Details

analyze0.0ms (0%)

Algorithm

1×

Search

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

Compiler

Compiled 12 to 9 computations (25% saved)

sample5.6s (65.6%)

Results

3.9s	4409×	body	2048	valid
1.2s	2081×	body	1024	valid
415.0ms	1011×	body	512	valid
116.0ms	755×	body	256	valid

preprocess18.0ms (0.2%)

Algorithm

2×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0

Outputs
0

Call 2

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

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

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify37.0ms (0.4%)

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

31.3b

Counts

2 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	31.3b	(-.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
✓	3.2b	(-.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))

rewrite52.0ms (0.6%)

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))))))))

simplify109.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

32 → 36

Calls

Call 1

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

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

eval9.0ms (0.1%)

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

prune7.0ms (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
✓	31.3b	(-.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))
▶	0.2b	(.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))

rewrite71.0ms (0.8%)

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%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

26 → 16

Calls

Call 1

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

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

localize11.0ms (0.1%)

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)

series5.0ms (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)

rewrite103.0ms (1.2%)

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))))))))

simplify209.0ms (2.5%)

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)))

localize11.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 26 to 10 computations (61.5% saved)

series4.0ms (0%)

Counts

2 → 24

Calls

6 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 (sin.f64 x) (sin.f64 x))
1.0ms	x	@	inf	(*.f64 (sin.f64 x) (sin.f64 x))
1.0ms	x	@	-inf	(*.f64 (sin.f64 x) (sin.f64 x))

rewrite111.0ms (1.3%)

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	20
1	179	12
2	2618	12

Stop Event

1×	node limit

Counts

2 → 68

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (neg.f64 (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 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))))))))

simplify75.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

932×	`distribute-rgt-out_binary64`
742×	`associate-/l/_binary64`
628×	`fma-def_binary64`
584×	`associate-l_binary64`
560×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	43	288
1	98	288
2	223	288
3	712	264
4	3461	264
5	5560	264
6	6976	264

Stop Event

1×	node limit

Counts

92 → 87

Calls

Call 1

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

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

eval97.0ms (1.1%)

Compiler: Compiled 1648 to 1048 computations (36.4% saved)

prune22.0ms (0.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	130	5	135
Fresh	0	0	0
Picked	1	0	1
Done	3	0	3
Total	134	5	139

Error

Counts

139 → 5

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.2b	(.f64 x (.f64 x 1/2))
▶	0.0b	(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
▶	31.3b	(-.f64 (+.f64 1 (.f64 1/2 (.f64 x x))) 1)
▶	0.0b	(+.f64 (.f64 (.f64 x (.f64 x -1/24)) (.f64 x x)) (.f64 1/2 (.f64 x x)))
▶	0.0b	(.f64 x (.f64 x (fma.f64 x (*.f64 x -1/24) 1/2)))

Compiler

Compiled 102 to 68 computations (33.3% saved)

localize19.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 x (.f64 x (fma.f64 x (*.f64 x -1/24) 1/2)))
✓	0.0b	(.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	@	0	(.f64 x (fma.f64 x (.f64 x -1/24) 1/2))
1.0ms	x	@	-inf	(.f64 x (fma.f64 x (.f64 x -1/24) 1/2))
1.0ms	x	@	inf	(.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)))
0.0ms	x	@	0	(.f64 x (.f64 x (fma.f64 x (*.f64 x -1/24) 1/2)))

rewrite63.0ms (0.7%)

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

((#(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)))))))))

simplify189.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

957×	`sqr-pow_binary64`
803×	`unswap-sqr_binary64`
635×	`cube-prod_binary64`
542×	`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	182	264
4	605	264
5	1180	264
6	2613	264
7	2732	264
8	2906	264
9	3121	264
10	3406	264
11	3780	264
12	4228	264
13	4781	264
14	5471	264
15	5928	264
16	6239	264
17	6509	264
18	6719	264
19	6907	264
20	7688	264

Stop Event

1×	node limit

Counts

54 → 39

Calls

Call 1

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

localize5.0ms (0.1%)

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

localize10.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(.f64 1/2 (.f64 x x))
✓	3.2b	(-.f64 (+.f64 1 (.f64 1/2 (.f64 x x))) 1)

