Details

analyze532.0ms (4.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
25%	74.9%	0.1%	7
37.4%	62.4%	0.1%	8
37.4%	62.4%	0.1%	9
56.2%	43.7%	0.1%	10
65.5%	34.3%	0.1%	11
65.5%	34.3%	0.1%	12

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample2.6s (20%)

Results

1.1s	5189×	body	256	valid
1.1s	2050×	body	1024	valid
367.0ms	1013×	body	512	valid
5.0ms	4×	body	2048	valid

preprocess22.0ms (0.2%)

Algorithm

2×	egg-herbie

Rules

16×	`fma-def_binary64`
8×	`*-commutative_binary64`
4×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	48
1	38	48
2	50	48
0	3	3

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0
1
2

Outputs
0
1
2

Call 2

Inputs
(+.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))
(+.f64 (.f64 y (cos.f64 x)) (.f64 z (sin.f64 x)))
(+.f64 (.f64 z (cos.f64 y)) (.f64 x (sin.f64 y)))
(+.f64 (.f64 x (cos.f64 z)) (.f64 y (sin.f64 z)))

Outputs
(+.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))
(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
(+.f64 (.f64 y (cos.f64 x)) (.f64 z (sin.f64 x)))
(fma.f64 y (cos.f64 x) (*.f64 z (sin.f64 x)))
(+.f64 (.f64 z (cos.f64 y)) (.f64 x (sin.f64 y)))
(fma.f64 z (cos.f64 y) (*.f64 x (sin.f64 y)))
(fma.f64 x (sin.f64 y) (*.f64 (cos.f64 y) z))
(+.f64 (.f64 x (cos.f64 z)) (.f64 y (sin.f64 z)))
(fma.f64 x (cos.f64 z) (*.f64 y (sin.f64 z)))

Compiler

Compiled 15 to 11 computations (26.7% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`fma-def_binary64`
2×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	12
1	13	12
2	16	12

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

Inputs
(+.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))

Outputs
(+.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))
(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))

eval1.0ms (0%)

Compiler: Compiled 20 to 9 computations (55% saved)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

0.1b

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.1b	(+.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))

Compiler

Compiled 12 to 8 computations (33.3% saved)

localize13.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 z (sin.f64 y))
✓	0.1b	(*.f64 x (cos.f64 y))

Compiler

Compiled 27 to 8 computations (70.4% saved)

series8.0ms (0.1%)

Counts

2 → 28

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(*.f64 x (cos.f64 y))
1.0ms	y	@	0	(*.f64 x (cos.f64 y))
1.0ms	z	@	0	(*.f64 z (sin.f64 y))
1.0ms	z	@	-inf	(*.f64 z (sin.f64 y))
1.0ms	y	@	0	(*.f64 z (sin.f64 y))

rewrite56.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

740×	`pow1_binary64`
673×	`add-log-exp_binary64`
673×	`log1p-expm1-u_binary64`
673×	`expm1-log1p-u_binary64`
657×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	155	12
2	1836	12

Stop Event

1×	node limit

Counts

2 → 26

Calls

Call 1

Inputs
(*.f64 x (cos.f64 y))
(*.f64 z (sin.f64 y))

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

Outputs

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

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

simplify189.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

722×	`cube-prod_binary64`
682×	`sqr-pow_binary64`
506×	`fabs-mul_binary64`
443×	`pow-sqr_binary64`
427×	`unpow3_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	46	260
1	122	257
2	344	240
3	1172	239
4	1870	239
5	2752	239
6	2938	239
7	3172	239
8	3439	239
9	3798	239
10	4213	239
11	4705	239
12	5277	239
13	5965	239
14	6473	239
15	6865	239
16	7255	239
17	7699	239

Stop Event

1×	node limit

Counts

54 → 41

Calls

Call 1

Inputs
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
x
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) x)
(+.f64 (.f64 1/24 (.f64 (pow.f64 y 4) x)) (+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) x))
(+.f64 (.f64 -1/720 (.f64 (pow.f64 y 6) x)) (+.f64 (.f64 1/24 (.f64 (pow.f64 y 4) x)) (+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) x)))
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 y z)
(+.f64 (.f64 -1/6 (.f64 (pow.f64 y 3) z)) (*.f64 y z))
(+.f64 (.f64 -1/6 (.f64 (pow.f64 y 3) z)) (+.f64 (.f64 y z) (.f64 1/120 (*.f64 (pow.f64 y 5) z))))
(+.f64 (.f64 -1/6 (.f64 (pow.f64 y 3) z)) (+.f64 (.f64 y z) (+.f64 (.f64 -1/5040 (.f64 (pow.f64 y 7) z)) (.f64 1/120 (*.f64 (pow.f64 y 5) z)))))

Outputs
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
x
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) x)
(fma.f64 -1/2 (.f64 x (.f64 y y)) x)
(.f64 x (fma.f64 -1/2 (.f64 y y) 1))
(.f64 x (fma.f64 (.f64 y -1/2) y 1))
(+.f64 (.f64 1/24 (.f64 (pow.f64 y 4) x)) (+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) x))
(fma.f64 1/24 (.f64 x (pow.f64 y 4)) (fma.f64 -1/2 (.f64 x (*.f64 y y)) x))
(fma.f64 x (fma.f64 1/24 (pow.f64 y 4) (.f64 y (.f64 y -1/2))) x)
(+.f64 (.f64 -1/720 (.f64 (pow.f64 y 6) x)) (+.f64 (.f64 1/24 (.f64 (pow.f64 y 4) x)) (+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) x)))
(fma.f64 -1/720 (.f64 x (pow.f64 y 6)) (fma.f64 1/24 (.f64 x (pow.f64 y 4)) (fma.f64 -1/2 (.f64 x (.f64 y y)) x)))
(fma.f64 x (fma.f64 -1/720 (pow.f64 y 6) (.f64 1/24 (pow.f64 y 4))) (.f64 x (fma.f64 -1/2 (*.f64 y y) 1)))
(.f64 x (+.f64 (fma.f64 (.f64 y -1/2) y 1) (fma.f64 -1/720 (pow.f64 y 6) (*.f64 1/24 (pow.f64 y 4)))))
(.f64 x (+.f64 (fma.f64 -1/2 (.f64 y y) 1) (fma.f64 -1/720 (pow.f64 y 6) (*.f64 1/24 (pow.f64 y 4)))))
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 y z)
(+.f64 (.f64 -1/6 (.f64 (pow.f64 y 3) z)) (*.f64 y z))
(fma.f64 -1/6 (.f64 z (pow.f64 y 3)) (.f64 y z))
(.f64 z (+.f64 y (.f64 -1/6 (pow.f64 y 3))))
(*.f64 z (fma.f64 -1/6 (pow.f64 y 3) y))
(+.f64 (.f64 -1/6 (.f64 (pow.f64 y 3) z)) (+.f64 (.f64 y z) (.f64 1/120 (*.f64 (pow.f64 y 5) z))))
(fma.f64 -1/6 (.f64 z (pow.f64 y 3)) (fma.f64 y z (.f64 1/120 (*.f64 z (pow.f64 y 5)))))
(fma.f64 -1/6 (.f64 z (pow.f64 y 3)) (.f64 z (+.f64 y (*.f64 1/120 (pow.f64 y 5)))))
(.f64 z (+.f64 (.f64 -1/6 (pow.f64 y 3)) (fma.f64 1/120 (pow.f64 y 5) y)))
(+.f64 (.f64 -1/6 (.f64 (pow.f64 y 3) z)) (+.f64 (.f64 y z) (+.f64 (.f64 -1/5040 (.f64 (pow.f64 y 7) z)) (.f64 1/120 (*.f64 (pow.f64 y 5) z)))))
(fma.f64 -1/6 (.f64 z (pow.f64 y 3)) (fma.f64 y z (fma.f64 -1/5040 (.f64 z (pow.f64 y 7)) (.f64 1/120 (.f64 z (pow.f64 y 5))))))
(fma.f64 -1/6 (.f64 z (pow.f64 y 3)) (fma.f64 y z (.f64 z (+.f64 (.f64 1/120 (pow.f64 y 5)) (.f64 -1/5040 (pow.f64 y 7))))))
(.f64 z (+.f64 (fma.f64 -1/5040 (pow.f64 y 7) (.f64 1/120 (pow.f64 y 5))) (fma.f64 -1/6 (pow.f64 y 3) y)))
(.f64 z (+.f64 (fma.f64 -1/6 (pow.f64 y 3) y) (fma.f64 1/120 (pow.f64 y 5) (.f64 -1/5040 (pow.f64 y 7)))))

eval10.0ms (0.1%)

Compiler: Compiled 589 to 264 computations (55.2% saved)

prune17.0ms (0.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	34	7	41
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	34	8	42

Error

0.1b

Counts

42 → 8

Alt Table

Click to see full alt table

Status	Error	Program
▶	30.2b	(+.f64 (cbrt.f64 (pow.f64 (.f64 x (cos.f64 y)) 3)) (.f64 z (sin.f64 y)))
✓	0.1b	(+.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))
	18.3b	(+.f64 (.f64 x (cos.f64 y)) (cbrt.f64 (pow.f64 (.f64 z (sin.f64 y)) 3)))
	30.5b	(+.f64 (pow.f64 (sqrt.f64 (.f64 x (cos.f64 y))) 2) (.f64 z (sin.f64 y)))
▶	20.3b	(+.f64 (.f64 x (cos.f64 y)) (.f64 y z))
▶	24.8b	(+.f64 (+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) x) (*.f64 z (sin.f64 y)))
▶	13.8b	(+.f64 x (*.f64 z (sin.f64 y)))
▶	0.5b	(+.f64 (.f64 x (cos.f64 y)) (pow.f64 (cbrt.f64 (.f64 z (sin.f64 y))) 3))

Compiler

Compiled 206 to 146 computations (29.1% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.f64 z (sin.f64 y))
	0.1b	(*.f64 x (cos.f64 y))
✓	0.6b	(pow.f64 (cbrt.f64 (*.f64 z (sin.f64 y))) 3)
✓	6.1b	(cbrt.f64 (*.f64 z (sin.f64 y)))

Compiler

Compiled 43 to 14 computations (67.4% saved)

series14.0ms (0.1%)

Counts

2 → 16

Calls

12 calls:

Time	Variable		Point	Expression
3.0ms	z	@	-inf	(pow.f64 (cbrt.f64 (*.f64 z (sin.f64 y))) 3)
2.0ms	y	@	inf	(cbrt.f64 (*.f64 z (sin.f64 y)))
2.0ms	y	@	-inf	(cbrt.f64 (*.f64 z (sin.f64 y)))
1.0ms	y	@	0	(pow.f64 (cbrt.f64 (*.f64 z (sin.f64 y))) 3)
1.0ms	y	@	-inf	(pow.f64 (cbrt.f64 (*.f64 z (sin.f64 y))) 3)

rewrite67.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

638×	`pow1_binary64`
596×	`add-log-exp_binary64`
596×	`log1p-expm1-u_binary64`
596×	`expm1-log1p-u_binary64`
581×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	166	14
2	1669	14

Stop Event

1×	node limit

Counts

2 → 52

Calls

Call 1

Inputs
(cbrt.f64 (*.f64 z (sin.f64 y)))
(pow.f64 (cbrt.f64 (*.f64 z (sin.f64 y))) 3)

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

Outputs

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

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

simplify183.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

1290×	`sqr-pow_binary64`
676×	`cube-prod_binary64`
666×	`pow-sqr_binary64`
556×	`fabs-mul_binary64`
373×	`unpow3_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	136
1	26	112
2	40	112
3	51	112
4	75	112
5	161	112
6	525	112
7	1190	112
8	1282	112
9	1420	112
10	1583	112
11	1822	112
12	2149	112
13	2576	112
14	3081	112
15	3688	112
16	4411	112
17	4734	112
18	5018	112
19	5242	112
20	5418	112
21	5498	112
22	6441	112
23	7418	112
24	7884	112

Stop Event

1×	node limit

Counts

68 → 54

Calls

Call 1

Inputs
(pow.f64 (*.f64 z (sin.f64 y)) 1/3)
(pow.f64 (*.f64 z (sin.f64 y)) 1/3)
(pow.f64 (*.f64 z (sin.f64 y)) 1/3)
(pow.f64 (*.f64 z (sin.f64 y)) 1/3)
(pow.f64 (*.f64 z (sin.f64 y)) 1/3)
(pow.f64 (*.f64 z (sin.f64 y)) 1/3)
(pow.f64 (*.f64 z (sin.f64 y)) 1/3)
(pow.f64 (*.f64 z (sin.f64 y)) 1/3)
(.f64 (pow.f64 1 1/3) (.f64 z (sin.f64 y)))
(.f64 (pow.f64 1 1/3) (.f64 z (sin.f64 y)))
(.f64 (pow.f64 1 1/3) (.f64 z (sin.f64 y)))
(.f64 (pow.f64 1 1/3) (.f64 z (sin.f64 y)))
(.f64 (pow.f64 1 1/3) (.f64 z (sin.f64 y)))
(.f64 (pow.f64 1 1/3) (.f64 z (sin.f64 y)))
(.f64 (pow.f64 1 1/3) (.f64 z (sin.f64 y)))
(.f64 (pow.f64 1 1/3) (.f64 z (sin.f64 y)))

Outputs
(pow.f64 (*.f64 z (sin.f64 y)) 1/3)
(cbrt.f64 (*.f64 z (sin.f64 y)))
(pow.f64 (*.f64 z (sin.f64 y)) 1/3)
(cbrt.f64 (*.f64 z (sin.f64 y)))
(pow.f64 (*.f64 z (sin.f64 y)) 1/3)
(cbrt.f64 (*.f64 z (sin.f64 y)))
(pow.f64 (*.f64 z (sin.f64 y)) 1/3)
(cbrt.f64 (*.f64 z (sin.f64 y)))
(pow.f64 (*.f64 z (sin.f64 y)) 1/3)
(cbrt.f64 (*.f64 z (sin.f64 y)))
(pow.f64 (*.f64 z (sin.f64 y)) 1/3)
(cbrt.f64 (*.f64 z (sin.f64 y)))
(pow.f64 (*.f64 z (sin.f64 y)) 1/3)
(cbrt.f64 (*.f64 z (sin.f64 y)))
(pow.f64 (*.f64 z (sin.f64 y)) 1/3)
(cbrt.f64 (*.f64 z (sin.f64 y)))
(.f64 (pow.f64 1 1/3) (.f64 z (sin.f64 y)))
(.f64 (.f64 z (sin.f64 y)) 1)
(*.f64 z (sin.f64 y))
(.f64 (pow.f64 1 1/3) (.f64 z (sin.f64 y)))
(.f64 (.f64 z (sin.f64 y)) 1)
(*.f64 z (sin.f64 y))
(.f64 (pow.f64 1 1/3) (.f64 z (sin.f64 y)))
(.f64 (.f64 z (sin.f64 y)) 1)
(*.f64 z (sin.f64 y))
(.f64 (pow.f64 1 1/3) (.f64 z (sin.f64 y)))
(.f64 (.f64 z (sin.f64 y)) 1)
(*.f64 z (sin.f64 y))
(.f64 (pow.f64 1 1/3) (.f64 z (sin.f64 y)))
(.f64 (.f64 z (sin.f64 y)) 1)
(*.f64 z (sin.f64 y))
(.f64 (pow.f64 1 1/3) (.f64 z (sin.f64 y)))
(.f64 (.f64 z (sin.f64 y)) 1)
(*.f64 z (sin.f64 y))
(.f64 (pow.f64 1 1/3) (.f64 z (sin.f64 y)))
(.f64 (.f64 z (sin.f64 y)) 1)
(*.f64 z (sin.f64 y))
(.f64 (pow.f64 1 1/3) (.f64 z (sin.f64 y)))
(.f64 (.f64 z (sin.f64 y)) 1)
(*.f64 z (sin.f64 y))

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (*.f64 z (sin.f64 y)))
	0.1b	(*.f64 z (sin.f64 y))

Compiler

Compiled 18 to 6 computations (66.7% saved)

series3.0ms (0%)

Counts

1 → 27

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(+.f64 x (*.f64 z (sin.f64 y)))
0.0ms	x	@	inf	(+.f64 x (*.f64 z (sin.f64 y)))
0.0ms	y	@	0	(+.f64 x (*.f64 z (sin.f64 y)))
0.0ms	x	@	-inf	(+.f64 x (*.f64 z (sin.f64 y)))
0.0ms	y	@	inf	(+.f64 x (*.f64 z (sin.f64 y)))

rewrite57.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

808×	`pow1_binary64`
747×	`add-log-exp_binary64`
747×	`log1p-expm1-u_binary64`
747×	`expm1-log1p-u_binary64`
730×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	147	7
2	2003	7

Stop Event

1×	node limit

Counts

1 → 35

Calls

Call 1

Inputs
(+.f64 x (*.f64 z (sin.f64 y)))

Outputs

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

simplify154.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

1295×	`fma-def_binary64`
788×	`sqr-pow_binary64`
544×	`associate-l_binary64`
487×	`*-commutative_binary64`
448×	`cube-prod_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	24	186
1	65	186
2	152	182
3	380	179
4	995	177
5	2360	177
6	2811	177
7	3453	177
8	3569	177
9	3741	177
10	3960	177
11	4946	177
12	5406	177
13	6006	177
14	6759	177
15	7693	177

Stop Event

1×	node limit

Counts

62 → 44

Calls

Call 1

Inputs
(*.f64 z (sin.f64 y))
x
(+.f64 (*.f64 z (sin.f64 y)) x)
(+.f64 (*.f64 z (sin.f64 y)) x)
(+.f64 (*.f64 z (sin.f64 y)) x)
x
(+.f64 (*.f64 z (sin.f64 y)) x)
(+.f64 (*.f64 z (sin.f64 y)) x)
(+.f64 (*.f64 z (sin.f64 y)) x)
x
(+.f64 (*.f64 z (sin.f64 y)) x)
(+.f64 (*.f64 z (sin.f64 y)) x)
(+.f64 (*.f64 z (sin.f64 y)) x)
(*.f64 z (sin.f64 y))
(*.f64 z (sin.f64 y))
x
(+.f64 (*.f64 y z) x)
(+.f64 (.f64 y z) (+.f64 (.f64 -1/6 (*.f64 (pow.f64 y 3) z)) x))
(+.f64 (.f64 y z) (+.f64 (.f64 -1/6 (.f64 (pow.f64 y 3) z)) (+.f64 (.f64 1/120 (*.f64 (pow.f64 y 5) z)) x)))
(+.f64 (*.f64 z (sin.f64 y)) x)
(+.f64 (*.f64 z (sin.f64 y)) x)
(+.f64 (*.f64 z (sin.f64 y)) x)
(+.f64 (*.f64 z (sin.f64 y)) x)
(+.f64 (*.f64 z (sin.f64 y)) x)
(+.f64 (*.f64 z (sin.f64 y)) x)
(+.f64 (*.f64 z (sin.f64 y)) x)
(+.f64 (*.f64 z (sin.f64 y)) x)

