Details

analyze404.0ms (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)

sample2.5s (25.2%)

Results

1.1s	1940×	body	1024	valid
1.0s	5314×	body	256	valid
327.0ms	997×	body	512	valid
4.0ms	5×	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 (sin.f64 y)) (.f64 z (cos.f64 y)))
(+.f64 (.f64 y (sin.f64 x)) (.f64 z (cos.f64 x)))
(+.f64 (.f64 z (sin.f64 y)) (.f64 x (cos.f64 y)))
(+.f64 (.f64 x (sin.f64 z)) (.f64 y (cos.f64 z)))

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

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

0.2b

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.2b	(+.f64 (.f64 x (sin.f64 y)) (.f64 z (cos.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 x (sin.f64 y))
✓	0.1b	(*.f64 z (cos.f64 y))

Compiler

Compiled 27 to 8 computations (70.4% saved)

series8.0ms (0.1%)

Counts

2 → 40

Calls

12 calls:

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

rewrite59.0ms (0.6%)

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

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

Outputs

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

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

simplify151.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

1987×	`fma-def_binary64`
682×	`sqr-pow_binary64`
443×	`pow-sqr_binary64`
420×	`*-commutative_binary64`
376×	`cube-prod_binary64`

Iterations

Useful iterations: 8 (0.0ms)

Iter	Nodes	Cost
0	49	336
1	129	329
2	359	314
3	1204	313
4	1950	313
5	2861	313
6	2999	313
7	3216	313
8	3430	305
9	5384	305
10	5803	305
11	6309	305
12	6910	305
13	7615	305

Stop Event

1×	node limit

Counts

66 → 42

Calls

Call 1

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

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

eval10.0ms (0.1%)

Compiler: Compiled 595 to 263 computations (55.8% saved)

prune63.0ms (0.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	33	9	42
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	33	10	43

Error

0.1b

Counts

43 → 10

Alt Table

Click to see full alt table

Status	Error	Program
	18.7b	(+.f64 (cbrt.f64 (pow.f64 (.f64 x (sin.f64 y)) 3)) (.f64 z (cos.f64 y)))
	31.9b	(+.f64 (.f64 x (sin.f64 y)) (pow.f64 (sqrt.f64 (.f64 z (cos.f64 y))) 2))
▶	30.1b	(+.f64 (pow.f64 (sqrt.f64 (.f64 x (sin.f64 y))) 2) (.f64 z (cos.f64 y)))
▶	13.8b	(+.f64 (*.f64 x (sin.f64 y)) z)
▶	0.6b	(+.f64 (pow.f64 (cbrt.f64 (.f64 x (sin.f64 y))) 3) (.f64 z (cos.f64 y)))
✓	0.2b	(+.f64 (.f64 x (sin.f64 y)) (.f64 z (cos.f64 y)))
	22.7b	(+.f64 (.f64 y x) (.f64 z (cos.f64 y)))
	26.2b	(+.f64 (cbrt.f64 (.f64 (pow.f64 (sin.f64 y) 3) (pow.f64 x 3))) (.f64 z (cos.f64 y)))
▶	0.9b	(+.f64 (.f64 x (sin.f64 y)) (pow.f64 (cbrt.f64 (.f64 z (cos.f64 y))) 3))
▶	25.7b	(+.f64 (.f64 x (sin.f64 y)) (+.f64 (.f64 -1/2 (*.f64 (pow.f64 y 2) z)) z))

Compiler

Compiled 270 to 194 computations (28.1% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.f64 x (sin.f64 y))
	0.1b	(*.f64 z (cos.f64 y))
✓	0.6b	(pow.f64 (cbrt.f64 (*.f64 x (sin.f64 y))) 3)
✓	8.0b	(cbrt.f64 (*.f64 x (sin.f64 y)))

Compiler

Compiled 43 to 14 computations (67.4% saved)

series70.0ms (0.7%)

Counts

2 → 16

Calls

12 calls:

Time	Variable		Point	Expression
58.0ms	x	@	-inf	(pow.f64 (cbrt.f64 (*.f64 x (sin.f64 y))) 3)
2.0ms	y	@	-inf	(cbrt.f64 (*.f64 x (sin.f64 y)))
2.0ms	y	@	inf	(cbrt.f64 (*.f64 x (sin.f64 y)))
1.0ms	y	@	0	(pow.f64 (cbrt.f64 (*.f64 x (sin.f64 y))) 3)
1.0ms	y	@	inf	(pow.f64 (cbrt.f64 (*.f64 x (sin.f64 y))) 3)

rewrite61.0ms (0.6%)

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 x (sin.f64 y)))
(pow.f64 (cbrt.f64 (*.f64 x (sin.f64 y))) 3)

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

Outputs

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

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

simplify187.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

1290×	`sqr-pow_binary64`
666×	`pow-sqr_binary64`
625×	`cube-prod_binary64`
559×	`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	169	112
6	541	112
7	1207	112
8	1299	112
9	1437	112
10	1600	112
11	1839	112
12	2166	112
13	2594	112
14	3100	112
15	3706	112
16	4429	112
17	4750	112
18	5034	112
19	5258	112
20	5438	112
21	5522	112
22	6465	112
23	7442	112
24	7908	112

Stop Event

1×	node limit

Counts

68 → 55

Calls

Call 1

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

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

localize12.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 18 to 6 computations (66.7% saved)

localize50.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 x (sin.f64 y)) (+.f64 (.f64 -1/2 (*.f64 (pow.f64 y 2) z)) z))
✓	0.0b	(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) z)) z)
	0.1b	(*.f64 x (sin.f64 y))
✓	6.3b	(*.f64 (pow.f64 y 2) z)

Compiler

Compiled 52 to 30 computations (42.3% saved)

series10.0ms (0.1%)

Counts

3 → 51

Calls

21 calls:

Time	Variable		Point	Expression
1.0ms	y	@	0	(*.f64 (pow.f64 y 2) z)
1.0ms	z	@	0	(*.f64 (pow.f64 y 2) z)
1.0ms	z	@	inf	(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) z)) z)
1.0ms	x	@	0	(+.f64 (.f64 x (sin.f64 y)) (+.f64 (.f64 -1/2 (*.f64 (pow.f64 y 2) z)) z))
1.0ms	y	@	inf	(*.f64 (pow.f64 y 2) z)

rewrite116.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

686×	`log-prod_binary64`
647×	`fma-def_binary64`
367×	`pow2_binary64`
347×	`fma-neg_binary64`
253×	`pow1/3_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	35
1	288	35
2	3850	35

Stop Event

1×	node limit

Counts

3 → 181

Calls

Call 1

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

Outputs

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((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 x (sin.f64 y) (fma.f64 (*.f64 y y) (*.f64 z -1/2) z)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 (*.f64 x (sin.f64 y)) 2) (fma.f64 x (sin.f64 y) (neg.f64 (fma.f64 (*.f64 y y) (*.f64 z -1/2) z)))) (/.f64 (pow.f64 (fma.f64 (*.f64 y y) (*.f64 z -1/2) z) 2) (fma.f64 x (sin.f64 y) (neg.f64 (fma.f64 (*.f64 y y) (*.f64 z -1/2) z)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 x (sin.f64 y) (fma.f64 (*.f64 y y) (*.f64 z -1/2) z)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 x (sin.f64 y) (fma.f64 (*.f64 y y) (*.f64 z -1/2) z)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (fma.f64 (*.f64 y y) (*.f64 z -1/2) z))) (pow.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (fma.f64 (*.f64 y y) (*.f64 z -1/2) z))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (fma.f64 (*.f64 y y) (*.f64 z -1/2) 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simplify103.0ms (1%)

Algorithm

1×	egg-herbie

Rules

653×	`distribute-lft-out_binary64`
595×	`distribute-rgt-neg-in_binary64`
589×	`fma-neg_binary64`
471×	`fma-def_binary64`
459×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	37	758
1	94	678
2	231	678
3	632	675
4	2135	674
5	4472	674

Stop Event

1×	node limit

Counts

232 → 199

Calls

Call 1

Inputs
z
(.f64 -1/2 (.f64 (pow.f64 y 2) z))
(.f64 -1/2 (.f64 (pow.f64 y 2) z))
(.f64 (+.f64 1 (.f64 -1/2 (pow.f64 y 2))) z)
(.f64 (+.f64 1 (.f64 -1/2 (pow.f64 y 2))) z)
(.f64 (+.f64 1 (.f64 -1/2 (pow.f64 y 2))) z)
(.f64 (+.f64 1 (.f64 -1/2 (pow.f64 y 2))) z)
(.f64 (+.f64 1 (.f64 -1/2 (pow.f64 y 2))) z)
(.f64 (+.f64 1 (.f64 -1/2 (pow.f64 y 2))) z)
(.f64 (+.f64 1 (.f64 -1/2 (pow.f64 y 2))) z)
(.f64 (+.f64 1 (.f64 -1/2 (pow.f64 y 2))) z)
(.f64 -1 (.f64 (-.f64 (*.f64 1/2 (pow.f64 y 2)) 1) z))
(.f64 -1 (.f64 (-.f64 (*.f64 1/2 (pow.f64 y 2)) 1) z))
(.f64 -1 (.f64 (-.f64 (*.f64 1/2 (pow.f64 y 2)) 1) z))
(.f64 -1 (.f64 (-.f64 (*.f64 1/2 (pow.f64 y 2)) 1) z))
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) z)) z)
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) z)) (+.f64 z (*.f64 (sin.f64 y) x)))
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) z)) (+.f64 z (*.f64 (sin.f64 y) x)))
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) z)) (+.f64 z (*.f64 (sin.f64 y) x)))
(*.f64 (sin.f64 y) x)
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) z)) (+.f64 z (*.f64 (sin.f64 y) x)))
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) z)) (+.f64 z (*.f64 (sin.f64 y) x)))
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) z)) (+.f64 z (*.f64 (sin.f64 y) x)))
(*.f64 (sin.f64 y) x)
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) z)) (+.f64 z (*.f64 (sin.f64 y) x)))
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) z)) (+.f64 z (*.f64 (sin.f64 y) x)))
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) z)) (+.f64 z (*.f64 (sin.f64 y) x)))
z
(+.f64 (*.f64 y x) z)
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) z)) (+.f64 (*.f64 y x) z))
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) z)) (+.f64 (.f64 y x) (+.f64 z (.f64 -1/6 (*.f64 (pow.f64 y 3) x)))))
(.f64 -1/2 (.f64 (pow.f64 y 2) z))
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) z)) (+.f64 z (*.f64 (sin.f64 y) x)))
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) z)) (+.f64 z (*.f64 (sin.f64 y) x)))
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) z)) (+.f64 z (*.f64 (sin.f64 y) x)))
(.f64 -1/2 (.f64 (pow.f64 y 2) z))
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) z)) (+.f64 z (*.f64 (sin.f64 y) x)))
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) z)) (+.f64 z (*.f64 (sin.f64 y) x)))
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) z)) (+.f64 z (*.f64 (sin.f64 y) x)))
(*.f64 (sin.f64 y) x)
(+.f64 (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 y 2))) z) (*.f64 (sin.f64 y) x))
(+.f64 (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 y 2))) z) (*.f64 (sin.f64 y) x))
(+.f64 (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 y 2))) z) (*.f64 (sin.f64 y) x))
(.f64 (+.f64 1 (.f64 -1/2 (pow.f64 y 2))) z)
(+.f64 (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 y 2))) z) (*.f64 (sin.f64 y) x))
(+.f64 (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 y 2))) z) (*.f64 (sin.f64 y) x))
(+.f64 (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 y 2))) z) (*.f64 (sin.f64 y) x))
(.f64 -1 (.f64 (-.f64 (*.f64 1/2 (pow.f64 y 2)) 1) z))
(+.f64 (.f64 -1 (.f64 (-.f64 (.f64 1/2 (pow.f64 y 2)) 1) z)) (.f64 (sin.f64 y) x))
(+.f64 (.f64 -1 (.f64 (-.f64 (.f64 1/2 (pow.f64 y 2)) 1) z)) (.f64 (sin.f64 y) x))
(+.f64 (.f64 -1 (.f64 (-.f64 (.f64 1/2 (pow.f64 y 2)) 1) z)) (.f64 (sin.f64 y) x))

