Details

analyze0.0ms (0%)

Algorithm

1×

Search

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

Compiler

Compiled 12 to 9 computations (25% saved)

sample4.5s (66.1%)

Results

3.2s	4399×	body	2048	valid
1.0s	2110×	body	1024	valid
264.0ms	1035×	body	512	valid
85.0ms	712×	body	256	valid

preprocess22.0ms (0.3%)

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)

simplify10.0ms (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

27.8b

Counts

2 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	27.8b	(-.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
✓	3.6b	(-.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))

rewrite45.0ms (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))))))))

simplify103.0ms (1.5%)

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))))

eval12.0ms (0.2%)

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

prune6.0ms (0.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	33	3	36
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	33	4	37

Error

0.0b

Counts

37 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	27.8b	(-.f64 1 (cos.f64 x))
▶	0.0b	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
▶	0.0b	(.f64 (.f64 x x) (fma.f64 x (*.f64 x -1/24) 1/2))
▶	0.3b	(.f64 1/2 (.f64 x x))

Compiler

Compiled 33 to 22 computations (33.3% 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))

rewrite43.0ms (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 (2.5%)

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)

rewrite57.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

2 → 26

Calls

Call 1

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

Outputs

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

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

simplify214.0ms (3.1%)

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)))

localize10.0ms (0.1%)

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)

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

rewrite69.0ms (1%)

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	26
1	179	18
2	2618	18

Stop Event

1×	node limit

Counts

3 → 99

Calls

Call 1

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

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

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

simplify60.0ms (0.9%)

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

131 → 127

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))

eval47.0ms (0.7%)

Compiler: Compiled 2276 to 1341 computations (41.1% saved)

prune22.0ms (0.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	171	4	175
Fresh	0	0	0
Picked	1	0	1
Done	2	1	3
Total	174	5	179

Error

Counts

179 → 5

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.0b	(+.f64 (.f64 (.f64 x (.f64 x -1/24)) (.f64 x x)) (.f64 1/2 (.f64 x x)))
▶	0.3b	(.f64 x (.f64 x 1/2))
▶	0.0b	(/.f64 (fma.f64 x x (*.f64 (pow.f64 x 4) -1/3)) (+.f64 1 (cos.f64 x)))
▶	0.0b	(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
✓	0.0b	(.f64 (.f64 x x) (fma.f64 x (*.f64 x -1/24) 1/2))

Compiler

Compiled 55 to 36 computations (34.5% saved)

localize5.0ms (0.1%)

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

localize36.0ms (0.5%)

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)))

rewrite52.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

1 → 15

Calls

Call 1

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

Outputs

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

simplify112.0ms (1.6%)

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 (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 (.f64 x (.f64 x -1/24)) (.f64 x x)) (.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)

series4.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

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

rewrite95.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

588×	`log-prod_binary64`
548×	`fma-def_binary64`
400×	`pow-prod-down_binary64`
275×	`pow2_binary64`
248×	`pow-unpow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	36
1	222	28
2	2994	28

Stop Event

1×	node limit

Counts

3 → 129

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 x (*.f64 x -1/24)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) (*.f64 x -1/24))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 x) (*.f64 x -1/24)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 x) (*.f64 x -1/24)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 x) (*.f64 x -1/24)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.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 (*.f64 (pow.f64 x 4) 1/576) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x (sqrt.f64 -1/24)) 6) 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 (exp.f64 x) (*.f64 x -1/24)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 x (*.f64 x -1/24)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 -1/24)) 6))))) (#(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 exp.f64 (*.f64 (log.f64 (*.f64 x (*.f64 x -1/24))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 x (sqrt.f64 -1/24)) 6)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 x (*.f64 x -1/24)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 x (sqrt.f64 -1/24))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 x (*.f64 x -1/24))) 1) 1))))))

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

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

simplify220.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

802×	`fma-def_binary64`
787×	`sqr-pow_binary64`
511×	`pow-sqr_binary64`
486×	`associate-l_binary64`
446×	`cube-prod_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	315
1	24	315
2	48	315
3	118	315
4	423	315
5	1599	315
6	2994	315
7	3642	315
8	3832	315
9	4043	315
10	4324	315
11	4689	315
12	5186	315
13	5715	315
14	6345	315
15	7094	315
16	7402	315
17	7628	315
18	7822	315
19	7878	315
20	7902	315

Stop Event

1×	node limit

Counts

165 → 136

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

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 (0.1%)

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 (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)))

rewrite96.0ms (1.4%)

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

simplify85.0ms (1.2%)

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)))))

eval126.0ms (1.8%)

Compiler: Compiled 5170 to 3488 computations (32.5% saved)

prune45.0ms (0.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	300	1	301
Fresh	0	0	0
Picked	1	0	1
Done	1	3	4
Total	302	4	306

Error

Counts

306 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.0b	(+.f64 (.f64 (.f64 x (.f64 x -1/24)) (.f64 x x)) (.f64 1/2 (.f64 x x)))
✓	0.3b	(.f64 x (.f64 x 1/2))
▶	0.0b	(.f64 x (.f64 x (fma.f64 x (*.f64 x -1/24) 1/2)))
✓	0.0b	(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))

Compiler

Compiled 41 to 26 computations (36.6% saved)

localize13.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 31 to 20 computations (35.5% saved)

series3.0ms (0%)

Counts

2 → 24

Calls

6 calls:

