.f64 1/3 x)
(+.f64 (.f64 1/3 (/.f64 1 x)) (.f64 -1/9 x))
(+.f64 (/.f64 1/3 x) (*.f64 x -1/9))
(fma.f64 x -1/9 (/.f64 1/3 x))
(+.f64 (.f64 1/3 (/.f64 1 x)) (+.f64 (.f64 -1/9 x) (*.f64 -1/135 (pow.f64 x 3))))
(+.f64 (/.f64 1/3 x) (fma.f64 -1/9 x (*.f64 (pow.f64 x 3) -1/135)))
(+.f64 (/.f64 1/3 x) (fma.f64 x -1/9 (*.f64 (pow.f64 x 3) -1/135)))
(fma.f64 (pow.f64 x 3) -1/135 (fma.f64 x -1/9 (/.f64 1/3 x)))
(fma.f64 x -1/9 (fma.f64 (pow.f64 x 3) -1/135 (/.f64 1/3 x)))
(+.f64 (.f64 -2/2835 (pow.f64 x 5)) (+.f64 (.f64 1/3 (/.f64 1 x)) (+.f64 (.f64 -1/9 x) (.f64 -1/135 (pow.f64 x 3)))))
(fma.f64 -2/2835 (pow.f64 x 5) (+.f64 (/.f64 1/3 x) (fma.f64 -1/9 x (*.f64 (pow.f64 x 3) -1/135))))
(+.f64 (fma.f64 x -1/9 (*.f64 (pow.f64 x 3) -1/135)) (fma.f64 (pow.f64 x 5) -2/2835 (/.f64 1/3 x)))
(fma.f64 (pow.f64 x 5) -2/2835 (fma.f64 (pow.f64 x 3) -1/135 (fma.f64 x -1/9 (/.f64 1/3 x))))
(fma.f64 x -1/9 (fma.f64 (pow.f64 x 5) -2/2835 (fma.f64 (pow.f64 x 3) -1/135 (/.f64 1/3 x))))
(*.f64 1/3 (/.f64 (cos.f64 x) (sin.f64 x)))
(*.f64 (cos.f64 x) (/.f64 1/3 (sin.f64 x)))
(*.f64 1/3 (/.f64 (cos.f64 x) (sin.f64 x)))
(*.f64 (cos.f64 x) (/.f64 1/3 (sin.f64 x)))
(*.f64 1/3 (/.f64 (cos.f64 x) (sin.f64 x)))
(*.f64 (cos.f64 x) (/.f64 1/3 (sin.f64 x)))
(*.f64 1/3 (/.f64 (cos.f64 x) (sin.f64 x)))
(*.f64 (cos.f64 x) (/.f64 1/3 (sin.f64 x)))
(*.f64 1/3 (/.f64 (cos.f64 x) (sin.f64 x)))
(*.f64 (cos.f64 x) (/.f64 1/3 (sin.f64 x)))
(*.f64 1/3 (/.f64 (cos.f64 x) (sin.f64 x)))
(*.f64 (cos.f64 x) (/.f64 1/3 (sin.f64 x)))
(*.f64 1/3 (/.f64 (cos.f64 x) (sin.f64 x)))
(*.f64 (cos.f64 x) (/.f64 1/3 (sin.f64 x)))
(*.f64 1/3 (/.f64 (cos.f64 x) (sin.f64 x)))
(*.f64 (cos.f64 x) (/.f64 1/3 (sin.f64 x)))

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.4b	(*.f64 1/3 x)
✓	0.7b	(cbrt.f64 (*.f64 1/3 x))
✓	0.7b	(pow.f64 (cbrt.f64 (*.f64 1/3 x)) 3)

Compiler

Compiled 17 to 13 computations (23.5% saved)

series8.0ms (0.1%)

Counts

2 → 0

Calls

6 calls:

Time	Variable		Point	Expression
3.0ms	x	@	inf	(cbrt.f64 (*.f64 1/3 x))
2.0ms	x	@	0	(pow.f64 (cbrt.f64 (*.f64 1/3 x)) 3)
2.0ms	x	@	-inf	(pow.f64 (cbrt.f64 (*.f64 1/3 x)) 3)
1.0ms	x	@	inf	(pow.f64 (cbrt.f64 (*.f64 1/3 x)) 3)
1.0ms	x	@	-inf	(cbrt.f64 (*.f64 1/3 x))

rewrite48.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

515×	`pow1_binary64`
508×	`add-sqr-sqrt_binary64`
487×	`add-log-exp_binary64`
487×	`log1p-expm1-u_binary64`
487×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	148	10
2	1376	10

Stop Event

1×	node limit

Counts

2 → 49

Calls

Call 1

Inputs
(pow.f64 (cbrt.f64 (*.f64 1/3 x)) 3)
(cbrt.f64 (*.f64 1/3 x))

Outputs

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

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

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

49 → 49

Calls

Call 1

Inputs

Outputs

eval325.0ms (2.1%)

Compiler: Compiled 5061 to 3750 computations (25.9% saved)

prune139.0ms (0.9%)

Pruning

17 alts after pruning (7 fresh and 10 done)

	Pruned	Kept	Total
New	308	3	311
Fresh	2	4	6
Picked	0	1	1
Done	3	9	12
Total	313	17	330

Error

Counts

330 → 17

Alt Table

Click to see full alt table

Status	Error	Program
	38.2b	(cbrt.f64 (.f64 (.f64 (pow.f64 (*.f64 1/3 x) 2) 1/3) x))
✓	1.0b	(*.f64 (pow.f64 1/27 1/3) x)
✓	28.7b	(/.f64 (.f64 1/3 (.f64 x x)) (tan.f64 x))
✓	60.1b	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))
✓	59.2b	(-.f64 (+.f64 1 (*.f64 1/3 x)) 1)
✓	1.8b	(pow.f64 (cbrt.f64 (*.f64 1/3 x)) 3)
	0.3b	(/.f64 (.f64 x 1/27) (+.f64 (.f64 1/2025 (pow.f64 x 4)) (-.f64 1/9 (.f64 (.f64 x x) 1/135))))
	28.7b	(.f64 (.f64 x x) (+.f64 (.f64 1/3 (/.f64 1 x)) (.f64 -1/9 x)))
	0.4b	(.f64 x (/.f64 (+.f64 (.f64 (.f64 (.f64 x (.f64 x 1/45)) (.f64 (.f64 x x) 1/2025)) (.f64 x x)) 1/27) (+.f64 (.f64 (.f64 1/45 (.f64 x x)) (.f64 1/45 (.f64 x x))) (-.f64 1/9 (.f64 (.f64 1/45 (.f64 x x)) 1/3)))))
✓	0.4b	(+.f64 (.f64 1/3 x) (+.f64 (.f64 2/945 (pow.f64 x 5)) (*.f64 1/45 (pow.f64 x 3))))
	42.4b	(sqrt.f64 (.f64 (.f64 x x) 1/9))
✓	0.6b	(*.f64 1/3 x)
✓	60.1b	(/.f64 (/.f64 (-.f64 (tan.f64 x) x) x) (tan.f64 x))
	28.6b	(.f64 (.f64 x x) (/.f64 1/3 x))
	38.2b	(cbrt.f64 (*.f64 (pow.f64 x 3) 1/27))
✓	0.4b	(+.f64 (.f64 1/3 x) (+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 1/4725 (pow.f64 x 7)))))
✓	0.4b	(.f64 x (+.f64 (.f64 1/45 (*.f64 x x)) 1/3))

Compiler

Compiled 208 to 151 computations (27.4% saved)

regimes45.0ms (0.3%)