Outputs
z
(.f64 -1/2 (.f64 (pow.f64 y 2) z))
(.f64 -1/2 (.f64 z (*.f64 y y)))
(.f64 z (.f64 -1/2 (*.f64 y y)))
(.f64 y (.f64 y (*.f64 z -1/2)))
(.f64 -1/2 (.f64 (pow.f64 y 2) z))
(.f64 -1/2 (.f64 z (*.f64 y y)))
(.f64 z (.f64 -1/2 (*.f64 y y)))
(.f64 y (.f64 y (*.f64 z -1/2)))
(.f64 (+.f64 1 (.f64 -1/2 (pow.f64 y 2))) z)
(.f64 z (+.f64 1 (.f64 -1/2 (*.f64 y y))))
(.f64 z (fma.f64 -1/2 (.f64 y y) 1))
(fma.f64 z (.f64 -1/2 (.f64 y y)) z)
(fma.f64 y (.f64 y (.f64 z -1/2)) z)
(.f64 (+.f64 1 (.f64 -1/2 (pow.f64 y 2))) z)
(.f64 z (+.f64 1 (.f64 -1/2 (*.f64 y y))))
(.f64 z (fma.f64 -1/2 (.f64 y y) 1))
(fma.f64 z (.f64 -1/2 (.f64 y y)) z)
(fma.f64 y (.f64 y (.f64 z -1/2)) z)
(.f64 (+.f64 1 (.f64 -1/2 (pow.f64 y 2))) z)
(.f64 z (+.f64 1 (.f64 -1/2 (*.f64 y y))))
(.f64 z (fma.f64 -1/2 (.f64 y y) 1))
(fma.f64 z (.f64 -1/2 (.f64 y y)) z)
(fma.f64 y (.f64 y (.f64 z -1/2)) z)
(.f64 (+.f64 1 (.f64 -1/2 (pow.f64 y 2))) z)
(.f64 z (+.f64 1 (.f64 -1/2 (*.f64 y y))))
(.f64 z (fma.f64 -1/2 (.f64 y y) 1))
(fma.f64 z (.f64 -1/2 (.f64 y y)) z)
(fma.f64 y (.f64 y (.f64 z -1/2)) z)
(.f64 (+.f64 1 (.f64 -1/2 (pow.f64 y 2))) z)
(.f64 z (+.f64 1 (.f64 -1/2 (*.f64 y y))))
(.f64 z (fma.f64 -1/2 (.f64 y y) 1))
(fma.f64 z (.f64 -1/2 (.f64 y y)) z)
(fma.f64 y (.f64 y (.f64 z -1/2)) z)
(.f64 (+.f64 1 (.f64 -1/2 (pow.f64 y 2))) z)
(.f64 z (+.f64 1 (.f64 -1/2 (*.f64 y y))))
(.f64 z (fma.f64 -1/2 (.f64 y y) 1))
(fma.f64 z (.f64 -1/2 (.f64 y y)) z)
(fma.f64 y (.f64 y (.f64 z -1/2)) z)
(.f64 (+.f64 1 (.f64 -1/2 (pow.f64 y 2))) z)
(.f64 z (+.f64 1 (.f64 -1/2 (*.f64 y y))))
(.f64 z (fma.f64 -1/2 (.f64 y y) 1))
(fma.f64 z (.f64 -1/2 (.f64 y y)) z)
(fma.f64 y (.f64 y (.f64 z -1/2)) z)
(.f64 (+.f64 1 (.f64 -1/2 (pow.f64 y 2))) z)
(.f64 z (+.f64 1 (.f64 -1/2 (*.f64 y y))))
(.f64 z (fma.f64 -1/2 (.f64 y y) 1))
(fma.f64 z (.f64 -1/2 (.f64 y y)) z)
(fma.f64 y (.f64 y (.f64 z -1/2)) z)
(.f64 -1 (.f64 (-.f64 (*.f64 1/2 (pow.f64 y 2)) 1) z))
(.f64 z (+.f64 1 (.f64 -1/2 (*.f64 y y))))
(.f64 z (fma.f64 -1/2 (.f64 y y) 1))
(fma.f64 z (.f64 -1/2 (.f64 y y)) z)
(fma.f64 y (.f64 y (.f64 z -1/2)) z)
(.f64 -1 (.f64 (-.f64 (*.f64 1/2 (pow.f64 y 2)) 1) z))
(.f64 z (+.f64 1 (.f64 -1/2 (*.f64 y y))))
(.f64 z (fma.f64 -1/2 (.f64 y y) 1))
(fma.f64 z (.f64 -1/2 (.f64 y y)) z)
(fma.f64 y (.f64 y (.f64 z -1/2)) z)
(.f64 -1 (.f64 (-.f64 (*.f64 1/2 (pow.f64 y 2)) 1) z))
(.f64 z (+.f64 1 (.f64 -1/2 (*.f64 y y))))
(.f64 z (fma.f64 -1/2 (.f64 y y) 1))
(fma.f64 z (.f64 -1/2 (.f64 y y)) z)
(fma.f64 y (.f64 y (.f64 z -1/2)) z)
(.f64 -1 (.f64 (-.f64 (*.f64 1/2 (pow.f64 y 2)) 1) z))
(.f64 z (+.f64 1 (.f64 -1/2 (*.f64 y y))))
(.f64 z (fma.f64 -1/2 (.f64 y y) 1))
(fma.f64 z (.f64 -1/2 (.f64 y y)) z)
(fma.f64 y (.f64 y (.f64 z -1/2)) z)
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) z)) z)
(.f64 z (+.f64 1 (.f64 -1/2 (*.f64 y y))))
(.f64 z (fma.f64 -1/2 (.f64 y y) 1))
(fma.f64 z (.f64 -1/2 (.f64 y y)) z)
(fma.f64 y (.f64 y (.f64 z -1/2)) z)
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) z)) (+.f64 z (*.f64 (sin.f64 y) x)))
(fma.f64 -1/2 (.f64 z (.f64 y y)) (+.f64 z (*.f64 (sin.f64 y) x)))
(fma.f64 z (fma.f64 -1/2 (.f64 y y) 1) (.f64 (sin.f64 y) x))
(fma.f64 z (.f64 -1/2 (.f64 y y)) (fma.f64 (sin.f64 y) x z))
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) z)) (+.f64 z (*.f64 (sin.f64 y) x)))
(fma.f64 -1/2 (.f64 z (.f64 y y)) (+.f64 z (*.f64 (sin.f64 y) x)))
(fma.f64 z (fma.f64 -1/2 (.f64 y y) 1) (.f64 (sin.f64 y) x))
(fma.f64 z (.f64 -1/2 (.f64 y y)) (fma.f64 (sin.f64 y) x z))
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) z)) (+.f64 z (*.f64 (sin.f64 y) x)))
(fma.f64 -1/2 (.f64 z (.f64 y y)) (+.f64 z (*.f64 (sin.f64 y) x)))
(fma.f64 z (fma.f64 -1/2 (.f64 y y) 1) (.f64 (sin.f64 y) x))
(fma.f64 z (.f64 -1/2 (.f64 y y)) (fma.f64 (sin.f64 y) x z))
(*.f64 (sin.f64 y) x)
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) z)) (+.f64 z (*.f64 (sin.f64 y) x)))
(fma.f64 -1/2 (.f64 z (.f64 y y)) (+.f64 z (*.f64 (sin.f64 y) x)))
(fma.f64 z (fma.f64 -1/2 (.f64 y y) 1) (.f64 (sin.f64 y) x))
(fma.f64 z (.f64 -1/2 (.f64 y y)) (fma.f64 (sin.f64 y) x z))
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) z)) (+.f64 z (*.f64 (sin.f64 y) x)))
(fma.f64 -1/2 (.f64 z (.f64 y y)) (+.f64 z (*.f64 (sin.f64 y) x)))
(fma.f64 z (fma.f64 -1/2 (.f64 y y) 1) (.f64 (sin.f64 y) x))
(fma.f64 z (.f64 -1/2 (.f64 y y)) (fma.f64 (sin.f64 y) x z))
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) z)) (+.f64 z (*.f64 (sin.f64 y) x)))
(fma.f64 -1/2 (.f64 z (.f64 y y)) (+.f64 z (*.f64 (sin.f64 y) x)))
(fma.f64 z (fma.f64 -1/2 (.f64 y y) 1) (.f64 (sin.f64 y) x))
(fma.f64 z (.f64 -1/2 (.f64 y y)) (fma.f64 (sin.f64 y) x z))
(*.f64 (sin.f64 y) x)
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) z)) (+.f64 z (*.f64 (sin.f64 y) x)))
(fma.f64 -1/2 (.f64 z (.f64 y y)) (+.f64 z (*.f64 (sin.f64 y) x)))
(fma.f64 z (fma.f64 -1/2 (.f64 y y) 1) (.f64 (sin.f64 y) x))
(fma.f64 z (.f64 -1/2 (.f64 y y)) (fma.f64 (sin.f64 y) x z))
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) z)) (+.f64 z (*.f64 (sin.f64 y) x)))
(fma.f64 -1/2 (.f64 z (.f64 y y)) (+.f64 z (*.f64 (sin.f64 y) x)))
(fma.f64 z (fma.f64 -1/2 (.f64 y y) 1) (.f64 (sin.f64 y) x))
(fma.f64 z (.f64 -1/2 (.f64 y y)) (fma.f64 (sin.f64 y) x z))
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) z)) (+.f64 z (*.f64 (sin.f64 y) x)))
(fma.f64 -1/2 (.f64 z (.f64 y y)) (+.f64 z (*.f64 (sin.f64 y) x)))
(fma.f64 z (fma.f64 -1/2 (.f64 y y) 1) (.f64 (sin.f64 y) x))
(fma.f64 z (.f64 -1/2 (.f64 y y)) (fma.f64 (sin.f64 y) x z))
z
(+.f64 (*.f64 y x) z)
(fma.f64 y x z)
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) z)) (+.f64 (*.f64 y x) z))
(fma.f64 -1/2 (.f64 z (.f64 y y)) (fma.f64 y x z))
(fma.f64 z (.f64 -1/2 (.f64 y y)) (fma.f64 y x z))
(fma.f64 z (fma.f64 -1/2 (.f64 y y) 1) (.f64 y x))
(fma.f64 y (+.f64 x (.f64 y (.f64 z -1/2))) z)
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) z)) (+.f64 (.f64 y x) (+.f64 z (.f64 -1/6 (*.f64 (pow.f64 y 3) x)))))
(fma.f64 -1/2 (.f64 z (.f64 y y)) (+.f64 (fma.f64 y x z) (.f64 -1/6 (.f64 x (pow.f64 y 3)))))
(fma.f64 -1/2 (.f64 z (.f64 y y)) (fma.f64 y x (fma.f64 -1/6 (*.f64 x (pow.f64 y 3)) z)))
(fma.f64 y x (fma.f64 z (.f64 -1/2 (.f64 y y)) (fma.f64 x (*.f64 -1/6 (pow.f64 y 3)) z)))
(fma.f64 z (fma.f64 -1/2 (.f64 y y) 1) (.f64 x (fma.f64 -1/6 (pow.f64 y 3) y)))
(fma.f64 z (.f64 -1/2 (.f64 y y)) (fma.f64 x (fma.f64 -1/6 (pow.f64 y 3) y) z))
(.f64 -1/2 (.f64 (pow.f64 y 2) z))
(.f64 -1/2 (.f64 z (*.f64 y y)))
(.f64 z (.f64 -1/2 (*.f64 y y)))
(.f64 y (.f64 y (*.f64 z -1/2)))
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) z)) (+.f64 z (*.f64 (sin.f64 y) x)))
(fma.f64 -1/2 (.f64 z (.f64 y y)) (+.f64 z (*.f64 (sin.f64 y) x)))
(fma.f64 z (fma.f64 -1/2 (.f64 y y) 1) (.f64 (sin.f64 y) x))
(fma.f64 z (.f64 -1/2 (.f64 y y)) (fma.f64 (sin.f64 y) x z))
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) z)) (+.f64 z (*.f64 (sin.f64 y) x)))
(fma.f64 -1/2 (.f64 z (.f64 y y)) (+.f64 z (*.f64 (sin.f64 y) x)))
(fma.f64 z (fma.f64 -1/2 (.f64 y y) 1) (.f64 (sin.f64 y) x))
(fma.f64 z (.f64 -1/2 (.f64 y y)) (fma.f64 (sin.f64 y) x z))
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) z)) (+.f64 z (*.f64 (sin.f64 y) x)))
(fma.f64 -1/2 (.f64 z (.f64 y y)) (+.f64 z (*.f64 (sin.f64 y) x)))
(fma.f64 z (fma.f64 -1/2 (.f64 y y) 1) (.f64 (sin.f64 y) x))
(fma.f64 z (.f64 -1/2 (.f64 y y)) (fma.f64 (sin.f64 y) x z))
(.f64 -1/2 (.f64 (pow.f64 y 2) z))
(.f64 -1/2 (.f64 z (*.f64 y y)))
(.f64 z (.f64 -1/2 (*.f64 y y)))
(.f64 y (.f64 y (*.f64 z -1/2)))
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) z)) (+.f64 z (*.f64 (sin.f64 y) x)))
(fma.f64 -1/2 (.f64 z (.f64 y y)) (+.f64 z (*.f64 (sin.f64 y) x)))
(fma.f64 z (fma.f64 -1/2 (.f64 y y) 1) (.f64 (sin.f64 y) x))
(fma.f64 z (.f64 -1/2 (.f64 y y)) (fma.f64 (sin.f64 y) x z))
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) z)) (+.f64 z (*.f64 (sin.f64 y) x)))
(fma.f64 -1/2 (.f64 z (.f64 y y)) (+.f64 z (*.f64 (sin.f64 y) x)))
(fma.f64 z (fma.f64 -1/2 (.f64 y y) 1) (.f64 (sin.f64 y) x))
(fma.f64 z (.f64 -1/2 (.f64 y y)) (fma.f64 (sin.f64 y) x z))
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) z)) (+.f64 z (*.f64 (sin.f64 y) x)))
(fma.f64 -1/2 (.f64 z (.f64 y y)) (+.f64 z (*.f64 (sin.f64 y) x)))
(fma.f64 z (fma.f64 -1/2 (.f64 y y) 1) (.f64 (sin.f64 y) x))
(fma.f64 z (.f64 -1/2 (.f64 y y)) (fma.f64 (sin.f64 y) x z))
(*.f64 (sin.f64 y) x)
(+.f64 (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 y 2))) z) (*.f64 (sin.f64 y) x))
(fma.f64 -1/2 (.f64 z (.f64 y y)) (+.f64 z (*.f64 (sin.f64 y) x)))
(fma.f64 z (fma.f64 -1/2 (.f64 y y) 1) (.f64 (sin.f64 y) x))
(fma.f64 z (.f64 -1/2 (.f64 y y)) (fma.f64 (sin.f64 y) x z))
(+.f64 (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 y 2))) z) (*.f64 (sin.f64 y) x))
(fma.f64 -1/2 (.f64 z (.f64 y y)) (+.f64 z (*.f64 (sin.f64 y) x)))
(fma.f64 z (fma.f64 -1/2 (.f64 y y) 1) (.f64 (sin.f64 y) x))
(fma.f64 z (.f64 -1/2 (.f64 y y)) (fma.f64 (sin.f64 y) x z))
(+.f64 (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 y 2))) z) (*.f64 (sin.f64 y) x))
(fma.f64 -1/2 (.f64 z (.f64 y y)) (+.f64 z (*.f64 (sin.f64 y) x)))
(fma.f64 z (fma.f64 -1/2 (.f64 y y) 1) (.f64 (sin.f64 y) x))
(fma.f64 z (.f64 -1/2 (.f64 y y)) (fma.f64 (sin.f64 y) x z))
(.f64 (+.f64 1 (.f64 -1/2 (pow.f64 y 2))) z)
(.f64 z (+.f64 1 (.f64 -1/2 (*.f64 y y))))
(.f64 z (fma.f64 -1/2 (.f64 y y) 1))
(fma.f64 z (.f64 -1/2 (.f64 y y)) z)
(fma.f64 y (.f64 y (.f64 z -1/2)) z)
(+.f64 (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 y 2))) z) (*.f64 (sin.f64 y) x))
(fma.f64 -1/2 (.f64 z (.f64 y y)) (+.f64 z (*.f64 (sin.f64 y) x)))
(fma.f64 z (fma.f64 -1/2 (.f64 y y) 1) (.f64 (sin.f64 y) x))
(fma.f64 z (.f64 -1/2 (.f64 y y)) (fma.f64 (sin.f64 y) x z))
(+.f64 (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 y 2))) z) (*.f64 (sin.f64 y) x))
(fma.f64 -1/2 (.f64 z (.f64 y y)) (+.f64 z (*.f64 (sin.f64 y) x)))
(fma.f64 z (fma.f64 -1/2 (.f64 y y) 1) (.f64 (sin.f64 y) x))
(fma.f64 z (.f64 -1/2 (.f64 y y)) (fma.f64 (sin.f64 y) x z))
(+.f64 (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 y 2))) z) (*.f64 (sin.f64 y) x))
(fma.f64 -1/2 (.f64 z (.f64 y y)) (+.f64 z (*.f64 (sin.f64 y) x)))
(fma.f64 z (fma.f64 -1/2 (.f64 y y) 1) (.f64 (sin.f64 y) x))
(fma.f64 z (.f64 -1/2 (.f64 y y)) (fma.f64 (sin.f64 y) x z))
(.f64 -1 (.f64 (-.f64 (*.f64 1/2 (pow.f64 y 2)) 1) z))
(.f64 z (+.f64 1 (.f64 -1/2 (*.f64 y y))))
(.f64 z (fma.f64 -1/2 (.f64 y y) 1))
(fma.f64 z (.f64 -1/2 (.f64 y y)) z)
(fma.f64 y (.f64 y (.f64 z -1/2)) z)
(+.f64 (.f64 -1 (.f64 (-.f64 (.f64 1/2 (pow.f64 y 2)) 1) z)) (.f64 (sin.f64 y) x))
(fma.f64 -1/2 (.f64 z (.f64 y y)) (+.f64 z (*.f64 (sin.f64 y) x)))
(fma.f64 z (fma.f64 -1/2 (.f64 y y) 1) (.f64 (sin.f64 y) x))
(fma.f64 z (.f64 -1/2 (.f64 y y)) (fma.f64 (sin.f64 y) x z))
(+.f64 (.f64 -1 (.f64 (-.f64 (.f64 1/2 (pow.f64 y 2)) 1) z)) (.f64 (sin.f64 y) x))
(fma.f64 -1/2 (.f64 z (.f64 y y)) (+.f64 z (*.f64 (sin.f64 y) x)))
(fma.f64 z (fma.f64 -1/2 (.f64 y y) 1) (.f64 (sin.f64 y) x))
(fma.f64 z (.f64 -1/2 (.f64 y y)) (fma.f64 (sin.f64 y) x z))
(+.f64 (.f64 -1 (.f64 (-.f64 (.f64 1/2 (pow.f64 y 2)) 1) z)) (.f64 (sin.f64 y) x))
(fma.f64 -1/2 (.f64 z (.f64 y y)) (+.f64 z (*.f64 (sin.f64 y) x)))
(fma.f64 z (fma.f64 -1/2 (.f64 y y) 1) (.f64 (sin.f64 y) x))
(fma.f64 z (.f64 -1/2 (.f64 y y)) (fma.f64 (sin.f64 y) x z))

