Details

analyze0.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	49.6%	50.4%	0
49.6%	0%	50.4%	1

Compiler

Compiled 12 to 9 computations (25% saved)

sample4.3s (67%)

Results

3.1s	4408×	body	2048	valid
857.0ms	2026×	body	1024	valid
270.0ms	1086×	body	512	valid
105.0ms	736×	body	256	valid

preprocess15.0ms (0.2%)

Algorithm

2×	egg-herbie

Rules

8×	`sub-neg_binary64`
6×	`fma-def_binary64`
4×	`+-commutative_binary64`
3×	`associate-+l-_binary64`
3×	`associate--r+_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	9	6
2	13	6
3	19	6
4	26	6
5	36	6
6	47	6
7	59	6
8	62	6
0	1	1

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0

Outputs
0

Call 2

Inputs
(-.f64 1 (cos.f64 x))

Outputs
(-.f64 1 (cos.f64 x))

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`sub-neg_binary64`
6×	`fma-def_binary64`
4×	`+-commutative_binary64`
3×	`associate-+l-_binary64`
3×	`associate--r+_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	9	6
2	13	6
3	19	6
4	26	6
5	36	6
6	47	6
7	59	6
8	62	6

Stop Event

1×

saturated

Counts

1 → 1

Calls

Call 1

Inputs
(-.f64 1 (cos.f64 x))

Outputs
(-.f64 1 (cos.f64 x))

eval0.0ms (0%)

Compiler: Compiled 5 to 4 computations (20% saved)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

29.0b

Counts

2 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	29.0b	(-.f64 1 (cos.f64 x))

Compiler

Compiled 5 to 4 computations (20% saved)

localize7.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	1.6b	(-.f64 1 (cos.f64 x))

Compiler

Compiled 9 to 5 computations (44.4% saved)

series2.0ms (0%)

Counts

1 → 4

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(-.f64 1 (cos.f64 x))
1.0ms	x	@	inf	(-.f64 1 (cos.f64 x))
1.0ms	x	@	-inf	(-.f64 1 (cos.f64 x))

rewrite63.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

517×	`pow1_binary64`
503×	`add-sqr-sqrt_binary64`
481×	`add-log-exp_binary64`
481×	`log1p-expm1-u_binary64`
481×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	102	6
2	1250	6

Stop Event

1×	node limit

Counts

1 → 28

Calls

Call 1

Inputs
(-.f64 1 (cos.f64 x))

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

Outputs

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

simplify106.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

601×	`distribute-rgt-out_binary64`
520×	`sqr-pow_binary64`
482×	`associate-+l+_binary64`
478×	`distribute-lft-out_binary64`
413×	`unswap-sqr_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	70
1	56	70
2	128	70
3	425	70
4	2012	70
5	4417	70
6	4794	70
7	5300	70
8	6290	70
9	7274	70
10	7713	70

Stop Event

1×	node limit

Counts

32 → 36

Calls

Call 1

Inputs
(*.f64 1/2 (pow.f64 x 2))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (+.f64 (.f64 -1/24 (pow.f64 x 4)) (*.f64 1/720 (pow.f64 x 6))))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (+.f64 (.f64 -1/24 (pow.f64 x 4)) (+.f64 (.f64 1/720 (pow.f64 x 6)) (.f64 -1/40320 (pow.f64 x 8)))))

Outputs
(*.f64 1/2 (pow.f64 x 2))
(.f64 1/2 (.f64 x x))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))
(fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4)))
(.f64 x (.f64 x (fma.f64 (*.f64 x x) -1/24 1/2)))
(.f64 (.f64 x x) (fma.f64 x (*.f64 x -1/24) 1/2))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (+.f64 (.f64 -1/24 (pow.f64 x 4)) (*.f64 1/720 (pow.f64 x 6))))
(fma.f64 1/2 (.f64 x x) (fma.f64 -1/24 (pow.f64 x 4) (.f64 1/720 (pow.f64 x 6))))
(fma.f64 1/2 (.f64 x x) (fma.f64 1/720 (pow.f64 x 6) (.f64 -1/24 (pow.f64 x 4))))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) -1/24 1/2) (*.f64 1/720 (pow.f64 x 6)))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (+.f64 (.f64 -1/24 (pow.f64 x 4)) (+.f64 (.f64 1/720 (pow.f64 x 6)) (.f64 -1/40320 (pow.f64 x 8)))))
(fma.f64 1/2 (.f64 x x) (fma.f64 -1/24 (pow.f64 x 4) (fma.f64 1/720 (pow.f64 x 6) (.f64 -1/40320 (pow.f64 x 8)))))
(fma.f64 1/2 (.f64 x x) (fma.f64 1/720 (pow.f64 x 6) (fma.f64 -1/40320 (pow.f64 x 8) (.f64 -1/24 (pow.f64 x 4)))))
(fma.f64 (pow.f64 x 4) (fma.f64 (pow.f64 x 4) -1/40320 -1/24) (fma.f64 1/720 (pow.f64 x 6) (.f64 1/2 (.f64 x x))))

eval8.0ms (0.1%)

Compiler: Compiled 390 to 244 computations (37.4% saved)

prune6.0ms (0.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	32	4	36
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	32	5	37

Error

0.0b

Counts

37 → 5

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.6b	(/.f64 1 (/.f64 (+.f64 1 (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 x))))
▶	0.0b	(.f64 (.f64 x x) (fma.f64 x (*.f64 x -1/24) 1/2))
▶	0.0b	(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))
▶	0.2b	(.f64 1/2 (.f64 x x))
✓	29.0b	(-.f64 1 (cos.f64 x))

Compiler

Compiled 47 to 34 computations (27.7% saved)

localize36.0ms (0.6%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 11 to 5 computations (54.5% saved)

series2.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite43.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

432×	`pow1_binary64`
420×	`add-sqr-sqrt_binary64`
411×	`*-un-lft-identity_binary64`
401×	`add-log-exp_binary64`
401×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	102	7
2	1147	7

Stop Event

1×	node limit

Counts

1 → 14

Calls

Call 1

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

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

Outputs

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

simplify179.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

1082×	`sqr-pow_binary64`
617×	`cube-prod_binary64`
554×	`fabs-mul_binary64`
523×	`pow-sqr_binary64`
456×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	84
1	12	84
2	22	84
3	44	84
4	106	84
5	334	84
6	1259	84
7	2136	84
8	2300	84
9	2484	84
10	2692	84
11	2991	84
12	3384	84
13	3865	84
14	4433	84
15	5121	84
16	5954	84
17	6346	84
18	6636	84
19	6910	84
20	6982	84
21	7018	84
22	7959	84

Stop Event

1×	node limit

Counts

26 → 16

Calls

Call 1

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

Outputs
(*.f64 1/2 (pow.f64 x 2))
(.f64 1/2 (.f64 x x))
(*.f64 1/2 (pow.f64 x 2))
(.f64 1/2 (.f64 x x))
(*.f64 1/2 (pow.f64 x 2))
(.f64 1/2 (.f64 x x))
(*.f64 1/2 (pow.f64 x 2))
(.f64 1/2 (.f64 x x))
(*.f64 1/2 (pow.f64 x 2))
(.f64 1/2 (.f64 x x))
(*.f64 1/2 (pow.f64 x 2))
(.f64 1/2 (.f64 x x))
(*.f64 1/2 (pow.f64 x 2))
(.f64 1/2 (.f64 x x))
(*.f64 1/2 (pow.f64 x 2))
(.f64 1/2 (.f64 x x))
(*.f64 1/2 (pow.f64 x 2))
(.f64 1/2 (.f64 x x))
(*.f64 1/2 (pow.f64 x 2))
(.f64 1/2 (.f64 x x))
(*.f64 1/2 (pow.f64 x 2))
(.f64 1/2 (.f64 x x))
(*.f64 1/2 (pow.f64 x 2))
(.f64 1/2 (.f64 x x))

localize11.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (.f64 x x) (fma.f64 x (*.f64 x -1/24) 1/2))
✓	0.3b	(*.f64 x -1/24)

Compiler

Compiled 26 to 15 computations (42.3% saved)

series4.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(.f64 (.f64 x x) (fma.f64 x (*.f64 x -1/24) 1/2))
1.0ms	x	@	inf	(.f64 (.f64 x x) (fma.f64 x (*.f64 x -1/24) 1/2))
1.0ms	x	@	inf	(*.f64 x -1/24)
1.0ms	x	@	0	(.f64 (.f64 x x) (fma.f64 x (*.f64 x -1/24) 1/2))
1.0ms	x	@	0	(*.f64 x -1/24)

rewrite53.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

735×	`pow1_binary64`
684×	`add-log-exp_binary64`
684×	`log1p-expm1-u_binary64`
684×	`expm1-log1p-u_binary64`
669×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	164	18
2	1884	18

Stop Event

1×	node limit

Counts

2 → 26

Calls

Call 1

Inputs
(*.f64 x -1/24)
(.f64 (.f64 x x) (fma.f64 x (*.f64 x -1/24) 1/2))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 x -1/24)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x -1/24) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x -1/24) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x -1/24)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 x -1/24)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (*.f64 x x) 1/576))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 x) -1/24))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x -1/24) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x -1/24)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x -1/24)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x -1/24)))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 x (*.f64 x -1/24)) (*.f64 x x)) (*.f64 1/2 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x -1/24))) (*.f64 (*.f64 x x) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x -1/24) 1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x -1/24) 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x -1/24) 1/2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x -1/24) 1/2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (sqrt.f64 (fma.f64 x (*.f64 x -1/24) 1/2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 x 4) (pow.f64 (fma.f64 x (*.f64 x -1/24) 1/2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (pow.f64 (exp.f64 x) x) (fma.f64 x (*.f64 x -1/24) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x -1/24) 1/2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (*.f64 x x) 3) (pow.f64 (fma.f64 x (*.f64 x -1/24) 1/2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (fma.f64 x (*.f64 x -1/24) 1/2) 3) (pow.f64 (*.f64 x x) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x -1/24) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x -1/24) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x -1/24) 1/2))))))))

simplify196.0ms (3%)