Counts

28 → 1

Calls

Call 1

Inputs
(*.f64 1/3 x)
(.f64 (.f64 x x) (/.f64 1/3 x))
(-.f64 (+.f64 1 (*.f64 1/3 x)) 1)
(.f64 x (+.f64 (.f64 1/45 (*.f64 x x)) 1/3))
(.f64 (.f64 x x) (+.f64 (.f64 1/3 (/.f64 1 x)) (.f64 -1/9 x)))
(.f64 x (/.f64 (+.f64 (.f64 (.f64 (.f64 x (.f64 x 1/45)) (.f64 (.f64 x x) 1/2025)) (.f64 x x)) 1/27) (+.f64 (.f64 (.f64 1/45 (.f64 x x)) (.f64 1/45 (.f64 x x))) (-.f64 1/9 (.f64 (.f64 1/45 (.f64 x x)) 1/3)))))
(*.f64 (pow.f64 1/27 1/3) x)
(sqrt.f64 (.f64 (.f64 x x) 1/9))
(/.f64 (.f64 1/3 (.f64 x x)) (tan.f64 x))
(.f64 x (fma.f64 1/45 (.f64 x x) 1/3))
(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))
(.f64 (.f64 x x) (*.f64 1/3 (/.f64 1 (tan.f64 x))))
(/.f64 (.f64 x 1/27) (+.f64 (.f64 1/2025 (pow.f64 x 4)) (-.f64 1/9 (.f64 (.f64 x x) 1/135))))
(.f64 x (/.f64 (+.f64 (pow.f64 (.f64 1/45 (.f64 x x)) 3) 1/27) (+.f64 (.f64 (.f64 1/45 (.f64 x x)) (.f64 1/45 (.f64 x x))) (-.f64 1/9 (.f64 (.f64 1/45 (*.f64 x x)) 1/3)))))
(exp.f64 (log.f64 (*.f64 1/3 x)))
(pow.f64 (cbrt.f64 (*.f64 1/3 x)) 3)
(cbrt.f64 (*.f64 (pow.f64 x 3) 1/27))
(pow.f64 (cbrt.f64 (*.f64 1/3 x)) 3)
(pow.f64 (sqrt.f64 (*.f64 1/3 x)) 2)
(cbrt.f64 (pow.f64 (*.f64 1/3 x) 3))
(.f64 (.f64 1/3 (sqrt.f64 x)) (sqrt.f64 x))
(/.f64 (/.f64 (-.f64 (tan.f64 x) x) x) (tan.f64 x))
(cbrt.f64 (.f64 (.f64 (pow.f64 (*.f64 1/3 x) 2) 1/3) x))
(/.f64 (/.f64 (*.f64 1/3 (pow.f64 x 3)) x) (tan.f64 x))
(+.f64 (.f64 1/3 x) (+.f64 (.f64 2/945 (pow.f64 x 5)) (*.f64 1/45 (pow.f64 x 3))))
(/.f64 (.f64 (+.f64 (.f64 1/2025 (pow.f64 x 4)) -1/9) x) (fma.f64 1/45 (*.f64 x x) -1/3))
(/.f64 (.f64 (+.f64 1/27 (pow.f64 (.f64 x (.f64 x 1/45)) 3)) x) (+.f64 (.f64 1/2025 (pow.f64 x 4)) (-.f64 1/9 (.f64 (.f64 x x) 1/135))))
(+.f64 (.f64 1/3 x) (+.f64 (.f64 2/945 (pow.f64 x 5)) (+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 1/4725 (pow.f64 x 7)))))

Outputs
(/.f64 (.f64 (+.f64 1/27 (pow.f64 (.f64 x (.f64 x 1/45)) 3)) x) (+.f64 (.f64 1/2025 (pow.f64 x 4)) (-.f64 1/9 (.f64 (.f64 x x) 1/135))))

Calls

2 calls:

32.0ms	x
4.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))

Results

Error	Segments	Branch
0.3b	1	`x`
0.3b	1	`(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))`

Compiler

Compiled 335 to 222 computations (33.7% saved)

regimes165.0ms (1%)