localize60.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.f64 x (sin.f64 y))
	0.1b	(*.f64 z (cos.f64 y))
✓	0.6b	(cbrt.f64 (*.f64 z (cos.f64 y)))
✓	0.8b	(pow.f64 (cbrt.f64 (*.f64 z (cos.f64 y))) 3)

Compiler

Compiled 43 to 14 computations (67.4% saved)

series30.0ms (0.3%)

Counts

2 → 24

Calls

12 calls:

Time	Variable		Point	Expression
11.0ms	y	@	0	(pow.f64 (cbrt.f64 (*.f64 z (cos.f64 y))) 3)
4.0ms	y	@	inf	(pow.f64 (cbrt.f64 (*.f64 z (cos.f64 y))) 3)
4.0ms	y	@	-inf	(pow.f64 (cbrt.f64 (*.f64 z (cos.f64 y))) 3)
2.0ms	z	@	-inf	(pow.f64 (cbrt.f64 (*.f64 z (cos.f64 y))) 3)
2.0ms	z	@	inf	(pow.f64 (cbrt.f64 (*.f64 z (cos.f64 y))) 3)

rewrite97.0ms (1%)

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
(pow.f64 (cbrt.f64 (*.f64 z (cos.f64 y))) 3)
(cbrt.f64 (*.f64 z (cos.f64 y)))

Outputs

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

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

simplify56.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

694×	`associate-r_binary64`
686×	`associate-l_binary64`
551×	`fma-def_binary64`
428×	`distribute-rgt-out_binary64`
229×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	89	496
1	286	453
2	979	401
3	5892	392