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

rewrite65.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

749×	`pow1_binary64`
695×	`add-log-exp_binary64`
695×	`log1p-expm1-u_binary64`
695×	`expm1-log1p-u_binary64`
682×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	25
1	163	25
2	1872	25

Stop Event

1×	node limit

Counts

2 → 30

Calls

Call 1

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

Outputs

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

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

simplify184.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

957×	`sqr-pow_binary64`
803×	`unswap-sqr_binary64`
635×	`cube-prod_binary64`
543×	`fabs-mul_binary64`
385×	`pow-sqr_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	264
1	38	264
2	75	264
3	183	264
4	604	264
5	1183	264
6	2616	264
7	2735	264
8	2909	264
9	3121	264
10	3406	264
11	3780	264
12	4228	264
13	4779	264
14	5473	264
15	5934	264
16	6247	264
17	6519	264
18	6727	264
19	6915	264
20	7696	264

Stop Event

1×	node limit

Counts

54 → 39

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

eval14.0ms (0.2%)

Compiler: Compiled 614 to 413 computations (32.7% saved)

prune10.0ms (0.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	50	1	51
Fresh	0	0	0
Picked	0	1	1
Done	1	2	3
Total	51	4	55

Error

Counts

55 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.0b	(.f64 x (.f64 x (fma.f64 x (*.f64 x -1/24) 1/2)))
	0.0b	(.f64 x (+.f64 (.f64 (.f64 x (.f64 x -1/24)) x) (*.f64 1/2 x)))
✓	0.3b	(.f64 x (.f64 x 1/2))
✓	0.0b	(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))

Compiler

Compiled 39 to 26 computations (33.3% saved)

regimes14.0ms (0.2%)

Counts

10 → 1

Calls

Call 1

Inputs
(.f64 x (.f64 x 1/2))
(.f64 1/2 (.f64 x x))
(.f64 x (+.f64 (.f64 (.f64 x (.f64 x -1/24)) x) (*.f64 1/2 x)))
(+.f64 (.f64 (.f64 x (.f64 x -1/24)) (.f64 x x)) (.f64 1/2 (.f64 x x)))
(-.f64 1 (cos.f64 x))
(.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 (sin.f64 x) (tan.f64 (/.f64 x 2)))
(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.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
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 103 to 60 computations (41.7% saved)

regimes15.0ms (0.2%)

Counts

7 → 1

Calls

Call 1

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

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

Calls

3 calls:

5.0ms	x
2.0ms	(-.f64 1 (cos.f64 x))
2.0ms	(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 73 to 43 computations (41.1% saved)

regimes15.0ms (0.2%)

Counts

5 → 1

Calls

Call 1

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

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

Calls

3 calls:

6.0ms	(-.f64 1 (cos.f64 x))
5.0ms	x
2.0ms	(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 53 to 32 computations (39.6% saved)

regimes4.0ms (0.1%)

Accuracy

Total -0.0b remaining (-2.6%)

Threshold costs -0.0b (-2.6%)

Counts

2 → 1

Calls

Call 1

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

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

Calls

1 calls:

4.0ms

Results

Error	Segments	Branch
0.3b	1	`x`

Compiler

Compiled 13 to 8 computations (38.5% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

9×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	51
1	30	51

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

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

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

Compiler

Compiled 39 to 26 computations (33.3% saved)

soundness96.0ms (1.4%)

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)

end34.0ms (0.5%)

Compiler: Compiled 36 to 23 computations (36.1% saved)

Details

analyze0.0ms (0%)

sample4.5s (66.1%)

preprocess22.0ms (0.3%)

simplify10.0ms (0.1%)

eval0.0ms (0%)

prune1.0ms (0%)

localize4.0ms (0.1%)

series1.0ms (0%)

rewrite45.0ms (0.7%)

simplify103.0ms (1.5%)

eval12.0ms (0.2%)

prune6.0ms (0.1%)

localize5.0ms (0.1%)

series2.0ms (0%)

rewrite43.0ms (0.6%)

simplify174.0ms (2.5%)

localize16.0ms (0.2%)

series4.0ms (0.1%)

rewrite57.0ms (0.8%)

simplify214.0ms (3.1%)

localize10.0ms (0.1%)

series4.0ms (0.1%)

rewrite69.0ms (1%)

simplify60.0ms (0.9%)

eval47.0ms (0.7%)

prune22.0ms (0.3%)

localize5.0ms (0.1%)

localize36.0ms (0.5%)

series4.0ms (0.1%)

rewrite52.0ms (0.8%)

simplify112.0ms (1.6%)

localize17.0ms (0.3%)

series4.0ms (0.1%)

rewrite95.0ms (1.4%)

simplify220.0ms (3.2%)

localize20.0ms (0.3%)

series4.0ms (0.1%)

rewrite96.0ms (1.4%)

simplify85.0ms (1.2%)

eval126.0ms (1.8%)

prune45.0ms (0.7%)

localize13.0ms (0.2%)

series3.0ms (0%)

rewrite65.0ms (0.9%)

simplify184.0ms (2.7%)

eval14.0ms (0.2%)

prune10.0ms (0.2%)

regimes14.0ms (0.2%)

regimes15.0ms (0.2%)

regimes15.0ms (0.2%)

regimes4.0ms (0.1%)

simplify5.0ms (0.1%)

soundness96.0ms (1.4%)

end34.0ms (0.5%)

Profiling