Counts

26 → 1

Calls

Call 1

Inputs
(*.f64 1/3 x)
(.f64 (.f64 x x) (/.f64 1/3 x))
(-.f64 (+.f64 1 (*.f64 1/3 x)) 1)
(.f64 x (+.f64 (.f64 1/45 (*.f64 x x)) 1/3))
(.f64 (.f64 x x) (+.f64 (.f64 1/3 (/.f64 1 x)) (.f64 -1/9 x)))
(.f64 x (/.f64 (+.f64 (.f64 (.f64 (.f64 x (.f64 x 1/45)) (.f64 (.f64 x x) 1/2025)) (.f64 x x)) 1/27) (+.f64 (.f64 (.f64 1/45 (.f64 x x)) (.f64 1/45 (.f64 x x))) (-.f64 1/9 (.f64 (.f64 1/45 (.f64 x x)) 1/3)))))
(*.f64 (pow.f64 1/27 1/3) x)
(sqrt.f64 (.f64 (.f64 x x) 1/9))
(/.f64 (.f64 1/3 (.f64 x x)) (tan.f64 x))
(.f64 x (fma.f64 1/45 (.f64 x x) 1/3))
(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))
(.f64 (.f64 x x) (*.f64 1/3 (/.f64 1 (tan.f64 x))))
(/.f64 (.f64 x 1/27) (+.f64 (.f64 1/2025 (pow.f64 x 4)) (-.f64 1/9 (.f64 (.f64 x x) 1/135))))
(.f64 x (/.f64 (+.f64 (pow.f64 (.f64 1/45 (.f64 x x)) 3) 1/27) (+.f64 (.f64 (.f64 1/45 (.f64 x x)) (.f64 1/45 (.f64 x x))) (-.f64 1/9 (.f64 (.f64 1/45 (*.f64 x x)) 1/3)))))
(exp.f64 (log.f64 (*.f64 1/3 x)))
(pow.f64 (cbrt.f64 (*.f64 1/3 x)) 3)
(cbrt.f64 (*.f64 (pow.f64 x 3) 1/27))
(pow.f64 (cbrt.f64 (*.f64 1/3 x)) 3)
(pow.f64 (sqrt.f64 (*.f64 1/3 x)) 2)
(cbrt.f64 (pow.f64 (*.f64 1/3 x) 3))
(.f64 (.f64 1/3 (sqrt.f64 x)) (sqrt.f64 x))
(/.f64 (/.f64 (-.f64 (tan.f64 x) x) x) (tan.f64 x))
(cbrt.f64 (.f64 (.f64 (pow.f64 (*.f64 1/3 x) 2) 1/3) x))
(/.f64 (/.f64 (*.f64 1/3 (pow.f64 x 3)) x) (tan.f64 x))
(+.f64 (.f64 1/3 x) (+.f64 (.f64 2/945 (pow.f64 x 5)) (*.f64 1/45 (pow.f64 x 3))))
(/.f64 (.f64 (+.f64 (.f64 1/2025 (pow.f64 x 4)) -1/9) x) (fma.f64 1/45 (*.f64 x x) -1/3))

Outputs
(/.f64 (.f64 x 1/27) (+.f64 (.f64 1/2025 (pow.f64 x 4)) (-.f64 1/9 (.f64 (.f64 x x) 1/135))))

Calls

2 calls:

153.0ms	x
4.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))

Results

Error	Segments	Branch
0.3b	1	`x`
0.3b	1	`(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))`

Compiler

Compiled 289 to 187 computations (35.3% saved)

regimes14.0ms (0.1%)

Counts

12 → 1

Calls

Call 1

Inputs
(*.f64 1/3 x)
(.f64 (.f64 x x) (/.f64 1/3 x))
(-.f64 (+.f64 1 (*.f64 1/3 x)) 1)
(.f64 x (+.f64 (.f64 1/45 (*.f64 x x)) 1/3))
(.f64 (.f64 x x) (+.f64 (.f64 1/3 (/.f64 1 x)) (.f64 -1/9 x)))
(.f64 x (/.f64 (+.f64 (.f64 (.f64 (.f64 x (.f64 x 1/45)) (.f64 (.f64 x x) 1/2025)) (.f64 x x)) 1/27) (+.f64 (.f64 (.f64 1/45 (.f64 x x)) (.f64 1/45 (.f64 x x))) (-.f64 1/9 (.f64 (.f64 1/45 (.f64 x x)) 1/3)))))
(*.f64 (pow.f64 1/27 1/3) x)
(sqrt.f64 (.f64 (.f64 x x) 1/9))
(/.f64 (.f64 1/3 (.f64 x x)) (tan.f64 x))
(.f64 x (fma.f64 1/45 (.f64 x x) 1/3))
(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))
(.f64 (.f64 x x) (*.f64 1/3 (/.f64 1 (tan.f64 x))))