Algorithm

1×	egg-herbie

Rules

1076×	`sqr-pow_binary64`
670×	`fma-def_binary64`
511×	`pow-sqr_binary64`
446×	`cube-prod_binary64`
427×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	195
1	24	195
2	46	195
3	115	195
4	367	195
5	1445	195
6	2770	195
7	3302	195
8	3493	195
9	3704	195
10	3983	195
11	4350	195
12	4833	195
13	5366	195
14	5990	195
15	6743	195
16	7055	195
17	7279	195
18	7475	195
19	7531	195
20	7553	195

Stop Event

1×	node limit

Counts

50 → 32

Calls

Call 1

Inputs
(*.f64 -1/24 x)
(*.f64 -1/24 x)
(*.f64 -1/24 x)
(*.f64 -1/24 x)
(*.f64 -1/24 x)
(*.f64 -1/24 x)
(*.f64 -1/24 x)
(*.f64 -1/24 x)
(*.f64 -1/24 x)
(*.f64 -1/24 x)
(*.f64 -1/24 x)
(*.f64 -1/24 x)
(*.f64 1/2 (pow.f64 x 2))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))
(*.f64 -1/24 (pow.f64 x 4))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))
(*.f64 -1/24 (pow.f64 x 4))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))

Outputs
(*.f64 -1/24 x)
(*.f64 -1/24 x)
(*.f64 -1/24 x)
(*.f64 -1/24 x)
(*.f64 -1/24 x)
(*.f64 -1/24 x)
(*.f64 -1/24 x)
(*.f64 -1/24 x)
(*.f64 -1/24 x)
(*.f64 -1/24 x)
(*.f64 -1/24 x)
(*.f64 -1/24 x)
(*.f64 1/2 (pow.f64 x 2))
(.f64 1/2 (.f64 x x))
(.f64 x (.f64 x 1/2))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))
(fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4)))
(fma.f64 -1/24 (pow.f64 x 4) (.f64 x (.f64 x 1/2)))
(.f64 x (.f64 x (fma.f64 -1/24 (*.f64 x x) 1/2)))
(fma.f64 -1/24 (pow.f64 x 4) (.f64 1/2 (.f64 x x)))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))
(fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4)))
(fma.f64 -1/24 (pow.f64 x 4) (.f64 x (.f64 x 1/2)))
(.f64 x (.f64 x (fma.f64 -1/24 (*.f64 x x) 1/2)))
(fma.f64 -1/24 (pow.f64 x 4) (.f64 1/2 (.f64 x x)))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))
(fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4)))
(fma.f64 -1/24 (pow.f64 x 4) (.f64 x (.f64 x 1/2)))
(.f64 x (.f64 x (fma.f64 -1/24 (*.f64 x x) 1/2)))
(fma.f64 -1/24 (pow.f64 x 4) (.f64 1/2 (.f64 x x)))
(*.f64 -1/24 (pow.f64 x 4))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))
(fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4)))
(fma.f64 -1/24 (pow.f64 x 4) (.f64 x (.f64 x 1/2)))
(.f64 x (.f64 x (fma.f64 -1/24 (*.f64 x x) 1/2)))
(fma.f64 -1/24 (pow.f64 x 4) (.f64 1/2 (.f64 x x)))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))
(fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4)))
(fma.f64 -1/24 (pow.f64 x 4) (.f64 x (.f64 x 1/2)))
(.f64 x (.f64 x (fma.f64 -1/24 (*.f64 x x) 1/2)))
(fma.f64 -1/24 (pow.f64 x 4) (.f64 1/2 (.f64 x x)))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))
(fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4)))
(fma.f64 -1/24 (pow.f64 x 4) (.f64 x (.f64 x 1/2)))
(.f64 x (.f64 x (fma.f64 -1/24 (*.f64 x x) 1/2)))
(fma.f64 -1/24 (pow.f64 x 4) (.f64 1/2 (.f64 x x)))
(*.f64 -1/24 (pow.f64 x 4))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))
(fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4)))
(fma.f64 -1/24 (pow.f64 x 4) (.f64 x (.f64 x 1/2)))
(.f64 x (.f64 x (fma.f64 -1/24 (*.f64 x x) 1/2)))
(fma.f64 -1/24 (pow.f64 x 4) (.f64 1/2 (.f64 x x)))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))
(fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4)))
(fma.f64 -1/24 (pow.f64 x 4) (.f64 x (.f64 x 1/2)))
(.f64 x (.f64 x (fma.f64 -1/24 (*.f64 x x) 1/2)))
(fma.f64 -1/24 (pow.f64 x 4) (.f64 1/2 (.f64 x x)))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))
(fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4)))
(fma.f64 -1/24 (pow.f64 x 4) (.f64 x (.f64 x 1/2)))
(.f64 x (.f64 x (fma.f64 -1/24 (*.f64 x x) 1/2)))
(fma.f64 -1/24 (pow.f64 x 4) (.f64 1/2 (.f64 x x)))

localize36.0ms (0.6%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))
✓	0.0b	(*.f64 1/2 (pow.f64 x 2))
✓	0.1b	(*.f64 -1/24 (pow.f64 x 4))

Compiler

Compiled 33 to 26 computations (21.2% saved)

series3.0ms (0.1%)

Counts

3 → 3

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(*.f64 -1/24 (pow.f64 x 4))
1.0ms	x	@	inf	(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))
0.0ms	x	@	inf	(*.f64 -1/24 (pow.f64 x 4))
0.0ms	x	@	inf	(*.f64 1/2 (pow.f64 x 2))
0.0ms	x	@	0	(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))

rewrite68.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

446×	`log-prod_binary64`
335×	`exp-prod_binary64`
304×	`fma-def_binary64`
298×	`prod-exp_binary64`
270×	`pow-prod-down_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	28
1	239	28
2	2731	28

Stop Event

1×	node limit

Counts

3 → 117

Calls

Call 1

Inputs
(*.f64 -1/24 (pow.f64 x 4))
(*.f64 1/2 (pow.f64 x 2))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 -1/24 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 -1/24) (pow.f64 x 4))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 -1/24) (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 -1/24) (pow.f64 x 4)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 -1/24) (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 -1/24 (pow.f64 x 4)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 -1/24 (pow.f64 x 4)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 x 8) 1/576) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 -1/24 (pow.f64 x 4))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (*.f64 x x) (sqrt.f64 -1/24)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 x 12) -1/13824) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (fma.f64 4 (log.f64 x) (log1p.f64 -25/24)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (fma.f64 4 (log.f64 x) (log1p.f64 -25/24))) 2)) (cbrt.f64 (fma.f64 4 (log.f64 x) (log1p.f64 -25/24))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (fma.f64 4 (log.f64 x) (log1p.f64 -25/24)))) (sqrt.f64 (fma.f64 4 (log.f64 x) (log1p.f64 -25/24))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 x 8) 1/576))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 -1/24) (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 -1/24 (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 x 12) -1/13824))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 -1/24 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 -1/24 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (fma.f64 4 (log.f64 x) (log1p.f64 -25/24)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (fma.f64 4 (log.f64 x) (log1p.f64 -25/24)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 -1/24 (pow.f64 x 4)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (*.f64 x x) (sqrt.f64 -1/24))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 x 12) -1/13824)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (fma.f64 4 (log.f64 x) (log1p.f64 -25/24)) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (fma.f64 4 (log.f64 x) (log1p.f64 -25/24)) 3) 1/3))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 x (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (exp.f64 x) x))) 2)) (log.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (exp.f64 x) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (sqrt.f64 (pow.f64 (exp.f64 x) x)))) (log.f64 (sqrt.f64 (sqrt.f64 (pow.f64 (exp.f64 x) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 x (*.f64 x 1/2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (*.f64 x 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 x 4) 1/4) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x (*.f64 x 1/2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (sqrt.f64 1/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 x 6) 1/8) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (fma.f64 2 (log.f64 x) (log1p.f64 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (fma.f64 2 (log.f64 x) (log1p.f64 -1/2))) 2)) (cbrt.f64 (fma.f64 2 (log.f64 x) (log1p.f64 -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (fma.f64 2 (log.f64 x) (log1p.f64 -1/2)))) (sqrt.f64 (fma.f64 2 (log.f64 x) (log1p.f64 -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 x 4) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (sqrt.f64 (pow.f64 (exp.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 x (*.f64 x 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 x 6) 1/8))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x (*.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x (*.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (fma.f64 2 (log.f64 x) (log1p.f64 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (fma.f64 2 (log.f64 x) (log1p.f64 -1/2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 x (*.f64 x 1/2)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 x (sqrt.f64 1/2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 x 6) 1/8)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (fma.f64 2 (log.f64 x) (log1p.f64 -1/2)) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (fma.f64 2 (log.f64 x) (log1p.f64 -1/2)) 3) 1/3))))))

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simplify188.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

1319×	`sqr-pow_binary64`
659×	`pow-sqr_binary64`
493×	`cube-prod_binary64`
407×	`fabs-mul_binary64`
391×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	21
1	19	21
2	38	21
3	93	21
4	297	21
5	1171	21
6	1937	21
7	2061	21
8	2230	21
9	2429	21
10	2702	21
11	3061	21
12	3514	21
13	4045	21
14	4677	21
15	5428	21
16	5740	21
17	5968	21
18	6164	21
19	6216	21
20	6238	21
21	7072	21
22	7985	21

Stop Event

1×	node limit

Counts

120 → 120

Calls

Call 1

Inputs
(*.f64 1/2 (pow.f64 x 2))
(*.f64 -1/24 (pow.f64 x 4))
(*.f64 -1/24 (pow.f64 x 4))