Outputs
(*.f64 z (sin.f64 y))
x
(+.f64 (*.f64 z (sin.f64 y)) x)
(fma.f64 z (sin.f64 y) x)
(+.f64 (*.f64 z (sin.f64 y)) x)
(fma.f64 z (sin.f64 y) x)
(+.f64 (*.f64 z (sin.f64 y)) x)
(fma.f64 z (sin.f64 y) x)
x
(+.f64 (*.f64 z (sin.f64 y)) x)
(fma.f64 z (sin.f64 y) x)
(+.f64 (*.f64 z (sin.f64 y)) x)
(fma.f64 z (sin.f64 y) x)
(+.f64 (*.f64 z (sin.f64 y)) x)
(fma.f64 z (sin.f64 y) x)
x
(+.f64 (*.f64 z (sin.f64 y)) x)
(fma.f64 z (sin.f64 y) x)
(+.f64 (*.f64 z (sin.f64 y)) x)
(fma.f64 z (sin.f64 y) x)
(+.f64 (*.f64 z (sin.f64 y)) x)
(fma.f64 z (sin.f64 y) x)
(*.f64 z (sin.f64 y))
(*.f64 z (sin.f64 y))
x
(+.f64 (*.f64 y z) x)
(fma.f64 y z x)
(fma.f64 z y x)
(+.f64 (.f64 y z) (+.f64 (.f64 -1/6 (*.f64 (pow.f64 y 3) z)) x))
(fma.f64 y z (fma.f64 -1/6 (*.f64 z (pow.f64 y 3)) x))
(fma.f64 z y (fma.f64 -1/6 (*.f64 z (pow.f64 y 3)) x))
(fma.f64 z (+.f64 y (*.f64 -1/6 (pow.f64 y 3))) x)
(fma.f64 z (fma.f64 -1/6 (pow.f64 y 3) y) x)
(+.f64 (.f64 y z) (+.f64 (.f64 -1/6 (.f64 (pow.f64 y 3) z)) (+.f64 (.f64 1/120 (*.f64 (pow.f64 y 5) z)) x)))
(fma.f64 y z (fma.f64 -1/6 (.f64 z (pow.f64 y 3)) (fma.f64 1/120 (.f64 z (pow.f64 y 5)) x)))
(fma.f64 z y (fma.f64 -1/6 (.f64 z (pow.f64 y 3)) (fma.f64 1/120 (.f64 z (pow.f64 y 5)) x)))
(fma.f64 z (fma.f64 -1/6 (pow.f64 y 3) (*.f64 1/120 (pow.f64 y 5))) (fma.f64 z y x))
(fma.f64 z (+.f64 (*.f64 1/120 (pow.f64 y 5)) (fma.f64 -1/6 (pow.f64 y 3) y)) x)
(fma.f64 z (fma.f64 -1/6 (pow.f64 y 3) (fma.f64 1/120 (pow.f64 y 5) y)) x)
(+.f64 (*.f64 z (sin.f64 y)) x)
(fma.f64 z (sin.f64 y) x)
(+.f64 (*.f64 z (sin.f64 y)) x)
(fma.f64 z (sin.f64 y) x)
(+.f64 (*.f64 z (sin.f64 y)) x)
(fma.f64 z (sin.f64 y) x)
(+.f64 (*.f64 z (sin.f64 y)) x)
(fma.f64 z (sin.f64 y) x)
(+.f64 (*.f64 z (sin.f64 y)) x)
(fma.f64 z (sin.f64 y) x)
(+.f64 (*.f64 z (sin.f64 y)) x)
(fma.f64 z (sin.f64 y) x)
(+.f64 (*.f64 z (sin.f64 y)) x)
(fma.f64 z (sin.f64 y) x)
(+.f64 (*.f64 z (sin.f64 y)) x)
(fma.f64 z (sin.f64 y) x)

localize10.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 x (cos.f64 y)) (.f64 y z))
	0.1b	(*.f64 x (cos.f64 y))

Compiler

Compiled 23 to 7 computations (69.6% saved)

series4.0ms (0%)

Counts

1 → 36

Calls

9 calls:

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

rewrite75.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

911×	`pow1_binary64`
841×	`add-log-exp_binary64`
841×	`log1p-expm1-u_binary64`
841×	`expm1-log1p-u_binary64`
822×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	168	10
2	2280	10

Stop Event

1×	node limit

Counts

1 → 37

Calls

Call 1

Inputs
(+.f64 (.f64 x (cos.f64 y)) (.f64 y z))

Outputs

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

simplify193.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

909×	`fma-def_binary64`
671×	`sqr-pow_binary64`
476×	`distribute-lft-out_binary64`
444×	`cube-prod_binary64`
426×	`*-commutative_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	23	324
1	58	324
2	139	321
3	375	321
4	1285	318
5	2767	318
6	3925	318
7	4006	318
8	4129	318
9	4284	318
10	4546	318
11	4805	318
12	5158	318
13	5535	318
14	6026	318
15	6613	318
16	7331	318
17	7661	318
18	7923	318

Stop Event

1×	node limit

Counts

73 → 48

Calls

Call 1

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

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

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) x)
✓	0.0b	(pow.f64 y 2)
	0.1b	(*.f64 z (sin.f64 y))
✓	7.6b	(*.f64 (pow.f64 y 2) x)

Compiler

Compiled 52 to 30 computations (42.3% saved)

series8.0ms (0.1%)

Counts

3 → 15

Calls

15 calls:

Time	Variable		Point	Expression
2.0ms	y	@	inf	(*.f64 (pow.f64 y 2) x)
1.0ms	y	@	0	(*.f64 (pow.f64 y 2) x)
1.0ms	x	@	0	(*.f64 (pow.f64 y 2) x)
1.0ms	y	@	-inf	(pow.f64 y 2)
1.0ms	y	@	inf	(pow.f64 y 2)

rewrite71.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

944×	`pow1_binary64`
879×	`add-log-exp_binary64`
878×	`log1p-expm1-u_binary64`
878×	`expm1-log1p-u_binary64`
861×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	22
1	197	22
2	2452	22

Stop Event

1×	node limit

Counts

3 → 68

Calls

Call 1

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

Outputs

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

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

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

simplify114.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

1107×	`fma-neg_binary64`
615×	`fma-def_binary64`
502×	`distribute-rgt-neg-in_binary64`
383×	`unswap-sqr_binary64`
345×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	177
1	39	153
2	94	153
3	273	153
4	836	153
5	1537	153
6	2678	153
7	3861	153
8	5388	153
9	6361	153
10	7072	153
11	7507	153

Stop Event

1×	node limit

Counts

83 → 74

Calls

Call 1

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

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

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.f64 z (sin.f64 y))
✓	0.1b	(pow.f64 (*.f64 x (cos.f64 y)) 3)
	0.1b	(*.f64 x (cos.f64 y))
✓	42.2b	(cbrt.f64 (pow.f64 (*.f64 x (cos.f64 y)) 3))

Compiler

Compiled 44 to 17 computations (61.4% saved)

series14.0ms (0.1%)

Counts

2 → 48

Calls

12 calls:

Time	Variable		Point	Expression
5.0ms	x	@	-inf	(cbrt.f64 (pow.f64 (*.f64 x (cos.f64 y)) 3))
2.0ms	y	@	0	(cbrt.f64 (pow.f64 (*.f64 x (cos.f64 y)) 3))
1.0ms	y	@	0	(pow.f64 (*.f64 x (cos.f64 y)) 3)
1.0ms	y	@	-inf	(pow.f64 (*.f64 x (cos.f64 y)) 3)
1.0ms	y	@	inf	(pow.f64 (*.f64 x (cos.f64 y)) 3)

rewrite64.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

645×	`pow1_binary64`
603×	`add-log-exp_binary64`
603×	`log1p-expm1-u_binary64`
603×	`expm1-log1p-u_binary64`
586×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	168	15
2	1728	15

Stop Event

1×	node limit

Counts

2 → 54

Calls

Call 1

Inputs
(cbrt.f64 (pow.f64 (*.f64 x (cos.f64 y)) 3))
(pow.f64 (*.f64 x (cos.f64 y)) 3)

Outputs

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

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

simplify71.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

649×	`distribute-rgt-out_binary64`
558×	`distribute-rgt-in_binary64`
552×	`fma-def_binary64`
549×	`distribute-lft-in_binary64`
452×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	66	596
1	208	584
2	787	556
3	4122	546
4	7923	546

Stop Event

1×	node limit

Counts

102 → 70

Calls

Call 1

Inputs
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(.f64 -1 (.f64 (cbrt.f64 -1) (*.f64 (cos.f64 y) x)))
(.f64 -1 (.f64 (cbrt.f64 -1) (*.f64 (cos.f64 y) x)))
(.f64 -1 (.f64 (cbrt.f64 -1) (*.f64 (cos.f64 y) x)))
(.f64 -1 (.f64 (cbrt.f64 -1) (*.f64 (cos.f64 y) x)))
x
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) x)
(+.f64 (.f64 1/24 (.f64 (pow.f64 y 4) x)) (+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) x))
(+.f64 (.f64 -1/720 (.f64 (pow.f64 y 6) x)) (+.f64 (.f64 1/24 (.f64 (pow.f64 y 4) x)) (+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) x)))
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(pow.f64 x 3)
(+.f64 (.f64 (pow.f64 y 2) (+.f64 (.f64 -1 (pow.f64 x 3)) (*.f64 -1/2 (pow.f64 x 3)))) (pow.f64 x 3))
(+.f64 (.f64 (+.f64 (.f64 x (+.f64 (.f64 1/4 (pow.f64 x 2)) (.f64 1/12 (pow.f64 x 2)))) (+.f64 (.f64 1/2 (pow.f64 x 3)) (.f64 1/24 (pow.f64 x 3)))) (pow.f64 y 4)) (+.f64 (.f64 (pow.f64 y 2) (+.f64 (.f64 -1 (pow.f64 x 3)) (*.f64 -1/2 (pow.f64 x 3)))) (pow.f64 x 3)))
(+.f64 (.f64 (+.f64 (.f64 x (+.f64 (.f64 1/4 (pow.f64 x 2)) (.f64 1/12 (pow.f64 x 2)))) (+.f64 (.f64 1/2 (pow.f64 x 3)) (.f64 1/24 (pow.f64 x 3)))) (pow.f64 y 4)) (+.f64 (.f64 (pow.f64 y 6) (+.f64 (.f64 -1/24 (pow.f64 x 3)) (+.f64 (.f64 -1/2 (.f64 (+.f64 (.f64 1/4 (pow.f64 x 2)) (.f64 1/12 (pow.f64 x 2))) x)) (+.f64 (.f64 (+.f64 (.f64 -1/360 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 2))) x) (.f64 -1/720 (pow.f64 x 3)))))) (+.f64 (.f64 (pow.f64 y 2) (+.f64 (.f64 -1 (pow.f64 x 3)) (*.f64 -1/2 (pow.f64 x 3)))) (pow.f64 x 3))))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))

Outputs
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(.f64 -1 (.f64 (cbrt.f64 -1) (*.f64 (cos.f64 y) x)))
(neg.f64 (.f64 (.f64 (cos.f64 y) x) (cbrt.f64 -1)))
(.f64 (.f64 (cos.f64 y) x) (neg.f64 (cbrt.f64 -1)))
(.f64 (cos.f64 y) (.f64 x (neg.f64 (cbrt.f64 -1))))
(.f64 -1 (.f64 (cbrt.f64 -1) (*.f64 (cos.f64 y) x)))
(neg.f64 (.f64 (.f64 (cos.f64 y) x) (cbrt.f64 -1)))
(.f64 (.f64 (cos.f64 y) x) (neg.f64 (cbrt.f64 -1)))
(.f64 (cos.f64 y) (.f64 x (neg.f64 (cbrt.f64 -1))))
(.f64 -1 (.f64 (cbrt.f64 -1) (*.f64 (cos.f64 y) x)))
(neg.f64 (.f64 (.f64 (cos.f64 y) x) (cbrt.f64 -1)))
(.f64 (.f64 (cos.f64 y) x) (neg.f64 (cbrt.f64 -1)))
(.f64 (cos.f64 y) (.f64 x (neg.f64 (cbrt.f64 -1))))
(.f64 -1 (.f64 (cbrt.f64 -1) (*.f64 (cos.f64 y) x)))
(neg.f64 (.f64 (.f64 (cos.f64 y) x) (cbrt.f64 -1)))
(.f64 (.f64 (cos.f64 y) x) (neg.f64 (cbrt.f64 -1)))
(.f64 (cos.f64 y) (.f64 x (neg.f64 (cbrt.f64 -1))))
x
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) x)
(fma.f64 -1/2 (.f64 x (.f64 y y)) x)
(fma.f64 (.f64 (.f64 -1/2 y) y) x x)
(.f64 x (fma.f64 -1/2 (.f64 y y) 1))
(fma.f64 x (.f64 y (.f64 y -1/2)) x)
(+.f64 (.f64 1/24 (.f64 (pow.f64 y 4) x)) (+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) x))
(fma.f64 1/24 (.f64 x (pow.f64 y 4)) (fma.f64 -1/2 (.f64 x (*.f64 y y)) x))
(fma.f64 1/24 (.f64 x (pow.f64 y 4)) (fma.f64 (.f64 (*.f64 -1/2 y) y) x x))
(fma.f64 x (fma.f64 1/24 (pow.f64 y 4) (.f64 y (.f64 y -1/2))) x)
(+.f64 (.f64 -1/720 (.f64 (pow.f64 y 6) x)) (+.f64 (.f64 1/24 (.f64 (pow.f64 y 4) x)) (+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) x)))
(fma.f64 -1/720 (.f64 x (pow.f64 y 6)) (fma.f64 1/24 (.f64 x (pow.f64 y 4)) (fma.f64 -1/2 (.f64 x (.f64 y y)) x)))
(fma.f64 -1/720 (.f64 x (pow.f64 y 6)) (fma.f64 1/24 (.f64 x (pow.f64 y 4)) (fma.f64 (.f64 (.f64 -1/2 y) y) x x)))
(fma.f64 x (fma.f64 -1/720 (pow.f64 y 6) (.f64 1/24 (pow.f64 y 4))) (.f64 x (fma.f64 -1/2 (*.f64 y y) 1)))
(.f64 x (+.f64 (fma.f64 -1/2 (.f64 y y) 1) (fma.f64 -1/720 (pow.f64 y 6) (*.f64 1/24 (pow.f64 y 4)))))
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(pow.f64 x 3)
(+.f64 (.f64 (pow.f64 y 2) (+.f64 (.f64 -1 (pow.f64 x 3)) (*.f64 -1/2 (pow.f64 x 3)))) (pow.f64 x 3))
(fma.f64 (.f64 y y) (.f64 (pow.f64 x 3) -3/2) (pow.f64 x 3))
(fma.f64 y (.f64 y (.f64 (pow.f64 x 3) -3/2)) (pow.f64 x 3))
(.f64 (+.f64 (.f64 (*.f64 -3/2 y) y) 1) (pow.f64 x 3))
(+.f64 (.f64 (+.f64 (.f64 x (+.f64 (.f64 1/4 (pow.f64 x 2)) (.f64 1/12 (pow.f64 x 2)))) (+.f64 (.f64 1/2 (pow.f64 x 3)) (.f64 1/24 (pow.f64 x 3)))) (pow.f64 y 4)) (+.f64 (.f64 (pow.f64 y 2) (+.f64 (.f64 -1 (pow.f64 x 3)) (*.f64 -1/2 (pow.f64 x 3)))) (pow.f64 x 3)))
(fma.f64 (fma.f64 x (.f64 (.f64 x x) 1/3) (.f64 (pow.f64 x 3) 13/24)) (pow.f64 y 4) (fma.f64 (.f64 y y) (*.f64 (pow.f64 x 3) -3/2) (pow.f64 x 3)))
(fma.f64 (pow.f64 y 4) (fma.f64 (pow.f64 x 3) 13/24 (.f64 (pow.f64 x 3) 1/3)) (fma.f64 (.f64 y y) (*.f64 (pow.f64 x 3) -3/2) (pow.f64 x 3)))
(fma.f64 y (.f64 y (.f64 (pow.f64 x 3) -3/2)) (fma.f64 (pow.f64 y 4) (*.f64 (pow.f64 x 3) 7/8) (pow.f64 x 3)))
(fma.f64 (pow.f64 y 4) (.f64 (pow.f64 x 3) 7/8) (.f64 (+.f64 (.f64 (.f64 -3/2 y) y) 1) (pow.f64 x 3)))
(+.f64 (.f64 (+.f64 (.f64 x (+.f64 (.f64 1/4 (pow.f64 x 2)) (.f64 1/12 (pow.f64 x 2)))) (+.f64 (.f64 1/2 (pow.f64 x 3)) (.f64 1/24 (pow.f64 x 3)))) (pow.f64 y 4)) (+.f64 (.f64 (pow.f64 y 6) (+.f64 (.f64 -1/24 (pow.f64 x 3)) (+.f64 (.f64 -1/2 (.f64 (+.f64 (.f64 1/4 (pow.f64 x 2)) (.f64 1/12 (pow.f64 x 2))) x)) (+.f64 (.f64 (+.f64 (.f64 -1/360 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 2))) x) (.f64 -1/720 (pow.f64 x 3)))))) (+.f64 (.f64 (pow.f64 y 2) (+.f64 (.f64 -1 (pow.f64 x 3)) (*.f64 -1/2 (pow.f64 x 3)))) (pow.f64 x 3))))
(fma.f64 (fma.f64 x (.f64 (.f64 x x) 1/3) (.f64 (pow.f64 x 3) 13/24)) (pow.f64 y 4) (fma.f64 (pow.f64 y 6) (fma.f64 -1/24 (pow.f64 x 3) (fma.f64 -1/2 (.f64 x (.f64 (.f64 x x) 1/3)) (fma.f64 (.f64 (.f64 x x) -2/45) x (.f64 -1/720 (pow.f64 x 3))))) (fma.f64 (.f64 y y) (*.f64 (pow.f64 x 3) -3/2) (pow.f64 x 3))))
(fma.f64 (pow.f64 y 4) (fma.f64 (pow.f64 x 3) 13/24 (.f64 (pow.f64 x 3) 1/3)) (fma.f64 (pow.f64 y 6) (fma.f64 (pow.f64 x 3) -1/24 (fma.f64 -1/2 (.f64 (pow.f64 x 3) 1/3) (fma.f64 -1/720 (pow.f64 x 3) (.f64 (pow.f64 x 3) -2/45)))) (fma.f64 (.f64 y y) (*.f64 (pow.f64 x 3) -3/2) (pow.f64 x 3))))
(fma.f64 (pow.f64 y 4) (.f64 (pow.f64 x 3) 7/8) (fma.f64 (pow.f64 y 6) (+.f64 (.f64 (pow.f64 x 3) -1/6) (fma.f64 (pow.f64 x 3) -1/24 (.f64 (pow.f64 x 3) -11/240))) (fma.f64 y (.f64 y (*.f64 (pow.f64 x 3) -3/2)) (pow.f64 x 3))))
(fma.f64 (pow.f64 y 4) (.f64 (pow.f64 x 3) 7/8) (fma.f64 (pow.f64 y 6) (fma.f64 x (.f64 (.f64 x x) -19/90) (.f64 (pow.f64 x 3) -31/720)) (.f64 (+.f64 (.f64 (*.f64 -3/2 y) y) 1) (pow.f64 x 3))))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))

eval129.0ms (1%)