Outputs

(*.f64 x (/.f64 (+.f64 (*.f64 (*.f64 (*.f64 x (*.f64 x 1/45)) (*.f64 (*.f64 x x) 1/2025)) (*.f64 x x)) 1/27) (+.f64 (*.f64 (*.f64 1/45 (*.f64 x x)) (*.f64 1/45 (*.f64 x x))) (-.f64 1/9 (*.f64 (*.f64 1/45 (*.f64 x x)) 1/3)))))

Calls

2 calls:

7.0ms	x
4.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))

Results

Error	Segments	Branch
0.4b	1	`x`
0.4b	1	`(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))`

Compiler

Compiled 137 to 82 computations (40.1% saved)

regimes6.0ms (0%)

Counts

5 → 1

Calls

Call 1

Inputs
(*.f64 1/3 x)
(.f64 (.f64 x x) (/.f64 1/3 x))
(-.f64 (+.f64 1 (*.f64 1/3 x)) 1)
(.f64 x (+.f64 (.f64 1/45 (*.f64 x x)) 1/3))
(.f64 (.f64 x x) (+.f64 (.f64 1/3 (/.f64 1 x)) (.f64 -1/9 x)))

Outputs
(.f64 x (+.f64 (.f64 1/45 (*.f64 x x)) 1/3))

Calls

1 calls:

4.0ms

Results

Error	Segments	Branch
0.4b	1	`x`

Compiler

Compiled 42 to 27 computations (35.7% saved)

regimes6.0ms (0%)

Accuracy

Total -58.6b remaining (-9883.1%)

Threshold costs -58.6b (-9883.1%)

Counts

3 → 1

Calls

Call 1

Inputs
(*.f64 1/3 x)
(.f64 (.f64 x x) (/.f64 1/3 x))
(-.f64 (+.f64 1 (*.f64 1/3 x)) 1)

Outputs
(*.f64 1/3 x)

Calls

1 calls:

3.0ms

Results

Error	Segments	Branch
0.6b	1	`x`

Compiler

Compiled 20 to 14 computations (30% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

19×	`*-commutative_binary64`
12×	`+-commutative_binary64`
7×	`distribute-rgt-neg-in_binary64`
7×	`sub-neg_binary64`
5×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	140
1	67	140
2	100	140
3	110	140
4	116	140
5	117	140

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(/.f64 (.f64 (+.f64 1/27 (pow.f64 (.f64 x (.f64 x 1/45)) 3)) x) (+.f64 (.f64 1/2025 (pow.f64 x 4)) (-.f64 1/9 (.f64 (.f64 x x) 1/135))))
(/.f64 (.f64 x 1/27) (+.f64 (.f64 1/2025 (pow.f64 x 4)) (-.f64 1/9 (.f64 (.f64 x x) 1/135))))
(.f64 x (/.f64 (+.f64 (.f64 (.f64 (.f64 x (.f64 x 1/45)) (.f64 (.f64 x x) 1/2025)) (.f64 x x)) 1/27) (+.f64 (.f64 (.f64 1/45 (.f64 x x)) (.f64 1/45 (.f64 x x))) (-.f64 1/9 (.f64 (.f64 1/45 (.f64 x x)) 1/3)))))
(.f64 x (+.f64 (.f64 1/45 (*.f64 x x)) 1/3))
(*.f64 1/3 x)