Stop Event

1×	node limit

Counts

76 → 71

Calls

Call 1

Inputs
(*.f64 (pow.f64 1 1/3) z)
(+.f64 (.f64 (+.f64 (.f64 -1/3 (.f64 (pow.f64 1 1/3) z)) (.f64 -1/6 (.f64 (pow.f64 1 1/3) z))) (pow.f64 y 2)) (.f64 (pow.f64 1 1/3) z))
(+.f64 (.f64 (+.f64 (.f64 -1/3 (.f64 (pow.f64 1 1/3) z)) (.f64 -1/6 (.f64 (pow.f64 1 1/3) z))) (pow.f64 y 2)) (+.f64 (.f64 (+.f64 (.f64 1/3 (.f64 (pow.f64 1 1/3) (-.f64 (.f64 1/24 z) (.f64 1/12 z)))) (+.f64 (.f64 (pow.f64 (.f64 1 z) 1/3) (+.f64 (.f64 2/3 (.f64 (pow.f64 (/.f64 1 z) 1/3) (-.f64 (.f64 1/24 z) (.f64 1/12 z)))) (.f64 1/36 (pow.f64 (.f64 1 (pow.f64 z 2)) 1/3)))) (.f64 1/18 (.f64 (pow.f64 1 1/3) z)))) (pow.f64 y 4)) (*.f64 (pow.f64 1 1/3) z)))
(+.f64 (.f64 (+.f64 (.f64 (pow.f64 (.f64 1 z) 1/3) (+.f64 (.f64 2/3 (.f64 (pow.f64 (/.f64 1 z) 1/3) (-.f64 (.f64 -1/720 z) (+.f64 (.f64 -1/216 z) (.f64 -1/3 (-.f64 (.f64 1/24 z) (.f64 1/12 z))))))) (.f64 -1/9 (.f64 (pow.f64 (/.f64 1 z) 1/3) (-.f64 (.f64 1/24 z) (.f64 1/12 z)))))) (+.f64 (.f64 1/3 (.f64 (pow.f64 1 1/3) (-.f64 (.f64 -1/720 z) (+.f64 (.f64 -1/216 z) (.f64 -1/3 (-.f64 (.f64 1/24 z) (.f64 1/12 z))))))) (+.f64 (.f64 -1/6 (.f64 (pow.f64 (.f64 1 z) 1/3) (+.f64 (.f64 2/3 (.f64 (pow.f64 (/.f64 1 z) 1/3) (-.f64 (.f64 1/24 z) (.f64 1/12 z)))) (.f64 1/36 (pow.f64 (.f64 1 (pow.f64 z 2)) 1/3))))) (.f64 -1/9 (.f64 (pow.f64 1 1/3) (-.f64 (.f64 1/24 z) (.f64 1/12 z))))))) (pow.f64 y 6)) (+.f64 (.f64 (+.f64 (.f64 -1/3 (.f64 (pow.f64 1 1/3) z)) (.f64 -1/6 (.f64 (pow.f64 1 1/3) z))) (pow.f64 y 2)) (+.f64 (.f64 (+.f64 (.f64 1/3 (.f64 (pow.f64 1 1/3) (-.f64 (.f64 1/24 z) (.f64 1/12 z)))) (+.f64 (.f64 (pow.f64 (.f64 1 z) 1/3) (+.f64 (.f64 2/3 (.f64 (pow.f64 (/.f64 1 z) 1/3) (-.f64 (.f64 1/24 z) (.f64 1/12 z)))) (.f64 1/36 (pow.f64 (.f64 1 (pow.f64 z 2)) 1/3)))) (.f64 1/18 (.f64 (pow.f64 1 1/3) z)))) (pow.f64 y 4)) (*.f64 (pow.f64 1 1/3) z))))
(.f64 (pow.f64 1 1/3) (.f64 z (cos.f64 y)))
(.f64 (pow.f64 1 1/3) (.f64 z (cos.f64 y)))
(.f64 (pow.f64 1 1/3) (.f64 z (cos.f64 y)))
(.f64 (pow.f64 1 1/3) (.f64 z (cos.f64 y)))
(.f64 (pow.f64 1 1/3) (.f64 z (cos.f64 y)))
(.f64 (pow.f64 1 1/3) (.f64 z (cos.f64 y)))
(.f64 (pow.f64 1 1/3) (.f64 z (cos.f64 y)))
(.f64 (pow.f64 1 1/3) (.f64 z (cos.f64 y)))
(pow.f64 z 1/3)
(+.f64 (pow.f64 z 1/3) (.f64 -1/6 (.f64 (pow.f64 (*.f64 1 z) 1/3) (pow.f64 y 2))))
(+.f64 (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 z 2)) 1/3) (.f64 (pow.f64 y 4) (-.f64 (.f64 1/24 z) (.f64 1/12 z))))) (+.f64 (pow.f64 z 1/3) (.f64 -1/6 (.f64 (pow.f64 (.f64 1 z) 1/3) (pow.f64 y 2)))))
(+.f64 (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 z 2)) 1/3) (.f64 (pow.f64 y 6) (-.f64 (.f64 -1/720 z) (+.f64 (.f64 -1/216 z) (.f64 -1/3 (-.f64 (.f64 1/24 z) (.f64 1/12 z)))))))) (+.f64 (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 z 2)) 1/3) (.f64 (pow.f64 y 4) (-.f64 (.f64 1/24 z) (.f64 1/12 z))))) (+.f64 (pow.f64 z 1/3) (.f64 -1/6 (.f64 (pow.f64 (.f64 1 z) 1/3) (pow.f64 y 2))))))
(pow.f64 (*.f64 (cos.f64 y) z) 1/3)
(pow.f64 (*.f64 (cos.f64 y) z) 1/3)
(pow.f64 (*.f64 (cos.f64 y) z) 1/3)
(pow.f64 (*.f64 (cos.f64 y) z) 1/3)
(pow.f64 (*.f64 (cos.f64 y) z) 1/3)
(pow.f64 (*.f64 (cos.f64 y) z) 1/3)
(pow.f64 (*.f64 (cos.f64 y) z) 1/3)
(pow.f64 (*.f64 (cos.f64 y) z) 1/3)