Compiler: Compiled 7107 to 2958 computations (58.4% saved)

prune155.0ms (1.2%)

Pruning

19 alts after pruning (16 fresh and 3 done)

	Pruned	Kept	Total
New	418	15	433
Fresh	1	1	2
Picked	0	1	1
Done	3	2	5
Total	422	19	441

Error

0.0b

Counts

441 → 19

Alt Table

Click to see full alt table

Status	Error	Program
✓	30.2b	(+.f64 (cbrt.f64 (pow.f64 (.f64 x (cos.f64 y)) 3)) (.f64 z (sin.f64 y)))
✓	0.1b	(+.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))
▶	14.3b	(+.f64 x (pow.f64 (cbrt.f64 (*.f64 z (sin.f64 y))) 3))
	14.4b	(+.f64 (.f64 (.f64 x (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	38.2b	x
	28.8b	(+.f64 (*.f64 y z) x)
	30.5b	(+.f64 (pow.f64 (sqrt.f64 (.f64 x (cos.f64 y))) 2) (.f64 z (sin.f64 y)))
▶	25.0b	(*.f64 (cos.f64 y) x)
▶	52.8b	(*.f64 y z)
	38.3b	(*.f64 z (sin.f64 y))
▶	0.7b	(+.f64 (.f64 x (cos.f64 y)) (pow.f64 (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 z)) 3))
	20.9b	(fma.f64 (pow.f64 (cbrt.f64 (.f64 x (cos.f64 y))) 2) (cbrt.f64 (.f64 x (cos.f64 y))) (*.f64 y z))
	0.8b	(+.f64 (.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (cos.f64 y))) (*.f64 z (sin.f64 y)))
	30.1b	(+.f64 (.f64 x (cos.f64 y)) (.f64 (*.f64 (sin.f64 y) (sqrt.f64 z)) (sqrt.f64 z)))
	33.9b	(+.f64 (.f64 x (cos.f64 y)) (.f64 (*.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
	30.0b	(+.f64 (+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) x) (*.f64 y z))
	30.5b	(+.f64 x (cbrt.f64 (pow.f64 (*.f64 z (sin.f64 y)) 3)))
✓	0.5b	(+.f64 (.f64 x (cos.f64 y)) (pow.f64 (cbrt.f64 (.f64 z (sin.f64 y))) 3))
▶	0.5b	(+.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 (pow.f64 (cbrt.f64 (.f64 z (sin.f64 y))) 2) (cbrt.f64 z)) (cbrt.f64 (sin.f64 y))))

Compiler

Compiled 462 to 309 computations (33.1% saved)

localize57.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(pow.f64 (cbrt.f64 (*.f64 z (sin.f64 y))) 2)
✓	0.6b	(cbrt.f64 (sin.f64 y))
✓	0.6b	(cbrt.f64 z)
	6.1b	(cbrt.f64 (*.f64 z (sin.f64 y)))

Compiler

Compiled 79 to 25 computations (68.4% saved)

series17.0ms (0.1%)

Counts

3 → 16

Calls

12 calls:

Time	Variable		Point	Expression
3.0ms	y	@	inf	(cbrt.f64 (sin.f64 y))
3.0ms	y	@	-inf	(cbrt.f64 (sin.f64 y))
3.0ms	z	@	inf	(pow.f64 (cbrt.f64 (*.f64 z (sin.f64 y))) 2)
1.0ms	z	@	-inf	(pow.f64 (cbrt.f64 (*.f64 z (sin.f64 y))) 2)
1.0ms	y	@	0	(pow.f64 (cbrt.f64 (*.f64 z (sin.f64 y))) 2)

rewrite101.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

790×	`pow1_binary64`
726×	`add-log-exp_binary64`
726×	`log1p-expm1-u_binary64`
726×	`expm1-log1p-u_binary64`
705×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	19
1	194	19
2	2080	19

Stop Event

1×	node limit

Counts

3 → 55

Calls

Call 1

Inputs
(cbrt.f64 z)
(cbrt.f64 (sin.f64 y))
(pow.f64 (cbrt.f64 (*.f64 z (sin.f64 y))) 2)

Outputs

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

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

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

simplify148.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

2214×	`associate-l_binary64`
1903×	`associate-r_binary64`
711×	`sqr-pow_binary64`
283×	`pow-sqr_binary64`
276×	`unswap-sqr_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	152
1	28	152
2	56	152
3	137	152
4	511	152
5	1058	152
6	1149	152
7	1288	152
8	1461	152
9	1650	152
10	1886	152
11	2163	152
12	2483	152
13	2853	152
14	3262	152
15	3695	152
16	3891	152
17	3995	152
18	4067	152
19	4121	152

Stop Event

1×	node limit

Counts

71 → 58

Calls

Call 1

Inputs
(pow.f64 (sin.f64 y) 1/3)
(pow.f64 (sin.f64 y) 1/3)
(pow.f64 (sin.f64 y) 1/3)
(pow.f64 (sin.f64 y) 1/3)
(pow.f64 (sin.f64 y) 1/3)
(pow.f64 (sin.f64 y) 1/3)
(pow.f64 (sin.f64 y) 1/3)
(pow.f64 (sin.f64 y) 1/3)
(pow.f64 (*.f64 (pow.f64 z 2) (pow.f64 (sin.f64 y) 2)) 1/3)
(pow.f64 (*.f64 (pow.f64 z 2) (pow.f64 (sin.f64 y) 2)) 1/3)
(pow.f64 (*.f64 (pow.f64 z 2) (pow.f64 (sin.f64 y) 2)) 1/3)
(pow.f64 (*.f64 (pow.f64 z 2) (pow.f64 (sin.f64 y) 2)) 1/3)
(pow.f64 (*.f64 (pow.f64 z 2) (pow.f64 (sin.f64 y) 2)) 1/3)
(pow.f64 (*.f64 (pow.f64 z 2) (pow.f64 (sin.f64 y) 2)) 1/3)
(pow.f64 (*.f64 (pow.f64 z 2) (pow.f64 (sin.f64 y) 2)) 1/3)
(pow.f64 (*.f64 (pow.f64 z 2) (pow.f64 (sin.f64 y) 2)) 1/3)

Outputs
(pow.f64 (sin.f64 y) 1/3)
(cbrt.f64 (sin.f64 y))
(pow.f64 (sin.f64 y) 1/3)
(cbrt.f64 (sin.f64 y))
(pow.f64 (sin.f64 y) 1/3)
(cbrt.f64 (sin.f64 y))
(pow.f64 (sin.f64 y) 1/3)
(cbrt.f64 (sin.f64 y))
(pow.f64 (sin.f64 y) 1/3)
(cbrt.f64 (sin.f64 y))
(pow.f64 (sin.f64 y) 1/3)
(cbrt.f64 (sin.f64 y))
(pow.f64 (sin.f64 y) 1/3)
(cbrt.f64 (sin.f64 y))
(pow.f64 (sin.f64 y) 1/3)
(cbrt.f64 (sin.f64 y))
(pow.f64 (*.f64 (pow.f64 z 2) (pow.f64 (sin.f64 y) 2)) 1/3)
(cbrt.f64 (.f64 (.f64 z z) (pow.f64 (sin.f64 y) 2)))
(cbrt.f64 (.f64 z (.f64 z (pow.f64 (sin.f64 y) 2))))
(pow.f64 (*.f64 (pow.f64 z 2) (pow.f64 (sin.f64 y) 2)) 1/3)
(cbrt.f64 (.f64 (.f64 z z) (pow.f64 (sin.f64 y) 2)))
(cbrt.f64 (.f64 z (.f64 z (pow.f64 (sin.f64 y) 2))))
(pow.f64 (*.f64 (pow.f64 z 2) (pow.f64 (sin.f64 y) 2)) 1/3)
(cbrt.f64 (.f64 (.f64 z z) (pow.f64 (sin.f64 y) 2)))
(cbrt.f64 (.f64 z (.f64 z (pow.f64 (sin.f64 y) 2))))
(pow.f64 (*.f64 (pow.f64 z 2) (pow.f64 (sin.f64 y) 2)) 1/3)
(cbrt.f64 (.f64 (.f64 z z) (pow.f64 (sin.f64 y) 2)))
(cbrt.f64 (.f64 z (.f64 z (pow.f64 (sin.f64 y) 2))))
(pow.f64 (*.f64 (pow.f64 z 2) (pow.f64 (sin.f64 y) 2)) 1/3)
(cbrt.f64 (.f64 (.f64 z z) (pow.f64 (sin.f64 y) 2)))
(cbrt.f64 (.f64 z (.f64 z (pow.f64 (sin.f64 y) 2))))
(pow.f64 (*.f64 (pow.f64 z 2) (pow.f64 (sin.f64 y) 2)) 1/3)
(cbrt.f64 (.f64 (.f64 z z) (pow.f64 (sin.f64 y) 2)))
(cbrt.f64 (.f64 z (.f64 z (pow.f64 (sin.f64 y) 2))))
(pow.f64 (*.f64 (pow.f64 z 2) (pow.f64 (sin.f64 y) 2)) 1/3)
(cbrt.f64 (.f64 (.f64 z z) (pow.f64 (sin.f64 y) 2)))
(cbrt.f64 (.f64 z (.f64 z (pow.f64 (sin.f64 y) 2))))
(pow.f64 (*.f64 (pow.f64 z 2) (pow.f64 (sin.f64 y) 2)) 1/3)
(cbrt.f64 (.f64 (.f64 z z) (pow.f64 (sin.f64 y) 2)))
(cbrt.f64 (.f64 z (.f64 z (pow.f64 (sin.f64 y) 2))))

localize8.0ms (0.1%)

Compiler: Compiled 8 to 4 computations (50% saved)

localize15.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (cos.f64 y) x)

Compiler

Compiled 11 to 5 computations (54.5% saved)

series3.0ms (0%)

Counts

1 → 4

Calls

6 calls:

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

rewrite65.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

462×	`pow1_binary64`
440×	`add-sqr-sqrt_binary64`
435×	`*-un-lft-identity_binary64`
422×	`add-log-exp_binary64`
422×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	97	6
2	1146	6

Stop Event

1×	node limit

Counts

1 → 11

Calls

Call 1

Inputs
(*.f64 (cos.f64 y) x)

Outputs

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

simplify130.0ms (1%)

Algorithm

1×	egg-herbie

Rules

629×	`distribute-lft-out_binary64`
610×	`distribute-rgt-out_binary64`
428×	`*-commutative_binary64`
420×	`associate-+l+_binary64`
420×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	21	64
1	54	64
2	148	58
3	481	55
4	2096	55
5	4262	55
6	4535	55
7	4866	55
8	5379	55
9	6128	55
10	6941	55

Stop Event

1×	node limit

Counts

15 → 18

Calls

Call 1

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

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

localize28.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (pow.f64 (cbrt.f64 (*.f64 z (sin.f64 y))) 3))
	0.1b	(*.f64 z (sin.f64 y))
	0.6b	(pow.f64 (cbrt.f64 (*.f64 z (sin.f64 y))) 3)
	6.1b	(cbrt.f64 (*.f64 z (sin.f64 y)))

Compiler

Compiled 34 to 12 computations (64.7% saved)

series8.0ms (0.1%)

Counts

1 → 24

Calls

9 calls:

Time	Variable		Point	Expression
3.0ms	x	@	0	(+.f64 x (pow.f64 (cbrt.f64 (*.f64 z (sin.f64 y))) 3))
1.0ms	z	@	inf	(+.f64 x (pow.f64 (cbrt.f64 (*.f64 z (sin.f64 y))) 3))
1.0ms	z	@	-inf	(+.f64 x (pow.f64 (cbrt.f64 (*.f64 z (sin.f64 y))) 3))
1.0ms	z	@	0	(+.f64 x (pow.f64 (cbrt.f64 (*.f64 z (sin.f64 y))) 3))
1.0ms	y	@	0	(+.f64 x (pow.f64 (cbrt.f64 (*.f64 z (sin.f64 y))) 3))

rewrite95.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

979×	`pow1_binary64`
914×	`add-log-exp_binary64`
914×	`log1p-expm1-u_binary64`
914×	`expm1-log1p-u_binary64`
99×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	9
1	216	7
2	2521	7

Stop Event

1×	node limit

Counts

1 → 37

Calls

Call 1

Inputs
(+.f64 x (pow.f64 (cbrt.f64 (*.f64 z (sin.f64 y))) 3))

Outputs

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

simplify3.2s (25.2%)