Outputs
(*.f64 1/2 (pow.f64 x 2))
(.f64 1/2 (.f64 x x))
(*.f64 -1/24 (pow.f64 x 4))
(*.f64 -1/24 (pow.f64 x 4))

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (sin.f64 x) (sin.f64 x))
✓	0.0b	(+.f64 1 (cos.f64 x))
✓	0.2b	(/.f64 (+.f64 1 (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 x)))
✓	0.7b	(/.f64 1 (/.f64 (+.f64 1 (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 x))))

Compiler

Compiled 38 to 15 computations (60.5% saved)

series6.0ms (0.1%)

Counts

4 → 44

Calls

12 calls:

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

rewrite102.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

483×	`log-prod_binary64`
386×	`prod-diff_binary64`
299×	`pow-prod-down_binary64`
254×	`pow2_binary64`
207×	`fma-def_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	43
1	207	27
2	3058	27

Stop Event

1×	node limit

Counts

4 → 210

Calls

Call 1

Inputs
(/.f64 1 (/.f64 (+.f64 1 (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 x))))
(/.f64 (+.f64 1 (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 x)))
(+.f64 1 (cos.f64 x))
(*.f64 (sin.f64 x) (sin.f64 x))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (neg.f64 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (.f64 -1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (.f64 (neg.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2)) (cbrt.f64 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (.f64 (neg.f64 (sqrt.f64 (cos.f64 x))) (sqrt.f64 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (-.f64 1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (-.f64 1 (cos.f64 x)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (-.f64 1 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (-.f64 1 (cos.f64 x))))) (log.f64 (sqrt.f64 (exp.f64 (-.f64 1 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 1 (cos.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (-.f64 1 (cos.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1/2 (+.f64 1 (cos.f64 x))) (/.f64 (.f64 (cos.f64 (+.f64 x x)) 1/2) (+.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (-.f64 1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (sin.f64 x) 2) (/.f64 1 (+.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 2) (cbrt.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (sqrt.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -1 (/.f64 1 (/.f64 -1 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 1 (cos.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (+.f64 1 (cos.f64 x))) (pow.f64 (sin.f64 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sin.f64 x) 1) (tan.f64 (/.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 x)) 4) 1) (/.f64 (pow.f64 (cbrt.f64 (sin.f64 x)) 2) (+.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (+.f64 1 (cos.f64 x))) -2) (/.f64 (pow.f64 (sin.f64 x) 2) (cbrt.f64 (+.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sin.f64 x) (pow.f64 (cbrt.f64 (+.f64 1 (cos.f64 x))) 2)) (/.f64 (sin.f64 x) (cbrt.f64 (+.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 x)) 4) (pow.f64 (cbrt.f64 (+.f64 1 (cos.f64 x))) 2)) (/.f64 (pow.f64 (cbrt.f64 (sin.f64 x)) 2) (cbrt.f64 (+.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (+.f64 1 (cos.f64 x)) -1/2) (/.f64 (pow.f64 (sin.f64 x) 2) (sqrt.f64 (+.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sin.f64 x) (sqrt.f64 (+.f64 1 (cos.f64 x)))) (/.f64 (sin.f64 x) (sqrt.f64 (+.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 x)) 4) (sqrt.f64 (+.f64 1 (cos.f64 x)))) (/.f64 (pow.f64 (cbrt.f64 (sin.f64 x)) 2) (sqrt.f64 (+.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (+.f64 -1 (neg.f64 (cos.f64 x)))) (neg.f64 (pow.f64 (sin.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (/.f64 1 (tan.f64 (/.f64 x 2)))) (sin.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 1 (pow.f64 (cos.f64 x) 3))) (fma.f64 (cos.f64 x) (-.f64 (cos.f64 x) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (cbrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) -2))) (cbrt.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (/.f64 1 (+.f64 1 (cos.f64 x))) 1) (pow.f64 (sin.f64 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (/.f64 1 (+.f64 1 (cos.f64 x))) (sin.f64 x)) (sin.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (/.f64 1 (+.f64 1 (cos.f64 x))) (pow.f64 (cbrt.f64 (sin.f64 x)) 4)) (pow.f64 (cbrt.f64 (sin.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (-.f64 1 (cos.f64 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 1 (cos.f64 x)) -2) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 1 (cos.f64 x)) -3) -1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (cbrt.f64 (-.f64 1 (cos.f64 x)))) -3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 1 (cos.f64 x)) -1/2) -2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 1 (cos.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (sin.f64 x) 6) (pow.f64 (+.f64 1 (cos.f64 x)) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (neg.f64 (/.f64 -1 (-.f64 1 (cos.f64 x)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sin.f64 x) (sqrt.f64 (+.f64 1 (cos.f64 x)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (sin.f64 x) 6) (pow.f64 (+.f64 1 (cos.f64 x)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log1p.f64 (neg.f64 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (neg.f64 (log1p.f64 (neg.f64 (cos.f64 x)))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log1p.f64 (neg.f64 (cos.f64 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 3 (log1p.f64 (neg.f64 (cos.f64 x)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 1/3 (log1p.f64 (neg.f64 (cos.f64 x)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 1/2 (log1p.f64 (neg.f64 (cos.f64 x)))) 2))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 1 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 1 (-.f64 1 (cos.f64 x))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 1 (-.f64 1 (cos.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 1 (-.f64 1 (cos.f64 x)))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 1 (-.f64 1 (cos.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 1 (-.f64 1 (cos.f64 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (/.f64 1 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 1 (cos.f64 x)) (pow.f64 (sin.f64 x) -2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (-.f64 1 (cos.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (cbrt.f64 (-.f64 1 (cos.f64 x)))) (cbrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) -2)) (/.f64 1 (cbrt.f64 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (+.f64 1 (cos.f64 x))) 2) (.f64 (cbrt.f64 (+.f64 1 (cos.f64 x))) (pow.f64 (sin.f64 x) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (-.f64 1 (cos.f64 x)) -1/2) (pow.f64 (-.f64 1 (cos.f64 x)) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (+.f64 1 (cos.f64 x))) (.f64 (sqrt.f64 (+.f64 1 (cos.f64 x))) (pow.f64 (sin.f64 x) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 -1 (neg.f64 (cos.f64 x))) (/.f64 1 (neg.f64 (pow.f64 (sin.f64 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (sin.f64 x) -2) (+.f64 1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (tan.f64 (/.f64 x 2))) (/.f64 1 (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 1 (cos.f64 x))) 2) 1) (/.f64 (cbrt.f64 (+.f64 1 (cos.f64 x))) (pow.f64 (sin.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (+.f64 1 (cos.f64 x))) 1) (/.f64 (sqrt.f64 (+.f64 1 (cos.f64 x))) (pow.f64 (sin.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (sin.f64 x)) (/.f64 1 (tan.f64 (/.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 1 (cos.f64 x))) 2) (sin.f64 x)) (/.f64 (cbrt.f64 (+.f64 1 (cos.f64 x))) (sin.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (pow.f64 (cbrt.f64 (sin.f64 x)) 4)) (/.f64 (+.f64 1 (cos.f64 x)) (pow.f64 (cbrt.f64 (sin.f64 x)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 1 (cos.f64 x))) 2) (pow.f64 (cbrt.f64 (sin.f64 x)) 4)) (/.f64 1 (cbrt.f64 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (+.f64 1 (cos.f64 x))) (pow.f64 (cbrt.f64 (sin.f64 x)) 4)) (/.f64 (sqrt.f64 (+.f64 1 (cos.f64 x))) (pow.f64 (cbrt.f64 (sin.f64 x)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (+.f64 1 (cos.f64 x)) (-.f64 1 (cos.f64 (+.f64 x x)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (-.f64 1 (cos.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 1 (cos.f64 x)) -2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 1 (cos.f64 x)) -3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 3) -1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (cbrt.f64 (-.f64 1 (cos.f64 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) -3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 1 (cos.f64 x)) -1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) -2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 1 (cos.f64 x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (+.f64 1 (cos.f64 x)) 3) (pow.f64 (sin.f64 x) 6)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 1 (cos.f64 x)) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (+.f64 1 (cos.f64 x)) (neg.f64 (pow.f64 (sin.f64 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) -2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 1 (-.f64 1 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) -3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (+.f64 1 (cos.f64 x)) 3) (pow.f64 (sin.f64 x) 6)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1 (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (neg.f64 (log1p.f64 (neg.f64 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (neg.f64 (log1p.f64 (neg.f64 (cos.f64 x)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (pow.f64 (-.f64 1 (cos.f64 x)) -3)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 1/3 (neg.f64 (log1p.f64 (neg.f64 (cos.f64 x))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (pow.f64 (-.f64 1 (cos.f64 x)) -1/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log1p.f64 (neg.f64 (cos.f64 x))) -1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1 (-.f64 1 (cos.f64 x))) (/.f64 (pow.f64 (cos.f64 x) 2) (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 1 (cos.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (+.f64 1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 1 (cos.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (sin.f64 x) 2) (/.f64 1 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (+.f64 1 (cos.f64 x))) (pow.f64 (cbrt.f64 (+.f64 1 (cos.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (+.f64 1 (cos.f64 x))) 2) (cbrt.f64 (+.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (+.f64 1 (cos.f64 x))) (sqrt.f64 (+.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 1 (pow.f64 (cos.f64 x) 3)) (/.f64 1 (fma.f64 (cos.f64 x) (-.f64 (cos.f64 x) 1) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 (cos.f64 x) (-.f64 (cos.f64 x) 1) 1) (+.f64 1 (pow.f64 (cos.f64 x) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 (sin.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (sin.f64 x) 2) (-.f64 1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (neg.f64 (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (-.f64 (cos.f64 x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (cos.f64 x) 3)) (fma.f64 (cos.f64 x) (-.f64 (cos.f64 x) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (cos.f64 x) 3)) (+.f64 (pow.f64 (cos.f64 x) 2) (-.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 1 (pow.f64 (cos.f64 x) 3))) (neg.f64 (fma.f64 (cos.f64 x) (-.f64 (cos.f64 x) 1) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1 (cos.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 (cos.f64 x)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 (cos.f64 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 1 (cos.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 1 (cos.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (fma.f64 (cos.f64 x) (-.f64 (cos.f64 x) 1) 1) (+.f64 1 (pow.f64 (cos.f64 x) 3))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 (sin.f64 x) 2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 (sin.f64 x) 6) (pow.f64 (-.f64 1 (cos.f64 x)) -3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 (cbrt.f64 (sin.f64 x)) 2) (/.f64 1 (cbrt.f64 (-.f64 1 (cos.f64 x))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (sin.f64 x) (pow.f64 (-.f64 1 (cos.f64 x)) -1/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 1 (cos.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 1 (cos.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log1p.f64 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log1p.f64 (cos.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 3 (log1p.f64 (cos.f64 x))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 1/3 (log1p.f64 (cos.f64 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 1/2 (log1p.f64 (cos.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (cos.f64 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (/.f64 1 (-.f64 1 (cos.f64 x))) (neg.f64 (/.f64 (pow.f64 (cos.f64 x) 2) (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cos.f64 x) 1 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 1 (cos.f64 x)) (pow.f64 (sin.f64 x) -2) (neg.f64 (/.f64 (pow.f64 (cos.f64 x) 2) (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (-.f64 1 (cos.f64 x))) 1 (neg.f64 (/.f64 (pow.f64 (cos.f64 x) 2) (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (cbrt.f64 (-.f64 1 (cos.f64 x)))) (cbrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) -2)) (neg.f64 (/.f64 (pow.f64 (cos.f64 x) 2) (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 (-.f64 1 (cos.f64 x)) -2)) (/.f64 1 (cbrt.f64 (-.f64 1 (cos.f64 x)))) (neg.f64 (/.f64 (pow.f64 (cos.f64 x) 2) (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 1 (cos.f64 x))) 2) (.f64 (cbrt.f64 (+.f64 1 (cos.f64 x))) (pow.f64 (sin.f64 x) -2)) (neg.f64 (/.f64 (pow.f64 (cos.f64 x) 2) (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (cos.f64 x)) (pow.f64 (cbrt.f64 (cos.f64 x)) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2) (cbrt.f64 (cos.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (-.f64 1 (cos.f64 x)) -1/2) (pow.f64 (-.f64 1 (cos.f64 x)) -1/2) (neg.f64 (/.f64 (pow.f64 (cos.f64 x) 2) (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 1 (cos.f64 x))) (*.f64 (sqrt.f64 (+.f64 1 (cos.f64 x))) (pow.f64 (sin.f64 x) -2)) (neg.f64 (/.f64 (pow.f64 (cos.f64 x) 2) (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (cos.f64 x)) (sqrt.f64 (cos.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 -1 (neg.f64 (cos.f64 x))) (/.f64 1 (neg.f64 (pow.f64 (sin.f64 x) 2))) (neg.f64 (/.f64 (pow.f64 (cos.f64 x) 2) (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (sin.f64 x) -2) (+.f64 1 (cos.f64 x)) (neg.f64 (/.f64 (pow.f64 (cos.f64 x) 2) (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (tan.f64 (/.f64 x 2))) (/.f64 1 (sin.f64 x)) (neg.f64 (/.f64 (pow.f64 (cos.f64 x) 2) (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 1 (cos.f64 x))) 2) 1) (/.f64 (cbrt.f64 (+.f64 1 (cos.f64 x))) (pow.f64 (sin.f64 x) 2)) (neg.f64 (/.f64 (pow.f64 (cos.f64 x) 2) (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (sqrt.f64 (+.f64 1 (cos.f64 x))) 1) (/.f64 (sqrt.f64 (+.f64 1 (cos.f64 x))) (pow.f64 (sin.f64 x) 2)) (neg.f64 (/.f64 (pow.f64 (cos.f64 x) 2) (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (sin.f64 x)) (/.f64 1 (tan.f64 (/.f64 x 2))) (neg.f64 (/.f64 (pow.f64 (cos.f64 x) 2) (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 1 (cos.f64 x))) 2) (sin.f64 x)) (/.f64 (cbrt.f64 (+.f64 1 (cos.f64 x))) (sin.f64 x)) (neg.f64 (/.f64 (pow.f64 (cos.f64 x) 2) (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (pow.f64 (cbrt.f64 (sin.f64 x)) 4)) (/.f64 (+.f64 1 (cos.f64 x)) (pow.f64 (cbrt.f64 (sin.f64 x)) 2)) (neg.f64 (/.f64 (pow.f64 (cos.f64 x) 2) (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 1 (cos.f64 x))) 2) (pow.f64 (cbrt.f64 (sin.f64 x)) 4)) (/.f64 1 (cbrt.f64 (-.f64 1 (cos.f64 x)))) (neg.f64 (/.f64 (pow.f64 (cos.f64 x) 2) (-.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (sqrt.f64 (+.f64 1 (cos.f64 x))) (pow.f64 (cbrt.f64 (sin.f64 x)) 4)) 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((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (neg.f64 (pow.f64 (cos.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (.f64 (neg.f64 (cos.f64 x)) (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (sin.f64 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1/2 (neg.f64 (.f64 (cos.f64 (+.f64 x x)) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1/2 (.f64 -1/2 (cos.f64 (+.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (sin.f64 x) 2))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (sin.f64 x) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (sin.f64 x) 2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (sin.f64 x) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 1 (pow.f64 (cos.f64 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 1/2 (.f64 (cos.f64 (+.f64 x x)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 1/2 (/.f64 (cos.f64 (+.f64 x x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (sin.f64 x) 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (pow.f64 (sin.f64 x) -2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 2 (-.f64 1 (cos.f64 (+.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (cos.f64 (+.f64 x x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1 (cos.f64 (+.f64 x x)))) -2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1/8 (pow.f64 (.f64 (cos.f64 (+.f64 x x)) 1/2) 3)) (+.f64 1/4 (+.f64 (pow.f64 (.f64 (cos.f64 (+.f64 x x)) 1/2) 2) (.f64 1/2 (.f64 (cos.f64 (+.f64 x x)) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (cos.f64 x) 4)) (+.f64 1 (pow.f64 (cos.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1/4 (pow.f64 (.f64 (cos.f64 (+.f64 x x)) 1/2) 2)) (pow.f64 (cos.f64 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (cos.f64 x) 6)) (+.f64 1 (+.f64 (pow.f64 (cos.f64 x) 4) (pow.f64 (cos.f64 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sin.f64 x) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sin.f64 x) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sin.f64 x) 3) 2/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sin.f64 x) 4) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sin.f64 x) 6) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sin.f64 x)) 6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (cbrt.f64 (sin.f64 x)) 2) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (sin.f64 x)) 4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sin.f64 x) -2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 2 (-.f64 1 (cos.f64 (+.f64 x x)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (sin.f64 x) 4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (sin.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (sin.f64 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (sin.f64 x) 6))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (sin.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (sin.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 2 (log.f64 (sin.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (sin.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 2 (log.f64 (sin.f64 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 -2 (log.f64 (sin.f64 x))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (pow.f64 (sin.f64 x) 6)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 2 (log.f64 (cbrt.f64 (sin.f64 x)))) 3))))))

