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)

sample5.3s (67.4%)

Results

3.8s	4327×	body	2048	valid
920.0ms	2088×	body	1024	valid
409.0ms	1074×	body	512	valid
179.0ms	767×	body	256	valid

preprocess18.0ms (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)

simplify8.0ms (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

28.6b

Counts

2 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	28.6b	(-.f64 1 (cos.f64 x))

Compiler

Compiled 5 to 4 computations (20% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.7b	(-.f64 1 (cos.f64 x))

Compiler

Compiled 9 to 5 computations (44.4% saved)

series1.0ms (0%)

Counts

1 → 4

Calls

3 calls:

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

rewrite56.0ms (0.7%)

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))))))))

simplify105.0ms (1.3%)

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)

prune8.0ms (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
▶	0.0b	(.f64 (.f64 (sin.f64 x) (sin.f64 x)) (/.f64 1 (+.f64 1 (cos.f64 x))))
✓	28.6b	(-.f64 1 (cos.f64 x))
▶	0.0b	(.f64 (.f64 x x) (fma.f64 x (*.f64 x -1/24) 1/2))
▶	0.0b	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
▶	0.2b	(.f64 1/2 (.f64 x x))

Compiler

Compiled 46 to 31 computations (32.6% saved)

localize5.0ms (0.1%)

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))

rewrite45.0ms (0.6%)

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))))))))

simplify174.0ms (2.2%)

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))

localize16.0ms (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)

rewrite58.0ms (0.7%)

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))))))))

simplify206.0ms (2.6%)

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)))

localize15.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 34 to 16 computations (52.9% saved)

series4.0ms (0.1%)

Counts

3 → 32

Calls

9 calls:

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

rewrite81.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

454×	`log-prod_binary64`
368×	`prod-diff_binary64`
340×	`exp-prod_binary64`
287×	`pow-prod-down_binary64`
241×	`pow2_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	26
1	202	18
2	2817	18

Stop Event

1×	node limit

Counts

3 → 149

Calls

Call 1

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

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

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

simplify62.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

886×	`distribute-rgt-out_binary64`
842×	`fma-def_binary64`
716×	`associate-l_binary64`
650×	`distribute-lft-in_binary64`
538×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	55	364
1	125	362
2	294	360
3	954	334
4	4359	334
5	6652	334

Stop Event

1×	node limit

Counts

181 → 176

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))
(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)
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)

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 (.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 x (.f64 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 (pow.f64 x 4) (fma.f64 (pow.f64 x 4) -1/40320 -1/24) (.f64 1/720 (pow.f64 x 6))))
(/.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)))
(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 (pow.f64 x 4) -1/3 (*.f64 x x))
(fma.f64 x x (*.f64 (pow.f64 x 4) -1/3))
(+.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)))
(fma.f64 x x (fma.f64 (pow.f64 x 4) -1/3 (*.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 (pow.f64 x 6) 2/45 (fma.f64 x x (*.f64 (pow.f64 x 8) -1/315))))
(fma.f64 x x (fma.f64 (pow.f64 x 4) -1/3 (fma.f64 (pow.f64 x 6) 2/45 (*.f64 (pow.f64 x 8) -1/315))))
(fma.f64 x x (fma.f64 (pow.f64 x 4) (fma.f64 (pow.f64 x 4) -1/315 -1/3) (*.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)
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 (pow.f64 x 4) 1/24 (.f64 x (.f64 x -1/2))))
(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 4) 1/24 (.f64 (pow.f64 x 6) -1/720)))
(+.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)))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x 1/24) -1/2) (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))

localize15.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 26 to 10 computations (61.5% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite59.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

993×	`pow1_binary64`
931×	`add-log-exp_binary64`
930×	`log1p-expm1-u_binary64`
930×	`expm1-log1p-u_binary64`
95×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	179	6
2	2618	6

Stop Event

1×	node limit

Counts

1 → 42

Calls

Call 1

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

simplify71.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

697×	`associate-/l/_binary64`
604×	`distribute-rgt-out_binary64`
478×	`distribute-lft-out_binary64`
425×	`unswap-sqr_binary64`
399×	`associate-/r/_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	32	182
1	68	182
2	142	182
3	454	158
4	2090	158
5	4579	158
6	5264	158
7	7348	158

Stop Event

1×	node limit

Counts

54 → 53

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))

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

eval113.0ms (1.4%)

Compiler: Compiled 5449 to 3167 computations (41.9% saved)

prune54.0ms (0.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	389	4	393
Fresh	0	0	0
Picked	1	0	1
Done	4	0	4
Total	394	4	398

Error

Counts

398 → 4

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.2b	(.f64 x (.f64 x 1/2))
▶	0.0b	(+.f64 (.f64 (.f64 x (.f64 x -1/24)) (.f64 x x)) (.f64 1/2 (.f64 x x)))
▶	0.0b	(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
▶	0.0b	(/.f64 (fma.f64 x x (*.f64 (pow.f64 x 4) -1/3)) (+.f64 1 (cos.f64 x)))

Compiler

Compiled 44 to 29 computations (34.1% saved)

localize6.0ms (0.1%)

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

localize10.0ms (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)

series4.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
1.0ms	x	@	-inf	(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
1.0ms	x	@	0	(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))

rewrite57.0ms (0.7%)

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)))))))))

simplify111.0ms (1.4%)

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))))

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(.f64 1/2 (.f64 x x))
✓	0.1b	(.f64 (.f64 x (.f64 x -1/24)) (.f64 x x))
✓	0.1b	(.f64 x (.f64 x -1/24))
	0.3b	(*.f64 x -1/24)

Compiler

Compiled 44 to 22 computations (50% saved)

series3.0ms (0%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(.f64 (.f64 x (.f64 x -1/24)) (.f64 x x))
1.0ms	x	@	0	(.f64 x (.f64 x -1/24))
0.0ms	x	@	inf	(.f64 x (.f64 x -1/24))
0.0ms	x	@	inf	(.f64 (.f64 x (.f64 x -1/24)) (.f64 x x))
0.0ms	x	@	-inf	(.f64 x (.f64 x -1/24))

rewrite58.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

651×	`pow1_binary64`
604×	`add-log-exp_binary64`
604×	`log1p-expm1-u_binary64`
604×	`expm1-log1p-u_binary64`
589×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	20
1	145	14
2	1748	14

Stop Event

1×	node limit

Counts

2 → 26

Calls

Call 1

Inputs
(.f64 x (.f64 x -1/24))
(.f64 (.f64 x (.f64 x -1/24)) (.f64 x x))

Outputs

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

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

simplify198.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

1319×	`sqr-pow_binary64`
659×	`pow-sqr_binary64`
576×	`cube-prod_binary64`
404×	`fabs-mul_binary64`
377×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	168
1	18	168
2	36	168
3	87	168
4	297	168
5	1115	168
6	1838	168
7	1962	168
8	2131	168
9	2330	168
10	2601	168
11	2960	168
12	3414	168
13	3945	168
14	4577	168
15	5328	168
16	5636	168
17	5860	168
18	6056	168
19	6110	168
20	6134	168
21	6968	168
22	7881	168