Algorithm

1×	egg-herbie

Rules

1991×	`sqr-pow_binary64`
1991×	`pow-base-1_binary64`
6×	`fma-def_binary64`
3×	`*-commutative_binary64`
2×	`+-commutative_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	185
1	27	131
2	43	131
3	50	131
4	54	131
5	58	131
6	62	131
7	66	131
8	70	131
9	74	131
10	78	131
11	82	131
12	86	131
13	90	131
14	94	131
15	98	131
16	102	131
17	106	131
18	110	131
19	114	131
20	118	131
21	122	131
22	126	131
23	130	131
24	134	131
25	138	131
26	142	131
27	146	131
28	150	131
29	154	131
30	158	131
31	162	131
32	166	131
33	170	131
34	174	131
35	178	131
36	182	131
37	186	131
38	190	131
39	194	131
40	198	131
41	202	131
42	206	131
43	210	131
44	214	131
45	218	131
46	222	131
47	226	131
48	230	131
49	234	131
50	238	131
51	242	131
52	246	131
53	250	131
54	254	131
55	258	131
56	262	131
57	266	131
58	270	131
59	274	131
60	278	131
61	282	131
62	286	131
63	290	131
64	294	131
65	298	131
66	302	131
67	306	131
68	310	131
69	314	131
70	318	131
71	322	131
72	326	131
73	330	131
74	334	131
75	338	131
76	342	131
77	346	131
78	350	131
79	354	131
80	358	131
81	362	131
82	366	131
83	370	131
84	374	131
85	378	131
86	382	131
87	386	131
88	390	131
89	394	131
90	398	131
91	402	131
92	406	131
93	410	131
94	414	131
95	418	131
96	422	131
97	426	131
98	430	131
99	434	131
100	438	131
101	442	131
102	446	131
103	450	131
104	454	131
105	458	131
106	462	131
107	466	131
108	470	131
109	474	131
110	478	131
111	482	131
112	486	131
113	490	131
114	494	131
115	498	131
116	502	131
117	506	131
118	510	131
119	514	131
120	518	131
121	522	131
122	526	131
123	530	131
124	534	131
125	538	131
126	542	131
127	546	131
128	550	131
129	554	131
130	558	131
131	562	131
132	566	131
133	570	131
134	574	131
135	578	131
136	582	131
137	586	131
138	590	131
139	594	131
140	598	131
141	602	131
142	606	131
143	610	131
144	614	131
145	618	131
146	622	131
147	626	131
148	630	131
149	634	131
150	638	131
151	642	131
152	646	131
153	650	131
154	654	131
155	658	131
156	662	131
157	666	131
158	670	131
159	674	131
160	678	131
161	682	131
162	686	131
163	690	131
164	694	131
165	698	131
166	702	131
167	706	131
168	710	131
169	714	131
170	718	131
171	722	131
172	726	131
173	730	131
174	734	131
175	738	131
176	742	131
177	746	131
178	750	131
179	754	131
180	758	131
181	762	131
182	766	131
183	770	131
184	774	131
185	778	131
186	782	131
187	786	131
188	790	131
189	794	131
190	798	131
191	802	131
192	806	131
193	810	131
194	814	131
195	818	131
196	822	131
197	826	131
198	830	131
199	834	131
200	838	131
201	842	131
202	846	131
203	850	131
204	854	131
205	858	131
206	862	131
207	866	131
208	870	131
209	874	131
210	878	131
211	882	131
212	886	131
213	890	131
214	894	131
215	898	131
216	902	131
217	906	131
218	910	131
219	914	131
220	918	131
221	922	131
222	926	131
223	930	131
224	934	131
225	938	131
226	942	131
227	946	131
228	950	131
229	954	131
230	958	131
231	962	131
232	966	131
233	970	131
234	974	131
235	978	131
236	982	131
237	986	131
238	990	131
239	994	131
240	998	131
241	1002	131
242	1006	131
243	1010	131
244	1014	131
245	1018	131
246	1022	131
247	1026	131
248	1030	131
249	1034	131
250	1038	131
251	1042	131
252	1046	131
253	1050	131
254	1054	131
255	1058	131
256	1062	131
257	1066	131
258	1070	131
259	1074	131
260	1078	131
261	1082	131
262	1086	131
263	1090	131
264	1094	131
265	1098	131
266	1102	131
267	1106	131
268	1110	131
269	1114	131
270	1118	131
271	1122	131
272	1126	131
273	1130	131
274	1134	131
275	1138	131
276	1142	131
277	1146	131
278	1150	131
279	1154	131
280	1158	131
281	1162	131
282	1166	131
283	1170	131
284	1174	131
285	1178	131
286	1182	131
287	1186	131
288	1190	131
289	1194	131
290	1198	131
291	1202	131
292	1206	131
293	1210	131
294	1214	131
295	1218	131
296	1222	131
297	1226	131
298	1230	131
299	1234	131
300	1238	131
301	1242	131
302	1246	131
303	1250	131
304	1254	131
305	1258	131
306	1262	131
307	1266	131
308	1270	131
309	1274	131
310	1278	131
311	1282	131
312	1286	131
313	1290	131
314	1294	131
315	1298	131
316	1302	131
317	1306	131
318	1310	131
319	1314	131
320	1318	131
321	1322	131
322	1326	131
323	1330	131
324	1334	131
325	1338	131
326	1342	131
327	1346	131
328	1350	131
329	1354	131
330	1358	131
331	1362	131
332	1366	131
333	1370	131
334	1374	131
335	1378	131
336	1382	131
337	1386	131
338	1390	131
339	1394	131
340	1398	131
341	1402	131
342	1406	131
343	1410	131
344	1414	131
345	1418	131
346	1422	131
347	1426	131
348	1430	131
349	1434	131
350	1438	131
351	1442	131
352	1446	131
353	1450	131
354	1454	131
355	1458	131
356	1462	131
357	1466	131
358	1470	131
359	1474	131
360	1478	131
361	1482	131
362	1486	131
363	1490	131
364	1494	131
365	1498	131
366	1502	131
367	1506	131
368	1510	131
369	1514	131
370	1518	131
371	1522	131
372	1526	131
373	1530	131
374	1534	131
375	1538	131
376	1542	131
377	1546	131
378	1550	131
379	1554	131
380	1558	131
381	1562	131
382	1566	131
383	1570	131
384	1574	131
385	1578	131
386	1582	131
387	1586	131
388	1590	131
389	1594	131
390	1598	131
391	1602	131
392	1606	131
393	1610	131
394	1614	131
395	1618	131
396	1622	131
397	1626	131
398	1630	131
399	1634	131
400	1638	131
401	1642	131
402	1646	131
403	1650	131
404	1654	131
405	1658	131
406	1662	131
407	1666	131
408	1670	131
409	1674	131
410	1678	131
411	1682	131
412	1686	131
413	1690	131
414	1694	131
415	1698	131
416	1702	131
417	1706	131
418	1710	131
419	1714	131
420	1718	131
421	1722	131
422	1726	131
423	1730	131
424	1734	131
425	1738	131
426	1742	131
427	1746	131
428	1750	131
429	1754	131
430	1758	131
431	1762	131
432	1766	131
433	1770	131
434	1774	131
435	1778	131
436	1782	131
437	1786	131
438	1790	131
439	1794	131
440	1798	131
441	1802	131
442	1806	131
443	1810	131
444	1814	131
445	1818	131
446	1822	131
447	1826	131
448	1830	131
449	1834	131
450	1838	131
451	1842	131
452	1846	131
453	1850	131
454	1854	131
455	1858	131
456	1862	131
457	1866	131
458	1870	131
459	1874	131
460	1878	131
461	1882	131
462	1886	131
463	1890	131
464	1894	131
465	1898	131
466	1902	131
467	1906	131
468	1910	131
469	1914	131
470	1918	131
471	1922	131
472	1926	131
473	1930	131
474	1934	131
475	1938	131
476	1942	131
477	1946	131
478	1950	131
479	1954	131
480	1958	131
481	1962	131
482	1966	131
483	1970	131
484	1974	131
485	1978	131
486	1982	131
487	1986	131
488	1990	131
489	1994	131
490	1998	131
491	2002	131
492	2006	131
493	2010	131
494	2014	131
495	2018	131
496	2022	131
497	2026	131
498	2030	131
499	2034	131
500	2038	131
501	2042	131
502	2046	131
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1443	5810	131
1444	5814	131
1445	5818	131
1446	5822	131
1447	5826	131
1448	5830	131
1449	5834	131
1450	5838	131
1451	5842	131
1452	5846	131
1453	5850	131
1454	5854	131
1455	5858	131
1456	5862	131
1457	5866	131
1458	5870	131
1459	5874	131
1460	5878	131
1461	5882	131
1462	5886	131
1463	5890	131
1464	5894	131
1465	5898	131
1466	5902	131
1467	5906	131
1468	5910	131
1469	5914	131
1470	5918	131
1471	5922	131
1472	5926	131
1473	5930	131
1474	5934	131
1475	5938	131
1476	5942	131
1477	5946	131
1478	5950	131
1479	5954	131
1480	5958	131
1481	5962	131
1482	5966	131
1483	5970	131
1484	5974	131
1485	5978	131
1486	5982	131
1487	5986	131
1488	5990	131
1489	5994	131
1490	5998	131
1491	6002	131
1492	6006	131
1493	6010	131
1494	6014	131
1495	6018	131
1496	6022	131
1497	6026	131
1498	6030	131
1499	6034	131
1500	6038	131
1501	6042	131
1502	6046	131
1503	6050	131
1504	6054	131
1505	6058	131
1506	6062	131
1507	6066	131
1508	6070	131
1509	6074	131
1510	6078	131
1511	6082	131
1512	6086	131
1513	6090	131
1514	6094	131
1515	6098	131
1516	6102	131
1517	6106	131
1518	6110	131
1519	6114	131
1520	6118	131
1521	6122	131
1522	6126	131
1523	6130	131
1524	6134	131
1525	6138	131
1526	6142	131
1527	6146	131
1528	6150	131
1529	6154	131
1530	6158	131
1531	6162	131
1532	6166	131
1533	6170	131
1534	6174	131
1535	6178	131
1536	6182	131
1537	6186	131
1538	6190	131
1539	6194	131
1540	6198	131
1541	6202	131
1542	6206	131
1543	6210	131
1544	6214	131
1545	6218	131
1546	6222	131
1547	6226	131
1548	6230	131
1549	6234	131
1550	6238	131
1551	6242	131
1552	6246	131
1553	6250	131
1554	6254	131
1555	6258	131
1556	6262	131
1557	6266	131
1558	6270	131
1559	6274	131
1560	6278	131
1561	6282	131
1562	6286	131
1563	6290	131
1564	6294	131
1565	6298	131
1566	6302	131
1567	6306	131
1568	6310	131
1569	6314	131
1570	6318	131
1571	6322	131
1572	6326	131
1573	6330	131
1574	6334	131
1575	6338	131
1576	6342	131
1577	6346	131
1578	6350	131
1579	6354	131
1580	6358	131
1581	6362	131
1582	6366	131
1583	6370	131
1584	6374	131
1585	6378	131
1586	6382	131
1587	6386	131
1588	6390	131
1589	6394	131
1590	6398	131
1591	6402	131
1592	6406	131
1593	6410	131
1594	6414	131
1595	6418	131
1596	6422	131
1597	6426	131
1598	6430	131
1599	6434	131
1600	6438	131
1601	6442	131
1602	6446	131
1603	6450	131
1604	6454	131
1605	6458	131
1606	6462	131
1607	6466	131
1608	6470	131
1609	6474	131
1610	6478	131
1611	6482	131
1612	6486	131
1613	6490	131
1614	6494	131
1615	6498	131
1616	6502	131
1617	6506	131
1618	6510	131
1619	6514	131
1620	6518	131
1621	6522	131
1622	6526	131
1623	6530	131
1624	6534	131
1625	6538	131
1626	6542	131
1627	6546	131
1628	6550	131
1629	6554	131
1630	6558	131
1631	6562	131
1632	6566	131
1633	6570	131
1634	6574	131
1635	6578	131
1636	6582	131
1637	6586	131
1638	6590	131
1639	6594	131
1640	6598	131
1641	6602	131
1642	6606	131
1643	6610	131
1644	6614	131
1645	6618	131
1646	6622	131
1647	6626	131
1648	6630	131
1649	6634	131
1650	6638	131
1651	6642	131
1652	6646	131
1653	6650	131
1654	6654	131
1655	6658	131
1656	6662	131
1657	6666	131
1658	6670	131
1659	6674	131
1660	6678	131
1661	6682	131
1662	6686	131
1663	6690	131
1664	6694	131
1665	6698	131
1666	6702	131
1667	6706	131
1668	6710	131
1669	6714	131
1670	6718	131
1671	6722	131
1672	6726	131
1673	6730	131
1674	6734	131
1675	6738	131
1676	6742	131
1677	6746	131
1678	6750	131
1679	6754	131
1680	6758	131
1681	6762	131
1682	6766	131
1683	6770	131
1684	6774	131
1685	6778	131
1686	6782	131
1687	6786	131
1688	6790	131
1689	6794	131
1690	6798	131
1691	6802	131
1692	6806	131
1693	6810	131
1694	6814	131
1695	6818	131
1696	6822	131
1697	6826	131
1698	6830	131
1699	6834	131
1700	6838	131
1701	6842	131
1702	6846	131
1703	6850	131
1704	6854	131
1705	6858	131
1706	6862	131
1707	6866	131
1708	6870	131
1709	6874	131
1710	6878	131
1711	6882	131
1712	6886	131
1713	6890	131
1714	6894	131
1715	6898	131
1716	6902	131
1717	6906	131
1718	6910	131
1719	6914	131
1720	6918	131
1721	6922	131
1722	6926	131
1723	6930	131
1724	6934	131
1725	6938	131
1726	6942	131
1727	6946	131
1728	6950	131
1729	6954	131
1730	6958	131
1731	6962	131
1732	6966	131
1733	6970	131
1734	6974	131
1735	6978	131
1736	6982	131
1737	6986	131
1738	6990	131
1739	6994	131
1740	6998	131
1741	7002	131
1742	7006	131
1743	7010	131
1744	7014	131
1745	7018	131
1746	7022	131
1747	7026	131
1748	7030	131
1749	7034	131
1750	7038	131
1751	7042	131
1752	7046	131
1753	7050	131
1754	7054	131
1755	7058	131
1756	7062	131
1757	7066	131
1758	7070	131
1759	7074	131
1760	7078	131
1761	7082	131
1762	7086	131
1763	7090	131
1764	7094	131
1765	7098	131
1766	7102	131
1767	7106	131
1768	7110	131
1769	7114	131
1770	7118	131
1771	7122	131
1772	7126	131
1773	7130	131
1774	7134	131
1775	7138	131
1776	7142	131
1777	7146	131
1778	7150	131
1779	7154	131
1780	7158	131
1781	7162	131
1782	7166	131
1783	7170	131
1784	7174	131
1785	7178	131
1786	7182	131
1787	7186	131
1788	7190	131
1789	7194	131
1790	7198	131
1791	7202	131
1792	7206	131
1793	7210	131
1794	7214	131
1795	7218	131
1796	7222	131
1797	7226	131
1798	7230	131
1799	7234	131
1800	7238	131
1801	7242	131
1802	7246	131
1803	7250	131
1804	7254	131
1805	7258	131
1806	7262	131
1807	7266	131
1808	7270	131
1809	7274	131
1810	7278	131
1811	7282	131
1812	7286	131
1813	7290	131
1814	7294	131
1815	7298	131
1816	7302	131
1817	7306	131
1818	7310	131
1819	7314	131
1820	7318	131
1821	7322	131
1822	7326	131
1823	7330	131
1824	7334	131
1825	7338	131
1826	7342	131
1827	7346	131
1828	7350	131
1829	7354	131
1830	7358	131
1831	7362	131
1832	7366	131
1833	7370	131
1834	7374	131
1835	7378	131
1836	7382	131
1837	7386	131
1838	7390	131
1839	7394	131
1840	7398	131
1841	7402	131
1842	7406	131
1843	7410	131
1844	7414	131
1845	7418	131
1846	7422	131
1847	7426	131
1848	7430	131
1849	7434	131
1850	7438	131
1851	7442	131
1852	7446	131
1853	7450	131
1854	7454	131
1855	7458	131
1856	7462	131
1857	7466	131
1858	7470	131
1859	7474	131
1860	7478	131
1861	7482	131
1862	7486	131
1863	7490	131
1864	7494	131
1865	7498	131
1866	7502	131
1867	7506	131
1868	7510	131
1869	7514	131
1870	7518	131
1871	7522	131
1872	7526	131
1873	7530	131
1874	7534	131
1875	7538	131
1876	7542	131
1877	7546	131
1878	7550	131
1879	7554	131
1880	7558	131
1881	7562	131
1882	7566	131
1883	7570	131
1884	7574	131
1885	7578	131
1886	7582	131
1887	7586	131
1888	7590	131
1889	7594	131
1890	7598	131
1891	7602	131
1892	7606	131
1893	7610	131
1894	7614	131
1895	7618	131
1896	7622	131
1897	7626	131
1898	7630	131
1899	7634	131
1900	7638	131
1901	7642	131
1902	7646	131
1903	7650	131
1904	7654	131
1905	7658	131
1906	7662	131
1907	7666	131
1908	7670	131
1909	7674	131
1910	7678	131
1911	7682	131
1912	7686	131
1913	7690	131
1914	7694	131
1915	7698	131
1916	7702	131
1917	7706	131
1918	7710	131
1919	7714	131
1920	7718	131
1921	7722	131
1922	7726	131
1923	7730	131
1924	7734	131
1925	7738	131
1926	7742	131
1927	7746	131
1928	7750	131
1929	7754	131
1930	7758	131
1931	7762	131
1932	7766	131
1933	7770	131
1934	7774	131
1935	7778	131
1936	7782	131
1937	7786	131
1938	7790	131
1939	7794	131
1940	7798	131
1941	7802	131
1942	7806	131
1943	7810	131
1944	7814	131
1945	7818	131
1946	7822	131
1947	7826	131
1948	7830	131
1949	7834	131
1950	7838	131
1951	7842	131
1952	7846	131
1953	7850	131
1954	7854	131
1955	7858	131
1956	7862	131
1957	7866	131
1958	7870	131
1959	7874	131
1960	7878	131
1961	7882	131
1962	7886	131
1963	7890	131
1964	7894	131
1965	7898	131
1966	7902	131
1967	7906	131
1968	7910	131
1969	7914	131
1970	7918	131
1971	7922	131
1972	7926	131
1973	7930	131
1974	7934	131
1975	7938	131
1976	7942	131
1977	7946	131
1978	7950	131
1979	7954	131
1980	7958	131
1981	7962	131
1982	7966	131
1983	7970	131
1984	7974	131
1985	7978	131
1986	7982	131
1987	7986	131
1988	7990	131
1989	7994	131
1990	7998	131

Stop Event

1×	node limit

Counts

61 → 41

Calls

Call 1

Inputs
(.f64 (pow.f64 1 1/3) (.f64 z (sin.f64 y)))
(+.f64 (.f64 (pow.f64 1 1/3) (.f64 z (sin.f64 y))) x)
(+.f64 (.f64 (pow.f64 1 1/3) (.f64 z (sin.f64 y))) x)
(+.f64 (.f64 (pow.f64 1 1/3) (.f64 z (sin.f64 y))) x)
x
(+.f64 (.f64 (pow.f64 1 1/3) (.f64 z (sin.f64 y))) x)
(+.f64 (.f64 (pow.f64 1 1/3) (.f64 z (sin.f64 y))) x)
(+.f64 (.f64 (pow.f64 1 1/3) (.f64 z (sin.f64 y))) x)
x
(+.f64 (.f64 (pow.f64 1 1/3) (.f64 z (sin.f64 y))) x)
(+.f64 (.f64 (pow.f64 1 1/3) (.f64 z (sin.f64 y))) x)
(+.f64 (.f64 (pow.f64 1 1/3) (.f64 z (sin.f64 y))) x)
x
x
x
x
(+.f64 (.f64 (pow.f64 1 1/3) (.f64 z (sin.f64 y))) x)
(+.f64 (.f64 (pow.f64 1 1/3) (.f64 z (sin.f64 y))) x)
(+.f64 (.f64 (pow.f64 1 1/3) (.f64 z (sin.f64 y))) x)
(+.f64 (.f64 (pow.f64 1 1/3) (.f64 z (sin.f64 y))) x)
(+.f64 (.f64 (pow.f64 1 1/3) (.f64 z (sin.f64 y))) x)
(+.f64 (.f64 (pow.f64 1 1/3) (.f64 z (sin.f64 y))) x)
(+.f64 (.f64 (pow.f64 1 1/3) (.f64 z (sin.f64 y))) x)
(+.f64 (.f64 (pow.f64 1 1/3) (.f64 z (sin.f64 y))) x)

Outputs
(.f64 (pow.f64 1 1/3) (.f64 z (sin.f64 y)))
(.f64 1 (.f64 z (sin.f64 y)))
(*.f64 z (sin.f64 y))
(+.f64 (.f64 (pow.f64 1 1/3) (.f64 z (sin.f64 y))) x)
(fma.f64 1 (*.f64 z (sin.f64 y)) x)
(fma.f64 z (sin.f64 y) x)
(+.f64 (.f64 (pow.f64 1 1/3) (.f64 z (sin.f64 y))) x)
(fma.f64 1 (*.f64 z (sin.f64 y)) x)
(fma.f64 z (sin.f64 y) x)
(+.f64 (.f64 (pow.f64 1 1/3) (.f64 z (sin.f64 y))) x)
(fma.f64 1 (*.f64 z (sin.f64 y)) x)
(fma.f64 z (sin.f64 y) x)
x
(+.f64 (.f64 (pow.f64 1 1/3) (.f64 z (sin.f64 y))) x)
(fma.f64 1 (*.f64 z (sin.f64 y)) x)
(fma.f64 z (sin.f64 y) x)
(+.f64 (.f64 (pow.f64 1 1/3) (.f64 z (sin.f64 y))) x)
(fma.f64 1 (*.f64 z (sin.f64 y)) x)
(fma.f64 z (sin.f64 y) x)
(+.f64 (.f64 (pow.f64 1 1/3) (.f64 z (sin.f64 y))) x)
(fma.f64 1 (*.f64 z (sin.f64 y)) x)
(fma.f64 z (sin.f64 y) x)
x
(+.f64 (.f64 (pow.f64 1 1/3) (.f64 z (sin.f64 y))) x)
(fma.f64 1 (*.f64 z (sin.f64 y)) x)
(fma.f64 z (sin.f64 y) x)
(+.f64 (.f64 (pow.f64 1 1/3) (.f64 z (sin.f64 y))) x)
(fma.f64 1 (*.f64 z (sin.f64 y)) x)
(fma.f64 z (sin.f64 y) x)
(+.f64 (.f64 (pow.f64 1 1/3) (.f64 z (sin.f64 y))) x)
(fma.f64 1 (*.f64 z (sin.f64 y)) x)
(fma.f64 z (sin.f64 y) x)
x
x
x
x
(+.f64 (.f64 (pow.f64 1 1/3) (.f64 z (sin.f64 y))) x)
(fma.f64 1 (*.f64 z (sin.f64 y)) x)
(fma.f64 z (sin.f64 y) x)
(+.f64 (.f64 (pow.f64 1 1/3) (.f64 z (sin.f64 y))) x)
(fma.f64 1 (*.f64 z (sin.f64 y)) x)
(fma.f64 z (sin.f64 y) x)
(+.f64 (.f64 (pow.f64 1 1/3) (.f64 z (sin.f64 y))) x)
(fma.f64 1 (*.f64 z (sin.f64 y)) x)
(fma.f64 z (sin.f64 y) x)
(+.f64 (.f64 (pow.f64 1 1/3) (.f64 z (sin.f64 y))) x)
(fma.f64 1 (*.f64 z (sin.f64 y)) x)
(fma.f64 z (sin.f64 y) x)
(+.f64 (.f64 (pow.f64 1 1/3) (.f64 z (sin.f64 y))) x)
(fma.f64 1 (*.f64 z (sin.f64 y)) x)
(fma.f64 z (sin.f64 y) x)
(+.f64 (.f64 (pow.f64 1 1/3) (.f64 z (sin.f64 y))) x)
(fma.f64 1 (*.f64 z (sin.f64 y)) x)
(fma.f64 z (sin.f64 y) x)
(+.f64 (.f64 (pow.f64 1 1/3) (.f64 z (sin.f64 y))) x)
(fma.f64 1 (*.f64 z (sin.f64 y)) x)
(fma.f64 z (sin.f64 y) x)
(+.f64 (.f64 (pow.f64 1 1/3) (.f64 z (sin.f64 y))) x)
(fma.f64 1 (*.f64 z (sin.f64 y)) x)
(fma.f64 z (sin.f64 y) x)

localize45.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 z))
	0.6b	(cbrt.f64 (sin.f64 y))
✓	0.6b	(pow.f64 (*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 z)) 3)
	0.6b	(cbrt.f64 z)