simplify80.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

968×	`fma-def_binary64`
705×	`associate-r_binary64`
663×	`distribute-lft-out_binary64`
472×	`associate-/l/_binary64`
360×	`unswap-sqr_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	70	534
1	157	532
2	372	530
3	1135	504
4	3863	504
5	5448	504
6	7577	504

Stop Event

1×	node limit

Counts

254 → 248

Calls

Call 1

Inputs
(*.f64 1/2 (pow.f64 x 2))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (+.f64 (.f64 -1/24 (pow.f64 x 4)) (*.f64 1/720 (pow.f64 x 6))))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (+.f64 (.f64 -1/24 (pow.f64 x 4)) (+.f64 (.f64 1/720 (pow.f64 x 6)) (.f64 -1/40320 (pow.f64 x 8)))))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 1 (cos.f64 x)))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 1 (cos.f64 x)))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 1 (cos.f64 x)))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 1 (cos.f64 x)))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 (cos.f64 x) 1))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 (cos.f64 x) 1))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 (cos.f64 x) 1))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 (cos.f64 x) 1))
(/.f64 2 (pow.f64 x 2))
(+.f64 1/6 (*.f64 2 (/.f64 1 (pow.f64 x 2))))
(+.f64 (.f64 1/120 (pow.f64 x 2)) (+.f64 1/6 (.f64 2 (/.f64 1 (pow.f64 x 2)))))
(+.f64 (.f64 1/120 (pow.f64 x 2)) (+.f64 1/6 (+.f64 (.f64 1/3024 (pow.f64 x 4)) (*.f64 2 (/.f64 1 (pow.f64 x 2))))))
(/.f64 (+.f64 1 (cos.f64 x)) (pow.f64 (sin.f64 x) 2))
(/.f64 (+.f64 1 (cos.f64 x)) (pow.f64 (sin.f64 x) 2))
(/.f64 (+.f64 1 (cos.f64 x)) (pow.f64 (sin.f64 x) 2))
(/.f64 (+.f64 1 (cos.f64 x)) (pow.f64 (sin.f64 x) 2))
(/.f64 (+.f64 (cos.f64 x) 1) (pow.f64 (sin.f64 x) 2))
(/.f64 (+.f64 (cos.f64 x) 1) (pow.f64 (sin.f64 x) 2))
(/.f64 (+.f64 (cos.f64 x) 1) (pow.f64 (sin.f64 x) 2))
(/.f64 (+.f64 (cos.f64 x) 1) (pow.f64 (sin.f64 x) 2))
2
(+.f64 2 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 2 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 1/24 (pow.f64 x 4))))
(+.f64 2 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (+.f64 (.f64 1/24 (pow.f64 x 4)) (*.f64 -1/720 (pow.f64 x 6)))))
(+.f64 (cos.f64 x) 1)
(+.f64 (cos.f64 x) 1)
(+.f64 (cos.f64 x) 1)
(+.f64 (cos.f64 x) 1)
(pow.f64 x 2)
(+.f64 (*.f64 -1/3 (pow.f64 x 4)) (pow.f64 x 2))
(+.f64 (.f64 -1/3 (pow.f64 x 4)) (+.f64 (.f64 2/45 (pow.f64 x 6)) (pow.f64 x 2)))
(+.f64 (.f64 -1/3 (pow.f64 x 4)) (+.f64 (.f64 -1/315 (pow.f64 x 8)) (+.f64 (*.f64 2/45 (pow.f64 x 6)) (pow.f64 x 2))))
(pow.f64 (sin.f64 x) 2)
(pow.f64 (sin.f64 x) 2)
(pow.f64 (sin.f64 x) 2)
(pow.f64 (sin.f64 x) 2)
(pow.f64 (sin.f64 x) 2)
(pow.f64 (sin.f64 x) 2)
(pow.f64 (sin.f64 x) 2)
(pow.f64 (sin.f64 x) 2)