Stop Event

1×	node limit

Counts

50 → 29

Calls

Call 1

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

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

localize20.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(+.f64 1 (cos.f64 x))
✓	0.0b	(/.f64 (fma.f64 x x (*.f64 (pow.f64 x 4) -1/3)) (+.f64 1 (cos.f64 x)))
✓	0.1b	(*.f64 (pow.f64 x 4) -1/3)

Compiler

Compiled 40 to 26 computations (35% saved)

series4.0ms (0%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(/.f64 (fma.f64 x x (*.f64 (pow.f64 x 4) -1/3)) (+.f64 1 (cos.f64 x)))
1.0ms	x	@	inf	(/.f64 (fma.f64 x x (*.f64 (pow.f64 x 4) -1/3)) (+.f64 1 (cos.f64 x)))
1.0ms	x	@	inf	(*.f64 (pow.f64 x 4) -1/3)
1.0ms	x	@	0	(/.f64 (fma.f64 x x (*.f64 (pow.f64 x 4) -1/3)) (+.f64 1 (cos.f64 x)))
1.0ms	x	@	0	(*.f64 (pow.f64 x 4) -1/3)

rewrite70.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

487×	`log-prod_binary64`
386×	`exp-prod_binary64`
324×	`prod-diff_binary64`
283×	`pow2_binary64`
280×	`pow-prod-down_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	26
1	234	26
2	2848	26

Stop Event

1×	node limit

Counts

2 → 73

Calls

Call 1

Inputs
(*.f64 (pow.f64 x 4) -1/3)
(/.f64 (fma.f64 x x (*.f64 (pow.f64 x 4) -1/3)) (+.f64 1 (cos.f64 x)))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (pow.f64 x 4) -1/3))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (*.f64 (pow.f64 x 4) -1/3))) 2)) (log.f64 (cbrt.f64 (exp.f64 (*.f64 (pow.f64 x 4) -1/3)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (*.f64 (pow.f64 x 4) -1/3)))) (log.f64 (sqrt.f64 (exp.f64 (*.f64 (pow.f64 x 4) -1/3)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 x 4) -1/3))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 x 4) -1/3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (log.f64 (*.f64 (pow.f64 x 4) -1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 1/9 (pow.f64 x 8)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (pow.f64 x 4) -1/3) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (pow.f64 x 4) -1/3)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (*.f64 x x) (sqrt.f64 -1/3)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 (pow.f64 x 4) -1/3))) 2)) (cbrt.f64 (log.f64 (*.f64 (pow.f64 x 4) -1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 (pow.f64 x 4) -1/3)))) (sqrt.f64 (log.f64 (*.f64 (pow.f64 x 4) -1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 1/9 (pow.f64 x 8)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (*.f64 (pow.f64 x 4) -1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (pow.f64 x 4) -1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (pow.f64 x 4) -1/3) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (pow.f64 x 4) -1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (pow.f64 x 4) -1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (pow.f64 x 4) -1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 x 4) -1/3)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (*.f64 (pow.f64 x 4) -1/3))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 (pow.f64 x 4) -1/3))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (*.f64 x x) (sqrt.f64 -1/3))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (pow.f64 x 4) -1/3)) 1) 1))))))

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

simplify83.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

535×	`distribute-rgt-out_binary64`
504×	`associate-*l/_binary64`
478×	`distribute-lft-out_binary64`
415×	`*-commutative_binary64`
413×	`unswap-sqr_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	38	346
1	83	346
2	166	346
3	509	346
4	2349	346
5	5712	328
6	6566	328
7	8000	328

Stop Event

1×	node limit

Counts

97 → 88

Calls

Call 1

Inputs
(*.f64 -1/3 (pow.f64 x 4))
(*.f64 -1/3 (pow.f64 x 4))
(*.f64 -1/3 (pow.f64 x 4))
(*.f64 -1/3 (pow.f64 x 4))
(*.f64 -1/3 (pow.f64 x 4))
(*.f64 -1/3 (pow.f64 x 4))
(*.f64 -1/3 (pow.f64 x 4))
(*.f64 -1/3 (pow.f64 x 4))
(*.f64 -1/3 (pow.f64 x 4))
(*.f64 -1/3 (pow.f64 x 4))
(*.f64 -1/3 (pow.f64 x 4))
(*.f64 -1/3 (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)))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (+.f64 (.f64 -1/24 (pow.f64 x 4)) (*.f64 -1/48 (pow.f64 x 6))))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (+.f64 (.f64 -1/24 (pow.f64 x 4)) (+.f64 (.f64 -1/48 (pow.f64 x 6)) (.f64 -23/5760 (pow.f64 x 8)))))
(*.f64 -1/3 (/.f64 (pow.f64 x 4) (+.f64 1 (cos.f64 x))))
(+.f64 (*.f64 -1/3 (/.f64 (pow.f64 x 4) (+.f64 1 (cos.f64 x)))) (/.f64 (pow.f64 x 2) (+.f64 1 (cos.f64 x))))
(+.f64 (*.f64 -1/3 (/.f64 (pow.f64 x 4) (+.f64 1 (cos.f64 x)))) (/.f64 (pow.f64 x 2) (+.f64 1 (cos.f64 x))))
(+.f64 (*.f64 -1/3 (/.f64 (pow.f64 x 4) (+.f64 1 (cos.f64 x)))) (/.f64 (pow.f64 x 2) (+.f64 1 (cos.f64 x))))
(*.f64 -1/3 (/.f64 (pow.f64 x 4) (+.f64 (cos.f64 x) 1)))
(+.f64 (*.f64 -1/3 (/.f64 (pow.f64 x 4) (+.f64 (cos.f64 x) 1))) (/.f64 (pow.f64 x 2) (+.f64 (cos.f64 x) 1)))
(+.f64 (*.f64 -1/3 (/.f64 (pow.f64 x 4) (+.f64 (cos.f64 x) 1))) (/.f64 (pow.f64 x 2) (+.f64 (cos.f64 x) 1)))
(+.f64 (*.f64 -1/3 (/.f64 (pow.f64 x 4) (+.f64 (cos.f64 x) 1))) (/.f64 (pow.f64 x 2) (+.f64 (cos.f64 x) 1)))