Compiler

Compiled 47 to 15 computations (68.1% saved)

series9.0ms (0.1%)

Counts

2 → 16

Calls

12 calls:

Time	Variable		Point	Expression
2.0ms	y	@	inf	(pow.f64 (*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 z)) 3)
2.0ms	y	@	-inf	(pow.f64 (*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 z)) 3)
1.0ms	y	@	0	(pow.f64 (*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 z)) 3)
1.0ms	z	@	-inf	(pow.f64 (*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 z)) 3)
1.0ms	z	@	inf	(pow.f64 (*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 z)) 3)

rewrite70.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

771×	`pow1_binary64`
717×	`add-log-exp_binary64`
717×	`log1p-expm1-u_binary64`
717×	`expm1-log1p-u_binary64`
695×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	19
1	186	14
2	2049	14

Stop Event

1×	node limit

Counts

2 → 41

Calls

Call 1

Inputs
(pow.f64 (*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 z)) 3)
(*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 z))

Outputs

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

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

simplify176.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

1290×	`sqr-pow_binary64`
666×	`pow-sqr_binary64`
625×	`cube-prod_binary64`
557×	`fabs-mul_binary64`
373×	`unpow3_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	136
1	26	112
2	40	112
3	51	112
4	75	112
5	162	112
6	543	112
7	1206	112
8	1298	112
9	1436	112
10	1599	112
11	1838	112
12	2165	112
13	2594	112
14	3099	112
15	3703	112
16	4426	112
17	4749	112
18	5035	112
19	5257	112
20	5435	112
21	5517	112
22	6460	112
23	7437	112
24	7903	112

Stop Event

1×	node limit

Counts

57 → 44

Calls

Call 1

Inputs
(.f64 (pow.f64 1 1/3) (.f64 z (sin.f64 y)))
(.f64 (pow.f64 1 1/3) (.f64 z (sin.f64 y)))
(.f64 (pow.f64 1 1/3) (.f64 z (sin.f64 y)))
(.f64 (pow.f64 1 1/3) (.f64 z (sin.f64 y)))
(.f64 (pow.f64 1 1/3) (.f64 z (sin.f64 y)))
(.f64 (pow.f64 1 1/3) (.f64 z (sin.f64 y)))
(.f64 (pow.f64 1 1/3) (.f64 z (sin.f64 y)))
(.f64 (pow.f64 1 1/3) (.f64 z (sin.f64 y)))
(pow.f64 (*.f64 z (sin.f64 y)) 1/3)
(pow.f64 (*.f64 z (sin.f64 y)) 1/3)
(pow.f64 (*.f64 z (sin.f64 y)) 1/3)
(pow.f64 (*.f64 z (sin.f64 y)) 1/3)
(pow.f64 (*.f64 z (sin.f64 y)) 1/3)
(pow.f64 (*.f64 z (sin.f64 y)) 1/3)
(pow.f64 (*.f64 z (sin.f64 y)) 1/3)
(pow.f64 (*.f64 z (sin.f64 y)) 1/3)

Outputs
(.f64 (pow.f64 1 1/3) (.f64 z (sin.f64 y)))
(.f64 1 (.f64 z (sin.f64 y)))
(*.f64 z (sin.f64 y))
(.f64 (pow.f64 1 1/3) (.f64 z (sin.f64 y)))
(.f64 1 (.f64 z (sin.f64 y)))
(*.f64 z (sin.f64 y))
(.f64 (pow.f64 1 1/3) (.f64 z (sin.f64 y)))
(.f64 1 (.f64 z (sin.f64 y)))
(*.f64 z (sin.f64 y))
(.f64 (pow.f64 1 1/3) (.f64 z (sin.f64 y)))
(.f64 1 (.f64 z (sin.f64 y)))
(*.f64 z (sin.f64 y))
(.f64 (pow.f64 1 1/3) (.f64 z (sin.f64 y)))
(.f64 1 (.f64 z (sin.f64 y)))
(*.f64 z (sin.f64 y))
(.f64 (pow.f64 1 1/3) (.f64 z (sin.f64 y)))
(.f64 1 (.f64 z (sin.f64 y)))
(*.f64 z (sin.f64 y))
(.f64 (pow.f64 1 1/3) (.f64 z (sin.f64 y)))
(.f64 1 (.f64 z (sin.f64 y)))
(*.f64 z (sin.f64 y))
(.f64 (pow.f64 1 1/3) (.f64 z (sin.f64 y)))
(.f64 1 (.f64 z (sin.f64 y)))
(*.f64 z (sin.f64 y))
(pow.f64 (*.f64 z (sin.f64 y)) 1/3)
(cbrt.f64 (*.f64 z (sin.f64 y)))
(pow.f64 (*.f64 z (sin.f64 y)) 1/3)
(cbrt.f64 (*.f64 z (sin.f64 y)))
(pow.f64 (*.f64 z (sin.f64 y)) 1/3)
(cbrt.f64 (*.f64 z (sin.f64 y)))
(pow.f64 (*.f64 z (sin.f64 y)) 1/3)
(cbrt.f64 (*.f64 z (sin.f64 y)))
(pow.f64 (*.f64 z (sin.f64 y)) 1/3)
(cbrt.f64 (*.f64 z (sin.f64 y)))
(pow.f64 (*.f64 z (sin.f64 y)) 1/3)
(cbrt.f64 (*.f64 z (sin.f64 y)))
(pow.f64 (*.f64 z (sin.f64 y)) 1/3)
(cbrt.f64 (*.f64 z (sin.f64 y)))
(pow.f64 (*.f64 z (sin.f64 y)) 1/3)
(cbrt.f64 (*.f64 z (sin.f64 y)))

eval92.0ms (0.7%)

Compiler: Compiled 4834 to 1753 computations (63.7% saved)

prune151.0ms (1.2%)

Pruning

19 alts after pruning (14 fresh and 5 done)

	Pruned	Kept	Total
New	284	10	294
Fresh	7	4	11
Picked	1	0	1
Done	2	5	7
Total	294	19	313

Error

0.0b

Counts

313 → 19

Alt Table

Click to see full alt table

Status	Error	Program
	41.0b	(pow.f64 (sqrt.f64 (*.f64 (cos.f64 y) x)) 2)
▶	37.1b	(+.f64 x (.f64 (.f64 (sin.f64 y) (sqrt.f64 z)) (sqrt.f64 z)))
✓	14.3b	(+.f64 x (pow.f64 (cbrt.f64 (*.f64 z (sin.f64 y))) 3))
▶	14.4b	(+.f64 (.f64 (.f64 x (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	14.2b	(+.f64 x (.f64 (.f64 (pow.f64 (cbrt.f64 (*.f64 z (sin.f64 y))) 2) (cbrt.f64 z)) (cbrt.f64 (sin.f64 y))))
✓	25.0b	(*.f64 (cos.f64 y) x)
	14.4b	(+.f64 x (pow.f64 (*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 z)) 3))
✓	52.8b	(*.f64 y z)
	30.5b	(+.f64 x (cbrt.f64 (pow.f64 (*.f64 z (sin.f64 y)) 3)))
	38.3b	(*.f64 z (sin.f64 y))
✓	0.5b	(+.f64 (.f64 x (cos.f64 y)) (pow.f64 (cbrt.f64 (.f64 z (sin.f64 y))) 3))
	38.2b	x
	20.9b	(fma.f64 (pow.f64 (cbrt.f64 (.f64 x (cos.f64 y))) 2) (cbrt.f64 (.f64 x (cos.f64 y))) (*.f64 y z))
▶	0.8b	(+.f64 (.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (cos.f64 y))) (*.f64 z (sin.f64 y)))
▶	51.8b	(cbrt.f64 (pow.f64 (*.f64 (cos.f64 y) x) 3))
	39.5b	(+.f64 x (.f64 (.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
✓	0.1b	(+.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))
▶	28.8b	(+.f64 (*.f64 y z) x)
	40.0b	(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) x)

Compiler

Compiled 400 to 270 computations (32.5% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (cbrt.f64 x) (cos.f64 y))
✓	0.3b	(.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (cos.f64 y)))
✓	0.4b	(pow.f64 (cbrt.f64 x) 2)
✓	0.5b	(cbrt.f64 x)

Compiler

Compiled 51 to 18 computations (64.7% saved)

series49.0ms (0.4%)

Counts

4 → 36

Calls

18 calls:

Time	Variable		Point	Expression
35.0ms	x	@	-inf	(cbrt.f64 x)
2.0ms	y	@	inf	(*.f64 (cbrt.f64 x) (cos.f64 y))
1.0ms	x	@	-inf	(.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (cos.f64 y)))
1.0ms	x	@	0	(pow.f64 (cbrt.f64 x) 2)
1.0ms	y	@	0	(*.f64 (cbrt.f64 x) (cos.f64 y))

rewrite72.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

769×	`pow1_binary64`
708×	`add-log-exp_binary64`
708×	`log1p-expm1-u_binary64`
708×	`expm1-log1p-u_binary64`
691×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	181	23
2	2013	23

Stop Event

1×	node limit

Counts

4 → 63

Calls

Call 1

Inputs
(cbrt.f64 x)
(pow.f64 (cbrt.f64 x) 2)
(.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (cos.f64 y)))
(*.f64 (cbrt.f64 x) (cos.f64 y))

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

simplify257.0ms (2%)

Algorithm

1×	egg-herbie

Rules

840×	`unswap-sqr_binary64`
754×	`distribute-rgt-out_binary64`
643×	`associate-+l+_binary64`
534×	`sqr-pow_binary64`
454×	`*-commutative_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	41	338
1	115	336
2	361	315
3	1303	312
4	2292	308
5	3898	308
6	5040	308
7	5479	308
8	5642	308
9	5857	308
10	6162	308
11	6523	308
12	6960	308
13	7710	308

Stop Event

1×	node limit

Counts

99 → 80

Calls

Call 1

Inputs
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
x
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) x)
(+.f64 (.f64 1/24 (.f64 (pow.f64 y 4) x)) (+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) x))
(+.f64 (.f64 -1/720 (.f64 (pow.f64 y 6) x)) (+.f64 (.f64 1/24 (.f64 (pow.f64 y 4) x)) (+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) x)))
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(pow.f64 x 1/3)
(+.f64 (pow.f64 x 1/3) (.f64 -1/2 (.f64 (pow.f64 (*.f64 1 x) 1/3) (pow.f64 y 2))))
(+.f64 (pow.f64 x 1/3) (+.f64 (.f64 -1/2 (.f64 (pow.f64 (.f64 1 x) 1/3) (pow.f64 y 2))) (.f64 1/24 (.f64 (pow.f64 (.f64 1 x) 1/3) (pow.f64 y 4)))))
(+.f64 (pow.f64 x 1/3) (+.f64 (.f64 -1/2 (.f64 (pow.f64 (.f64 1 x) 1/3) (pow.f64 y 2))) (+.f64 (.f64 -1/720 (.f64 (pow.f64 (.f64 1 x) 1/3) (pow.f64 y 6))) (.f64 1/24 (.f64 (pow.f64 (*.f64 1 x) 1/3) (pow.f64 y 4))))))
(.f64 (pow.f64 (.f64 1 x) 1/3) (cos.f64 y))
(.f64 (pow.f64 (.f64 1 x) 1/3) (cos.f64 y))
(.f64 (pow.f64 (.f64 1 x) 1/3) (cos.f64 y))
(.f64 (pow.f64 (.f64 1 x) 1/3) (cos.f64 y))
(.f64 (pow.f64 (.f64 1 x) 1/3) (cos.f64 y))
(.f64 (pow.f64 (.f64 1 x) 1/3) (cos.f64 y))
(.f64 (pow.f64 (.f64 1 x) 1/3) (cos.f64 y))
(.f64 (pow.f64 (.f64 1 x) 1/3) (cos.f64 y))

Outputs
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
x
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) x)
(fma.f64 -1/2 (.f64 x (.f64 y y)) x)
(fma.f64 -1/2 (.f64 y (.f64 y x)) x)
(.f64 x (fma.f64 -1/2 (.f64 y y) 1))
(+.f64 (.f64 1/24 (.f64 (pow.f64 y 4) x)) (+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) x))
(fma.f64 1/24 (.f64 x (pow.f64 y 4)) (fma.f64 -1/2 (.f64 x (*.f64 y y)) x))
(fma.f64 1/24 (.f64 x (pow.f64 y 4)) (fma.f64 -1/2 (.f64 y (*.f64 y x)) x))
(fma.f64 x (fma.f64 1/24 (pow.f64 y 4) (.f64 y (.f64 y -1/2))) x)
(+.f64 (.f64 -1/720 (.f64 (pow.f64 y 6) x)) (+.f64 (.f64 1/24 (.f64 (pow.f64 y 4) x)) (+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) x)))
(fma.f64 -1/720 (.f64 x (pow.f64 y 6)) (fma.f64 1/24 (.f64 x (pow.f64 y 4)) (fma.f64 -1/2 (.f64 x (.f64 y y)) x)))
(fma.f64 -1/720 (.f64 x (pow.f64 y 6)) (fma.f64 1/24 (.f64 x (pow.f64 y 4)) (fma.f64 -1/2 (.f64 y (.f64 y x)) x)))
(.f64 x (+.f64 (fma.f64 -1/720 (pow.f64 y 6) (.f64 1/24 (pow.f64 y 4))) (fma.f64 -1/2 (*.f64 y y) 1)))
(.f64 x (+.f64 (fma.f64 -1/2 (.f64 y y) 1) (fma.f64 -1/720 (pow.f64 y 6) (*.f64 1/24 (pow.f64 y 4)))))
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(pow.f64 x 1/3)
(cbrt.f64 x)
(+.f64 (pow.f64 x 1/3) (.f64 -1/2 (.f64 (pow.f64 (*.f64 1 x) 1/3) (pow.f64 y 2))))
(+.f64 (cbrt.f64 x) (.f64 -1/2 (.f64 (*.f64 y y) (cbrt.f64 x))))
(fma.f64 -1/2 (.f64 (.f64 y y) (cbrt.f64 x)) (cbrt.f64 x))
(.f64 (fma.f64 -1/2 (.f64 y y) 1) (cbrt.f64 x))
(.f64 (cbrt.f64 x) (fma.f64 -1/2 (.f64 y y) 1))
(+.f64 (pow.f64 x 1/3) (+.f64 (.f64 -1/2 (.f64 (pow.f64 (.f64 1 x) 1/3) (pow.f64 y 2))) (.f64 1/24 (.f64 (pow.f64 (.f64 1 x) 1/3) (pow.f64 y 4)))))
(+.f64 (cbrt.f64 x) (fma.f64 -1/2 (.f64 (.f64 y y) (cbrt.f64 x)) (.f64 1/24 (.f64 (pow.f64 y 4) (cbrt.f64 x)))))
(+.f64 (cbrt.f64 x) (fma.f64 1/24 (.f64 (pow.f64 y 4) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (.f64 -1/2 (.f64 y y)))))
(+.f64 (cbrt.f64 x) (.f64 (cbrt.f64 x) (fma.f64 1/24 (pow.f64 y 4) (.f64 y (*.f64 y -1/2)))))
(.f64 (cbrt.f64 x) (+.f64 (.f64 1/24 (pow.f64 y 4)) (fma.f64 -1/2 (*.f64 y y) 1)))
(.f64 (cbrt.f64 x) (+.f64 1 (fma.f64 1/24 (pow.f64 y 4) (.f64 y (*.f64 y -1/2)))))
(+.f64 (pow.f64 x 1/3) (+.f64 (.f64 -1/2 (.f64 (pow.f64 (.f64 1 x) 1/3) (pow.f64 y 2))) (+.f64 (.f64 -1/720 (.f64 (pow.f64 (.f64 1 x) 1/3) (pow.f64 y 6))) (.f64 1/24 (.f64 (pow.f64 (*.f64 1 x) 1/3) (pow.f64 y 4))))))
(+.f64 (cbrt.f64 x) (fma.f64 -1/2 (.f64 (.f64 y y) (cbrt.f64 x)) (fma.f64 -1/720 (.f64 (pow.f64 y 6) (cbrt.f64 x)) (.f64 1/24 (*.f64 (pow.f64 y 4) (cbrt.f64 x))))))
(+.f64 (fma.f64 -1/2 (.f64 (.f64 y y) (cbrt.f64 x)) (cbrt.f64 x)) (fma.f64 1/24 (.f64 (pow.f64 y 4) (cbrt.f64 x)) (.f64 (pow.f64 y 6) (*.f64 -1/720 (cbrt.f64 x)))))
(+.f64 (.f64 (fma.f64 -1/2 (.f64 y y) 1) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (fma.f64 -1/720 (pow.f64 y 6) (.f64 1/24 (pow.f64 y 4)))))
(+.f64 (cbrt.f64 x) (.f64 (cbrt.f64 x) (+.f64 (.f64 -1/720 (pow.f64 y 6)) (fma.f64 1/24 (pow.f64 y 4) (.f64 y (.f64 y -1/2))))))
(.f64 (cbrt.f64 x) (+.f64 (fma.f64 -1/2 (.f64 y y) 1) (fma.f64 -1/720 (pow.f64 y 6) (*.f64 1/24 (pow.f64 y 4)))))
(.f64 (pow.f64 (.f64 1 x) 1/3) (cos.f64 y))
(*.f64 (cos.f64 y) (cbrt.f64 x))
(.f64 (pow.f64 (.f64 1 x) 1/3) (cos.f64 y))
(*.f64 (cos.f64 y) (cbrt.f64 x))
(.f64 (pow.f64 (.f64 1 x) 1/3) (cos.f64 y))
(*.f64 (cos.f64 y) (cbrt.f64 x))
(.f64 (pow.f64 (.f64 1 x) 1/3) (cos.f64 y))
(*.f64 (cos.f64 y) (cbrt.f64 x))
(.f64 (pow.f64 (.f64 1 x) 1/3) (cos.f64 y))
(*.f64 (cos.f64 y) (cbrt.f64 x))
(.f64 (pow.f64 (.f64 1 x) 1/3) (cos.f64 y))
(*.f64 (cos.f64 y) (cbrt.f64 x))
(.f64 (pow.f64 (.f64 1 x) 1/3) (cos.f64 y))
(*.f64 (cos.f64 y) (cbrt.f64 x))
(.f64 (pow.f64 (.f64 1 x) 1/3) (cos.f64 y))
(*.f64 (cos.f64 y) (cbrt.f64 x))

localize27.0ms (0.2%)

Compiler: Compiled 14 to 5 computations (64.3% saved)

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(pow.f64 (*.f64 (cos.f64 y) x) 3)
	0.1b	(*.f64 (cos.f64 y) x)
✓	42.2b	(cbrt.f64 (pow.f64 (*.f64 (cos.f64 y) x) 3))

Compiler

Compiled 25 to 11 computations (56% saved)

series3.0ms (0%)

Counts

2 → 48

Calls

12 calls:

Time	Variable		Point	Expression
0.0ms	y	@	0	(cbrt.f64 (pow.f64 (*.f64 (cos.f64 y) x) 3))
0.0ms	y	@	0	(pow.f64 (*.f64 (cos.f64 y) x) 3)
0.0ms	x	@	-inf	(cbrt.f64 (pow.f64 (*.f64 (cos.f64 y) x) 3))
0.0ms	y	@	inf	(cbrt.f64 (pow.f64 (*.f64 (cos.f64 y) x) 3))
0.0ms	y	@	-inf	(cbrt.f64 (pow.f64 (*.f64 (cos.f64 y) x) 3))

rewrite67.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

645×	`pow1_binary64`
603×	`add-log-exp_binary64`
603×	`log1p-expm1-u_binary64`
603×	`expm1-log1p-u_binary64`
586×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	168	15
2	1728	15

Stop Event

1×	node limit

Counts

2 → 54

Calls

Call 1

Inputs
(cbrt.f64 (pow.f64 (*.f64 (cos.f64 y) x) 3))
(pow.f64 (*.f64 (cos.f64 y) x) 3)

Outputs

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

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

simplify116.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

654×	`distribute-rgt-out_binary64`
558×	`distribute-rgt-in_binary64`
552×	`fma-def_binary64`
549×	`distribute-lft-in_binary64`
448×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	66	596
1	208	584
2	783	556
3	4107	546
4	7914	546

Stop Event

1×	node limit

Counts

102 → 70

Calls

Call 1

Inputs
x
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) x)
(+.f64 (.f64 1/24 (.f64 (pow.f64 y 4) x)) (+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) x))
(+.f64 (.f64 -1/720 (.f64 (pow.f64 y 6) x)) (+.f64 (.f64 1/24 (.f64 (pow.f64 y 4) x)) (+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) x)))
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(.f64 -1 (.f64 (cbrt.f64 -1) (*.f64 (cos.f64 y) x)))
(.f64 -1 (.f64 (cbrt.f64 -1) (*.f64 (cos.f64 y) x)))
(.f64 -1 (.f64 (cbrt.f64 -1) (*.f64 (cos.f64 y) x)))
(.f64 -1 (.f64 (cbrt.f64 -1) (*.f64 (cos.f64 y) x)))
(pow.f64 x 3)
(+.f64 (.f64 (pow.f64 y 2) (+.f64 (.f64 -1 (pow.f64 x 3)) (*.f64 -1/2 (pow.f64 x 3)))) (pow.f64 x 3))
(+.f64 (.f64 (+.f64 (.f64 x (+.f64 (.f64 1/4 (pow.f64 x 2)) (.f64 1/12 (pow.f64 x 2)))) (+.f64 (.f64 1/2 (pow.f64 x 3)) (.f64 1/24 (pow.f64 x 3)))) (pow.f64 y 4)) (+.f64 (.f64 (pow.f64 y 2) (+.f64 (.f64 -1 (pow.f64 x 3)) (*.f64 -1/2 (pow.f64 x 3)))) (pow.f64 x 3)))
(+.f64 (.f64 (+.f64 (.f64 x (+.f64 (.f64 1/4 (pow.f64 x 2)) (.f64 1/12 (pow.f64 x 2)))) (+.f64 (.f64 1/2 (pow.f64 x 3)) (.f64 1/24 (pow.f64 x 3)))) (pow.f64 y 4)) (+.f64 (.f64 (pow.f64 y 6) (+.f64 (.f64 -1/24 (pow.f64 x 3)) (+.f64 (.f64 -1/2 (.f64 (+.f64 (.f64 1/4 (pow.f64 x 2)) (.f64 1/12 (pow.f64 x 2))) x)) (+.f64 (.f64 (+.f64 (.f64 -1/360 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 2))) x) (.f64 -1/720 (pow.f64 x 3)))))) (+.f64 (.f64 (pow.f64 y 2) (+.f64 (.f64 -1 (pow.f64 x 3)) (*.f64 -1/2 (pow.f64 x 3)))) (pow.f64 x 3))))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))

Outputs
x
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) x)
(fma.f64 -1/2 (.f64 x (.f64 y y)) x)
(fma.f64 (.f64 (.f64 -1/2 y) y) x x)
(.f64 x (fma.f64 -1/2 (.f64 y y) 1))
(+.f64 (.f64 1/24 (.f64 (pow.f64 y 4) x)) (+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) x))
(fma.f64 1/24 (.f64 x (pow.f64 y 4)) (fma.f64 -1/2 (.f64 x (*.f64 y y)) x))
(fma.f64 1/24 (.f64 x (pow.f64 y 4)) (fma.f64 (.f64 (*.f64 -1/2 y) y) x x))
(fma.f64 x (fma.f64 1/24 (pow.f64 y 4) (.f64 -1/2 (.f64 y y))) x)
(+.f64 (.f64 -1/720 (.f64 (pow.f64 y 6) x)) (+.f64 (.f64 1/24 (.f64 (pow.f64 y 4) x)) (+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) x)))
(fma.f64 -1/720 (.f64 x (pow.f64 y 6)) (fma.f64 1/24 (.f64 x (pow.f64 y 4)) (fma.f64 -1/2 (.f64 x (.f64 y y)) x)))
(fma.f64 -1/720 (.f64 x (pow.f64 y 6)) (fma.f64 1/24 (.f64 x (pow.f64 y 4)) (fma.f64 (.f64 (.f64 -1/2 y) y) x x)))
(fma.f64 x (fma.f64 -1/720 (pow.f64 y 6) (.f64 1/24 (pow.f64 y 4))) (.f64 x (fma.f64 -1/2 (*.f64 y y) 1)))
(.f64 x (+.f64 (fma.f64 -1/2 (.f64 y y) 1) (fma.f64 -1/720 (pow.f64 y 6) (*.f64 1/24 (pow.f64 y 4)))))
(*.f64 (cos.f64 y) x)
(*.f64 x (cos.f64 y))
(*.f64 (cos.f64 y) x)
(*.f64 x (cos.f64 y))
(*.f64 (cos.f64 y) x)
(*.f64 x (cos.f64 y))
(*.f64 (cos.f64 y) x)
(*.f64 x (cos.f64 y))
(*.f64 (cos.f64 y) x)
(*.f64 x (cos.f64 y))
(*.f64 (cos.f64 y) x)
(*.f64 x (cos.f64 y))
(*.f64 (cos.f64 y) x)
(*.f64 x (cos.f64 y))
(*.f64 (cos.f64 y) x)
(*.f64 x (cos.f64 y))
(*.f64 (cos.f64 y) x)
(*.f64 x (cos.f64 y))
(*.f64 (cos.f64 y) x)
(*.f64 x (cos.f64 y))
(*.f64 (cos.f64 y) x)
(*.f64 x (cos.f64 y))
(*.f64 (cos.f64 y) x)
(*.f64 x (cos.f64 y))
(*.f64 (cos.f64 y) x)
(*.f64 x (cos.f64 y))
(*.f64 (cos.f64 y) x)
(*.f64 x (cos.f64 y))
(*.f64 (cos.f64 y) x)
(*.f64 x (cos.f64 y))
(*.f64 (cos.f64 y) x)
(*.f64 x (cos.f64 y))
(.f64 -1 (.f64 (cbrt.f64 -1) (*.f64 (cos.f64 y) x)))
(neg.f64 (.f64 (.f64 (cbrt.f64 -1) (cos.f64 y)) x))
(.f64 (.f64 x (cos.f64 y)) (neg.f64 (cbrt.f64 -1)))
(.f64 x (.f64 (cos.f64 y) (neg.f64 (cbrt.f64 -1))))
(.f64 (cos.f64 y) (.f64 x (neg.f64 (cbrt.f64 -1))))
(.f64 -1 (.f64 (cbrt.f64 -1) (*.f64 (cos.f64 y) x)))
(neg.f64 (.f64 (.f64 (cbrt.f64 -1) (cos.f64 y)) x))
(.f64 (.f64 x (cos.f64 y)) (neg.f64 (cbrt.f64 -1)))
(.f64 x (.f64 (cos.f64 y) (neg.f64 (cbrt.f64 -1))))
(.f64 (cos.f64 y) (.f64 x (neg.f64 (cbrt.f64 -1))))
(.f64 -1 (.f64 (cbrt.f64 -1) (*.f64 (cos.f64 y) x)))
(neg.f64 (.f64 (.f64 (cbrt.f64 -1) (cos.f64 y)) x))
(.f64 (.f64 x (cos.f64 y)) (neg.f64 (cbrt.f64 -1)))
(.f64 x (.f64 (cos.f64 y) (neg.f64 (cbrt.f64 -1))))
(.f64 (cos.f64 y) (.f64 x (neg.f64 (cbrt.f64 -1))))
(.f64 -1 (.f64 (cbrt.f64 -1) (*.f64 (cos.f64 y) x)))
(neg.f64 (.f64 (.f64 (cbrt.f64 -1) (cos.f64 y)) x))
(.f64 (.f64 x (cos.f64 y)) (neg.f64 (cbrt.f64 -1)))
(.f64 x (.f64 (cos.f64 y) (neg.f64 (cbrt.f64 -1))))
(.f64 (cos.f64 y) (.f64 x (neg.f64 (cbrt.f64 -1))))
(pow.f64 x 3)
(+.f64 (.f64 (pow.f64 y 2) (+.f64 (.f64 -1 (pow.f64 x 3)) (*.f64 -1/2 (pow.f64 x 3)))) (pow.f64 x 3))
(fma.f64 (.f64 y y) (.f64 (pow.f64 x 3) -3/2) (pow.f64 x 3))
(fma.f64 y (.f64 (pow.f64 x 3) (.f64 -3/2 y)) (pow.f64 x 3))
(.f64 (+.f64 (.f64 (*.f64 -3/2 y) y) 1) (pow.f64 x 3))
(+.f64 (.f64 (+.f64 (.f64 x (+.f64 (.f64 1/4 (pow.f64 x 2)) (.f64 1/12 (pow.f64 x 2)))) (+.f64 (.f64 1/2 (pow.f64 x 3)) (.f64 1/24 (pow.f64 x 3)))) (pow.f64 y 4)) (+.f64 (.f64 (pow.f64 y 2) (+.f64 (.f64 -1 (pow.f64 x 3)) (*.f64 -1/2 (pow.f64 x 3)))) (pow.f64 x 3)))
(fma.f64 (fma.f64 x (.f64 (.f64 x x) 1/3) (.f64 (pow.f64 x 3) 13/24)) (pow.f64 y 4) (fma.f64 (.f64 y y) (*.f64 (pow.f64 x 3) -3/2) (pow.f64 x 3)))
(fma.f64 (pow.f64 y 4) (fma.f64 (pow.f64 x 3) 13/24 (.f64 (pow.f64 x 3) 1/3)) (fma.f64 (.f64 y y) (*.f64 (pow.f64 x 3) -3/2) (pow.f64 x 3)))
(fma.f64 (pow.f64 y 4) (.f64 (pow.f64 x 3) 7/8) (fma.f64 y (.f64 (pow.f64 x 3) (*.f64 -3/2 y)) (pow.f64 x 3)))
(fma.f64 (pow.f64 y 4) (.f64 (pow.f64 x 3) 7/8) (.f64 (+.f64 (.f64 (.f64 -3/2 y) y) 1) (pow.f64 x 3)))
(+.f64 (.f64 (+.f64 (.f64 x (+.f64 (.f64 1/4 (pow.f64 x 2)) (.f64 1/12 (pow.f64 x 2)))) (+.f64 (.f64 1/2 (pow.f64 x 3)) (.f64 1/24 (pow.f64 x 3)))) (pow.f64 y 4)) (+.f64 (.f64 (pow.f64 y 6) (+.f64 (.f64 -1/24 (pow.f64 x 3)) (+.f64 (.f64 -1/2 (.f64 (+.f64 (.f64 1/4 (pow.f64 x 2)) (.f64 1/12 (pow.f64 x 2))) x)) (+.f64 (.f64 (+.f64 (.f64 -1/360 (pow.f64 x 2)) (.f64 -1/24 (pow.f64 x 2))) x) (.f64 -1/720 (pow.f64 x 3)))))) (+.f64 (.f64 (pow.f64 y 2) (+.f64 (.f64 -1 (pow.f64 x 3)) (*.f64 -1/2 (pow.f64 x 3)))) (pow.f64 x 3))))
(fma.f64 (fma.f64 x (.f64 (.f64 x x) 1/3) (.f64 (pow.f64 x 3) 13/24)) (pow.f64 y 4) (fma.f64 (pow.f64 y 6) (fma.f64 -1/24 (pow.f64 x 3) (fma.f64 -1/2 (.f64 x (.f64 (.f64 x x) 1/3)) (fma.f64 (.f64 (.f64 x x) -2/45) x (.f64 -1/720 (pow.f64 x 3))))) (fma.f64 (.f64 y y) (*.f64 (pow.f64 x 3) -3/2) (pow.f64 x 3))))
(fma.f64 (pow.f64 y 4) (fma.f64 (pow.f64 x 3) 13/24 (.f64 (pow.f64 x 3) 1/3)) (fma.f64 (pow.f64 y 6) (fma.f64 (pow.f64 x 3) -1/24 (fma.f64 -1/2 (.f64 (pow.f64 x 3) 1/3) (fma.f64 -1/720 (pow.f64 x 3) (.f64 (pow.f64 x 3) -2/45)))) (fma.f64 (.f64 y y) (*.f64 (pow.f64 x 3) -3/2) (pow.f64 x 3))))
(fma.f64 (pow.f64 y 4) (.f64 (pow.f64 x 3) 7/8) (fma.f64 (pow.f64 y 6) (+.f64 (.f64 (pow.f64 x 3) -1/6) (fma.f64 (pow.f64 x 3) -1/24 (.f64 (pow.f64 x 3) -11/240))) (fma.f64 y (.f64 (pow.f64 x 3) (*.f64 -3/2 y)) (pow.f64 x 3))))
(fma.f64 (pow.f64 y 4) (.f64 (pow.f64 x 3) 7/8) (fma.f64 (pow.f64 y 6) (fma.f64 x (.f64 (.f64 x x) -19/90) (.f64 (pow.f64 x 3) -31/720)) (.f64 (+.f64 (.f64 (*.f64 -3/2 y) y) 1) (pow.f64 x 3))))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 x 3) (pow.f64 (cos.f64 y) 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 x 3) (pow.f64 (cos.f64 y) 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 x 3) (pow.f64 (cos.f64 y) 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 x 3) (pow.f64 (cos.f64 y) 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 x 3) (pow.f64 (cos.f64 y) 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 x 3) (pow.f64 (cos.f64 y) 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 x 3) (pow.f64 (cos.f64 y) 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 x 3) (pow.f64 (cos.f64 y) 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 x 3) (pow.f64 (cos.f64 y) 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 x 3) (pow.f64 (cos.f64 y) 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 x 3) (pow.f64 (cos.f64 y) 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 x 3) (pow.f64 (cos.f64 y) 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 x 3) (pow.f64 (cos.f64 y) 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 x 3) (pow.f64 (cos.f64 y) 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 x 3) (pow.f64 (cos.f64 y) 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 x 3) (pow.f64 (cos.f64 y) 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 x 3) (pow.f64 (cos.f64 y) 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 x 3) (pow.f64 (cos.f64 y) 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 x 3) (pow.f64 (cos.f64 y) 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 x 3) (pow.f64 (cos.f64 y) 3))

localize44.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (sin.f64 y) (sqrt.f64 z))
✓	0.1b	(.f64 (.f64 (sin.f64 y) (sqrt.f64 z)) (sqrt.f64 z))

Compiler

Compiled 33 to 8 computations (75.8% saved)

series7.0ms (0.1%)

Counts

2 → 36

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	z	@	-inf	(.f64 (.f64 (sin.f64 y) (sqrt.f64 z)) (sqrt.f64 z))
1.0ms	z	@	0	(*.f64 (sin.f64 y) (sqrt.f64 z))
1.0ms	z	@	-inf	(*.f64 (sin.f64 y) (sqrt.f64 z))
1.0ms	y	@	0	(*.f64 (sin.f64 y) (sqrt.f64 z))
1.0ms	y	@	inf	(*.f64 (sin.f64 y) (sqrt.f64 z))

rewrite60.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

641×	`pow1_binary64`
588×	`add-log-exp_binary64`
588×	`log1p-expm1-u_binary64`
588×	`expm1-log1p-u_binary64`
573×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	14
1	138	14
2	1640	14

Stop Event

1×	node limit

Counts

2 → 22

Calls

Call 1

Inputs
(.f64 (.f64 (sin.f64 y) (sqrt.f64 z)) (sqrt.f64 z))
(*.f64 (sin.f64 y) (sqrt.f64 z))

Outputs

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

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

simplify88.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

1003×	`fma-def_binary64`
599×	`associate-r_binary64`
446×	`neg-sub0_binary64`
437×	`neg-mul-1_binary64`
351×	`distribute-rgt-out_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	48	356
1	132	343
2	390	316
3	1180	312
4	3294	312
5	5591	312
6	7685	312

Stop Event

1×	node limit

Counts

58 → 40

Calls

Call 1

Inputs
(*.f64 y z)
(+.f64 (.f64 -1/6 (.f64 (pow.f64 y 3) z)) (*.f64 y z))
(+.f64 (.f64 -1/6 (.f64 (pow.f64 y 3) z)) (+.f64 (.f64 y z) (.f64 1/120 (*.f64 (pow.f64 y 5) z))))
(+.f64 (.f64 -1/6 (.f64 (pow.f64 y 3) z)) (+.f64 (.f64 y z) (+.f64 (.f64 -1/5040 (.f64 (pow.f64 y 7) z)) (.f64 1/120 (*.f64 (pow.f64 y 5) z)))))
(*.f64 z (sin.f64 y))
(*.f64 z (sin.f64 y))
(*.f64 z (sin.f64 y))
(*.f64 z (sin.f64 y))
(*.f64 z (sin.f64 y))
(*.f64 z (sin.f64 y))
(*.f64 z (sin.f64 y))
(*.f64 z (sin.f64 y))
(*.f64 z (sin.f64 y))
(*.f64 z (sin.f64 y))
(*.f64 z (sin.f64 y))
(*.f64 z (sin.f64 y))
(*.f64 z (sin.f64 y))
(*.f64 z (sin.f64 y))
(*.f64 z (sin.f64 y))
(*.f64 z (sin.f64 y))
(.f64 -1 (.f64 (pow.f64 (sqrt.f64 -1) 2) (*.f64 z (sin.f64 y))))
(.f64 -1 (.f64 (pow.f64 (sqrt.f64 -1) 2) (*.f64 z (sin.f64 y))))
(.f64 -1 (.f64 (pow.f64 (sqrt.f64 -1) 2) (*.f64 z (sin.f64 y))))
(.f64 -1 (.f64 (pow.f64 (sqrt.f64 -1) 2) (*.f64 z (sin.f64 y))))
(*.f64 y (sqrt.f64 z))
(+.f64 (.f64 y (sqrt.f64 z)) (.f64 -1/6 (*.f64 (pow.f64 y 3) (sqrt.f64 z))))
(+.f64 (.f64 y (sqrt.f64 z)) (+.f64 (.f64 -1/6 (.f64 (pow.f64 y 3) (sqrt.f64 z))) (.f64 1/120 (*.f64 (pow.f64 y 5) (sqrt.f64 z)))))
(+.f64 (.f64 y (sqrt.f64 z)) (+.f64 (.f64 -1/6 (.f64 (pow.f64 y 3) (sqrt.f64 z))) (+.f64 (.f64 -1/5040 (.f64 (pow.f64 y 7) (sqrt.f64 z))) (.f64 1/120 (*.f64 (pow.f64 y 5) (sqrt.f64 z))))))
(*.f64 (sqrt.f64 z) (sin.f64 y))
(*.f64 (sqrt.f64 z) (sin.f64 y))
(*.f64 (sqrt.f64 z) (sin.f64 y))
(*.f64 (sqrt.f64 z) (sin.f64 y))
(*.f64 (sqrt.f64 z) (sin.f64 y))
(*.f64 (sqrt.f64 z) (sin.f64 y))
(*.f64 (sqrt.f64 z) (sin.f64 y))
(*.f64 (sqrt.f64 z) (sin.f64 y))