Outputs
(*.f64 (pow.f64 1 1/3) z)
z
(+.f64 (.f64 (+.f64 (.f64 -1/3 (.f64 (pow.f64 1 1/3) z)) (.f64 -1/6 (.f64 (pow.f64 1 1/3) z))) (pow.f64 y 2)) (.f64 (pow.f64 1 1/3) z))
(fma.f64 (.f64 z -1/2) (.f64 y y) z)
(fma.f64 z (.f64 (.f64 y y) -1/2) z)
(+.f64 (.f64 (+.f64 (.f64 -1/3 (.f64 (pow.f64 1 1/3) z)) (.f64 -1/6 (.f64 (pow.f64 1 1/3) z))) (pow.f64 y 2)) (+.f64 (.f64 (+.f64 (.f64 1/3 (.f64 (pow.f64 1 1/3) (-.f64 (.f64 1/24 z) (.f64 1/12 z)))) (+.f64 (.f64 (pow.f64 (.f64 1 z) 1/3) (+.f64 (.f64 2/3 (.f64 (pow.f64 (/.f64 1 z) 1/3) (-.f64 (.f64 1/24 z) (.f64 1/12 z)))) (.f64 1/36 (pow.f64 (.f64 1 (pow.f64 z 2)) 1/3)))) (.f64 1/18 (.f64 (pow.f64 1 1/3) z)))) (pow.f64 y 4)) (*.f64 (pow.f64 1 1/3) z)))
(fma.f64 (.f64 z -1/2) (.f64 y y) (fma.f64 (+.f64 (.f64 1/3 (.f64 z -1/24)) (fma.f64 (cbrt.f64 z) (fma.f64 2/3 (.f64 (.f64 z -1/24) (cbrt.f64 (/.f64 1 z))) (.f64 1/36 (cbrt.f64 (.f64 z z)))) (*.f64 z 1/18))) (pow.f64 y 4) z))
(fma.f64 (.f64 z -1/2) (.f64 y y) (fma.f64 (fma.f64 1/3 (.f64 z -1/24) (fma.f64 (cbrt.f64 z) (fma.f64 2/3 (.f64 z (.f64 -1/24 (cbrt.f64 (/.f64 1 z)))) (.f64 1/36 (cbrt.f64 (.f64 z z)))) (.f64 z 1/18))) (pow.f64 y 4) z))
(fma.f64 (fma.f64 z 1/18 (fma.f64 (cbrt.f64 z) (fma.f64 (cbrt.f64 (/.f64 1 z)) (.f64 z -1/36) (.f64 1/36 (cbrt.f64 (.f64 z z)))) (.f64 z -1/72))) (pow.f64 y 4) (fma.f64 z (.f64 (.f64 y y) -1/2) z))
(fma.f64 (fma.f64 (cbrt.f64 z) (fma.f64 (cbrt.f64 (/.f64 1 z)) (.f64 z -1/36) (.f64 1/36 (cbrt.f64 (.f64 z z)))) (.f64 z 1/24)) (pow.f64 y 4) (fma.f64 z (.f64 (.f64 y y) -1/2) z))
(+.f64 (.f64 (+.f64 (.f64 (pow.f64 (.f64 1 z) 1/3) (+.f64 (.f64 2/3 (.f64 (pow.f64 (/.f64 1 z) 1/3) (-.f64 (.f64 -1/720 z) (+.f64 (.f64 -1/216 z) (.f64 -1/3 (-.f64 (.f64 1/24 z) (.f64 1/12 z))))))) (.f64 -1/9 (.f64 (pow.f64 (/.f64 1 z) 1/3) (-.f64 (.f64 1/24 z) (.f64 1/12 z)))))) (+.f64 (.f64 1/3 (.f64 (pow.f64 1 1/3) (-.f64 (.f64 -1/720 z) (+.f64 (.f64 -1/216 z) (.f64 -1/3 (-.f64 (.f64 1/24 z) (.f64 1/12 z))))))) (+.f64 (.f64 -1/6 (.f64 (pow.f64 (.f64 1 z) 1/3) (+.f64 (.f64 2/3 (.f64 (pow.f64 (/.f64 1 z) 1/3) (-.f64 (.f64 1/24 z) (.f64 1/12 z)))) (.f64 1/36 (pow.f64 (.f64 1 (pow.f64 z 2)) 1/3))))) (.f64 -1/9 (.f64 (pow.f64 1 1/3) (-.f64 (.f64 1/24 z) (.f64 1/12 z))))))) (pow.f64 y 6)) (+.f64 (.f64 (+.f64 (.f64 -1/3 (.f64 (pow.f64 1 1/3) z)) (.f64 -1/6 (.f64 (pow.f64 1 1/3) z))) (pow.f64 y 2)) (+.f64 (.f64 (+.f64 (.f64 1/3 (.f64 (pow.f64 1 1/3) (-.f64 (.f64 1/24 z) (.f64 1/12 z)))) (+.f64 (.f64 (pow.f64 (.f64 1 z) 1/3) (+.f64 (.f64 2/3 (.f64 (pow.f64 (/.f64 1 z) 1/3) (-.f64 (.f64 1/24 z) (.f64 1/12 z)))) (.f64 1/36 (pow.f64 (.f64 1 (pow.f64 z 2)) 1/3)))) (.f64 1/18 (.f64 (pow.f64 1 1/3) z)))) (pow.f64 y 4)) (*.f64 (pow.f64 1 1/3) z))))
(fma.f64 (fma.f64 (cbrt.f64 z) (fma.f64 2/3 (.f64 (cbrt.f64 (/.f64 1 z)) (-.f64 (.f64 z -1/720) (fma.f64 -1/216 z (.f64 -1/3 (.f64 z -1/24))))) (.f64 (.f64 (.f64 z -1/24) (cbrt.f64 (/.f64 1 z))) -1/9)) (+.f64 (.f64 1/3 (-.f64 (.f64 z -1/720) (fma.f64 -1/216 z (.f64 -1/3 (.f64 z -1/24))))) (fma.f64 -1/6 (.f64 (cbrt.f64 z) (fma.f64 2/3 (.f64 (.f64 z -1/24) (cbrt.f64 (/.f64 1 z))) (.f64 1/36 (cbrt.f64 (.f64 z z))))) (.f64 -1/9 (.f64 z -1/24))))) (pow.f64 y 6) (fma.f64 (.f64 z -1/2) (.f64 y y) (fma.f64 (+.f64 (.f64 1/3 (.f64 z -1/24)) (fma.f64 (cbrt.f64 z) (fma.f64 2/3 (.f64 (.f64 z -1/24) (cbrt.f64 (/.f64 1 z))) (.f64 1/36 (cbrt.f64 (.f64 z z)))) (*.f64 z 1/18))) (pow.f64 y 4) z)))
(fma.f64 (fma.f64 (cbrt.f64 z) (fma.f64 2/3 (.f64 (cbrt.f64 (/.f64 1 z)) (-.f64 (.f64 z 7/2160) (.f64 z 1/72))) (.f64 (cbrt.f64 (/.f64 1 z)) (.f64 (.f64 -1/9 z) -1/24))) (fma.f64 1/3 (-.f64 (.f64 z 7/2160) (.f64 z 1/72)) (fma.f64 (.f64 -1/6 (cbrt.f64 z)) (fma.f64 2/3 (.f64 z (.f64 -1/24 (cbrt.f64 (/.f64 1 z)))) (.f64 1/36 (cbrt.f64 (.f64 z z)))) (.f64 (.f64 -1/9 z) -1/24)))) (pow.f64 y 6) (fma.f64 (.f64 z -1/2) (.f64 y y) (fma.f64 (fma.f64 1/3 (.f64 z -1/24) (fma.f64 (cbrt.f64 z) (fma.f64 2/3 (.f64 z (.f64 -1/24 (cbrt.f64 (/.f64 1 z)))) (.f64 1/36 (cbrt.f64 (.f64 z z)))) (*.f64 z 1/18))) (pow.f64 y 4) z)))
(fma.f64 z (.f64 (.f64 y y) -1/2) (fma.f64 (fma.f64 1/3 (.f64 z -23/2160) (fma.f64 (cbrt.f64 z) (.f64 (cbrt.f64 (/.f64 1 z)) (+.f64 (.f64 2/3 (.f64 z -23/2160)) (.f64 z 1/216))) (fma.f64 (fma.f64 (cbrt.f64 (/.f64 1 z)) (.f64 z -1/36) (.f64 1/36 (cbrt.f64 (.f64 z z)))) (.f64 -1/6 (cbrt.f64 z)) (.f64 z 1/216)))) (pow.f64 y 6) (fma.f64 (fma.f64 z 1/18 (fma.f64 (cbrt.f64 z) (fma.f64 (cbrt.f64 (/.f64 1 z)) (.f64 z -1/36) (.f64 1/36 (cbrt.f64 (.f64 z z)))) (.f64 z -1/72))) (pow.f64 y 4) z)))
(fma.f64 z (.f64 (.f64 y y) -1/2) (fma.f64 (+.f64 (.f64 (cbrt.f64 z) (+.f64 (.f64 (cbrt.f64 (/.f64 1 z)) (+.f64 (.f64 2/3 (.f64 z -23/2160)) (.f64 z 1/216))) (.f64 -1/6 (fma.f64 (cbrt.f64 (/.f64 1 z)) (.f64 z -1/36) (.f64 1/36 (cbrt.f64 (.f64 z z))))))) (fma.f64 1/3 (.f64 z -23/2160) (.f64 z 1/216))) (pow.f64 y 6) (fma.f64 (fma.f64 (cbrt.f64 z) (fma.f64 (cbrt.f64 (/.f64 1 z)) (.f64 z -1/36) (.f64 1/36 (cbrt.f64 (.f64 z z)))) (*.f64 z 1/24)) (pow.f64 y 4) z)))
(.f64 (pow.f64 1 1/3) (.f64 z (cos.f64 y)))
(*.f64 z (cos.f64 y))
(.f64 (pow.f64 1 1/3) (.f64 z (cos.f64 y)))
(*.f64 z (cos.f64 y))
(.f64 (pow.f64 1 1/3) (.f64 z (cos.f64 y)))
(*.f64 z (cos.f64 y))
(.f64 (pow.f64 1 1/3) (.f64 z (cos.f64 y)))
(*.f64 z (cos.f64 y))
(.f64 (pow.f64 1 1/3) (.f64 z (cos.f64 y)))
(*.f64 z (cos.f64 y))
(.f64 (pow.f64 1 1/3) (.f64 z (cos.f64 y)))
(*.f64 z (cos.f64 y))
(.f64 (pow.f64 1 1/3) (.f64 z (cos.f64 y)))
(*.f64 z (cos.f64 y))
(.f64 (pow.f64 1 1/3) (.f64 z (cos.f64 y)))
(*.f64 z (cos.f64 y))
(pow.f64 z 1/3)
(cbrt.f64 z)
(+.f64 (pow.f64 z 1/3) (.f64 -1/6 (.f64 (pow.f64 (*.f64 1 z) 1/3) (pow.f64 y 2))))
(+.f64 (cbrt.f64 z) (.f64 -1/6 (.f64 (*.f64 y y) (cbrt.f64 z))))
(fma.f64 -1/6 (.f64 y (.f64 y (cbrt.f64 z))) (cbrt.f64 z))
(fma.f64 -1/6 (.f64 (.f64 y y) (cbrt.f64 z)) (cbrt.f64 z))
(+.f64 (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 z 2)) 1/3) (.f64 (pow.f64 y 4) (-.f64 (.f64 1/24 z) (.f64 1/12 z))))) (+.f64 (pow.f64 z 1/3) (.f64 -1/6 (.f64 (pow.f64 (.f64 1 z) 1/3) (pow.f64 y 2)))))
(fma.f64 1/3 (.f64 (cbrt.f64 (/.f64 1 (.f64 z z))) (.f64 (.f64 z -1/24) (pow.f64 y 4))) (+.f64 (cbrt.f64 z) (.f64 -1/6 (.f64 (*.f64 y y) (cbrt.f64 z)))))
(fma.f64 1/3 (.f64 (.f64 z -1/24) (.f64 (pow.f64 y 4) (cbrt.f64 (/.f64 1 (.f64 z z))))) (fma.f64 -1/6 (.f64 y (.f64 y (cbrt.f64 z))) (cbrt.f64 z)))
(fma.f64 -1/6 (.f64 (.f64 y y) (cbrt.f64 z)) (fma.f64 (cbrt.f64 (/.f64 1 (.f64 z z))) (.f64 (*.f64 z -1/72) (pow.f64 y 4)) (cbrt.f64 z)))
(+.f64 (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 z 2)) 1/3) (.f64 (pow.f64 y 6) (-.f64 (.f64 -1/720 z) (+.f64 (.f64 -1/216 z) (.f64 -1/3 (-.f64 (.f64 1/24 z) (.f64 1/12 z)))))))) (+.f64 (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 z 2)) 1/3) (.f64 (pow.f64 y 4) (-.f64 (.f64 1/24 z) (.f64 1/12 z))))) (+.f64 (pow.f64 z 1/3) (.f64 -1/6 (.f64 (pow.f64 (.f64 1 z) 1/3) (pow.f64 y 2))))))
(fma.f64 1/3 (.f64 (cbrt.f64 (/.f64 1 (.f64 z z))) (.f64 (-.f64 (.f64 z -1/720) (fma.f64 -1/216 z (.f64 -1/3 (.f64 z -1/24)))) (pow.f64 y 6))) (fma.f64 1/3 (.f64 (cbrt.f64 (/.f64 1 (.f64 z z))) (.f64 (.f64 z -1/24) (pow.f64 y 4))) (+.f64 (cbrt.f64 z) (.f64 -1/6 (.f64 (*.f64 y y) (cbrt.f64 z))))))
(+.f64 (fma.f64 -1/6 (.f64 y (.f64 y (cbrt.f64 z))) (cbrt.f64 z)) (.f64 (.f64 1/3 (cbrt.f64 (/.f64 1 (.f64 z z)))) (+.f64 (.f64 (-.f64 (.f64 z 7/2160) (.f64 z 1/72)) (pow.f64 y 6)) (.f64 z (.f64 -1/24 (pow.f64 y 4))))))
(fma.f64 (.f64 1/3 (cbrt.f64 (/.f64 1 (.f64 z z)))) (fma.f64 (.f64 z -23/2160) (pow.f64 y 6) (.f64 z (.f64 (pow.f64 y 4) -1/24))) (fma.f64 -1/6 (.f64 (*.f64 y y) (cbrt.f64 z)) (cbrt.f64 z)))
(pow.f64 (*.f64 (cos.f64 y) z) 1/3)
(cbrt.f64 (*.f64 z (cos.f64 y)))
(pow.f64 (*.f64 (cos.f64 y) z) 1/3)
(cbrt.f64 (*.f64 z (cos.f64 y)))
(pow.f64 (*.f64 (cos.f64 y) z) 1/3)
(cbrt.f64 (*.f64 z (cos.f64 y)))
(pow.f64 (*.f64 (cos.f64 y) z) 1/3)
(cbrt.f64 (*.f64 z (cos.f64 y)))
(pow.f64 (*.f64 (cos.f64 y) z) 1/3)
(cbrt.f64 (*.f64 z (cos.f64 y)))
(pow.f64 (*.f64 (cos.f64 y) z) 1/3)
(cbrt.f64 (*.f64 z (cos.f64 y)))
(pow.f64 (*.f64 (cos.f64 y) z) 1/3)
(cbrt.f64 (*.f64 z (cos.f64 y)))
(pow.f64 (*.f64 (cos.f64 y) z) 1/3)
(cbrt.f64 (*.f64 z (cos.f64 y)))

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.f64 x (sin.f64 y))
	0.1b	(*.f64 z (cos.f64 y))
✓	0.2b	(pow.f64 (sqrt.f64 (*.f64 x (sin.f64 y))) 2)
✓	7.5b	(sqrt.f64 (*.f64 x (sin.f64 y)))

Compiler

Compiled 43 to 14 computations (67.4% saved)

series11.0ms (0.1%)

Counts

2 → 16

Calls

12 calls:

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

rewrite57.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

613×	`pow1_binary64`
565×	`add-log-exp_binary64`
565×	`log1p-expm1-u_binary64`
565×	`expm1-log1p-u_binary64`
551×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	163	14
2	1592	14

Stop Event

1×	node limit

Counts

2 → 50

Calls

Call 1

Inputs
(sqrt.f64 (*.f64 x (sin.f64 y)))
(pow.f64 (sqrt.f64 (*.f64 x (sin.f64 y))) 2)