Outputs
(*.f64 -1/3 (pow.f64 x 4))
(*.f64 -1/3 (pow.f64 x 4))
(*.f64 -1/3 (pow.f64 x 4))
(*.f64 -1/3 (pow.f64 x 4))
(*.f64 -1/3 (pow.f64 x 4))
(*.f64 -1/3 (pow.f64 x 4))
(*.f64 -1/3 (pow.f64 x 4))
(*.f64 -1/3 (pow.f64 x 4))
(*.f64 -1/3 (pow.f64 x 4))
(*.f64 -1/3 (pow.f64 x 4))
(*.f64 -1/3 (pow.f64 x 4))
(*.f64 -1/3 (pow.f64 x 4))
(*.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 (pow.f64 x 4) -1/24))
(fma.f64 (pow.f64 x 4) -1/24 (.f64 1/2 (.f64 x x)))
(fma.f64 x (.f64 x 1/2) (.f64 (pow.f64 x 4) -1/24))
(.f64 x (.f64 x (fma.f64 x (*.f64 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 -1/48 (pow.f64 x 6))))
(fma.f64 1/2 (.f64 x x) (fma.f64 -1/24 (pow.f64 x 4) (.f64 -1/48 (pow.f64 x 6))))
(fma.f64 1/2 (.f64 x x) (fma.f64 (pow.f64 x 4) -1/24 (.f64 -1/48 (pow.f64 x 6))))
(fma.f64 x (.f64 x 1/2) (fma.f64 (pow.f64 x 4) -1/24 (.f64 -1/48 (pow.f64 x 6))))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x -1/24) 1/2) (*.f64 -1/48 (pow.f64 x 6)))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (+.f64 (.f64 -1/24 (pow.f64 x 4)) (+.f64 (.f64 -1/48 (pow.f64 x 6)) (.f64 -23/5760 (pow.f64 x 8)))))
(fma.f64 1/2 (.f64 x x) (fma.f64 -1/24 (pow.f64 x 4) (fma.f64 -1/48 (pow.f64 x 6) (.f64 -23/5760 (pow.f64 x 8)))))
(fma.f64 1/2 (.f64 x x) (fma.f64 (pow.f64 x 4) -1/24 (fma.f64 -1/48 (pow.f64 x 6) (.f64 -23/5760 (pow.f64 x 8)))))
(fma.f64 x (.f64 x 1/2) (fma.f64 (pow.f64 x 4) -1/24 (fma.f64 -23/5760 (pow.f64 x 8) (.f64 -1/48 (pow.f64 x 6)))))
(fma.f64 (pow.f64 x 4) (fma.f64 (pow.f64 x 4) -23/5760 -1/24) (fma.f64 x (.f64 x 1/2) (.f64 -1/48 (pow.f64 x 6))))
(fma.f64 x (.f64 x 1/2) (fma.f64 (pow.f64 x 4) -1/24 (fma.f64 -1/48 (pow.f64 x 6) (.f64 -23/5760 (pow.f64 x 8)))))
(*.f64 -1/3 (/.f64 (pow.f64 x 4) (+.f64 1 (cos.f64 x))))
(*.f64 (pow.f64 x 4) (/.f64 -1/3 (+.f64 1 (cos.f64 x))))
(+.f64 (*.f64 -1/3 (/.f64 (pow.f64 x 4) (+.f64 1 (cos.f64 x)))) (/.f64 (pow.f64 x 2) (+.f64 1 (cos.f64 x))))
(fma.f64 -1/3 (/.f64 (pow.f64 x 4) (+.f64 1 (cos.f64 x))) (/.f64 (*.f64 x x) (+.f64 1 (cos.f64 x))))
(fma.f64 -1/3 (/.f64 (pow.f64 x 4) (+.f64 1 (cos.f64 x))) (*.f64 (/.f64 x (+.f64 1 (cos.f64 x))) x))
(fma.f64 -1/3 (/.f64 (pow.f64 x 4) (+.f64 1 (cos.f64 x))) (*.f64 x (/.f64 x (+.f64 1 (cos.f64 x)))))
(.f64 (+.f64 (.f64 -1/3 (.f64 x x)) 1) (.f64 x (/.f64 x (+.f64 1 (cos.f64 x)))))
(.f64 (+.f64 1 (.f64 -1/3 (.f64 x x))) (.f64 x (/.f64 x (+.f64 1 (cos.f64 x)))))
(+.f64 (*.f64 -1/3 (/.f64 (pow.f64 x 4) (+.f64 1 (cos.f64 x)))) (/.f64 (pow.f64 x 2) (+.f64 1 (cos.f64 x))))
(fma.f64 -1/3 (/.f64 (pow.f64 x 4) (+.f64 1 (cos.f64 x))) (/.f64 (*.f64 x x) (+.f64 1 (cos.f64 x))))
(fma.f64 -1/3 (/.f64 (pow.f64 x 4) (+.f64 1 (cos.f64 x))) (*.f64 (/.f64 x (+.f64 1 (cos.f64 x))) x))
(fma.f64 -1/3 (/.f64 (pow.f64 x 4) (+.f64 1 (cos.f64 x))) (*.f64 x (/.f64 x (+.f64 1 (cos.f64 x)))))
(.f64 (+.f64 (.f64 -1/3 (.f64 x x)) 1) (.f64 x (/.f64 x (+.f64 1 (cos.f64 x)))))
(.f64 (+.f64 1 (.f64 -1/3 (.f64 x x))) (.f64 x (/.f64 x (+.f64 1 (cos.f64 x)))))
(+.f64 (*.f64 -1/3 (/.f64 (pow.f64 x 4) (+.f64 1 (cos.f64 x)))) (/.f64 (pow.f64 x 2) (+.f64 1 (cos.f64 x))))
(fma.f64 -1/3 (/.f64 (pow.f64 x 4) (+.f64 1 (cos.f64 x))) (/.f64 (*.f64 x x) (+.f64 1 (cos.f64 x))))
(fma.f64 -1/3 (/.f64 (pow.f64 x 4) (+.f64 1 (cos.f64 x))) (*.f64 (/.f64 x (+.f64 1 (cos.f64 x))) x))
(fma.f64 -1/3 (/.f64 (pow.f64 x 4) (+.f64 1 (cos.f64 x))) (*.f64 x (/.f64 x (+.f64 1 (cos.f64 x)))))
(.f64 (+.f64 (.f64 -1/3 (.f64 x x)) 1) (.f64 x (/.f64 x (+.f64 1 (cos.f64 x)))))
(.f64 (+.f64 1 (.f64 -1/3 (.f64 x x))) (.f64 x (/.f64 x (+.f64 1 (cos.f64 x)))))
(*.f64 -1/3 (/.f64 (pow.f64 x 4) (+.f64 (cos.f64 x) 1)))
(*.f64 -1/3 (/.f64 (pow.f64 x 4) (+.f64 1 (cos.f64 x))))
(*.f64 (pow.f64 x 4) (/.f64 -1/3 (+.f64 1 (cos.f64 x))))
(+.f64 (*.f64 -1/3 (/.f64 (pow.f64 x 4) (+.f64 (cos.f64 x) 1))) (/.f64 (pow.f64 x 2) (+.f64 (cos.f64 x) 1)))
(fma.f64 -1/3 (/.f64 (pow.f64 x 4) (+.f64 1 (cos.f64 x))) (/.f64 (*.f64 x x) (+.f64 1 (cos.f64 x))))
(fma.f64 -1/3 (/.f64 (pow.f64 x 4) (+.f64 1 (cos.f64 x))) (*.f64 (/.f64 x (+.f64 1 (cos.f64 x))) x))
(fma.f64 -1/3 (/.f64 (pow.f64 x 4) (+.f64 1 (cos.f64 x))) (*.f64 x (/.f64 x (+.f64 1 (cos.f64 x)))))
(.f64 (+.f64 (.f64 -1/3 (.f64 x x)) 1) (.f64 x (/.f64 x (+.f64 1 (cos.f64 x)))))
(.f64 (+.f64 1 (.f64 -1/3 (.f64 x x))) (.f64 x (/.f64 x (+.f64 1 (cos.f64 x)))))
(+.f64 (*.f64 -1/3 (/.f64 (pow.f64 x 4) (+.f64 (cos.f64 x) 1))) (/.f64 (pow.f64 x 2) (+.f64 (cos.f64 x) 1)))
(fma.f64 -1/3 (/.f64 (pow.f64 x 4) (+.f64 1 (cos.f64 x))) (/.f64 (*.f64 x x) (+.f64 1 (cos.f64 x))))
(fma.f64 -1/3 (/.f64 (pow.f64 x 4) (+.f64 1 (cos.f64 x))) (*.f64 (/.f64 x (+.f64 1 (cos.f64 x))) x))
(fma.f64 -1/3 (/.f64 (pow.f64 x 4) (+.f64 1 (cos.f64 x))) (*.f64 x (/.f64 x (+.f64 1 (cos.f64 x)))))
(.f64 (+.f64 (.f64 -1/3 (.f64 x x)) 1) (.f64 x (/.f64 x (+.f64 1 (cos.f64 x)))))
(.f64 (+.f64 1 (.f64 -1/3 (.f64 x x))) (.f64 x (/.f64 x (+.f64 1 (cos.f64 x)))))
(+.f64 (*.f64 -1/3 (/.f64 (pow.f64 x 4) (+.f64 (cos.f64 x) 1))) (/.f64 (pow.f64 x 2) (+.f64 (cos.f64 x) 1)))
(fma.f64 -1/3 (/.f64 (pow.f64 x 4) (+.f64 1 (cos.f64 x))) (/.f64 (*.f64 x x) (+.f64 1 (cos.f64 x))))
(fma.f64 -1/3 (/.f64 (pow.f64 x 4) (+.f64 1 (cos.f64 x))) (*.f64 (/.f64 x (+.f64 1 (cos.f64 x))) x))
(fma.f64 -1/3 (/.f64 (pow.f64 x 4) (+.f64 1 (cos.f64 x))) (*.f64 x (/.f64 x (+.f64 1 (cos.f64 x)))))
(.f64 (+.f64 (.f64 -1/3 (.f64 x x)) 1) (.f64 x (/.f64 x (+.f64 1 (cos.f64 x)))))
(.f64 (+.f64 1 (.f64 -1/3 (.f64 x x))) (.f64 x (/.f64 x (+.f64 1 (cos.f64 x)))))