Compiler

Compiled 28 to 16 computations (42.9% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite59.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

816×	`pow1_binary64`
767×	`add-log-exp_binary64`
766×	`log1p-expm1-u_binary64`
766×	`expm1-log1p-u_binary64`
754×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	178	7
2	2396	7

Stop Event

1×	node limit

Counts

1 → 46

Calls

Call 1

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

Outputs

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

simplify178.0ms (2.1%)

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

58 → 47

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))

localize29.0ms (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%)

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)))
1.0ms	x	@	0	(.f64 x (.f64 x -1/24))
0.0ms	x	@	inf	(.f64 x (.f64 x -1/24))
0.0ms	x	@	inf	(.f64 (.f64 x (.f64 x -1/24)) (.f64 x x))

rewrite83.0ms (1%)

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))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 x (fma.f64 -1/24 (pow.f64 x 3) (*.f64 x 1/2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 (*.f64 (pow.f64 x 4) -1/24) 2) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x -1/24) -1/2))) (/.f64 (*.f64 1/4 (pow.f64 x 4)) (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x -1/24) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (fma.f64 -1/24 (pow.f64 x 3) (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (fma.f64 x 1/2 (*.f64 -1/24 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (*.f64 x (fma.f64 x (*.f64 x -1/24) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x x) (fma.f64 x (*.f64 x -1/24) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x (fma.f64 -1/24 (pow.f64 x 3) (*.f64 x 1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 x (fma.f64 -1/24 (pow.f64 x 3) (*.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (cbrt.f64 x) x) (*.f64 (pow.f64 (cbrt.f64 x) 2) (fma.f64 x (*.f64 x -1/24) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 x (fma.f64 -1/24 (pow.f64 x 3) (*.f64 x 1/2)))) (cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 (fma.f64 x (*.f64 x -1/24) 1/2))) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 (fma.f64 x (*.f64 x -1/24) 1/2))) 4)) (cbrt.f64 (*.f64 x (fma.f64 -1/24 (pow.f64 x 3) (*.f64 x 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x (sqrt.f64 (fma.f64 x (*.f64 x -1/24) 1/2))) (*.f64 x (sqrt.f64 (fma.f64 x (*.f64 x -1/24) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 1/8 (pow.f64 x 6) (pow.f64 (*.f64 (pow.f64 x 4) -1/24) 3)) (/.f64 1 (fma.f64 (*.f64 x (*.f64 x 1/2)) (-.f64 (*.f64 x (*.f64 x 1/2)) (*.f64 (pow.f64 x 4) -1/24)) (pow.f64 (*.f64 (pow.f64 x 4) -1/24) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 (*.f64 (pow.f64 x 4) -1/24) 2) (*.f64 1/4 (pow.f64 x 4))) (/.f64 1 (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x -1/24) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 x (*.f64 x -1/24) 1/2) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 (*.f64 x (*.f64 x 1/2)) (-.f64 (*.f64 x (*.f64 x 1/2)) (*.f64 (pow.f64 x 4) -1/24)) (pow.f64 (*.f64 (pow.f64 x 4) -1/24) 2)) (fma.f64 1/8 (pow.f64 x 6) (pow.f64 (*.f64 (pow.f64 x 4) -1/24) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (*.f64 (*.f64 x x) (fma.f64 x (*.f64 x -1/24) -1/2)) (-.f64 (pow.f64 (*.f64 (pow.f64 x 4) -1/24) 2) (*.f64 1/4 (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 1/8 (pow.f64 x 6) (pow.f64 (*.f64 (pow.f64 x 4) -1/24) 3)) (fma.f64 (*.f64 x (*.f64 x 1/2)) (-.f64 (*.f64 x (*.f64 x 1/2)) (*.f64 (pow.f64 x 4) -1/24)) (pow.f64 (*.f64 (pow.f64 x 4) -1/24) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 1/8 (pow.f64 x 6) (pow.f64 (*.f64 (pow.f64 x 4) -1/24) 3)) 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log.f64 (*.f64 (sqrt.f64 (pow.f64 (exp.f64 x) x)) (+.f64 1 (expm1.f64 (*.f64 (pow.f64 x 4) -1/24)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (*.f64 x (*.f64 x 1/2)))) (+.f64 1 (expm1.f64 (*.f64 (pow.f64 x 4) -1/24)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 (fma.f64 x (*.f64 x -1/24) 1/2))) 6))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x (fma.f64 -1/24 (pow.f64 x 3) (*.f64 x 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x (fma.f64 -1/24 (pow.f64 x 3) (*.f64 x 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x (fma.f64 -1/24 (pow.f64 x 3) (*.f64 x 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 x (fma.f64 -1/24 (pow.f64 x 3) (*.f64 x 1/2)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 x (sqrt.f64 (fma.f64 x (*.f64 x -1/24) 1/2))) 6)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 x (fma.f64 -1/24 (pow.f64 x 3) (*.f64 x 1/2))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 x (sqrt.f64 (fma.f64 x (*.f64 x -1/24) 1/2)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 x (fma.f64 -1/24 (pow.f64 x 3) (*.f64 x 1/2)))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x (*.f64 x 1/2) (*.f64 (pow.f64 x 4) -1/24))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x (*.f64 -1/24 (pow.f64 x 3)) (*.f64 x (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x -1/24) (pow.f64 x 3) (*.f64 x (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x (*.f64 x -1/24)) (*.f64 x x) (*.f64 x (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x x) (*.f64 x (*.f64 x -1/24)) (*.f64 x (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x x) 1/2 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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)))))))