Outputs
(*.f64 1/2 (pow.f64 x 2))
(.f64 1/2 (.f64 x x))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))
(fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4)))
(.f64 (.f64 x x) (fma.f64 x (*.f64 x -1/24) 1/2))
(.f64 x (.f64 x (fma.f64 x (*.f64 x -1/24) 1/2)))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (+.f64 (.f64 -1/24 (pow.f64 x 4)) (*.f64 1/720 (pow.f64 x 6))))
(fma.f64 1/2 (.f64 x x) (fma.f64 -1/24 (pow.f64 x 4) (.f64 1/720 (pow.f64 x 6))))
(fma.f64 1/2 (.f64 x x) (fma.f64 1/720 (pow.f64 x 6) (.f64 -1/24 (pow.f64 x 4))))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (+.f64 (.f64 -1/24 (pow.f64 x 4)) (+.f64 (.f64 1/720 (pow.f64 x 6)) (.f64 -1/40320 (pow.f64 x 8)))))
(fma.f64 1/2 (.f64 x x) (fma.f64 -1/24 (pow.f64 x 4) (fma.f64 1/720 (pow.f64 x 6) (.f64 -1/40320 (pow.f64 x 8)))))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 1 (cos.f64 x)))
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 1 (cos.f64 x)))
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 1 (cos.f64 x)))
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 1 (cos.f64 x)))
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 (cos.f64 x) 1))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 1 (cos.f64 x)))
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 (cos.f64 x) 1))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 1 (cos.f64 x)))
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 (cos.f64 x) 1))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 1 (cos.f64 x)))
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 (cos.f64 x) 1))
(/.f64 (pow.f64 (sin.f64 x) 2) (+.f64 1 (cos.f64 x)))
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(+.f64 1/6 (*.f64 2 (/.f64 1 (pow.f64 x 2))))
(+.f64 1/6 (/.f64 2 (*.f64 x x)))
(+.f64 (.f64 1/120 (pow.f64 x 2)) (+.f64 1/6 (.f64 2 (/.f64 1 (pow.f64 x 2)))))
(fma.f64 1/120 (.f64 x x) (+.f64 1/6 (/.f64 2 (.f64 x x))))
(+.f64 (/.f64 2 (.f64 x x)) (fma.f64 (.f64 x x) 1/120 1/6))
(+.f64 1/6 (fma.f64 x (.f64 x 1/120) (/.f64 2 (.f64 x x))))
(+.f64 (.f64 1/120 (pow.f64 x 2)) (+.f64 1/6 (+.f64 (.f64 1/3024 (pow.f64 x 4)) (*.f64 2 (/.f64 1 (pow.f64 x 2))))))
(fma.f64 1/120 (.f64 x x) (+.f64 1/6 (fma.f64 1/3024 (pow.f64 x 4) (/.f64 2 (.f64 x x)))))
(+.f64 (fma.f64 (pow.f64 x 4) 1/3024 (/.f64 2 (.f64 x x))) (fma.f64 (.f64 x x) 1/120 1/6))
(fma.f64 x (.f64 x 1/120) (fma.f64 (pow.f64 x 4) 1/3024 (+.f64 1/6 (/.f64 2 (.f64 x x)))))
(+.f64 (/.f64 2 (.f64 x x)) (fma.f64 (pow.f64 x 4) 1/3024 (fma.f64 x (.f64 x 1/120) 1/6)))
(/.f64 (+.f64 1 (cos.f64 x)) (pow.f64 (sin.f64 x) 2))
(/.f64 (+.f64 1 (cos.f64 x)) (pow.f64 (sin.f64 x) 2))
(/.f64 (+.f64 1 (cos.f64 x)) (pow.f64 (sin.f64 x) 2))
(/.f64 (+.f64 1 (cos.f64 x)) (pow.f64 (sin.f64 x) 2))
(/.f64 (+.f64 (cos.f64 x) 1) (pow.f64 (sin.f64 x) 2))
(/.f64 (+.f64 1 (cos.f64 x)) (pow.f64 (sin.f64 x) 2))
(/.f64 (+.f64 (cos.f64 x) 1) (pow.f64 (sin.f64 x) 2))
(/.f64 (+.f64 1 (cos.f64 x)) (pow.f64 (sin.f64 x) 2))
(/.f64 (+.f64 (cos.f64 x) 1) (pow.f64 (sin.f64 x) 2))
(/.f64 (+.f64 1 (cos.f64 x)) (pow.f64 (sin.f64 x) 2))
(/.f64 (+.f64 (cos.f64 x) 1) (pow.f64 (sin.f64 x) 2))
(/.f64 (+.f64 1 (cos.f64 x)) (pow.f64 (sin.f64 x) 2))
2
(+.f64 2 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 2 (.f64 (.f64 x x) -1/2))
(fma.f64 (*.f64 x x) -1/2 2)
(fma.f64 x (*.f64 x -1/2) 2)
(+.f64 2 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 1/24 (pow.f64 x 4))))
(+.f64 2 (fma.f64 -1/2 (.f64 x x) (.f64 (pow.f64 x 4) 1/24)))
(+.f64 2 (fma.f64 (.f64 x x) -1/2 (.f64 (pow.f64 x 4) 1/24)))
(fma.f64 (pow.f64 x 4) 1/24 (fma.f64 x (*.f64 x -1/2) 2))
(fma.f64 x (*.f64 x -1/2) (fma.f64 (pow.f64 x 4) 1/24 2))
(+.f64 2 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (+.f64 (.f64 1/24 (pow.f64 x 4)) (*.f64 -1/720 (pow.f64 x 6)))))
(+.f64 2 (fma.f64 -1/2 (.f64 x x) (fma.f64 1/24 (pow.f64 x 4) (.f64 (pow.f64 x 6) -1/720))))
(+.f64 (fma.f64 (.f64 x x) -1/2 2) (fma.f64 (pow.f64 x 6) -1/720 (.f64 (pow.f64 x 4) 1/24)))
(+.f64 2 (fma.f64 (pow.f64 x 4) 1/24 (fma.f64 x (.f64 x -1/2) (.f64 (pow.f64 x 6) -1/720))))
(fma.f64 x (*.f64 x -1/2) (fma.f64 (pow.f64 x 4) 1/24 (fma.f64 (pow.f64 x 6) -1/720 2)))
(+.f64 (cos.f64 x) 1)
(+.f64 1 (cos.f64 x))
(+.f64 (cos.f64 x) 1)
(+.f64 1 (cos.f64 x))
(+.f64 (cos.f64 x) 1)
(+.f64 1 (cos.f64 x))
(+.f64 (cos.f64 x) 1)
(+.f64 1 (cos.f64 x))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 -1/3 (pow.f64 x 4)) (pow.f64 x 2))
(fma.f64 -1/3 (pow.f64 x 4) (*.f64 x x))
(fma.f64 x x (*.f64 (pow.f64 x 4) -1/3))
(fma.f64 (pow.f64 x 4) -1/3 (*.f64 x x))
(+.f64 (.f64 -1/3 (pow.f64 x 4)) (+.f64 (.f64 2/45 (pow.f64 x 6)) (pow.f64 x 2)))
(fma.f64 -1/3 (pow.f64 x 4) (fma.f64 2/45 (pow.f64 x 6) (*.f64 x x)))
(fma.f64 (pow.f64 x 4) -1/3 (fma.f64 x x (*.f64 (pow.f64 x 6) 2/45)))
(+.f64 (.f64 -1/3 (pow.f64 x 4)) (+.f64 (.f64 -1/315 (pow.f64 x 8)) (+.f64 (*.f64 2/45 (pow.f64 x 6)) (pow.f64 x 2))))
(fma.f64 -1/3 (pow.f64 x 4) (fma.f64 -1/315 (pow.f64 x 8) (fma.f64 2/45 (pow.f64 x 6) (*.f64 x x))))
(fma.f64 (pow.f64 x 4) -1/3 (fma.f64 (pow.f64 x 8) -1/315 (fma.f64 x x (*.f64 (pow.f64 x 6) 2/45))))
(fma.f64 (pow.f64 x 4) -1/3 (fma.f64 x x (fma.f64 (pow.f64 x 8) -1/315 (*.f64 (pow.f64 x 6) 2/45))))
(pow.f64 (sin.f64 x) 2)
(pow.f64 (sin.f64 x) 2)
(pow.f64 (sin.f64 x) 2)
(pow.f64 (sin.f64 x) 2)
(pow.f64 (sin.f64 x) 2)
(pow.f64 (sin.f64 x) 2)
(pow.f64 (sin.f64 x) 2)
(pow.f64 (sin.f64 x) 2)

eval256.0ms (3.9%)