eval99.0ms (1.3%)

Compiler: Compiled 4036 to 2622 computations (35% saved)

prune57.0ms (0.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	231	1	232
Fresh	0	0	0
Picked	1	0	1
Done	0	3	3
Total	232	4	236

Error

Counts

236 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.2b	(.f64 x (.f64 x 1/2))
✓	0.0b	(+.f64 (.f64 (.f64 x (.f64 x -1/24)) (.f64 x x)) (.f64 1/2 (.f64 x x)))
▶	0.0b	(.f64 (+.f64 1 (.f64 -1/3 (.f64 x x))) (.f64 x (/.f64 x (+.f64 1 (cos.f64 x)))))
✓	0.0b	(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))

Compiler

Compiled 47 to 31 computations (34% saved)

localize47.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 1 (cos.f64 x))
✓	0.0b	(*.f64 x (/.f64 x (+.f64 1 (cos.f64 x))))
✓	0.0b	(.f64 (+.f64 1 (.f64 -1/3 (.f64 x x))) (.f64 x (/.f64 x (+.f64 1 (cos.f64 x)))))
✓	0.2b	(.f64 -1/3 (.f64 x x))

Compiler

Compiled 55 to 29 computations (47.3% saved)

series9.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

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

rewrite126.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

663×	`log-prod_binary64`
504×	`prod-diff_binary64`
481×	`fma-def_binary64`
232×	`pow1/3_binary64`
225×	`expm1-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	43
1	261	41
2	3623	41