Outputs
(/.f64 (.f64 (+.f64 1/27 (pow.f64 (.f64 x (.f64 x 1/45)) 3)) x) (+.f64 (.f64 1/2025 (pow.f64 x 4)) (-.f64 1/9 (.f64 (.f64 x x) 1/135))))
(/.f64 (.f64 x (+.f64 1/27 (pow.f64 (.f64 x (.f64 x 1/45)) 3))) (+.f64 (.f64 1/2025 (pow.f64 x 4)) (-.f64 1/9 (.f64 (.f64 x x) 1/135))))
(/.f64 (.f64 x 1/27) (+.f64 (.f64 1/2025 (pow.f64 x 4)) (-.f64 1/9 (.f64 (.f64 x x) 1/135))))
(/.f64 (.f64 1/27 x) (+.f64 (.f64 1/2025 (pow.f64 x 4)) (-.f64 1/9 (.f64 (.f64 x x) 1/135))))
(.f64 x (/.f64 (+.f64 (.f64 (.f64 (.f64 x (.f64 x 1/45)) (.f64 (.f64 x x) 1/2025)) (.f64 x x)) 1/27) (+.f64 (.f64 (.f64 1/45 (.f64 x x)) (.f64 1/45 (.f64 x x))) (-.f64 1/9 (.f64 (.f64 1/45 (.f64 x x)) 1/3)))))
(.f64 x (/.f64 (+.f64 1/27 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x 1/45)) (.f64 1/2025 (.f64 x x))))) (+.f64 (.f64 (.f64 1/45 (.f64 x x)) (.f64 1/45 (.f64 x x))) (-.f64 1/9 (.f64 (.f64 1/45 (.f64 x x)) 1/3)))))
(.f64 x (/.f64 (+.f64 1/27 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x 1/45)) (.f64 1/2025 (.f64 x x))))) (+.f64 (.f64 (.f64 1/45 (.f64 x x)) (.f64 1/45 (.f64 x x))) (+.f64 1/9 (.f64 (.f64 1/45 (.f64 x x)) -1/3)))))
(.f64 x (+.f64 (.f64 1/45 (*.f64 x x)) 1/3))
(*.f64 1/3 x)
(*.f64 x 1/3)

Compiler

Compiled 100 to 69 computations (31% saved)

soundness214.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

675×	`sqr-pow_binary64`
624×	`unswap-sqr_binary64`
594×	`cube-prod_binary64`
554×	`fma-def_binary64`
417×	`fabs-mul_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	30	168
1	74	162
2	153	162
3	367	162
4	677	162
5	1437	162
6	2099	162
7	3090	162
8	3307	162
9	3633	162
10	4034	162
11	4566	162
12	5297	162
13	6300	162
14	6946	162
15	7455	162
16	7858	162

Stop Event

1×	node limit

Compiler

Compiled 63 to 44 computations (30.2% saved)

end63.0ms (0.4%)

Compiler: Compiled 96 to 62 computations (35.4% saved)

Iter	Nodes	Cost
0	7	12
1	11	12
2	17	12
3	25	12
4	35	12
5	53	12
6	90	12
7	124	12
8	168	12
9	204	12
10	230	12
11	232	12
0	1	1

Iter	Nodes	Cost
0	7	12
1	11	12
2	17	12
3	25	12
4	35	12
5	53	12
6	90	12
7	124	12
8	168	12
9	204	12
10	230	12
11	232	12

Iter	Nodes	Cost
0	7	12
1	11	12
2	17	12
3	25	12
4	35	12
5	53	12
6	90	12
7	124	12
8	168	12
9	204	12
10	230	12
11	232	12
0	1	1

Iter	Nodes	Cost
0	7	12
1	11	12
2	17	12
3	25	12
4	35	12
5	53	12
6	90	12
7	124	12
8	168	12
9	204	12
10	230	12
11	232	12

Iter	Nodes	Cost
0	7	12
1	11	12
2	17	12
3	25	12
4	35	12
5	53	12
6	90	12
7	124	12
8	168	12
9	204	12
10	230	12
11	232	12
0	1	1

Iter	Nodes	Cost
0	7	12
1	11	12
2	17	12
3	25	12
4	35	12
5	53	12
6	90	12
7	124	12
8	168	12
9	204	12
10	230	12
11	232	12