Compiler: Compiled 6369 to 4278 computations (32.8% saved)

prune54.0ms (0.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	413	3	416
Fresh	0	0	0
Picked	1	0	1
Done	3	1	4
Total	417	4	421

Error

Counts

421 → 4

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.0b	(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
✓	0.0b	(.f64 (.f64 x x) (fma.f64 x (*.f64 x -1/24) 1/2))
▶	0.1b	(.f64 x (.f64 x 1/2))
▶	0.6b	(/.f64 1 (+.f64 1/6 (/.f64 2 (*.f64 x x))))

Compiler

Compiled 35 to 25 computations (28.6% saved)

localize5.0ms (0.1%)

Compiler: Compiled 11 to 7 computations (36.4% saved)

localize9.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))

Compiler

Compiled 19 to 12 computations (36.8% saved)

series6.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
4.0ms	x	@	0	(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
1.0ms	x	@	inf	(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
1.0ms	x	@	-inf	(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))

rewrite51.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

709×	`pow1_binary64`
657×	`add-log-exp_binary64`
657×	`log1p-expm1-u_binary64`
657×	`expm1-log1p-u_binary64`
645×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	149	11
2	1777	11

Stop Event

1×	node limit

Counts

1 → 15

Calls

Call 1

Inputs
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))

Outputs

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

simplify113.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

600×	`distribute-rgt-out_binary64`
520×	`sqr-pow_binary64`
480×	`associate-+l+_binary64`
478×	`distribute-lft-out_binary64`
413×	`unswap-sqr_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	222
1	66	222
2	140	222
3	432	222
4	2017	222
5	4405	222
6	4780	222
7	5286	222
8	6276	222
9	7260	222
10	7699	222

Stop Event

1×	node limit

Counts

27 → 25

Calls

Call 1

Inputs
(*.f64 1/2 (pow.f64 x 2))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (+.f64 (.f64 -1/24 (pow.f64 x 4)) (*.f64 1/720 (pow.f64 x 6))))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (+.f64 (.f64 -1/24 (pow.f64 x 4)) (+.f64 (.f64 1/720 (pow.f64 x 6)) (.f64 -1/40320 (pow.f64 x 8)))))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))

Outputs
(*.f64 1/2 (pow.f64 x 2))
(.f64 1/2 (.f64 x x))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))
(fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4)))
(.f64 (.f64 x x) (fma.f64 (*.f64 x x) -1/24 1/2))
(.f64 (.f64 x x) (fma.f64 x (*.f64 x -1/24) 1/2))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (+.f64 (.f64 -1/24 (pow.f64 x 4)) (*.f64 1/720 (pow.f64 x 6))))
(fma.f64 1/2 (.f64 x x) (fma.f64 -1/24 (pow.f64 x 4) (.f64 1/720 (pow.f64 x 6))))
(fma.f64 1/2 (.f64 x x) (fma.f64 1/720 (pow.f64 x 6) (.f64 -1/24 (pow.f64 x 4))))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) -1/24 1/2) (*.f64 1/720 (pow.f64 x 6)))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (+.f64 (.f64 -1/24 (pow.f64 x 4)) (+.f64 (.f64 1/720 (pow.f64 x 6)) (.f64 -1/40320 (pow.f64 x 8)))))
(fma.f64 1/2 (.f64 x x) (fma.f64 -1/24 (pow.f64 x 4) (fma.f64 1/720 (pow.f64 x 6) (.f64 -1/40320 (pow.f64 x 8)))))
(fma.f64 1/2 (.f64 x x) (fma.f64 -1/40320 (pow.f64 x 8) (fma.f64 1/720 (pow.f64 x 6) (.f64 -1/24 (pow.f64 x 4)))))
(fma.f64 1/2 (.f64 x x) (fma.f64 (pow.f64 x 4) (fma.f64 (pow.f64 x 4) -1/40320 -1/24) (.f64 1/720 (pow.f64 x 6))))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(.f64 (sin.f64 (.f64 1/2 x)) (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))))
(.f64 (sin.f64 x) (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(.f64 (sin.f64 (.f64 1/2 x)) (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))))
(.f64 (sin.f64 x) (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(.f64 (sin.f64 (.f64 1/2 x)) (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))))
(.f64 (sin.f64 x) (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(.f64 (sin.f64 (.f64 1/2 x)) (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))))
(.f64 (sin.f64 x) (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(.f64 (sin.f64 (.f64 1/2 x)) (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))))
(.f64 (sin.f64 x) (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(.f64 (sin.f64 (.f64 1/2 x)) (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))))
(.f64 (sin.f64 x) (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(.f64 (sin.f64 (.f64 1/2 x)) (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))))
(.f64 (sin.f64 x) (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 1/2 x))) (cos.f64 (*.f64 1/2 x)))
(.f64 (sin.f64 (.f64 1/2 x)) (/.f64 (sin.f64 x) (cos.f64 (*.f64 1/2 x))))
(.f64 (sin.f64 x) (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (*.f64 1/2 x))))

localize13.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1/6 (/.f64 2 (*.f64 x x)))
✓	0.2b	(/.f64 2 (*.f64 x x))
✓	0.7b	(/.f64 1 (+.f64 1/6 (/.f64 2 (*.f64 x x))))

Compiler

Compiled 29 to 17 computations (41.4% saved)

series4.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(/.f64 1 (+.f64 1/6 (/.f64 2 (*.f64 x x))))
1.0ms	x	@	inf	(/.f64 1 (+.f64 1/6 (/.f64 2 (*.f64 x x))))
0.0ms	x	@	0	(/.f64 2 (*.f64 x x))
0.0ms	x	@	inf	(/.f64 2 (*.f64 x x))
0.0ms	x	@	-inf	(/.f64 1 (+.f64 1/6 (/.f64 2 (*.f64 x x))))

rewrite76.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

939×	`pow1_binary64`
882×	`add-log-exp_binary64`
881×	`log1p-expm1-u_binary64`
881×	`expm1-log1p-u_binary64`
97×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	30
1	199	26
2	2457	26

Stop Event

1×	node limit

Counts

3 → 82

Calls

Call 1

Inputs
(/.f64 1 (+.f64 1/6 (/.f64 2 (*.f64 x x))))
(/.f64 2 (*.f64 x x))
(+.f64 1/6 (/.f64 2 (*.f64 x x)))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 1 (fma.f64 2 (pow.f64 x -2) 1/6)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 1 (fma.f64 2 (pow.f64 x -2) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (fma.f64 2 (pow.f64 x -2) 1/6)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (fma.f64 2 (pow.f64 x -2) 1/6))) (cbrt.f64 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1/6) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1/6) -2)) (/.f64 1 (cbrt.f64 (fma.f64 2 (pow.f64 x -2) 1/6))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1/6) -1/2) (pow.f64 (fma.f64 2 (pow.f64 x -2) 1/6) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 1 (neg.f64 (fma.f64 2 (pow.f64 x -2) 1/6))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (fma.f64 2 (pow.f64 x -2) 1/6)) 2) -1) (pow.f64 (cbrt.f64 (fma.f64 2 (pow.f64 x -2) 1/6)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (fma.f64 2 (pow.f64 x -2) 1/6)) -1) (pow.f64 (sqrt.f64 (fma.f64 2 (pow.f64 x -2) 1/6)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 1/216 (*.f64 8 (pow.f64 (pow.f64 x -2) 3)))) (+.f64 1/36 (-.f64 (/.f64 4 (pow.f64 x 4)) (/.f64 1/3 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (-.f64 1/36 (/.f64 4 (pow.f64 x 4)))) (+.f64 1/6 (*.f64 -2 (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 2 (pow.f64 x -2) 1/6) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (fma.f64 2 (pow.f64 x -2) 1/6)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 1 (fma.f64 2 (pow.f64 x -2) 1/6)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (cbrt.f64 (fma.f64 2 (pow.f64 x -2) 1/6))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1/6) -1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1/6) -2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1 (fma.f64 2 (pow.f64 x -2) 1/6))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 1 (fma.f64 2 (pow.f64 x -2) 1/6)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 1 (fma.f64 2 (pow.f64 x -2) 1/6)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1 (fma.f64 2 (pow.f64 x -2) 1/6))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1 (fma.f64 2 (pow.f64 x -2) 1/6))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (neg.f64 (log.f64 (fma.f64 2 (pow.f64 x -2) 1/6))))))))