Stop Event

1×	node limit

Counts

3 → 147

Calls

Call 1

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

Outputs

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((#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (*.f64 x x) (+.f64 1 (cos.f64 x))) (*.f64 (*.f64 -1/3 (*.f64 x x)) (/.f64 (*.f64 x x) (+.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (*.f64 x x) (+.f64 1 (cos.f64 x))) (*.f64 (/.f64 (*.f64 x x) (+.f64 1 (cos.f64 x))) (*.f64 -1/3 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (fma.f64 -1/3 (*.f64 x x) 1) (/.f64 (*.f64 x x) (+.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 -1/3 (*.f64 x x)) (/.f64 (*.f64 x x) (+.f64 1 (cos.f64 x)))) (/.f64 (*.f64 x x) (+.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (/.f64 (*.f64 x x) (+.f64 1 (cos.f64 x))) (*.f64 -1/3 (*.f64 x x))) (/.f64 (*.f64 x x) (+.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (pow.f64 (exp.f64 (/.f64 (*.f64 x x) (+.f64 1 (cos.f64 x)))) (fma.f64 -1/3 (*.f64 x x) 1))) (cbrt.f64 (pow.f64 (exp.f64 (/.f64 (*.f64 x x) (+.f64 1 (cos.f64 x)))) (fma.f64 -1/3 (*.f64 x x) 1))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (/.f64 (*.f64 x x) (+.f64 1 (cos.f64 x)))) (fma.f64 -1/3 (*.f64 x x) 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (/.f64 (*.f64 x x) (+.f64 1 (cos.f64 x)))) (fma.f64 -1/3 (*.f64 x x) 1)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (/.f64 (*.f64 x x) (+.f64 1 (cos.f64 x)))) (fma.f64 -1/3 (*.f64 x x) 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (fma.f64 -1/3 (*.f64 x x) 1) (/.f64 (*.f64 x x) (+.f64 1 (cos.f64 x)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 x (fma.f64 -1/3 (*.f64 x x) 1)) (/.f64 (+.f64 1 (cos.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (fma.f64 -1/27 (pow.f64 (*.f64 x x) 3) 1) (*.f64 x x)) (*.f64 (+.f64 1 (fma.f64 1/9 (pow.f64 x 4) (*.f64 1/3 (*.f64 x x)))) (+.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1 (*.f64 1/9 (pow.f64 x 4))) (*.f64 x x)) (*.f64 (+.f64 1 (*.f64 1/3 (*.f64 x x))) (+.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 x x) (fma.f64 -1/27 (pow.f64 (*.f64 x x) 3) 1)) (*.f64 (+.f64 1 (cos.f64 x)) (+.f64 1 (fma.f64 1/9 (pow.f64 x 4) (*.f64 1/3 (*.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 x x) (-.f64 1 (*.f64 1/9 (pow.f64 x 4)))) (*.f64 (+.f64 1 (cos.f64 x)) (+.f64 1 (*.f64 1/3 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (fma.f64 -1/27 (pow.f64 (*.f64 x x) 3) 1) (/.f64 (*.f64 x x) (+.f64 1 (cos.f64 x)))) (+.f64 1 (fma.f64 1/9 (pow.f64 x 4) (*.f64 1/3 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1 (*.f64 1/9 (pow.f64 x 4))) (/.f64 (*.f64 x x) (+.f64 1 (cos.f64 x)))) (+.f64 1 (*.f64 1/3 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 x x) (fma.f64 -1/3 (*.f64 x x) 1)) (+.f64 1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (fma.f64 -1/3 (*.f64 x x) 1) (*.f64 x x)) (+.f64 1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 (*.f64 x x) (+.f64 1 (cos.f64 x))) (fma.f64 -1/27 (pow.f64 (*.f64 x x) 3) 1)) (+.f64 1 (fma.f64 1/9 (pow.f64 x 4) (*.f64 1/3 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 (*.f64 x x) (+.f64 1 (cos.f64 x))) (-.f64 1 (*.f64 1/9 (pow.f64 x 4)))) (+.f64 1 (*.f64 1/3 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 x (fma.f64 -1/3 (*.f64 x x) 1)) x) (+.f64 1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 x (fma.f64 -1/3 (*.f64 x x) 1)) 1) (/.f64 (+.f64 1 (cos.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 x (fma.f64 -1/3 (*.f64 x x) 1)) (neg.f64 x)) (+.f64 (neg.f64 (cos.f64 x)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (fma.f64 -1/3 (*.f64 x x) 1) (/.f64 (*.f64 x x) (+.f64 1 (cos.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (fma.f64 -1/3 (*.f64 x x) 1) (/.f64 (*.f64 x x) (+.f64 1 (cos.f64 x)))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (fma.f64 -1/3 (*.f64 x x) 1) (/.f64 (*.f64 x x) (+.f64 1 (cos.f64 x))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 x (sqrt.f64 (+.f64 1 (cos.f64 x)))) (hypot.f64 1 (*.f64 x (sqrt.f64 -1/3)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (fma.f64 -1/3 (*.f64 x x) 1) 3) (pow.f64 (/.f64 (*.f64 x x) (+.f64 1 (cos.f64 x))) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (/.f64 (*.f64 x x) (+.f64 1 (cos.f64 x))) 3) (pow.f64 (fma.f64 -1/3 (*.f64 x x) 1) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (fma.f64 -1/3 (*.f64 x x) 1) (/.f64 (*.f64 x x) (+.f64 1 (cos.f64 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (/.f64 (*.f64 x x) (+.f64 1 (cos.f64 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((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (*.f64 x x) (+.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (/.f64 (*.f64 x x) (+.f64 1 (cos.f64 x))))) (cbrt.f64 (exp.f64 (/.f64 (*.f64 x x) (+.f64 1 (cos.f64 x))))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (*.f64 x x) (+.f64 1 (cos.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (*.f64 x x) (+.f64 1 (cos.f64 x)))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (*.f64 x x) (+.f64 1 (cos.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (*.f64 x x) (+.f64 1 (cos.f64 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 x (/.f64 (+.f64 1 (cos.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 x x) (+.f64 1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1 (cos.f64 x)) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (pow.f64 x 4)) (/.f64 (+.f64 1 (cos.f64 x)) (pow.f64 (cbrt.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 x x)) (+.f64 (neg.f64 (cos.f64 x)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (neg.f64 x) x) (+.f64 (neg.f64 (cos.f64 x)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 x (neg.f64 x)) (+.f64 (neg.f64 (cos.f64 x)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 x x) (sqrt.f64 (+.f64 1 (cos.f64 x)))) (sqrt.f64 (+.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 x x) 1) (+.f64 1 (cos.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 x x) (pow.f64 (cbrt.f64 (+.f64 1 (cos.f64 x))) 2)) (cbrt.f64 (+.f64 1 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (*.f64 x x) (+.f64 1 (cos.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (*.f64 x x) (+.f64 1 (cos.f64 x))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (*.f64 x x) (+.f64 1 (cos.f64 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 x (sqrt.f64 (+.f64 1 (cos.f64 x)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (*.f64 x x) 3) (pow.f64 (+.f64 1 (cos.f64 x)) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 x 3) (pow.f64 (/.f64 x (+.f64 1 (cos.f64 x))) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (/.f64 x (+.f64 1 (cos.f64 x))) 3) (pow.f64 x 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (+.f64 1 (cos.f64 x)) (*.f64 x x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (pow.f64 x 4) (pow.f64 (+.f64 1 (cos.f64 x)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (*.f64 x x) (+.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (*.f64 x x) (+.f64 1 (cos.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (*.f64 x x) (+.f64 1 (cos.f64 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (*.f64 x x) 3) (pow.f64 (+.f64 1 (cos.f64 x)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 x 3) (pow.f64 (/.f64 x (+.f64 1 (cos.f64 x))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (/.f64 x (+.f64 1 (cos.f64 x))) 3) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (*.f64 x x) (+.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (*.f64 x x) (+.f64 1 (cos.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (*.f64 2 (log.f64 x)) (log1p.f64 (cos.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (-.f64 (*.f64 2 (log.f64 x)) (log1p.f64 (cos.f64 x))) 1))))))

simplify101.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

946×	`distribute-rgt-out_binary64`
629×	`fma-def_binary64`
608×	`associate-l_binary64`
524×	`distribute-lft-in_binary64`
490×	`associate-r_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	512
1	115	512
2	248	512
3	789	512
4	3788	512
5	6436	512
6	7818	512

Stop Event

1×	node limit

Counts

183 → 172

Calls

Call 1

Inputs
(*.f64 -1/3 (pow.f64 x 2))
(*.f64 -1/3 (pow.f64 x 2))
(*.f64 -1/3 (pow.f64 x 2))
(*.f64 -1/3 (pow.f64 x 2))
(*.f64 -1/3 (pow.f64 x 2))
(*.f64 -1/3 (pow.f64 x 2))
(*.f64 -1/3 (pow.f64 x 2))
(*.f64 -1/3 (pow.f64 x 2))
(*.f64 -1/3 (pow.f64 x 2))
(*.f64 -1/3 (pow.f64 x 2))
(*.f64 -1/3 (pow.f64 x 2))
(*.f64 -1/3 (pow.f64 x 2))
(*.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 -1/48 (pow.f64 x 6))))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (+.f64 (.f64 -1/24 (pow.f64 x 4)) (+.f64 (.f64 -1/48 (pow.f64 x 6)) (.f64 -23/5760 (pow.f64 x 8)))))
(*.f64 -1/3 (/.f64 (pow.f64 x 4) (+.f64 1 (cos.f64 x))))
(+.f64 (*.f64 -1/3 (/.f64 (pow.f64 x 4) (+.f64 1 (cos.f64 x)))) (/.f64 (pow.f64 x 2) (+.f64 1 (cos.f64 x))))
(+.f64 (*.f64 -1/3 (/.f64 (pow.f64 x 4) (+.f64 1 (cos.f64 x)))) (/.f64 (pow.f64 x 2) (+.f64 1 (cos.f64 x))))
(+.f64 (*.f64 -1/3 (/.f64 (pow.f64 x 4) (+.f64 1 (cos.f64 x)))) (/.f64 (pow.f64 x 2) (+.f64 1 (cos.f64 x))))
(*.f64 -1/3 (/.f64 (pow.f64 x 4) (+.f64 (cos.f64 x) 1)))
(+.f64 (*.f64 -1/3 (/.f64 (pow.f64 x 4) (+.f64 (cos.f64 x) 1))) (/.f64 (pow.f64 x 2) (+.f64 (cos.f64 x) 1)))
(+.f64 (*.f64 -1/3 (/.f64 (pow.f64 x 4) (+.f64 (cos.f64 x) 1))) (/.f64 (pow.f64 x 2) (+.f64 (cos.f64 x) 1)))
(+.f64 (*.f64 -1/3 (/.f64 (pow.f64 x 4) (+.f64 (cos.f64 x) 1))) (/.f64 (pow.f64 x 2) (+.f64 (cos.f64 x) 1)))
(*.f64 1/2 (pow.f64 x 2))
(+.f64 (.f64 1/8 (pow.f64 x 4)) (.f64 1/2 (pow.f64 x 2)))
(+.f64 (.f64 1/8 (pow.f64 x 4)) (+.f64 (.f64 1/2 (pow.f64 x 2)) (*.f64 1/48 (pow.f64 x 6))))
(+.f64 (.f64 1/8 (pow.f64 x 4)) (+.f64 (.f64 1/2 (pow.f64 x 2)) (+.f64 (.f64 17/5760 (pow.f64 x 8)) (.f64 1/48 (pow.f64 x 6)))))
(/.f64 (pow.f64 x 2) (+.f64 1 (cos.f64 x)))
(/.f64 (pow.f64 x 2) (+.f64 1 (cos.f64 x)))
(/.f64 (pow.f64 x 2) (+.f64 1 (cos.f64 x)))
(/.f64 (pow.f64 x 2) (+.f64 1 (cos.f64 x)))
(/.f64 (pow.f64 x 2) (+.f64 (cos.f64 x) 1))
(/.f64 (pow.f64 x 2) (+.f64 (cos.f64 x) 1))
(/.f64 (pow.f64 x 2) (+.f64 (cos.f64 x) 1))
(/.f64 (pow.f64 x 2) (+.f64 (cos.f64 x) 1))