Outputs

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

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

simplify25.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	112
1	7	112

Stop Event

1×

saturated

Counts

66 → 51

Calls

Call 1

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

Outputs
(sqrt.f64 (*.f64 (sin.f64 y) x))
(sqrt.f64 (*.f64 (sin.f64 y) x))
(sqrt.f64 (*.f64 (sin.f64 y) x))
(sqrt.f64 (*.f64 (sin.f64 y) x))
(sqrt.f64 (*.f64 (sin.f64 y) x))
(sqrt.f64 (*.f64 (sin.f64 y) x))
(sqrt.f64 (*.f64 (sin.f64 y) x))
(sqrt.f64 (*.f64 (sin.f64 y) x))
(*.f64 (sin.f64 y) x)
(*.f64 (sin.f64 y) x)
(*.f64 (sin.f64 y) x)
(*.f64 (sin.f64 y) x)
(*.f64 (sin.f64 y) x)
(*.f64 (sin.f64 y) x)
(*.f64 (sin.f64 y) x)
(*.f64 (sin.f64 y) x)

eval169.0ms (1.7%)

Compiler: Compiled 10037 to 4271 computations (57.4% saved)

prune119.0ms (1.2%)

Pruning

23 alts after pruning (21 fresh and 2 done)

	Pruned	Kept	Total
New	525	19	544
Fresh	2	2	4
Picked	1	0	1
Done	3	2	5
Total	531	23	554

Error

0.0b

Counts

554 → 23

Alt Table

Click to see full alt table

Status	Error	Program
	30.2b	(+.f64 (pow.f64 (pow.f64 (pow.f64 (.f64 x (sin.f64 y)) 1/4) 2) 2) (.f64 z (cos.f64 y)))
	41.2b	(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) z)) z)
	14.3b	(+.f64 (pow.f64 (cbrt.f64 (*.f64 x (sin.f64 y))) 3) z)
	32.7b	(+.f64 (.f64 (.f64 x (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))) (*.f64 z (cos.f64 y)))
	37.3b	(+.f64 (cbrt.f64 (*.f64 (pow.f64 (sin.f64 y) 3) (pow.f64 x 3))) z)
	48.6b	(+.f64 (pow.f64 (.f64 (sqrt.f64 (sin.f64 y)) (sqrt.f64 x)) 2) (.f64 z (cos.f64 y)))
▶	30.8b	(+.f64 (*.f64 y x) z)
▶	31.9b	(+.f64 (.f64 x (sin.f64 y)) (pow.f64 (sqrt.f64 (.f64 z (cos.f64 y))) 2))
	1.0b	(+.f64 (.f64 x (sin.f64 y)) (pow.f64 (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 z)) 3))
	31.9b	(+.f64 (.f64 x (sin.f64 y)) (.f64 (*.f64 (cos.f64 y) (sqrt.f64 z)) (sqrt.f64 z)))
	30.8b	(fma.f64 y x z)
▶	14.6b	(+.f64 (.f64 x (sin.f64 y)) (.f64 (*.f64 z (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))))
	36.3b	(*.f64 (sin.f64 y) x)
	26.2b	(+.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 (pow.f64 (sin.f64 y) 3) (pow.f64 x 3)))) 3) (.f64 z (cos.f64 y)))
✓	0.2b	(+.f64 (.f64 x (sin.f64 y)) (.f64 z (cos.f64 y)))
	0.8b	(+.f64 (pow.f64 (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 x)) 3) (.f64 z (cos.f64 y)))
	23.3b	(+.f64 (.f64 y x) (pow.f64 (cbrt.f64 (.f64 z (cos.f64 y))) 3))
	22.7b	(+.f64 (.f64 y x) (.f64 z (cos.f64 y)))
▶	0.4b	(+.f64 (.f64 x (sin.f64 y)) (.f64 (pow.f64 (cbrt.f64 (cos.f64 y)) 2) (*.f64 (cbrt.f64 (cos.f64 y)) z)))
▶	29.9b	(+.f64 (cbrt.f64 (pow.f64 (*.f64 x (sin.f64 y)) 3)) z)
	0.9b	(+.f64 (.f64 x (sin.f64 y)) (.f64 (pow.f64 (cbrt.f64 z) 2) (*.f64 (cbrt.f64 z) (cos.f64 y))))
	37.5b	(+.f64 (pow.f64 (sqrt.f64 (*.f64 x (sin.f64 y))) 2) z)
✓	13.8b	(+.f64 (*.f64 x (sin.f64 y)) z)

Compiler

Compiled 615 to 432 computations (29.8% saved)

localize25.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.f64 x (sin.f64 y))
✓	0.1b	(*.f64 (cbrt.f64 (cos.f64 y)) z)
✓	0.3b	(pow.f64 (cbrt.f64 (cos.f64 y)) 2)
✓	0.3b	(cbrt.f64 (cos.f64 y))

Compiler

Compiled 55 to 18 computations (67.3% saved)

series16.0ms (0.2%)

Counts

3 → 48

Calls

12 calls:

Time	Variable		Point	Expression
4.0ms	y	@	-inf	(*.f64 (cbrt.f64 (cos.f64 y)) z)
2.0ms	z	@	0	(*.f64 (cbrt.f64 (cos.f64 y)) z)
2.0ms	y	@	inf	(*.f64 (cbrt.f64 (cos.f64 y)) z)
2.0ms	y	@	inf	(cbrt.f64 (cos.f64 y))
2.0ms	y	@	-inf	(cbrt.f64 (cos.f64 y))

rewrite56.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

659×	`pow1_binary64`
607×	`add-log-exp_binary64`
607×	`log1p-expm1-u_binary64`
607×	`expm1-log1p-u_binary64`
592×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	21
1	159	21
2	1730	21

Stop Event

1×	node limit

Counts

3 → 49

Calls

Call 1

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

Outputs

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

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

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

simplify212.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

1201×	`fma-def_binary64`
703×	`sqr-pow_binary64`
671×	`cube-prod_binary64`
407×	`unpow3_binary64`
402×	`fabs-mul_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	50	432
1	128	423
2	328	414
3	1012	411
4	2280	411
5	2865	411
6	3010	411
7	3201	411
8	3416	411
9	3695	411
10	4476	411
11	4956	411
12	5535	411
13	6217	411
14	6552	411
15	6885	411
16	7211	411
17	7515	411
18	7753	411

Stop Event

1×	node limit

Counts

97 → 73

Calls

Call 1

Inputs
1
(+.f64 1 (*.f64 -1/6 (pow.f64 y 2)))
(+.f64 (.f64 -1/72 (pow.f64 y 4)) (+.f64 1 (.f64 -1/6 (pow.f64 y 2))))
(+.f64 (.f64 -23/6480 (pow.f64 y 6)) (+.f64 (.f64 -1/72 (pow.f64 y 4)) (+.f64 1 (*.f64 -1/6 (pow.f64 y 2)))))
(pow.f64 (cos.f64 y) 1/3)
(pow.f64 (cos.f64 y) 1/3)
(pow.f64 (cos.f64 y) 1/3)
(pow.f64 (cos.f64 y) 1/3)
(pow.f64 (cos.f64 y) 1/3)
(pow.f64 (cos.f64 y) 1/3)
(pow.f64 (cos.f64 y) 1/3)
(pow.f64 (cos.f64 y) 1/3)
1
(+.f64 1 (*.f64 -1/3 (pow.f64 y 2)))
(+.f64 1 (+.f64 (.f64 -1/3 (pow.f64 y 2)) (.f64 -1/405 (pow.f64 y 6))))
(+.f64 1 (+.f64 (.f64 -1/1701 (pow.f64 y 8)) (+.f64 (.f64 -1/3 (pow.f64 y 2)) (*.f64 -1/405 (pow.f64 y 6)))))
(pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)
(pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)
(pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)
(pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)
(pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)
(pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)
(pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)
(pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)
z
(+.f64 (.f64 -1/6 (.f64 (pow.f64 y 2) z)) z)
(+.f64 (.f64 -1/72 (.f64 (pow.f64 y 4) z)) (+.f64 (.f64 -1/6 (.f64 (pow.f64 y 2) z)) z))
(+.f64 (.f64 -1/72 (.f64 (pow.f64 y 4) z)) (+.f64 (.f64 -23/6480 (.f64 (pow.f64 y 6) z)) (+.f64 (.f64 -1/6 (.f64 (pow.f64 y 2) z)) z)))
(.f64 (pow.f64 (.f64 1 (cos.f64 y)) 1/3) z)
(.f64 (pow.f64 (.f64 1 (cos.f64 y)) 1/3) z)
(.f64 (pow.f64 (.f64 1 (cos.f64 y)) 1/3) z)
(.f64 (pow.f64 (.f64 1 (cos.f64 y)) 1/3) z)
(.f64 (pow.f64 (.f64 1 (cos.f64 y)) 1/3) z)
(.f64 (pow.f64 (.f64 1 (cos.f64 y)) 1/3) z)
(.f64 (pow.f64 (.f64 1 (cos.f64 y)) 1/3) z)
(.f64 (pow.f64 (.f64 1 (cos.f64 y)) 1/3) z)
(.f64 (pow.f64 (.f64 1 (cos.f64 y)) 1/3) z)
(.f64 (pow.f64 (.f64 1 (cos.f64 y)) 1/3) z)
(.f64 (pow.f64 (.f64 1 (cos.f64 y)) 1/3) z)
(.f64 (pow.f64 (.f64 1 (cos.f64 y)) 1/3) z)
(.f64 (pow.f64 (.f64 1 (cos.f64 y)) 1/3) z)
(.f64 (pow.f64 (.f64 1 (cos.f64 y)) 1/3) z)
(.f64 (pow.f64 (.f64 1 (cos.f64 y)) 1/3) z)
(.f64 (pow.f64 (.f64 1 (cos.f64 y)) 1/3) z)
(.f64 (pow.f64 (.f64 1 (cos.f64 y)) 1/3) z)
(.f64 (pow.f64 (.f64 1 (cos.f64 y)) 1/3) z)
(.f64 (pow.f64 (.f64 1 (cos.f64 y)) 1/3) z)
(.f64 (pow.f64 (.f64 1 (cos.f64 y)) 1/3) z)