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

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 2 (pow.f64 x -2) 1/6))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1/36 (+.f64 1/6 (*.f64 -2 (pow.f64 x -2)))) (/.f64 (/.f64 4 (pow.f64 x 4)) (+.f64 1/6 (*.f64 -2 (pow.f64 x -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 2 (pow.f64 x -2) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 2 (pow.f64 x -2) 1/6) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 2 (pow.f64 x -2) 1/6)) (pow.f64 (cbrt.f64 (fma.f64 2 (pow.f64 x -2) 1/6)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 2 (pow.f64 x -2) 1/6)) 2) (cbrt.f64 (fma.f64 2 (pow.f64 x -2) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 2 (pow.f64 x -2) 1/6)) (sqrt.f64 (fma.f64 2 (pow.f64 x -2) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1/216 (*.f64 8 (pow.f64 (pow.f64 x -2) 3))) (/.f64 1 (+.f64 1/36 (-.f64 (/.f64 4 (pow.f64 x 4)) (/.f64 1/3 (*.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1/36 (/.f64 4 (pow.f64 x 4))) (/.f64 1 (+.f64 1/6 (*.f64 -2 (pow.f64 x -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 1 (fma.f64 2 (pow.f64 x -2) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1/36 (-.f64 (/.f64 4 (pow.f64 x 4)) (/.f64 1/3 (*.f64 x x)))) (+.f64 1/216 (*.f64 8 (pow.f64 (pow.f64 x -2) 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1/6 (*.f64 -2 (pow.f64 x -2))) (-.f64 1/36 (/.f64 4 (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 2 (pow.f64 x -2) 1/6) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (cbrt.f64 (fma.f64 2 (pow.f64 x -2) 1/6)) 2) (/.f64 1 (cbrt.f64 (fma.f64 2 (pow.f64 x -2) 1/6))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (fma.f64 2 (pow.f64 x -2) 1/6)) (pow.f64 (fma.f64 2 (pow.f64 x -2) 1/6) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (fma.f64 2 (pow.f64 x -2) 1/6)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1/216 (*.f64 8 (pow.f64 (pow.f64 x -2) 3))) (+.f64 1/36 (-.f64 (/.f64 4 (pow.f64 x 4)) (/.f64 1/3 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1/216 (*.f64 8 (pow.f64 (pow.f64 x -2) 3))) (+.f64 (/.f64 4 (pow.f64 x 4)) (-.f64 1/36 (/.f64 1/3 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1/36 (/.f64 4 (pow.f64 x 4))) (+.f64 1/6 (*.f64 -2 (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 1/216 (*.f64 8 (pow.f64 (pow.f64 x -2) 3)))) (neg.f64 (+.f64 1/36 (-.f64 (/.f64 4 (pow.f64 x 4)) (/.f64 1/3 (*.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1/36 (/.f64 4 (pow.f64 x 4)))) (neg.f64 (+.f64 1/6 (*.f64 -2 (pow.f64 x -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (/.f64 4 (pow.f64 x 4)) 1/36) (-.f64 (*.f64 2 (pow.f64 x -2)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 2 (pow.f64 x -2) 1/6) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1/6) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 2 (pow.f64 x -2) 1/6)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 2 (pow.f64 x -2) 1/6)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1/6) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 2 (pow.f64 x -2) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 2 (pow.f64 x -2) 1/6))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 2 (pow.f64 x -2) 1/6) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 2 (pow.f64 x -2) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 2 (pow.f64 x -2) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 2 (pow.f64 x -2) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 2 (pow.f64 x -2)) 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 2 (pow.f64 x -2) 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (/.f64 4 (pow.f64 x 4))) (cbrt.f64 (*.f64 2 (pow.f64 x -2))) 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (sqrt.f64 2) x) (/.f64 (sqrt.f64 2) x) 1/6)))))

simplify51.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

625×	`times-frac_binary64`
478×	`distribute-lft-out_binary64`
413×	`unswap-sqr_binary64`
410×	`associate-/l/_binary64`
393×	`fma-def_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	369
1	103	369
2	249	369
3	724	369
4	3145	369

Stop Event

1×	node limit

Counts

118 → 102

Calls

Call 1

Inputs
(*.f64 1/2 (pow.f64 x 2))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))
(+.f64 (.f64 1/288 (pow.f64 x 6)) (+.f64 (.f64 1/2 (pow.f64 x 2)) (*.f64 -1/24 (pow.f64 x 4))))
(+.f64 (.f64 1/288 (pow.f64 x 6)) (+.f64 (.f64 -1/3456 (pow.f64 x 8)) (+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))))
6
(-.f64 6 (*.f64 72 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 6 (.f64 864 (/.f64 1 (pow.f64 x 4)))) (.f64 72 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 6 (.f64 864 (/.f64 1 (pow.f64 x 4)))) (+.f64 (.f64 72 (/.f64 1 (pow.f64 x 2))) (*.f64 10368 (/.f64 1 (pow.f64 x 6)))))
6
(-.f64 6 (*.f64 72 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 6 (.f64 864 (/.f64 1 (pow.f64 x 4)))) (.f64 72 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 6 (.f64 864 (/.f64 1 (pow.f64 x 4)))) (+.f64 (.f64 72 (/.f64 1 (pow.f64 x 2))) (*.f64 10368 (/.f64 1 (pow.f64 x 6)))))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (pow.f64 x 2))
(+.f64 1/6 (*.f64 2 (/.f64 1 (pow.f64 x 2))))
(+.f64 1/6 (*.f64 2 (/.f64 1 (pow.f64 x 2))))
(+.f64 1/6 (*.f64 2 (/.f64 1 (pow.f64 x 2))))
1/6
(+.f64 1/6 (*.f64 2 (/.f64 1 (pow.f64 x 2))))
(+.f64 1/6 (*.f64 2 (/.f64 1 (pow.f64 x 2))))
(+.f64 1/6 (*.f64 2 (/.f64 1 (pow.f64 x 2))))
1/6
(+.f64 1/6 (*.f64 2 (/.f64 1 (pow.f64 x 2))))
(+.f64 1/6 (*.f64 2 (/.f64 1 (pow.f64 x 2))))
(+.f64 1/6 (*.f64 2 (/.f64 1 (pow.f64 x 2))))

Outputs
(*.f64 1/2 (pow.f64 x 2))
(.f64 1/2 (.f64 x x))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))
(fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4)))
(fma.f64 -1/24 (pow.f64 x 4) (.f64 1/2 (.f64 x x)))
(+.f64 (.f64 1/288 (pow.f64 x 6)) (+.f64 (.f64 1/2 (pow.f64 x 2)) (*.f64 -1/24 (pow.f64 x 4))))
(fma.f64 1/288 (pow.f64 x 6) (fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4))))
(fma.f64 -1/24 (pow.f64 x 4) (fma.f64 1/288 (pow.f64 x 6) (.f64 1/2 (.f64 x x))))
(fma.f64 1/288 (pow.f64 x 6) (fma.f64 -1/24 (pow.f64 x 4) (.f64 1/2 (.f64 x x))))
(+.f64 (.f64 1/288 (pow.f64 x 6)) (+.f64 (.f64 -1/3456 (pow.f64 x 8)) (+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))))
(fma.f64 1/288 (pow.f64 x 6) (fma.f64 -1/3456 (pow.f64 x 8) (fma.f64 1/2 (.f64 x x) (.f64 -1/24 (pow.f64 x 4)))))
(fma.f64 -1/3456 (pow.f64 x 8) (fma.f64 -1/24 (pow.f64 x 4) (fma.f64 1/288 (pow.f64 x 6) (.f64 1/2 (.f64 x x)))))
(fma.f64 1/2 (.f64 x x) (fma.f64 (pow.f64 x 4) (fma.f64 (pow.f64 x 4) -1/3456 -1/24) (.f64 1/288 (pow.f64 x 6))))
(fma.f64 1/2 (.f64 x x) (fma.f64 -1/24 (pow.f64 x 4) (fma.f64 1/288 (pow.f64 x 6) (.f64 -1/3456 (pow.f64 x 8)))))
6
(-.f64 6 (*.f64 72 (/.f64 1 (pow.f64 x 2))))
(-.f64 6 (/.f64 72 (*.f64 x x)))
(+.f64 6 (/.f64 -72 (*.f64 x x)))
(-.f64 (+.f64 6 (.f64 864 (/.f64 1 (pow.f64 x 4)))) (.f64 72 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 6 (/.f64 864 (pow.f64 x 4))) (/.f64 72 (*.f64 x x)))
(+.f64 (/.f64 864 (pow.f64 x 4)) (-.f64 6 (/.f64 72 (*.f64 x x))))
(+.f64 6 (+.f64 (/.f64 864 (pow.f64 x 4)) (/.f64 -72 (*.f64 x x))))
(-.f64 (+.f64 6 (.f64 864 (/.f64 1 (pow.f64 x 4)))) (+.f64 (.f64 72 (/.f64 1 (pow.f64 x 2))) (*.f64 10368 (/.f64 1 (pow.f64 x 6)))))
(+.f64 6 (-.f64 (/.f64 864 (pow.f64 x 4)) (+.f64 (/.f64 72 (*.f64 x x)) (/.f64 10368 (pow.f64 x 6)))))
(+.f64 (/.f64 864 (pow.f64 x 4)) (-.f64 6 (+.f64 (/.f64 72 (*.f64 x x)) (/.f64 10368 (pow.f64 x 6)))))
(+.f64 (/.f64 -72 (*.f64 x x)) (+.f64 (+.f64 6 (/.f64 864 (pow.f64 x 4))) (/.f64 -10368 (pow.f64 x 6))))
(+.f64 (+.f64 6 (/.f64 -72 (*.f64 x x))) (+.f64 (/.f64 864 (pow.f64 x 4)) (/.f64 -10368 (pow.f64 x 6))))
(+.f64 6 (+.f64 (/.f64 864 (pow.f64 x 4)) (+.f64 (/.f64 -72 (*.f64 x x)) (/.f64 -10368 (pow.f64 x 6)))))
6
(-.f64 6 (*.f64 72 (/.f64 1 (pow.f64 x 2))))
(-.f64 6 (/.f64 72 (*.f64 x x)))
(+.f64 6 (/.f64 -72 (*.f64 x x)))
(-.f64 (+.f64 6 (.f64 864 (/.f64 1 (pow.f64 x 4)))) (.f64 72 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 6 (/.f64 864 (pow.f64 x 4))) (/.f64 72 (*.f64 x x)))
(+.f64 (/.f64 864 (pow.f64 x 4)) (-.f64 6 (/.f64 72 (*.f64 x x))))
(+.f64 6 (+.f64 (/.f64 864 (pow.f64 x 4)) (/.f64 -72 (*.f64 x x))))
(-.f64 (+.f64 6 (.f64 864 (/.f64 1 (pow.f64 x 4)))) (+.f64 (.f64 72 (/.f64 1 (pow.f64 x 2))) (*.f64 10368 (/.f64 1 (pow.f64 x 6)))))
(+.f64 6 (-.f64 (/.f64 864 (pow.f64 x 4)) (+.f64 (/.f64 72 (*.f64 x x)) (/.f64 10368 (pow.f64 x 6)))))
(+.f64 (/.f64 864 (pow.f64 x 4)) (-.f64 6 (+.f64 (/.f64 72 (*.f64 x x)) (/.f64 10368 (pow.f64 x 6)))))
(+.f64 (/.f64 -72 (*.f64 x x)) (+.f64 (+.f64 6 (/.f64 864 (pow.f64 x 4))) (/.f64 -10368 (pow.f64 x 6))))
(+.f64 (+.f64 6 (/.f64 -72 (*.f64 x x))) (+.f64 (/.f64 864 (pow.f64 x 4)) (/.f64 -10368 (pow.f64 x 6))))
(+.f64 6 (+.f64 (/.f64 864 (pow.f64 x 4)) (+.f64 (/.f64 -72 (*.f64 x x)) (/.f64 -10368 (pow.f64 x 6)))))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(/.f64 2 (pow.f64 x 2))
(/.f64 2 (*.f64 x x))
(+.f64 1/6 (*.f64 2 (/.f64 1 (pow.f64 x 2))))
(+.f64 1/6 (/.f64 2 (*.f64 x x)))
(+.f64 1/6 (*.f64 2 (/.f64 1 (pow.f64 x 2))))
(+.f64 1/6 (/.f64 2 (*.f64 x x)))
(+.f64 1/6 (*.f64 2 (/.f64 1 (pow.f64 x 2))))
(+.f64 1/6 (/.f64 2 (*.f64 x x)))
1/6
(+.f64 1/6 (*.f64 2 (/.f64 1 (pow.f64 x 2))))
(+.f64 1/6 (/.f64 2 (*.f64 x x)))
(+.f64 1/6 (*.f64 2 (/.f64 1 (pow.f64 x 2))))
(+.f64 1/6 (/.f64 2 (*.f64 x x)))
(+.f64 1/6 (*.f64 2 (/.f64 1 (pow.f64 x 2))))
(+.f64 1/6 (/.f64 2 (*.f64 x x)))
1/6
(+.f64 1/6 (*.f64 2 (/.f64 1 (pow.f64 x 2))))
(+.f64 1/6 (/.f64 2 (*.f64 x x)))
(+.f64 1/6 (*.f64 2 (/.f64 1 (pow.f64 x 2))))
(+.f64 1/6 (/.f64 2 (*.f64 x x)))
(+.f64 1/6 (*.f64 2 (/.f64 1 (pow.f64 x 2))))
(+.f64 1/6 (/.f64 2 (*.f64 x x)))