Outputs
(*.f64 -1/3 (pow.f64 x 2))
(.f64 -1/3 (.f64 x x))
(*.f64 -1/3 (pow.f64 x 2))
(.f64 -1/3 (.f64 x x))
(*.f64 -1/3 (pow.f64 x 2))
(.f64 -1/3 (.f64 x x))
(*.f64 -1/3 (pow.f64 x 2))
(.f64 -1/3 (.f64 x x))
(*.f64 -1/3 (pow.f64 x 2))
(.f64 -1/3 (.f64 x x))
(*.f64 -1/3 (pow.f64 x 2))
(.f64 -1/3 (.f64 x x))
(*.f64 -1/3 (pow.f64 x 2))
(.f64 -1/3 (.f64 x x))
(*.f64 -1/3 (pow.f64 x 2))
(.f64 -1/3 (.f64 x x))
(*.f64 -1/3 (pow.f64 x 2))
(.f64 -1/3 (.f64 x x))
(*.f64 -1/3 (pow.f64 x 2))
(.f64 -1/3 (.f64 x x))
(*.f64 -1/3 (pow.f64 x 2))
(.f64 -1/3 (.f64 x x))
(*.f64 -1/3 (pow.f64 x 2))
(.f64 -1/3 (.f64 x x))
(*.f64 1/2 (pow.f64 x 2))
(.f64 (.f64 x x) 1/2)
(.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 (.f64 x x) 1/2 (.f64 -1/24 (pow.f64 x 4)))
(fma.f64 x (.f64 x 1/2) (.f64 -1/24 (pow.f64 x 4)))
(.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 -1/48 (pow.f64 x 6))))
(fma.f64 1/2 (.f64 x x) (fma.f64 -1/24 (pow.f64 x 4) (.f64 -1/48 (pow.f64 x 6))))
(fma.f64 (.f64 x x) 1/2 (fma.f64 -1/24 (pow.f64 x 4) (.f64 -1/48 (pow.f64 x 6))))
(fma.f64 x (.f64 x 1/2) (fma.f64 -1/24 (pow.f64 x 4) (.f64 -1/48 (pow.f64 x 6))))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x -1/24) 1/2) (*.f64 -1/48 (pow.f64 x 6)))
(+.f64 (.f64 1/2 (pow.f64 x 2)) (+.f64 (.f64 -1/24 (pow.f64 x 4)) (+.f64 (.f64 -1/48 (pow.f64 x 6)) (.f64 -23/5760 (pow.f64 x 8)))))
(fma.f64 1/2 (.f64 x x) (fma.f64 -1/24 (pow.f64 x 4) (fma.f64 -1/48 (pow.f64 x 6) (.f64 -23/5760 (pow.f64 x 8)))))
(fma.f64 (.f64 x x) 1/2 (fma.f64 -1/24 (pow.f64 x 4) (fma.f64 -1/48 (pow.f64 x 6) (.f64 -23/5760 (pow.f64 x 8)))))
(fma.f64 x (.f64 x 1/2) (fma.f64 -1/24 (pow.f64 x 4) (fma.f64 -1/48 (pow.f64 x 6) (.f64 -23/5760 (pow.f64 x 8)))))
(fma.f64 x (.f64 x 1/2) (fma.f64 -1/48 (pow.f64 x 6) (fma.f64 -1/24 (pow.f64 x 4) (.f64 -23/5760 (pow.f64 x 8)))))
(*.f64 -1/3 (/.f64 (pow.f64 x 4) (+.f64 1 (cos.f64 x))))
(*.f64 (pow.f64 x 4) (/.f64 -1/3 (+.f64 1 (cos.f64 x))))
(+.f64 (*.f64 -1/3 (/.f64 (pow.f64 x 4) (+.f64 1 (cos.f64 x)))) (/.f64 (pow.f64 x 2) (+.f64 1 (cos.f64 x))))
(fma.f64 -1/3 (/.f64 (pow.f64 x 4) (+.f64 1 (cos.f64 x))) (/.f64 (*.f64 x x) (+.f64 1 (cos.f64 x))))
(fma.f64 -1/3 (/.f64 (pow.f64 x 4) (+.f64 1 (cos.f64 x))) (*.f64 (/.f64 x (+.f64 1 (cos.f64 x))) x))
(fma.f64 -1/3 (/.f64 (pow.f64 x 4) (+.f64 1 (cos.f64 x))) (*.f64 x (/.f64 x (+.f64 1 (cos.f64 x)))))
(+.f64 (*.f64 -1/3 (/.f64 (pow.f64 x 4) (+.f64 1 (cos.f64 x)))) (/.f64 (pow.f64 x 2) (+.f64 1 (cos.f64 x))))
(fma.f64 -1/3 (/.f64 (pow.f64 x 4) (+.f64 1 (cos.f64 x))) (/.f64 (*.f64 x x) (+.f64 1 (cos.f64 x))))
(fma.f64 -1/3 (/.f64 (pow.f64 x 4) (+.f64 1 (cos.f64 x))) (*.f64 (/.f64 x (+.f64 1 (cos.f64 x))) x))
(fma.f64 -1/3 (/.f64 (pow.f64 x 4) (+.f64 1 (cos.f64 x))) (*.f64 x (/.f64 x (+.f64 1 (cos.f64 x)))))
(+.f64 (*.f64 -1/3 (/.f64 (pow.f64 x 4) (+.f64 1 (cos.f64 x)))) (/.f64 (pow.f64 x 2) (+.f64 1 (cos.f64 x))))
(fma.f64 -1/3 (/.f64 (pow.f64 x 4) (+.f64 1 (cos.f64 x))) (/.f64 (*.f64 x x) (+.f64 1 (cos.f64 x))))
(fma.f64 -1/3 (/.f64 (pow.f64 x 4) (+.f64 1 (cos.f64 x))) (*.f64 (/.f64 x (+.f64 1 (cos.f64 x))) x))
(fma.f64 -1/3 (/.f64 (pow.f64 x 4) (+.f64 1 (cos.f64 x))) (*.f64 x (/.f64 x (+.f64 1 (cos.f64 x)))))
(*.f64 -1/3 (/.f64 (pow.f64 x 4) (+.f64 (cos.f64 x) 1)))
(*.f64 -1/3 (/.f64 (pow.f64 x 4) (+.f64 1 (cos.f64 x))))
(*.f64 (pow.f64 x 4) (/.f64 -1/3 (+.f64 1 (cos.f64 x))))
(+.f64 (*.f64 -1/3 (/.f64 (pow.f64 x 4) (+.f64 (cos.f64 x) 1))) (/.f64 (pow.f64 x 2) (+.f64 (cos.f64 x) 1)))
(fma.f64 -1/3 (/.f64 (pow.f64 x 4) (+.f64 1 (cos.f64 x))) (/.f64 (*.f64 x x) (+.f64 1 (cos.f64 x))))
(fma.f64 -1/3 (/.f64 (pow.f64 x 4) (+.f64 1 (cos.f64 x))) (*.f64 (/.f64 x (+.f64 1 (cos.f64 x))) x))