Outputs
(*.f64 y z)
(+.f64 (.f64 -1/6 (.f64 (pow.f64 y 3) z)) (*.f64 y z))
(fma.f64 -1/6 (.f64 z (pow.f64 y 3)) (.f64 y z))
(.f64 z (+.f64 y (.f64 -1/6 (pow.f64 y 3))))
(*.f64 z (fma.f64 -1/6 (pow.f64 y 3) y))
(+.f64 (.f64 -1/6 (.f64 (pow.f64 y 3) z)) (+.f64 (.f64 y z) (.f64 1/120 (*.f64 (pow.f64 y 5) z))))
(fma.f64 -1/6 (.f64 z (pow.f64 y 3)) (fma.f64 y z (.f64 1/120 (*.f64 z (pow.f64 y 5)))))
(fma.f64 -1/6 (.f64 z (pow.f64 y 3)) (.f64 z (+.f64 y (*.f64 1/120 (pow.f64 y 5)))))
(.f64 z (+.f64 (fma.f64 -1/6 (pow.f64 y 3) y) (.f64 1/120 (pow.f64 y 5))))
(*.f64 z (fma.f64 -1/6 (pow.f64 y 3) (fma.f64 1/120 (pow.f64 y 5) y)))
(+.f64 (.f64 -1/6 (.f64 (pow.f64 y 3) z)) (+.f64 (.f64 y z) (+.f64 (.f64 -1/5040 (.f64 (pow.f64 y 7) z)) (.f64 1/120 (*.f64 (pow.f64 y 5) z)))))
(fma.f64 -1/6 (.f64 z (pow.f64 y 3)) (fma.f64 y z (fma.f64 -1/5040 (.f64 z (pow.f64 y 7)) (.f64 1/120 (.f64 z (pow.f64 y 5))))))
(fma.f64 -1/6 (.f64 z (pow.f64 y 3)) (fma.f64 y z (.f64 z (+.f64 (.f64 -1/5040 (pow.f64 y 7)) (.f64 1/120 (pow.f64 y 5))))))
(.f64 z (+.f64 (fma.f64 -1/6 (pow.f64 y 3) y) (fma.f64 1/120 (pow.f64 y 5) (.f64 -1/5040 (pow.f64 y 7)))))
(.f64 z (+.f64 (.f64 -1/5040 (pow.f64 y 7)) (fma.f64 -1/6 (pow.f64 y 3) (fma.f64 1/120 (pow.f64 y 5) y))))
(.f64 z (+.f64 y (fma.f64 -1/6 (pow.f64 y 3) (fma.f64 1/120 (pow.f64 y 5) (.f64 -1/5040 (pow.f64 y 7))))))
(*.f64 z (sin.f64 y))
(*.f64 z (sin.f64 y))
(*.f64 z (sin.f64 y))
(*.f64 z (sin.f64 y))
(*.f64 z (sin.f64 y))
(*.f64 z (sin.f64 y))
(*.f64 z (sin.f64 y))
(*.f64 z (sin.f64 y))
(*.f64 z (sin.f64 y))
(*.f64 z (sin.f64 y))
(*.f64 z (sin.f64 y))
(*.f64 z (sin.f64 y))
(*.f64 z (sin.f64 y))
(*.f64 z (sin.f64 y))
(*.f64 z (sin.f64 y))
(*.f64 z (sin.f64 y))
(.f64 -1 (.f64 (pow.f64 (sqrt.f64 -1) 2) (*.f64 z (sin.f64 y))))
(*.f64 z (sin.f64 y))
(.f64 -1 (.f64 (pow.f64 (sqrt.f64 -1) 2) (*.f64 z (sin.f64 y))))
(*.f64 z (sin.f64 y))
(.f64 -1 (.f64 (pow.f64 (sqrt.f64 -1) 2) (*.f64 z (sin.f64 y))))
(*.f64 z (sin.f64 y))
(.f64 -1 (.f64 (pow.f64 (sqrt.f64 -1) 2) (*.f64 z (sin.f64 y))))
(*.f64 z (sin.f64 y))
(*.f64 y (sqrt.f64 z))
(+.f64 (.f64 y (sqrt.f64 z)) (.f64 -1/6 (*.f64 (pow.f64 y 3) (sqrt.f64 z))))
(fma.f64 y (sqrt.f64 z) (.f64 -1/6 (.f64 (pow.f64 y 3) (sqrt.f64 z))))
(.f64 (sqrt.f64 z) (+.f64 y (.f64 -1/6 (pow.f64 y 3))))
(*.f64 (sqrt.f64 z) (fma.f64 -1/6 (pow.f64 y 3) y))
(+.f64 (.f64 y (sqrt.f64 z)) (+.f64 (.f64 -1/6 (.f64 (pow.f64 y 3) (sqrt.f64 z))) (.f64 1/120 (*.f64 (pow.f64 y 5) (sqrt.f64 z)))))
(fma.f64 y (sqrt.f64 z) (fma.f64 -1/6 (.f64 (pow.f64 y 3) (sqrt.f64 z)) (.f64 1/120 (*.f64 (pow.f64 y 5) (sqrt.f64 z)))))
(fma.f64 y (sqrt.f64 z) (.f64 (sqrt.f64 z) (+.f64 (.f64 1/120 (pow.f64 y 5)) (*.f64 -1/6 (pow.f64 y 3)))))
(.f64 (sqrt.f64 z) (+.f64 (fma.f64 -1/6 (pow.f64 y 3) y) (.f64 1/120 (pow.f64 y 5))))
(*.f64 (sqrt.f64 z) (fma.f64 -1/6 (pow.f64 y 3) (fma.f64 1/120 (pow.f64 y 5) y)))
(+.f64 (.f64 y (sqrt.f64 z)) (+.f64 (.f64 -1/6 (.f64 (pow.f64 y 3) (sqrt.f64 z))) (+.f64 (.f64 -1/5040 (.f64 (pow.f64 y 7) (sqrt.f64 z))) (.f64 1/120 (*.f64 (pow.f64 y 5) (sqrt.f64 z))))))
(fma.f64 y (sqrt.f64 z) (fma.f64 -1/6 (.f64 (pow.f64 y 3) (sqrt.f64 z)) (fma.f64 -1/5040 (.f64 (pow.f64 y 7) (sqrt.f64 z)) (.f64 1/120 (.f64 (pow.f64 y 5) (sqrt.f64 z))))))
(+.f64 (.f64 (sqrt.f64 z) (+.f64 y (.f64 -1/6 (pow.f64 y 3)))) (.f64 (sqrt.f64 z) (+.f64 (.f64 -1/5040 (pow.f64 y 7)) (*.f64 1/120 (pow.f64 y 5)))))
(.f64 (sqrt.f64 z) (+.f64 (fma.f64 -1/6 (pow.f64 y 3) y) (fma.f64 1/120 (pow.f64 y 5) (.f64 -1/5040 (pow.f64 y 7)))))
(.f64 (sqrt.f64 z) (+.f64 (.f64 -1/5040 (pow.f64 y 7)) (fma.f64 -1/6 (pow.f64 y 3) (fma.f64 1/120 (pow.f64 y 5) y))))
(.f64 (sqrt.f64 z) (+.f64 y (fma.f64 -1/6 (pow.f64 y 3) (fma.f64 1/120 (pow.f64 y 5) (.f64 -1/5040 (pow.f64 y 7))))))
(*.f64 (sqrt.f64 z) (sin.f64 y))
(*.f64 (sin.f64 y) (sqrt.f64 z))
(*.f64 (sqrt.f64 z) (sin.f64 y))
(*.f64 (sin.f64 y) (sqrt.f64 z))
(*.f64 (sqrt.f64 z) (sin.f64 y))
(*.f64 (sin.f64 y) (sqrt.f64 z))
(*.f64 (sqrt.f64 z) (sin.f64 y))
(*.f64 (sin.f64 y) (sqrt.f64 z))
(*.f64 (sqrt.f64 z) (sin.f64 y))
(*.f64 (sin.f64 y) (sqrt.f64 z))
(*.f64 (sqrt.f64 z) (sin.f64 y))
(*.f64 (sin.f64 y) (sqrt.f64 z))
(*.f64 (sqrt.f64 z) (sin.f64 y))
(*.f64 (sin.f64 y) (sqrt.f64 z))
(*.f64 (sqrt.f64 z) (sin.f64 y))
(*.f64 (sin.f64 y) (sqrt.f64 z))

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (cos.f64 y))
✓	0.1b	(.f64 (.f64 x (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y)))
✓	0.1b	(*.f64 x (sqrt.f64 (cos.f64 y)))
	0.1b	(*.f64 z (sin.f64 y))

Compiler

Compiled 45 to 10 computations (77.8% saved)

series47.0ms (0.4%)

Counts

3 → 52

Calls

15 calls:

Time	Variable		Point	Expression
41.0ms	y	@	inf	(*.f64 x (sqrt.f64 (cos.f64 y)))
1.0ms	y	@	-inf	(*.f64 x (sqrt.f64 (cos.f64 y)))
1.0ms	x	@	0	(*.f64 x (sqrt.f64 (cos.f64 y)))
1.0ms	y	@	0	(*.f64 x (sqrt.f64 (cos.f64 y)))
1.0ms	x	@	-inf	(*.f64 x (sqrt.f64 (cos.f64 y)))

rewrite134.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

641×	`pow1_binary64`
588×	`add-log-exp_binary64`
588×	`log1p-expm1-u_binary64`
588×	`expm1-log1p-u_binary64`
573×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	19
1	138	19
2	1640	19

Stop Event

1×	node limit

Counts

3 → 42

Calls

Call 1

Inputs
(*.f64 x (sqrt.f64 (cos.f64 y)))
(.f64 (.f64 x (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y)))
(sqrt.f64 (cos.f64 y))

Outputs

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

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

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

simplify106.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

1000×	`fma-def_binary64`
957×	`distribute-rgt-out_binary64`
748×	`distribute-lft-out_binary64`
662×	`associate-l_binary64`
492×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	44	458
1	112	455
2	302	441
3	987	436
4	4055	436
5	7341	436
6	7732	436
7	7962	436

Stop Event

1×	node limit

Counts

94 → 64

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 (cos.f64 y)) x)
(*.f64 (sqrt.f64 (cos.f64 y)) x)
(*.f64 (sqrt.f64 (cos.f64 y)) x)
(*.f64 (sqrt.f64 (cos.f64 y)) x)
(*.f64 (sqrt.f64 (cos.f64 y)) x)
(*.f64 (sqrt.f64 (cos.f64 y)) x)
(*.f64 (sqrt.f64 (cos.f64 y)) x)
(*.f64 (sqrt.f64 (cos.f64 y)) x)
(*.f64 (sqrt.f64 (cos.f64 y)) x)
(*.f64 (sqrt.f64 (cos.f64 y)) x)
(*.f64 (sqrt.f64 (cos.f64 y)) x)
(*.f64 (sqrt.f64 (cos.f64 y)) x)
x
(+.f64 (.f64 -1/4 (.f64 (pow.f64 y 2) x)) x)
(+.f64 (.f64 -1/96 (.f64 (pow.f64 y 4) x)) (+.f64 (.f64 -1/4 (.f64 (pow.f64 y 2) x)) x))
(+.f64 (.f64 -19/5760 (.f64 (pow.f64 y 6) x)) (+.f64 (.f64 -1/96 (.f64 (pow.f64 y 4) x)) (+.f64 (.f64 -1/4 (.f64 (pow.f64 y 2) x)) x)))
(*.f64 (sqrt.f64 (cos.f64 y)) x)
(*.f64 (sqrt.f64 (cos.f64 y)) x)
(*.f64 (sqrt.f64 (cos.f64 y)) x)
(*.f64 (sqrt.f64 (cos.f64 y)) x)
(*.f64 (sqrt.f64 (cos.f64 y)) x)
(*.f64 (sqrt.f64 (cos.f64 y)) x)
(*.f64 (sqrt.f64 (cos.f64 y)) x)
(*.f64 (sqrt.f64 (cos.f64 y)) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
x
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) x)
(+.f64 (.f64 1/24 (.f64 (pow.f64 y 4) x)) (+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) x))
(+.f64 (.f64 -1/720 (.f64 (pow.f64 y 6) x)) (+.f64 (.f64 1/24 (.f64 (pow.f64 y 4) x)) (+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) x)))
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
1
(+.f64 (*.f64 -1/4 (pow.f64 y 2)) 1)
(+.f64 (.f64 -1/4 (pow.f64 y 2)) (+.f64 1 (.f64 -1/96 (pow.f64 y 4))))
(+.f64 (.f64 -1/4 (pow.f64 y 2)) (+.f64 1 (+.f64 (.f64 -1/96 (pow.f64 y 4)) (*.f64 -19/5760 (pow.f64 y 6)))))

Outputs
(*.f64 (sqrt.f64 (cos.f64 y)) x)
(*.f64 (sqrt.f64 (cos.f64 y)) x)
(*.f64 (sqrt.f64 (cos.f64 y)) x)
(*.f64 (sqrt.f64 (cos.f64 y)) x)
(*.f64 (sqrt.f64 (cos.f64 y)) x)
(*.f64 (sqrt.f64 (cos.f64 y)) x)
(*.f64 (sqrt.f64 (cos.f64 y)) x)
(*.f64 (sqrt.f64 (cos.f64 y)) x)
(*.f64 (sqrt.f64 (cos.f64 y)) x)
(*.f64 (sqrt.f64 (cos.f64 y)) x)
(*.f64 (sqrt.f64 (cos.f64 y)) x)
(*.f64 (sqrt.f64 (cos.f64 y)) x)
x
(+.f64 (.f64 -1/4 (.f64 (pow.f64 y 2) x)) x)
(fma.f64 -1/4 (.f64 x (.f64 y y)) x)
(.f64 (fma.f64 -1/4 (.f64 y y) 1) x)
(fma.f64 x (.f64 -1/4 (.f64 y y)) x)
(fma.f64 -1/4 (.f64 y (.f64 y x)) x)
(+.f64 (.f64 -1/96 (.f64 (pow.f64 y 4) x)) (+.f64 (.f64 -1/4 (.f64 (pow.f64 y 2) x)) x))
(fma.f64 -1/96 (.f64 x (pow.f64 y 4)) (fma.f64 -1/4 (.f64 x (*.f64 y y)) x))
(fma.f64 -1/96 (.f64 x (pow.f64 y 4)) (.f64 (fma.f64 -1/4 (*.f64 y y) 1) x))
(.f64 x (fma.f64 y (.f64 y -1/4) (fma.f64 -1/96 (pow.f64 y 4) 1)))
(.f64 x (fma.f64 (.f64 y y) (fma.f64 (*.f64 y y) -1/96 -1/4) 1))
(+.f64 (.f64 -19/5760 (.f64 (pow.f64 y 6) x)) (+.f64 (.f64 -1/96 (.f64 (pow.f64 y 4) x)) (+.f64 (.f64 -1/4 (.f64 (pow.f64 y 2) x)) x)))
(fma.f64 -19/5760 (.f64 x (pow.f64 y 6)) (fma.f64 -1/96 (.f64 x (pow.f64 y 4)) (fma.f64 -1/4 (.f64 x (.f64 y y)) x)))
(+.f64 (.f64 (fma.f64 -1/4 (.f64 y y) 1) x) (.f64 x (fma.f64 -1/96 (pow.f64 y 4) (.f64 -19/5760 (pow.f64 y 6)))))
(+.f64 x (.f64 x (fma.f64 y (.f64 y -1/4) (fma.f64 -1/96 (pow.f64 y 4) (*.f64 -19/5760 (pow.f64 y 6))))))
(.f64 x (fma.f64 y (.f64 y -1/4) (fma.f64 -19/5760 (pow.f64 y 6) (fma.f64 -1/96 (pow.f64 y 4) 1))))
(fma.f64 x (fma.f64 -1/96 (pow.f64 y 4) (fma.f64 -1/4 (.f64 y y) (.f64 -19/5760 (pow.f64 y 6)))) x)
(*.f64 (sqrt.f64 (cos.f64 y)) x)
(*.f64 (sqrt.f64 (cos.f64 y)) x)
(*.f64 (sqrt.f64 (cos.f64 y)) x)
(*.f64 (sqrt.f64 (cos.f64 y)) x)
(*.f64 (sqrt.f64 (cos.f64 y)) x)
(*.f64 (sqrt.f64 (cos.f64 y)) x)
(*.f64 (sqrt.f64 (cos.f64 y)) x)
(*.f64 (sqrt.f64 (cos.f64 y)) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
x
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) x)
(fma.f64 -1/2 (.f64 x (.f64 y y)) x)
(fma.f64 (.f64 y (.f64 y x)) -1/2 x)
(fma.f64 (.f64 x (.f64 y y)) -1/2 x)
(fma.f64 y (.f64 x (.f64 y -1/2)) x)
(+.f64 (.f64 1/24 (.f64 (pow.f64 y 4) x)) (+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) x))
(fma.f64 1/24 (.f64 x (pow.f64 y 4)) (fma.f64 -1/2 (.f64 x (*.f64 y y)) x))
(fma.f64 (.f64 x (pow.f64 y 4)) 1/24 (fma.f64 (.f64 y (*.f64 y x)) -1/2 x))
(fma.f64 x (fma.f64 (pow.f64 y 4) 1/24 (.f64 y (.f64 y -1/2))) x)
(fma.f64 x (.f64 (.f64 y y) (fma.f64 (*.f64 y y) 1/24 -1/2)) x)
(.f64 x (fma.f64 (pow.f64 y 4) 1/24 (fma.f64 y (.f64 y -1/2) 1)))
(+.f64 (.f64 -1/720 (.f64 (pow.f64 y 6) x)) (+.f64 (.f64 1/24 (.f64 (pow.f64 y 4) x)) (+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) x)))
(fma.f64 -1/720 (.f64 x (pow.f64 y 6)) (fma.f64 1/24 (.f64 x (pow.f64 y 4)) (fma.f64 -1/2 (.f64 x (.f64 y y)) x)))
(fma.f64 (.f64 x (pow.f64 y 6)) -1/720 (fma.f64 (.f64 x (pow.f64 y 4)) 1/24 (fma.f64 (.f64 y (.f64 y x)) -1/2 x)))
(fma.f64 x (.f64 (pow.f64 y 6) -1/720) (fma.f64 x (fma.f64 (pow.f64 y 4) 1/24 (.f64 y (*.f64 y -1/2))) x))
(fma.f64 x (fma.f64 (pow.f64 y 6) -1/720 (.f64 (.f64 y y) (fma.f64 (*.f64 y y) 1/24 -1/2))) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
(*.f64 (cos.f64 y) x)
1
(+.f64 (*.f64 -1/4 (pow.f64 y 2)) 1)
(fma.f64 -1/4 (*.f64 y y) 1)
(fma.f64 y (*.f64 y -1/4) 1)
(+.f64 (.f64 -1/4 (pow.f64 y 2)) (+.f64 1 (.f64 -1/96 (pow.f64 y 4))))
(fma.f64 -1/4 (.f64 y y) (+.f64 1 (.f64 -1/96 (pow.f64 y 4))))
(fma.f64 -1/4 (*.f64 y y) (fma.f64 -1/96 (pow.f64 y 4) 1))
(fma.f64 y (*.f64 y -1/4) (fma.f64 -1/96 (pow.f64 y 4) 1))
(fma.f64 (.f64 y y) (fma.f64 (.f64 y y) -1/96 -1/4) 1)
(+.f64 (.f64 -1/4 (pow.f64 y 2)) (+.f64 1 (+.f64 (.f64 -1/96 (pow.f64 y 4)) (*.f64 -19/5760 (pow.f64 y 6)))))
(+.f64 (fma.f64 -1/4 (.f64 y y) 1) (fma.f64 -1/96 (pow.f64 y 4) (.f64 -19/5760 (pow.f64 y 6))))
(fma.f64 -1/4 (*.f64 y y) (fma.f64 -1/96 (pow.f64 y 4) (fma.f64 -19/5760 (pow.f64 y 6) 1)))
(fma.f64 y (*.f64 y -1/4) (fma.f64 -19/5760 (pow.f64 y 6) (fma.f64 -1/96 (pow.f64 y 4) 1)))
(fma.f64 (.f64 y y) (fma.f64 (.f64 y y) -1/96 -1/4) (fma.f64 -19/5760 (pow.f64 y 6) 1))

eval151.0ms (1.2%)