simplify222.0ms (2.6%)

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))

localize10.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 19 to 12 computations (36.8% saved)

series6.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

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

rewrite51.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

1 → 15

Calls

Call 1

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

Outputs

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

simplify111.0ms (1.3%)

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))))

eval107.0ms (1.3%)

Compiler: Compiled 4200 to 2840 computations (32.4% saved)

prune40.0ms (0.5%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	286	1	287
Fresh	0	0	0
Picked	0	1	1
Done	1	3	4
Total	287	5	292

Error

Counts

292 → 5

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.2b	(.f64 x (.f64 x 1/2))
✓	0.0b	(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
✓	31.3b	(-.f64 (+.f64 1 (.f64 1/2 (.f64 x x))) 1)
▶	0.0b	(.f64 x (+.f64 (.f64 (.f64 x (.f64 x -1/24)) x) (*.f64 1/2 x)))
✓	0.0b	(.f64 x (.f64 x (fma.f64 x (*.f64 x -1/24) 1/2)))

Compiler

Compiled 49 to 34 computations (30.6% saved)

localize27.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 46 to 29 computations (37% saved)

series11.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
6.0ms	x	@	0	(.f64 x (+.f64 (.f64 (.f64 x (.f64 x -1/24)) x) (*.f64 1/2 x)))
1.0ms	x	@	inf	(.f64 x (+.f64 (.f64 (.f64 x (.f64 x -1/24)) x) (*.f64 1/2 x)))
1.0ms	x	@	0	(.f64 (.f64 x (*.f64 x -1/24)) x)
1.0ms	x	@	-inf	(.f64 x (+.f64 (.f64 (.f64 x (.f64 x -1/24)) x) (*.f64 1/2 x)))
1.0ms	x	@	inf	(.f64 (.f64 x (*.f64 x -1/24)) x)

rewrite104.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

591×	`log-prod_binary64`
452×	`fma-def_binary64`
414×	`pow-prod-down_binary64`
283×	`pow2_binary64`
219×	`pow-unpow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	26
1	223	21
2	3028	21

Stop Event

1×	node limit

Counts

2 → 86

Calls

Call 1

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

Outputs

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

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

simplify196.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	231
1	33	231
2	69	231
3	165	231
4	556	231
5	1117	231
6	2565	231
7	2689	231
8	2863	231
9	3078	231
10	3361	231
11	3733	231
12	4180	231
13	4734	231
14	5428	231
15	5885	231
16	6192	231
17	6460	231
18	6672	231
19	6862	231
20	7643	231

Stop Event

1×	node limit

Counts

110 → 92

Calls

Call 1

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

eval54.0ms (0.6%)