eval48.0ms (0.7%)

Compiler: Compiled 1655 to 1384 computations (16.4% saved)

prune20.0ms (0.3%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	126	1	127
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	126	5	131

Error

Counts

131 → 5

Alt Table

Click to see full alt table

Status	Error	Program
	61.4b	6
✓	0.0b	(.f64 (.f64 x x) (fma.f64 x (*.f64 x -1/24) 1/2))
✓	0.0b	(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
✓	0.1b	(.f64 x (.f64 x 1/2))
✓	0.6b	(/.f64 1 (+.f64 1/6 (/.f64 2 (*.f64 x x))))

Compiler

Compiled 37 to 27 computations (27% saved)

eval0.0ms (0%)

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

prune2.0ms (0%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	4	4
Total	5	5

Error

Counts

5 → 5

Alt Table

Click to see full alt table

Status	Error	Program
	61.4b	6
✓	0.0b	(.f64 (.f64 x x) (fma.f64 x (*.f64 x -1/24) 1/2))
✓	0.0b	(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
✓	0.1b	(.f64 x (.f64 x 1/2))
✓	0.6b	(/.f64 1 (+.f64 1/6 (/.f64 2 (*.f64 x x))))

Compiler

Compiled 37 to 27 computations (27% saved)

regimes20.0ms (0.3%)

Counts

9 → 1

Calls

Call 1

Inputs
6
(.f64 x (.f64 x 1/2))
(.f64 1/2 (.f64 x x))
(/.f64 1 (+.f64 1/6 (/.f64 2 (*.f64 x x))))
(-.f64 1 (cos.f64 x))
(.f64 (.f64 x x) (fma.f64 x (*.f64 x -1/24) 1/2))
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 4)))
(/.f64 1 (/.f64 (+.f64 1 (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 x))))

Outputs
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))

Calls

5 calls:

6.0ms	x
5.0ms	(-.f64 1 (cos.f64 x))
2.0ms	(cos.f64 x)
2.0ms	(cos.f64 x)
2.0ms	(-.f64 1 (cos.f64 x))

Results

Error	Segments	Branch
0.0b	1	`x`
0.0b	1	`(-.f64 1 (cos.f64 x))`
0.0b	1	`(-.f64 1 (cos.f64 x))`
0.0b	1	`(cos.f64 x)`
0.0b	1	`(cos.f64 x)`

Compiler

Compiled 83 to 55 computations (33.7% saved)

regimes19.0ms (0.3%)

Counts

6 → 1

Calls

Call 1

Inputs
6
(.f64 x (.f64 x 1/2))
(.f64 1/2 (.f64 x x))
(/.f64 1 (+.f64 1/6 (/.f64 2 (*.f64 x x))))
(-.f64 1 (cos.f64 x))
(.f64 (.f64 x x) (fma.f64 x (*.f64 x -1/24) 1/2))

Outputs
(.f64 (.f64 x x) (fma.f64 x (*.f64 x -1/24) 1/2))

Calls

5 calls:

6.0ms	(cos.f64 x)
5.0ms	x
2.0ms	(cos.f64 x)
2.0ms	(-.f64 1 (cos.f64 x))
2.0ms	(-.f64 1 (cos.f64 x))

Results

Error	Segments	Branch
0.0b	1	`x`
0.0b	1	`(-.f64 1 (cos.f64 x))`
0.0b	1	`(-.f64 1 (cos.f64 x))`
0.0b	1	`(cos.f64 x)`
0.0b	1	`(cos.f64 x)`

Compiler

Compiled 53 to 35 computations (34% saved)

regimes16.0ms (0.3%)

Accuracy

Total -61.6b remaining (-43951%)

Threshold costs -61.6b (-43951%)

Counts

5 → 1

Calls

Call 1

Inputs
6
(.f64 x (.f64 x 1/2))
(.f64 1/2 (.f64 x x))
(/.f64 1 (+.f64 1/6 (/.f64 2 (*.f64 x x))))
(-.f64 1 (cos.f64 x))

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

Calls

5 calls:

5.0ms	(cos.f64 x)
4.0ms	x
2.0ms	(-.f64 1 (cos.f64 x))
2.0ms	(-.f64 1 (cos.f64 x))
2.0ms	(cos.f64 x)

Results

Error	Segments	Branch
0.1b	1	`x`
0.1b	1	`(-.f64 1 (cos.f64 x))`
0.1b	1	`(-.f64 1 (cos.f64 x))`
0.1b	1	`(cos.f64 x)`
0.1b	1	`(cos.f64 x)`

Compiler

Compiled 43 to 30 computations (30.2% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	33
1	21	33

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
(.f64 (.f64 x x) (fma.f64 x (*.f64 x -1/24) 1/2))
(.f64 x (.f64 x 1/2))
6

Outputs
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
(.f64 (.f64 x x) (fma.f64 x (*.f64 x -1/24) 1/2))
(.f64 x (.f64 x 1/2))
6

Compiler

Compiled 27 to 19 computations (29.6% saved)

soundness101.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

968×	`fma-def_binary64`
705×	`associate-r_binary64`
663×	`distribute-lft-out_binary64`
472×	`associate-/l/_binary64`
360×	`unswap-sqr_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	70	534
1	157	532
2	372	530
3	1135	504
4	3863	504
5	5448	504
6	7577	504

Stop Event

1×	node limit

Compiler

Compiled 40 to 28 computations (30% saved)

end29.0ms (0.4%)

Compiler: Compiled 24 to 16 computations (33.3% saved)

Details

analyze0.0ms (0%)

sample4.3s (67%)

preprocess15.0ms (0.2%)

simplify9.0ms (0.1%)

eval0.0ms (0%)

prune1.0ms (0%)

localize7.0ms (0.1%)

series2.0ms (0%)

rewrite63.0ms (1%)

simplify106.0ms (1.6%)

eval8.0ms (0.1%)

prune6.0ms (0.1%)

localize36.0ms (0.6%)

series2.0ms (0%)

rewrite43.0ms (0.7%)

simplify179.0ms (2.8%)

localize11.0ms (0.2%)

series4.0ms (0.1%)

rewrite53.0ms (0.8%)

simplify196.0ms (3%)

localize36.0ms (0.6%)

series3.0ms (0.1%)

rewrite68.0ms (1.1%)

simplify188.0ms (2.9%)

localize12.0ms (0.2%)

series6.0ms (0.1%)

rewrite102.0ms (1.6%)

simplify80.0ms (1.2%)

eval256.0ms (3.9%)

prune54.0ms (0.8%)

localize5.0ms (0.1%)

localize9.0ms (0.1%)

series6.0ms (0.1%)

rewrite51.0ms (0.8%)

simplify113.0ms (1.7%)

localize13.0ms (0.2%)

series4.0ms (0.1%)

rewrite76.0ms (1.2%)

simplify51.0ms (0.8%)

eval48.0ms (0.7%)

prune20.0ms (0.3%)

eval0.0ms (0%)

prune2.0ms (0%)

regimes20.0ms (0.3%)

regimes19.0ms (0.3%)

regimes16.0ms (0.3%)

simplify5.0ms (0.1%)

soundness101.0ms (1.6%)

end29.0ms (0.4%)

Profiling