(fma.f64 -1/3 (/.f64 (pow.f64 x 4) (+.f64 1 (cos.f64 x))) (*.f64 x (/.f64 x (+.f64 1 (cos.f64 x)))))
(+.f64 (*.f64 -1/3 (/.f64 (pow.f64 x 4) (+.f64 (cos.f64 x) 1))) (/.f64 (pow.f64 x 2) (+.f64 (cos.f64 x) 1)))
(fma.f64 -1/3 (/.f64 (pow.f64 x 4) (+.f64 1 (cos.f64 x))) (/.f64 (*.f64 x x) (+.f64 1 (cos.f64 x))))
(fma.f64 -1/3 (/.f64 (pow.f64 x 4) (+.f64 1 (cos.f64 x))) (*.f64 (/.f64 x (+.f64 1 (cos.f64 x))) x))
(fma.f64 -1/3 (/.f64 (pow.f64 x 4) (+.f64 1 (cos.f64 x))) (*.f64 x (/.f64 x (+.f64 1 (cos.f64 x)))))
(+.f64 (*.f64 -1/3 (/.f64 (pow.f64 x 4) (+.f64 (cos.f64 x) 1))) (/.f64 (pow.f64 x 2) (+.f64 (cos.f64 x) 1)))
(fma.f64 -1/3 (/.f64 (pow.f64 x 4) (+.f64 1 (cos.f64 x))) (/.f64 (*.f64 x x) (+.f64 1 (cos.f64 x))))
(fma.f64 -1/3 (/.f64 (pow.f64 x 4) (+.f64 1 (cos.f64 x))) (*.f64 (/.f64 x (+.f64 1 (cos.f64 x))) x))
(fma.f64 -1/3 (/.f64 (pow.f64 x 4) (+.f64 1 (cos.f64 x))) (*.f64 x (/.f64 x (+.f64 1 (cos.f64 x)))))
(*.f64 1/2 (pow.f64 x 2))
(.f64 (.f64 x x) 1/2)
(.f64 x (.f64 x 1/2))
(+.f64 (.f64 1/8 (pow.f64 x 4)) (.f64 1/2 (pow.f64 x 2)))
(fma.f64 1/8 (pow.f64 x 4) (.f64 (.f64 x x) 1/2))
(fma.f64 (.f64 x x) 1/2 (.f64 (pow.f64 x 4) 1/8))
(.f64 x (.f64 x (fma.f64 x (*.f64 x 1/8) 1/2)))
(+.f64 (.f64 1/8 (pow.f64 x 4)) (+.f64 (.f64 1/2 (pow.f64 x 2)) (*.f64 1/48 (pow.f64 x 6))))
(fma.f64 1/8 (pow.f64 x 4) (fma.f64 1/2 (.f64 x x) (.f64 (pow.f64 x 6) 1/48)))
(fma.f64 (pow.f64 x 4) 1/8 (fma.f64 (.f64 x x) 1/2 (.f64 (pow.f64 x 6) 1/48)))
(fma.f64 x (.f64 x 1/2) (fma.f64 (pow.f64 x 6) 1/48 (.f64 (pow.f64 x 4) 1/8)))
(fma.f64 x (.f64 x 1/2) (fma.f64 (pow.f64 x 4) 1/8 (.f64 (pow.f64 x 6) 1/48)))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x 1/8) 1/2) (*.f64 (pow.f64 x 6) 1/48))
(+.f64 (.f64 1/8 (pow.f64 x 4)) (+.f64 (.f64 1/2 (pow.f64 x 2)) (+.f64 (.f64 17/5760 (pow.f64 x 8)) (.f64 1/48 (pow.f64 x 6)))))
(fma.f64 1/8 (pow.f64 x 4) (fma.f64 1/2 (.f64 x x) (fma.f64 17/5760 (pow.f64 x 8) (.f64 (pow.f64 x 6) 1/48))))
(fma.f64 (pow.f64 x 4) 1/8 (fma.f64 (.f64 x x) 1/2 (fma.f64 (pow.f64 x 6) 1/48 (.f64 (pow.f64 x 8) 17/5760))))
(fma.f64 (pow.f64 x 4) 1/8 (fma.f64 x (.f64 x 1/2) (fma.f64 (pow.f64 x 6) 1/48 (.f64 (pow.f64 x 8) 17/5760))))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x 1/8) 1/2) (fma.f64 (pow.f64 x 6) 1/48 (*.f64 (pow.f64 x 8) 17/5760)))
(/.f64 (pow.f64 x 2) (+.f64 1 (cos.f64 x)))
(/.f64 (*.f64 x x) (+.f64 1 (cos.f64 x)))
(*.f64 (/.f64 x (+.f64 1 (cos.f64 x))) x)
(*.f64 x (/.f64 x (+.f64 1 (cos.f64 x))))
(/.f64 (pow.f64 x 2) (+.f64 1 (cos.f64 x)))
(/.f64 (*.f64 x x) (+.f64 1 (cos.f64 x)))
(*.f64 (/.f64 x (+.f64 1 (cos.f64 x))) x)
(*.f64 x (/.f64 x (+.f64 1 (cos.f64 x))))
(/.f64 (pow.f64 x 2) (+.f64 1 (cos.f64 x)))
(/.f64 (*.f64 x x) (+.f64 1 (cos.f64 x)))
(*.f64 (/.f64 x (+.f64 1 (cos.f64 x))) x)
(*.f64 x (/.f64 x (+.f64 1 (cos.f64 x))))
(/.f64 (pow.f64 x 2) (+.f64 1 (cos.f64 x)))
(/.f64 (*.f64 x x) (+.f64 1 (cos.f64 x)))
(*.f64 (/.f64 x (+.f64 1 (cos.f64 x))) x)
(*.f64 x (/.f64 x (+.f64 1 (cos.f64 x))))
(/.f64 (pow.f64 x 2) (+.f64 (cos.f64 x) 1))
(/.f64 (*.f64 x x) (+.f64 1 (cos.f64 x)))
(*.f64 (/.f64 x (+.f64 1 (cos.f64 x))) x)
(*.f64 x (/.f64 x (+.f64 1 (cos.f64 x))))
(/.f64 (pow.f64 x 2) (+.f64 (cos.f64 x) 1))
(/.f64 (*.f64 x x) (+.f64 1 (cos.f64 x)))
(*.f64 (/.f64 x (+.f64 1 (cos.f64 x))) x)
(*.f64 x (/.f64 x (+.f64 1 (cos.f64 x))))
(/.f64 (pow.f64 x 2) (+.f64 (cos.f64 x) 1))
(/.f64 (*.f64 x x) (+.f64 1 (cos.f64 x)))
(*.f64 (/.f64 x (+.f64 1 (cos.f64 x))) x)
(*.f64 x (/.f64 x (+.f64 1 (cos.f64 x))))
(/.f64 (pow.f64 x 2) (+.f64 (cos.f64 x) 1))
(/.f64 (*.f64 x x) (+.f64 1 (cos.f64 x)))
(*.f64 (/.f64 x (+.f64 1 (cos.f64 x))) x)
(*.f64 x (/.f64 x (+.f64 1 (cos.f64 x))))