Compiler: Compiled 5469 to 2294 computations (58.1% saved)

prune121.0ms (0.9%)

Pruning

22 alts after pruning (13 fresh and 9 done)

	Pruned	Kept	Total
New	330	8	338
Fresh	4	5	9
Picked	0	1	1
Done	1	8	9
Total	335	22	357

Error

0.0b

Counts

357 → 22

Alt Table

Click to see full alt table

Status	Error	Program
✓	51.8b	(cbrt.f64 (pow.f64 (*.f64 (cos.f64 y) x) 3))
	14.4b	(+.f64 (.f64 (.f64 x (-.f64 (+.f64 1 (sqrt.f64 (cos.f64 y))) 1)) (sqrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	33.0b	(.f64 (.f64 x (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y)))
	39.5b	(+.f64 x (.f64 (.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
	41.0b	(pow.f64 (sqrt.f64 (*.f64 (cos.f64 y) x)) 2)
	30.5b	(+.f64 x (cbrt.f64 (pow.f64 (*.f64 (sin.f64 y) z) 3)))
✓	37.1b	(+.f64 x (.f64 (.f64 (sin.f64 y) (sqrt.f64 z)) (sqrt.f64 z)))
✓	14.3b	(+.f64 x (pow.f64 (cbrt.f64 (*.f64 z (sin.f64 y))) 3))
✓	14.4b	(+.f64 (.f64 (.f64 x (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	14.2b	(+.f64 x (.f64 (.f64 (pow.f64 (cbrt.f64 (*.f64 z (sin.f64 y))) 2) (cbrt.f64 z)) (cbrt.f64 (sin.f64 y))))
	40.0b	(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) x)
✓	28.8b	(+.f64 (*.f64 y z) x)
✓	25.0b	(*.f64 (cos.f64 y) x)
	38.2b	x
	14.4b	(+.f64 x (pow.f64 (*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 z)) 3))
	38.3b	(*.f64 z (sin.f64 y))
✓	0.5b	(+.f64 (.f64 x (cos.f64 y)) (pow.f64 (cbrt.f64 (.f64 z (sin.f64 y))) 3))
✓	0.1b	(+.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))
	8.5b	(+.f64 (.f64 (sqrt.f64 (.f64 x (cbrt.f64 x))) (.f64 (cbrt.f64 x) (cos.f64 y))) (.f64 z (sin.f64 y)))
✓	52.8b	(*.f64 y z)
	25.6b	(.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (cos.f64 y)))
	25.8b	(.f64 (pow.f64 (cbrt.f64 (.f64 (cos.f64 y) x)) 2) (cbrt.f64 (*.f64 (cos.f64 y) x)))

Compiler

Compiled 272 to 184 computations (32.4% saved)

regimes258.0ms (2%)

Counts

41 → 1

Calls

Call 1

Inputs
x
x
x
(*.f64 y z)
(+.f64 (*.f64 y z) x)
(*.f64 z (sin.f64 y))
(*.f64 (cos.f64 y) x)
(*.f64 z (sin.f64 y))
(+.f64 x (*.f64 z (sin.f64 y)))
(+.f64 (.f64 x (cos.f64 y)) (.f64 y z))
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) x)
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) x)
(+.f64 (+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) x) (*.f64 y z))
(+.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))
(+.f64 (+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) x) (*.f64 z (sin.f64 y)))
(pow.f64 (sqrt.f64 (*.f64 (cos.f64 y) x)) 2)
(cbrt.f64 (pow.f64 (*.f64 (cos.f64 y) x) 3))
(+.f64 x (cbrt.f64 (pow.f64 (*.f64 (sin.f64 y) z) 3)))
(+.f64 x (cbrt.f64 (pow.f64 (*.f64 z (sin.f64 y)) 3)))
(+.f64 x (pow.f64 (cbrt.f64 (*.f64 z (sin.f64 y))) 3))
(+.f64 x (cbrt.f64 (pow.f64 (*.f64 z (sin.f64 y)) 3)))
(+.f64 x (.f64 (.f64 (sin.f64 y) (sqrt.f64 z)) (sqrt.f64 z)))
(.f64 (.f64 x (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y)))
(.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (cos.f64 y)))
(+.f64 x (pow.f64 (*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 z)) 3))
(+.f64 x (.f64 (.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
(+.f64 (cbrt.f64 (pow.f64 (.f64 x (cos.f64 y)) 3)) (.f64 z (sin.f64 y)))
(+.f64 (.f64 x (cos.f64 y)) (cbrt.f64 (pow.f64 (.f64 z (sin.f64 y)) 3)))
(+.f64 (pow.f64 (sqrt.f64 (.f64 x (cos.f64 y))) 2) (.f64 z (sin.f64 y)))
(+.f64 (.f64 x (cos.f64 y)) (pow.f64 (cbrt.f64 (.f64 z (sin.f64 y))) 3))
(+.f64 (.f64 x (cos.f64 y)) (.f64 (*.f64 (sin.f64 y) (sqrt.f64 z)) (sqrt.f64 z)))
(.f64 (pow.f64 (cbrt.f64 (.f64 (cos.f64 y) x)) 2) (cbrt.f64 (*.f64 (cos.f64 y) x)))
(+.f64 (.f64 x (cos.f64 y)) (pow.f64 (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 z)) 3))
(+.f64 (.f64 (.f64 x (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
(+.f64 (.f64 x (cos.f64 y)) (.f64 (*.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
(+.f64 (.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (cos.f64 y))) (*.f64 z (sin.f64 y)))
(+.f64 (.f64 (sqrt.f64 (.f64 x (cbrt.f64 x))) (.f64 (cbrt.f64 x) (cos.f64 y))) (.f64 z (sin.f64 y)))
(+.f64 (.f64 (.f64 x (-.f64 (+.f64 1 (sqrt.f64 (cos.f64 y))) 1)) (sqrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
(+.f64 x (.f64 (.f64 (pow.f64 (cbrt.f64 (*.f64 z (sin.f64 y))) 2) (cbrt.f64 z)) (cbrt.f64 (sin.f64 y))))
(fma.f64 (pow.f64 (cbrt.f64 (.f64 x (cos.f64 y))) 2) (cbrt.f64 (.f64 x (cos.f64 y))) (*.f64 y z))
(+.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 (pow.f64 (cbrt.f64 (.f64 z (sin.f64 y))) 2) (cbrt.f64 z)) (cbrt.f64 (sin.f64 y))))

Outputs
(+.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))

Calls

4 calls:

68.0ms	(+.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))
67.0ms	z
52.0ms	y
48.0ms	x

Results

Error	Segments	Branch
0.1b	1	`x`
0.1b	1	`y`
0.1b	1	`z`
0.1b	1	`(+.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))`

Compiler

Compiled 433 to 155 computations (64.2% saved)

regimes125.0ms (1%)

Counts

13 → 3

Calls

Call 1

Inputs
x
x
x
(*.f64 y z)
(+.f64 (*.f64 y z) x)
(*.f64 z (sin.f64 y))
(*.f64 (cos.f64 y) x)
(*.f64 z (sin.f64 y))
(+.f64 x (*.f64 z (sin.f64 y)))
(+.f64 (.f64 x (cos.f64 y)) (.f64 y z))
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) x)
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) x)
(+.f64 (+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) x)) x) (*.f64 y z))

Outputs
(+.f64 x (*.f64 z (sin.f64 y)))
(*.f64 (cos.f64 y) x)
(+.f64 x (*.f64 z (sin.f64 y)))

Calls

3 calls:

59.0ms	x
46.0ms	z
15.0ms	y

Results

Error	Segments	Branch
7.3b	3	`x`
12.0b	2	`y`
5.7b	3	`z`

Compiler

Compiled 83 to 40 computations (51.8% saved)

bsearch210.0ms (1.6%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
146.0ms	1.1228791439375612e-58	1.0534743273697433e-42
64.0ms	-0.5522434277288263	-3.865674960128869e-5

Compiler

Compiled 18 to 13 computations (27.8% saved)

regimes227.0ms (1.8%)

Counts

8 → 5

Calls

Call 1

Inputs
x
x
x
(*.f64 y z)
(+.f64 (*.f64 y z) x)
(*.f64 z (sin.f64 y))
(*.f64 (cos.f64 y) x)
(*.f64 z (sin.f64 y))

Outputs
(*.f64 z (sin.f64 y))
(*.f64 (cos.f64 y) x)
(*.f64 z (sin.f64 y))
(+.f64 (*.f64 y z) x)
(*.f64 (cos.f64 y) x)

Calls

3 calls:

155.0ms	y
37.0ms	x
32.0ms	z

Results

Error	Segments	Branch
14.3b	4	`x`
11.7b	5	`y`
13.3b	4	`z`

Compiler

Compiled 38 to 18 computations (52.6% saved)

bsearch585.0ms (4.5%)

Algorithm

4×	binary-search

Steps

Time	Left	Right
157.0ms	0.005942722395923747	79.86688634909905
79.0ms	-959.0349490808583	-4.690189031088517e-10
73.0ms	-1.3948637207315615e+61	-5.6331254089158625e+56
276.0ms	-1.6168061700794143e+169	-6.228842761369212e+167

Compiler

Compiled 18 to 13 computations (27.8% saved)

regimes128.0ms (1%)

Counts

6 → 3

Calls

Call 1

Inputs
x
x
x
(*.f64 y z)
(+.f64 (*.f64 y z) x)
(*.f64 z (sin.f64 y))

Outputs
(*.f64 z (sin.f64 y))
(+.f64 (*.f64 y z) x)
(*.f64 z (sin.f64 y))

Calls

3 calls:

58.0ms	x
48.0ms	y
19.0ms	z

Results

Error	Segments	Branch
23.7b	3	`x`
15.1b	3	`y`
22.9b	3	`z`

Compiler

Compiled 30 to 16 computations (46.7% saved)

bsearch208.0ms (1.6%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
37.0ms	1.8081290083886633e-7	0.005942722395923747
171.0ms	-959.0349490808583	-4.690189031088517e-10

Compiler

Compiled 18 to 13 computations (27.8% saved)

regimes53.0ms (0.4%)

Counts

5 → 1

Calls

Call 1

Inputs
x
x
x
(*.f64 y z)
(+.f64 (*.f64 y z) x)

Outputs
(+.f64 (*.f64 y z) x)

Calls

3 calls:

41.0ms	z
6.0ms	x
5.0ms	y

Results

Error	Segments	Branch
28.8b	1	`x`
28.8b	1	`y`
28.8b	1	`z`

Compiler

Compiled 26 to 14 computations (46.2% saved)

regimes36.0ms (0.3%)

Counts

4 → 3

Calls

Call 1

Inputs
x
x
x
(*.f64 y z)

Outputs
x
(*.f64 y z)
x

Calls

3 calls:

14.0ms	y
13.0ms	x
8.0ms	z

Results

Error	Segments	Branch
34.3b	3	`x`
37.0b	3	`y`
37.0b	2	`z`

Compiler

Compiled 21 to 13 computations (38.1% saved)

bsearch193.0ms (1.5%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
129.0ms	6.898425995386248e-203	1.1759978495780932e-201
64.0ms	-1.6037008546249173e-173	-3.545546476856473e-178

Compiler

Compiled 18 to 13 computations (27.8% saved)

regimes16.0ms (0.1%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0.0b (-0%)

Counts

3 → 1

Calls

Call 1

Inputs
x
x
x

Outputs
x

Calls

3 calls:

6.0ms	z
4.0ms	y
4.0ms	x

Results

Error	Segments	Branch
38.2b	1	`x`
38.2b	1	`y`
38.2b	1	`z`

Compiler

Compiled 18 to 12 computations (33.3% saved)

simplify13.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
3×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	162
1	48	162

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(+.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))
(if (<=.f64 z -4974166590674695/9007199254740992) (+.f64 x (.f64 z (sin.f64 y))) (if (<=.f64 z 396791143913389/3533694129556768659166595001485837031654967793751237916243212402585239552) (.f64 (cos.f64 y) x) (+.f64 x (*.f64 z (sin.f64 y)))))
(if (<=.f64 y -16168061700794143434200876931800779253130732190464746870848223349410265696449839733423360702244652267853879462379323705094800462288402507403322244963331123870533741969408) (.f64 z (sin.f64 y)) (if (<=.f64 y -13948637207315614754675125809002374336675864510959908198285312) (.f64 (cos.f64 y) x) (if (<=.f64 y -4217880311831871/4398046511104) (.f64 z (sin.f64 y)) (if (<=.f64 y 6851492446169213/1152921504606846976) (+.f64 (.f64 y z) x) (*.f64 (cos.f64 y) x)))))
(if (<=.f64 y -4217880311831871/4398046511104) (.f64 z (sin.f64 y)) (if (<=.f64 y 6830918260735161/37778931862957161709568) (+.f64 (.f64 y z) x) (*.f64 z (sin.f64 y))))
(+.f64 (*.f64 y z) x)
(if (<=.f64 x -8931628317451355/556938551955834377275533643273961343370755433013740225900780336657626363184653001282460059975265063449541297555370411048668054775558525146271076821255153099151854818647493280039413353545728) x (if (<=.f64 x 3043945516263499/44125218104815898389829825659447310364864904872680898823178155169729591099393726561029280015550468702670279148410687446533176513529349858556664892007608532912981188929417439383947376132698492620683708741856789536964608) (*.f64 y z) x))
x

Outputs
(+.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))
(+.f64 (.f64 z (sin.f64 y)) (.f64 x (cos.f64 y)))
(if (<=.f64 z -4974166590674695/9007199254740992) (+.f64 x (.f64 z (sin.f64 y))) (if (<=.f64 z 396791143913389/3533694129556768659166595001485837031654967793751237916243212402585239552) (.f64 (cos.f64 y) x) (+.f64 x (*.f64 z (sin.f64 y)))))
(if (<=.f64 z -4974166590674695/9007199254740992) (+.f64 x (.f64 z (sin.f64 y))) (if (<=.f64 z 396791143913389/3533694129556768659166595001485837031654967793751237916243212402585239552) (.f64 x (cos.f64 y)) (+.f64 x (*.f64 z (sin.f64 y)))))
(if (<=.f64 y -16168061700794143434200876931800779253130732190464746870848223349410265696449839733423360702244652267853879462379323705094800462288402507403322244963331123870533741969408) (.f64 z (sin.f64 y)) (if (<=.f64 y -13948637207315614754675125809002374336675864510959908198285312) (.f64 (cos.f64 y) x) (if (<=.f64 y -4217880311831871/4398046511104) (.f64 z (sin.f64 y)) (if (<=.f64 y 6851492446169213/1152921504606846976) (+.f64 (.f64 y z) x) (*.f64 (cos.f64 y) x)))))
(if (<=.f64 y -16168061700794143434200876931800779253130732190464746870848223349410265696449839733423360702244652267853879462379323705094800462288402507403322244963331123870533741969408) (.f64 z (sin.f64 y)) (if (<=.f64 y -13948637207315614754675125809002374336675864510959908198285312) (.f64 x (cos.f64 y)) (if (<=.f64 y -4217880311831871/4398046511104) (.f64 z (sin.f64 y)) (if (<=.f64 y 6851492446169213/1152921504606846976) (+.f64 x (.f64 y z)) (*.f64 x (cos.f64 y))))))
(if (<=.f64 y -4217880311831871/4398046511104) (.f64 z (sin.f64 y)) (if (<=.f64 y 6830918260735161/37778931862957161709568) (+.f64 (.f64 y z) x) (*.f64 z (sin.f64 y))))
(if (<=.f64 y -4217880311831871/4398046511104) (.f64 z (sin.f64 y)) (if (<=.f64 y 6830918260735161/37778931862957161709568) (+.f64 x (.f64 y z)) (*.f64 z (sin.f64 y))))
(+.f64 (*.f64 y z) x)
(+.f64 x (*.f64 y z))
(if (<=.f64 x -8931628317451355/556938551955834377275533643273961343370755433013740225900780336657626363184653001282460059975265063449541297555370411048668054775558525146271076821255153099151854818647493280039413353545728) x (if (<=.f64 x 3043945516263499/44125218104815898389829825659447310364864904872680898823178155169729591099393726561029280015550468702670279148410687446533176513529349858556664892007608532912981188929417439383947376132698492620683708741856789536964608) (*.f64 y z) x))
x

Compiler

Compiled 131 to 74 computations (43.5% saved)

soundness0.0ms (0%)

end65.0ms (0.5%)

Compiler: Compiled 113 to 41 computations (63.7% saved)