Compiler: Compiled 2079 to 1439 computations (30.8% saved)

prune18.0ms (0.2%)

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	127	0	127
Fresh	0	0	0
Picked	0	1	1
Done	0	4	4
Total	127	5	132

Error

Counts

132 → 5

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.2b	(.f64 x (.f64 x 1/2))
✓	0.0b	(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
✓	31.3b	(-.f64 (+.f64 1 (.f64 1/2 (.f64 x x))) 1)
✓	0.0b	(.f64 x (+.f64 (.f64 (.f64 x (.f64 x -1/24)) x) (*.f64 1/2 x)))
✓	0.0b	(.f64 x (.f64 x (fma.f64 x (*.f64 x -1/24) 1/2)))

Compiler

Compiled 49 to 34 computations (30.6% saved)

regimes19.0ms (0.2%)

Counts

10 → 1

Calls

Call 1

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

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

Calls

3 calls:

8.0ms	(cos.f64 x)
6.0ms	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 99 to 58 computations (41.4% saved)

regimes13.0ms (0.2%)

Counts

6 → 1

Calls

Call 1

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

8.0ms	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 62 to 38 computations (38.7% saved)

regimes5.0ms (0.1%)

Accuracy

Total -31.1b remaining (-13992.3%)

Threshold costs -31.1b (-13992.3%)

Counts

3 → 1

Calls

Call 1

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

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

Calls

1 calls:

4.0ms

Results

Error	Segments	Branch
0.2b	1	`x`

Compiler

Compiled 22 to 14 computations (36.4% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	40
1	24	40

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(.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 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 31 to 20 computations (35.5% saved)

soundness116.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

932×	`distribute-rgt-out_binary64`
742×	`associate-/l/_binary64`
628×	`fma-def_binary64`
584×	`associate-l_binary64`
560×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	43	288
1	98	288
2	223	288
3	712	264
4	3461	264
5	5560	264
6	6976	264

Stop Event

1×	node limit

Compiler

Compiled 153 to 118 computations (22.9% saved)

end35.0ms (0.4%)

Compiler: Compiled 29 to 18 computations (37.9% saved)

Details

analyze0.0ms (0%)

sample5.6s (65.6%)

preprocess18.0ms (0.2%)

simplify37.0ms (0.4%)

eval0.0ms (0%)

prune1.0ms (0%)

localize4.0ms (0.1%)

series1.0ms (0%)

rewrite52.0ms (0.6%)

simplify109.0ms (1.3%)

eval9.0ms (0.1%)

prune7.0ms (0.1%)

localize5.0ms (0.1%)

series2.0ms (0%)

rewrite71.0ms (0.8%)

simplify174.0ms (2%)

localize11.0ms (0.1%)

series5.0ms (0.1%)

rewrite103.0ms (1.2%)

simplify209.0ms (2.5%)

localize11.0ms (0.1%)

series4.0ms (0%)

rewrite111.0ms (1.3%)

simplify75.0ms (0.9%)

eval97.0ms (1.1%)

prune22.0ms (0.3%)

localize19.0ms (0.2%)

series3.0ms (0%)

rewrite63.0ms (0.7%)

simplify189.0ms (2.2%)

localize5.0ms (0.1%)

localize10.0ms (0.1%)

series1.0ms (0%)

rewrite59.0ms (0.7%)

simplify178.0ms (2.1%)

localize29.0ms (0.3%)

series4.0ms (0%)

rewrite83.0ms (1%)

simplify222.0ms (2.6%)

localize10.0ms (0.1%)

series6.0ms (0.1%)

rewrite51.0ms (0.6%)

simplify111.0ms (1.3%)

eval107.0ms (1.3%)

prune40.0ms (0.5%)

localize27.0ms (0.3%)

series11.0ms (0.1%)

rewrite104.0ms (1.2%)

simplify196.0ms (2.3%)

eval54.0ms (0.6%)

prune18.0ms (0.2%)

regimes19.0ms (0.2%)

regimes13.0ms (0.2%)

regimes5.0ms (0.1%)

simplify4.0ms (0%)

soundness116.0ms (1.4%)

end35.0ms (0.4%)

Profiling