eval102.0ms (1.3%)

Compiler: Compiled 5273 to 3054 computations (42.1% saved)

prune32.0ms (0.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	233	1	234
Fresh	0	0	0
Picked	1	0	1
Done	0	3	3
Total	234	4	238

Error

Counts

238 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.2b	(.f64 x (.f64 x 1/2))
	0.2b	(.f64 (+.f64 1 (.f64 -1/3 (.f64 x x))) (.f64 x (/.f64 x 2)))
✓	0.0b	(+.f64 (.f64 (.f64 x (.f64 x -1/24)) (.f64 x x)) (.f64 1/2 (.f64 x x)))
✓	0.0b	(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))

Compiler

Compiled 44 to 29 computations (34.1% saved)

regimes14.0ms (0.2%)

Counts

11 → 1

Calls

Call 1

Inputs
(.f64 x (.f64 x 1/2))
(.f64 1/2 (.f64 x x))
(.f64 (+.f64 1 (.f64 -1/3 (.f64 x x))) (.f64 x (/.f64 x 2)))
(+.f64 (.f64 (.f64 x (.f64 x -1/24)) (.f64 x x)) (.f64 1/2 (.f64 x x)))
(-.f64 1 (cos.f64 x))
(.f64 (.f64 x x) (fma.f64 x (*.f64 x -1/24) 1/2))
(.f64 (+.f64 1 (.f64 -1/3 (.f64 x x))) (.f64 x (/.f64 x (+.f64 1 (cos.f64 x)))))
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
(.f64 (.f64 (sin.f64 x) (sin.f64 x)) (/.f64 1 (+.f64 1 (cos.f64 x))))
(/.f64 (fma.f64 x x (*.f64 (pow.f64 x 4) -1/3)) (+.f64 1 (cos.f64 x)))

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

Calls

3 calls:

6.0ms	x
3.0ms	(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	`(cos.f64 x)`

Compiler

Compiled 121 to 68 computations (43.8% saved)

regimes17.0ms (0.2%)

Counts

7 → 1

Calls

Call 1

Inputs
(.f64 x (.f64 x 1/2))
(.f64 1/2 (.f64 x x))
(.f64 (+.f64 1 (.f64 -1/3 (.f64 x x))) (.f64 x (/.f64 x 2)))
(+.f64 (.f64 (.f64 x (.f64 x -1/24)) (.f64 x x)) (.f64 1/2 (.f64 x x)))
(-.f64 1 (cos.f64 x))
(.f64 (.f64 x x) (fma.f64 x (*.f64 x -1/24) 1/2))
(.f64 (+.f64 1 (.f64 -1/3 (.f64 x x))) (.f64 x (/.f64 x (+.f64 1 (cos.f64 x)))))

Outputs
(+.f64 (.f64 (.f64 x (.f64 x -1/24)) (.f64 x x)) (.f64 1/2 (.f64 x x)))

Calls

3 calls:

11.0ms	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	`(cos.f64 x)`

Compiler

Compiled 79 to 46 computations (41.8% saved)

regimes5.0ms (0.1%)

Accuracy

Total -0.0b remaining (-17.1%)

Threshold costs -0.0b (-17.1%)

Counts

3 → 1

Calls

Call 1

Inputs
(.f64 x (.f64 x 1/2))
(.f64 1/2 (.f64 x x))
(.f64 (+.f64 1 (.f64 -1/3 (.f64 x x))) (.f64 x (/.f64 x 2)))

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

Calls

1 calls:

4.0ms

Results

Error	Segments	Branch
0.2b	1	`x`

Compiler

Compiled 26 to 16 computations (38.5% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

7×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	40
1	25	40

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

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

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

Compiler

Compiled 30 to 19 computations (36.7% saved)

soundness89.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

886×	`distribute-rgt-out_binary64`
842×	`fma-def_binary64`
716×	`associate-l_binary64`
650×	`distribute-lft-in_binary64`
538×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	55	364
1	125	362
2	294	360
3	954	334
4	4359	334
5	6652	334

Stop Event

1×	node limit

Compiler

Compiled 40 to 28 computations (30% saved)

end23.0ms (0.3%)

Compiler: Compiled 28 to 17 computations (39.3% saved)

Details

analyze0.0ms (0%)

sample5.3s (67.4%)

preprocess18.0ms (0.2%)

simplify8.0ms (0.1%)

eval0.0ms (0%)

prune1.0ms (0%)

localize4.0ms (0.1%)

series1.0ms (0%)

rewrite56.0ms (0.7%)

simplify105.0ms (1.3%)

eval8.0ms (0.1%)

prune8.0ms (0.1%)

localize5.0ms (0.1%)

series2.0ms (0%)

rewrite45.0ms (0.6%)

simplify174.0ms (2.2%)

localize16.0ms (0.2%)

series4.0ms (0.1%)

rewrite58.0ms (0.7%)

simplify206.0ms (2.6%)

localize15.0ms (0.2%)

series4.0ms (0.1%)

rewrite81.0ms (1%)

simplify62.0ms (0.8%)

localize15.0ms (0.2%)

series1.0ms (0%)

rewrite59.0ms (0.8%)

simplify71.0ms (0.9%)

eval113.0ms (1.4%)

prune54.0ms (0.7%)

localize6.0ms (0.1%)

localize10.0ms (0.1%)

series4.0ms (0.1%)

rewrite57.0ms (0.7%)

simplify111.0ms (1.4%)

localize17.0ms (0.2%)

series3.0ms (0%)

rewrite58.0ms (0.7%)

simplify198.0ms (2.5%)

localize20.0ms (0.3%)

series4.0ms (0%)

rewrite70.0ms (0.9%)

simplify83.0ms (1.1%)

eval99.0ms (1.3%)

prune57.0ms (0.7%)

localize47.0ms (0.6%)

series9.0ms (0.1%)

rewrite126.0ms (1.6%)

simplify101.0ms (1.3%)

eval102.0ms (1.3%)

prune32.0ms (0.4%)

regimes14.0ms (0.2%)

regimes17.0ms (0.2%)

regimes5.0ms (0.1%)

simplify4.0ms (0.1%)

soundness89.0ms (1.1%)

end23.0ms (0.3%)

Profiling