Outputs
1
(+.f64 1 (*.f64 -1/6 (pow.f64 y 2)))
(+.f64 1 (.f64 -1/6 (.f64 y y)))
(fma.f64 -1/6 (*.f64 y y) 1)
(+.f64 (.f64 -1/72 (pow.f64 y 4)) (+.f64 1 (.f64 -1/6 (pow.f64 y 2))))
(fma.f64 -1/72 (pow.f64 y 4) (+.f64 1 (.f64 -1/6 (.f64 y y))))
(fma.f64 -1/72 (pow.f64 y 4) (fma.f64 -1/6 (*.f64 y y) 1))
(fma.f64 -1/6 (*.f64 y y) (fma.f64 -1/72 (pow.f64 y 4) 1))
(+.f64 (.f64 -23/6480 (pow.f64 y 6)) (+.f64 (.f64 -1/72 (pow.f64 y 4)) (+.f64 1 (*.f64 -1/6 (pow.f64 y 2)))))
(fma.f64 -23/6480 (pow.f64 y 6) (fma.f64 -1/72 (pow.f64 y 4) (+.f64 1 (.f64 -1/6 (.f64 y y)))))
(fma.f64 -23/6480 (pow.f64 y 6) (fma.f64 -1/72 (pow.f64 y 4) (fma.f64 -1/6 (*.f64 y y) 1)))
(fma.f64 -1/72 (pow.f64 y 4) (fma.f64 -23/6480 (pow.f64 y 6) (fma.f64 -1/6 (*.f64 y y) 1)))
(fma.f64 -1/6 (*.f64 y y) (fma.f64 -1/72 (pow.f64 y 4) (fma.f64 -23/6480 (pow.f64 y 6) 1)))
(fma.f64 (.f64 y y) (fma.f64 y (.f64 y -1/72) -1/6) (fma.f64 -23/6480 (pow.f64 y 6) 1))
(fma.f64 -1/6 (*.f64 y y) (fma.f64 -23/6480 (pow.f64 y 6) (fma.f64 -1/72 (pow.f64 y 4) 1)))
(pow.f64 (cos.f64 y) 1/3)
(cbrt.f64 (cos.f64 y))
(pow.f64 (cos.f64 y) 1/3)
(cbrt.f64 (cos.f64 y))
(pow.f64 (cos.f64 y) 1/3)
(cbrt.f64 (cos.f64 y))
(pow.f64 (cos.f64 y) 1/3)
(cbrt.f64 (cos.f64 y))
(pow.f64 (cos.f64 y) 1/3)
(cbrt.f64 (cos.f64 y))
(pow.f64 (cos.f64 y) 1/3)
(cbrt.f64 (cos.f64 y))
(pow.f64 (cos.f64 y) 1/3)
(cbrt.f64 (cos.f64 y))
(pow.f64 (cos.f64 y) 1/3)
(cbrt.f64 (cos.f64 y))
1
(+.f64 1 (*.f64 -1/3 (pow.f64 y 2)))
(+.f64 1 (.f64 (.f64 y y) -1/3))
(fma.f64 (*.f64 y y) -1/3 1)
(fma.f64 y (*.f64 y -1/3) 1)
(+.f64 1 (+.f64 (.f64 -1/3 (pow.f64 y 2)) (.f64 -1/405 (pow.f64 y 6))))
(+.f64 1 (fma.f64 -1/3 (.f64 y y) (.f64 (pow.f64 y 6) -1/405)))
(+.f64 1 (fma.f64 (pow.f64 y 6) -1/405 (.f64 y (.f64 y -1/3))))
(fma.f64 y (*.f64 y -1/3) (fma.f64 (pow.f64 y 6) -1/405 1))
(+.f64 1 (+.f64 (.f64 -1/1701 (pow.f64 y 8)) (+.f64 (.f64 -1/3 (pow.f64 y 2)) (*.f64 -1/405 (pow.f64 y 6)))))
(+.f64 1 (fma.f64 -1/1701 (pow.f64 y 8) (fma.f64 -1/3 (.f64 y y) (.f64 (pow.f64 y 6) -1/405))))
(+.f64 1 (fma.f64 -1/1701 (pow.f64 y 8) (fma.f64 (pow.f64 y 6) -1/405 (.f64 y (.f64 y -1/3)))))
(fma.f64 -1/1701 (pow.f64 y 8) (fma.f64 y (*.f64 y -1/3) (fma.f64 (pow.f64 y 6) -1/405 1)))
(fma.f64 (pow.f64 y 6) -1/405 (fma.f64 y (*.f64 y -1/3) (fma.f64 -1/1701 (pow.f64 y 8) 1)))
(fma.f64 y (*.f64 y -1/3) (fma.f64 (pow.f64 y 6) -1/405 (fma.f64 -1/1701 (pow.f64 y 8) 1)))
(fma.f64 (pow.f64 y 6) (fma.f64 (.f64 y y) -1/1701 -1/405) (fma.f64 (.f64 y y) -1/3 1))
(fma.f64 (*.f64 y y) (fma.f64 (pow.f64 y 6) -1/1701 -1/3) (fma.f64 (pow.f64 y 6) -1/405 1))
(pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)
(cbrt.f64 (pow.f64 (cos.f64 y) 2))
(pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)
(cbrt.f64 (pow.f64 (cos.f64 y) 2))
(pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)
(cbrt.f64 (pow.f64 (cos.f64 y) 2))
(pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)
(cbrt.f64 (pow.f64 (cos.f64 y) 2))
(pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)
(cbrt.f64 (pow.f64 (cos.f64 y) 2))
(pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)
(cbrt.f64 (pow.f64 (cos.f64 y) 2))
(pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)
(cbrt.f64 (pow.f64 (cos.f64 y) 2))
(pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)
(cbrt.f64 (pow.f64 (cos.f64 y) 2))
z
(+.f64 (.f64 -1/6 (.f64 (pow.f64 y 2) z)) z)
(fma.f64 -1/6 (.f64 (.f64 y y) z) z)
(.f64 (fma.f64 -1/6 (.f64 y y) 1) z)
(fma.f64 y (.f64 -1/6 (.f64 y z)) z)
(fma.f64 y (.f64 z (.f64 -1/6 y)) z)
(+.f64 (.f64 -1/72 (.f64 (pow.f64 y 4) z)) (+.f64 (.f64 -1/6 (.f64 (pow.f64 y 2) z)) z))
(fma.f64 -1/72 (.f64 (pow.f64 y 4) z) (fma.f64 -1/6 (.f64 (*.f64 y y) z) z))
(fma.f64 -1/72 (.f64 (pow.f64 y 4) z) (.f64 (fma.f64 -1/6 (*.f64 y y) 1) z))
(fma.f64 z (fma.f64 -1/6 (.f64 y y) (.f64 -1/72 (pow.f64 y 4))) z)
(fma.f64 z (.f64 (.f64 y y) (fma.f64 y (*.f64 y -1/72) -1/6)) z)
(.f64 (fma.f64 -1/72 (pow.f64 y 4) (fma.f64 -1/6 (.f64 y y) 1)) z)
(+.f64 (.f64 -1/72 (.f64 (pow.f64 y 4) z)) (+.f64 (.f64 -23/6480 (.f64 (pow.f64 y 6) z)) (+.f64 (.f64 -1/6 (.f64 (pow.f64 y 2) z)) z)))
(fma.f64 -1/72 (.f64 (pow.f64 y 4) z) (fma.f64 -23/6480 (.f64 (pow.f64 y 6) z) (fma.f64 -1/6 (.f64 (.f64 y y) z) z)))
(+.f64 (.f64 (fma.f64 -1/6 (.f64 y y) 1) z) (.f64 z (fma.f64 -23/6480 (pow.f64 y 6) (.f64 -1/72 (pow.f64 y 4)))))
(fma.f64 -1/72 (.f64 (pow.f64 y 4) z) (fma.f64 z (fma.f64 -1/6 (.f64 y y) (*.f64 -23/6480 (pow.f64 y 6))) z))
(fma.f64 z (fma.f64 -1/6 (.f64 y y) (fma.f64 -1/72 (pow.f64 y 4) (.f64 -23/6480 (pow.f64 y 6)))) z)
(.f64 z (fma.f64 (.f64 y y) (fma.f64 y (*.f64 y -1/72) -1/6) (fma.f64 -23/6480 (pow.f64 y 6) 1)))
(fma.f64 z (.f64 (.f64 y y) (fma.f64 y (fma.f64 -23/6480 (pow.f64 y 3) (*.f64 y -1/72)) -1/6)) z)
(.f64 (pow.f64 (.f64 1 (cos.f64 y)) 1/3) z)
(*.f64 z (cbrt.f64 (cos.f64 y)))
(.f64 (pow.f64 (.f64 1 (cos.f64 y)) 1/3) z)
(*.f64 z (cbrt.f64 (cos.f64 y)))
(.f64 (pow.f64 (.f64 1 (cos.f64 y)) 1/3) z)
(*.f64 z (cbrt.f64 (cos.f64 y)))
(.f64 (pow.f64 (.f64 1 (cos.f64 y)) 1/3) z)
(*.f64 z (cbrt.f64 (cos.f64 y)))
(.f64 (pow.f64 (.f64 1 (cos.f64 y)) 1/3) z)
(*.f64 z (cbrt.f64 (cos.f64 y)))
(.f64 (pow.f64 (.f64 1 (cos.f64 y)) 1/3) z)
(*.f64 z (cbrt.f64 (cos.f64 y)))
(.f64 (pow.f64 (.f64 1 (cos.f64 y)) 1/3) z)
(*.f64 z (cbrt.f64 (cos.f64 y)))
(.f64 (pow.f64 (.f64 1 (cos.f64 y)) 1/3) z)
(*.f64 z (cbrt.f64 (cos.f64 y)))
(.f64 (pow.f64 (.f64 1 (cos.f64 y)) 1/3) z)
(*.f64 z (cbrt.f64 (cos.f64 y)))
(.f64 (pow.f64 (.f64 1 (cos.f64 y)) 1/3) z)
(*.f64 z (cbrt.f64 (cos.f64 y)))
(.f64 (pow.f64 (.f64 1 (cos.f64 y)) 1/3) z)
(*.f64 z (cbrt.f64 (cos.f64 y)))
(.f64 (pow.f64 (.f64 1 (cos.f64 y)) 1/3) z)
(*.f64 z (cbrt.f64 (cos.f64 y)))
(.f64 (pow.f64 (.f64 1 (cos.f64 y)) 1/3) z)
(*.f64 z (cbrt.f64 (cos.f64 y)))
(.f64 (pow.f64 (.f64 1 (cos.f64 y)) 1/3) z)
(*.f64 z (cbrt.f64 (cos.f64 y)))
(.f64 (pow.f64 (.f64 1 (cos.f64 y)) 1/3) z)
(*.f64 z (cbrt.f64 (cos.f64 y)))
(.f64 (pow.f64 (.f64 1 (cos.f64 y)) 1/3) z)
(*.f64 z (cbrt.f64 (cos.f64 y)))
(.f64 (pow.f64 (.f64 1 (cos.f64 y)) 1/3) z)
(*.f64 z (cbrt.f64 (cos.f64 y)))
(.f64 (pow.f64 (.f64 1 (cos.f64 y)) 1/3) z)
(*.f64 z (cbrt.f64 (cos.f64 y)))
(.f64 (pow.f64 (.f64 1 (cos.f64 y)) 1/3) z)
(*.f64 z (cbrt.f64 (cos.f64 y)))
(.f64 (pow.f64 (.f64 1 (cos.f64 y)) 1/3) z)
(*.f64 z (cbrt.f64 (cos.f64 y)))

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 14 to 5 computations (64.3% saved)

series3.0ms (0%)

Counts

1 → 9

Calls

9 calls:

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

rewrite57.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

707×	`pow1_binary64`
655×	`add-log-exp_binary64`
655×	`log1p-expm1-u_binary64`
655×	`expm1-log1p-u_binary64`
640×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	5
1	129	5
2	1775	5

Stop Event

1×	node limit

Counts

1 → 35

Calls

Call 1

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

Outputs

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

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	24
1	6	24

Stop Event

1×

saturated

Counts

44 → 37

Calls

Call 1

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

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

localize31.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.1b	(*.f64 x (sin.f64 y))
✓	0.2b	(pow.f64 (*.f64 x (sin.f64 y)) 3)
✓	34.0b	(cbrt.f64 (pow.f64 (*.f64 x (sin.f64 y)) 3))

Compiler

Compiled 35 to 15 computations (57.1% saved)

series21.0ms (0.2%)

Counts

2 → 48

Calls

12 calls:

Time	Variable		Point	Expression
8.0ms	y	@	inf	(pow.f64 (*.f64 x (sin.f64 y)) 3)
6.0ms	y	@	0	(pow.f64 (*.f64 x (sin.f64 y)) 3)
2.0ms	x	@	-inf	(cbrt.f64 (pow.f64 (*.f64 x (sin.f64 y)) 3))
1.0ms	y	@	-inf	(pow.f64 (*.f64 x (sin.f64 y)) 3)
1.0ms	x	@	-inf	(pow.f64 (*.f64 x (sin.f64 y)) 3)

rewrite96.0ms (1%)

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 (sin.f64 y)) 3))
(pow.f64 (*.f64 x (sin.f64 y)) 3)

Outputs

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

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

simplify200.0ms (2%)

Algorithm

1×	egg-herbie

Rules

708×	`fma-def_binary64`
486×	`associate-l_binary64`
460×	`distribute-rgt-out_binary64`
452×	`associate-r_binary64`
425×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	73	632
1	229	617
2	872	572
3	4541	568
4	7031	565
5	7155	565
6	7291	565
7	7445	565
8	7633	565
9	7823	565

Stop Event

1×	node limit

Counts

102 → 71

Calls

Call 1

Inputs
(*.f64 (sin.f64 y) x)
(*.f64 (sin.f64 y) x)
(*.f64 (sin.f64 y) x)
(*.f64 (sin.f64 y) x)
(*.f64 (sin.f64 y) x)
(*.f64 (sin.f64 y) x)
(*.f64 (sin.f64 y) x)
(*.f64 (sin.f64 y) x)
(.f64 -1 (.f64 (cbrt.f64 -1) (*.f64 (sin.f64 y) x)))
(.f64 -1 (.f64 (cbrt.f64 -1) (*.f64 (sin.f64 y) x)))
(.f64 -1 (.f64 (cbrt.f64 -1) (*.f64 (sin.f64 y) x)))
(.f64 -1 (.f64 (cbrt.f64 -1) (*.f64 (sin.f64 y) x)))
(*.f64 y x)
(+.f64 (.f64 y x) (.f64 -1/6 (*.f64 (pow.f64 y 3) x)))
(+.f64 (.f64 1/120 (.f64 (pow.f64 y 5) x)) (+.f64 (.f64 y x) (.f64 -1/6 (*.f64 (pow.f64 y 3) x))))
(+.f64 (.f64 1/120 (.f64 (pow.f64 y 5) x)) (+.f64 (.f64 y x) (+.f64 (.f64 -1/5040 (.f64 (pow.f64 y 7) x)) (.f64 -1/6 (*.f64 (pow.f64 y 3) x)))))
(*.f64 (sin.f64 y) x)
(*.f64 (sin.f64 y) x)
(*.f64 (sin.f64 y) x)
(*.f64 (sin.f64 y) x)
(*.f64 (sin.f64 y) x)
(*.f64 (sin.f64 y) x)
(*.f64 (sin.f64 y) x)
(*.f64 (sin.f64 y) x)
(*.f64 (pow.f64 (sin.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (sin.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (sin.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (sin.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (sin.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (sin.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (sin.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (sin.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (sin.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (sin.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (sin.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (sin.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 y 3) (pow.f64 x 3))
(+.f64 (.f64 (pow.f64 y 5) (+.f64 (.f64 -1/6 (pow.f64 x 3)) (.f64 -1/3 (pow.f64 x 3)))) (.f64 (pow.f64 y 3) (pow.f64 x 3)))
(+.f64 (.f64 (pow.f64 y 7) (+.f64 (.f64 (+.f64 (.f64 1/36 (pow.f64 x 2)) (.f64 1/60 (pow.f64 x 2))) x) (+.f64 (.f64 1/18 (pow.f64 x 3)) (.f64 1/120 (pow.f64 x 3))))) (+.f64 (.f64 (pow.f64 y 5) (+.f64 (.f64 -1/6 (pow.f64 x 3)) (.f64 -1/3 (pow.f64 x 3)))) (.f64 (pow.f64 y 3) (pow.f64 x 3))))
(+.f64 (.f64 (pow.f64 y 7) (+.f64 (.f64 (+.f64 (.f64 1/36 (pow.f64 x 2)) (.f64 1/60 (pow.f64 x 2))) x) (+.f64 (.f64 1/18 (pow.f64 x 3)) (.f64 1/120 (pow.f64 x 3))))) (+.f64 (.f64 (pow.f64 y 5) (+.f64 (.f64 -1/6 (pow.f64 x 3)) (.f64 -1/3 (pow.f64 x 3)))) (+.f64 (.f64 (pow.f64 y 3) (pow.f64 x 3)) (.f64 (pow.f64 y 9) (+.f64 (.f64 -1/6 (.f64 (+.f64 (.f64 1/36 (pow.f64 x 2)) (.f64 1/60 (pow.f64 x 2))) x)) (+.f64 (.f64 -1/360 (pow.f64 x 3)) (+.f64 (.f64 (+.f64 (.f64 -1/2520 (pow.f64 x 2)) (.f64 -1/360 (pow.f64 x 2))) x) (.f64 -1/5040 (pow.f64 x 3)))))))))
(*.f64 (pow.f64 (sin.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (sin.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (sin.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (sin.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (sin.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (sin.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (sin.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (sin.f64 y) 3) (pow.f64 x 3))

Outputs
(*.f64 (sin.f64 y) x)
(*.f64 (sin.f64 y) x)
(*.f64 (sin.f64 y) x)
(*.f64 (sin.f64 y) x)
(*.f64 (sin.f64 y) x)
(*.f64 (sin.f64 y) x)
(*.f64 (sin.f64 y) x)
(*.f64 (sin.f64 y) x)
(.f64 -1 (.f64 (cbrt.f64 -1) (*.f64 (sin.f64 y) x)))
(neg.f64 (.f64 (.f64 (sin.f64 y) x) (cbrt.f64 -1)))
(.f64 (.f64 (sin.f64 y) x) (neg.f64 (cbrt.f64 -1)))
(.f64 (sin.f64 y) (.f64 x (neg.f64 (cbrt.f64 -1))))
(.f64 (sin.f64 y) (.f64 (cbrt.f64 -1) (neg.f64 x)))
(.f64 -1 (.f64 (cbrt.f64 -1) (*.f64 (sin.f64 y) x)))
(neg.f64 (.f64 (.f64 (sin.f64 y) x) (cbrt.f64 -1)))
(.f64 (.f64 (sin.f64 y) x) (neg.f64 (cbrt.f64 -1)))
(.f64 (sin.f64 y) (.f64 x (neg.f64 (cbrt.f64 -1))))
(.f64 (sin.f64 y) (.f64 (cbrt.f64 -1) (neg.f64 x)))
(.f64 -1 (.f64 (cbrt.f64 -1) (*.f64 (sin.f64 y) x)))
(neg.f64 (.f64 (.f64 (sin.f64 y) x) (cbrt.f64 -1)))
(.f64 (.f64 (sin.f64 y) x) (neg.f64 (cbrt.f64 -1)))
(.f64 (sin.f64 y) (.f64 x (neg.f64 (cbrt.f64 -1))))
(.f64 (sin.f64 y) (.f64 (cbrt.f64 -1) (neg.f64 x)))
(.f64 -1 (.f64 (cbrt.f64 -1) (*.f64 (sin.f64 y) x)))
(neg.f64 (.f64 (.f64 (sin.f64 y) x) (cbrt.f64 -1)))
(.f64 (.f64 (sin.f64 y) x) (neg.f64 (cbrt.f64 -1)))
(.f64 (sin.f64 y) (.f64 x (neg.f64 (cbrt.f64 -1))))
(.f64 (sin.f64 y) (.f64 (cbrt.f64 -1) (neg.f64 x)))
(*.f64 y x)
(+.f64 (.f64 y x) (.f64 -1/6 (*.f64 (pow.f64 y 3) x)))
(fma.f64 y x (.f64 -1/6 (.f64 x (pow.f64 y 3))))
(.f64 x (+.f64 y (.f64 -1/6 (pow.f64 y 3))))
(*.f64 x (fma.f64 -1/6 (pow.f64 y 3) y))
(+.f64 (.f64 1/120 (.f64 (pow.f64 y 5) x)) (+.f64 (.f64 y x) (.f64 -1/6 (*.f64 (pow.f64 y 3) x))))
(fma.f64 1/120 (.f64 x (pow.f64 y 5)) (fma.f64 y x (.f64 -1/6 (*.f64 x (pow.f64 y 3)))))
(fma.f64 1/120 (.f64 x (pow.f64 y 5)) (.f64 x (+.f64 y (*.f64 -1/6 (pow.f64 y 3)))))
(.f64 x (+.f64 (.f64 -1/6 (pow.f64 y 3)) (fma.f64 1/120 (pow.f64 y 5) y)))
(.f64 x (+.f64 (.f64 1/120 (pow.f64 y 5)) (fma.f64 -1/6 (pow.f64 y 3) y)))
(+.f64 (.f64 1/120 (.f64 (pow.f64 y 5) x)) (+.f64 (.f64 y x) (+.f64 (.f64 -1/5040 (.f64 (pow.f64 y 7) x)) (.f64 -1/6 (*.f64 (pow.f64 y 3) x)))))
(fma.f64 1/120 (.f64 x (pow.f64 y 5)) (fma.f64 y x (fma.f64 -1/5040 (.f64 x (pow.f64 y 7)) (.f64 -1/6 (.f64 x (pow.f64 y 3))))))
(fma.f64 1/120 (.f64 x (pow.f64 y 5)) (fma.f64 y x (.f64 x (+.f64 (.f64 -1/6 (pow.f64 y 3)) (.f64 -1/5040 (pow.f64 y 7))))))
(.f64 x (+.f64 (fma.f64 -1/6 (pow.f64 y 3) (.f64 -1/5040 (pow.f64 y 7))) (fma.f64 1/120 (pow.f64 y 5) y)))
(.f64 x (+.f64 (fma.f64 1/120 (pow.f64 y 5) y) (fma.f64 -1/5040 (pow.f64 y 7) (.f64 -1/6 (pow.f64 y 3)))))
(*.f64 (sin.f64 y) x)
(*.f64 (sin.f64 y) x)
(*.f64 (sin.f64 y) x)
(*.f64 (sin.f64 y) x)
(*.f64 (sin.f64 y) x)
(*.f64 (sin.f64 y) x)
(*.f64 (sin.f64 y) x)
(*.f64 (sin.f64 y) x)
(*.f64 (pow.f64 (sin.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (sin.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (sin.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (sin.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (sin.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (sin.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (sin.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (sin.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (sin.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (sin.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (sin.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (sin.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 y 3) (pow.f64 x 3))
(pow.f64 (*.f64 y x) 3)
(+.f64 (.f64 (pow.f64 y 5) (+.f64 (.f64 -1/6 (pow.f64 x 3)) (.f64 -1/3 (pow.f64 x 3)))) (.f64 (pow.f64 y 3) (pow.f64 x 3)))
(fma.f64 (pow.f64 y 5) (.f64 (pow.f64 x 3) -1/2) (.f64 (pow.f64 y 3) (pow.f64 x 3)))
(fma.f64 (pow.f64 y 3) (pow.f64 x 3) (.f64 (pow.f64 y 5) (.f64 (pow.f64 x 3) -1/2)))
(.f64 (pow.f64 x 3) (+.f64 (pow.f64 y 3) (.f64 (pow.f64 y 5) -1/2)))
(+.f64 (.f64 (pow.f64 y 7) (+.f64 (.f64 (+.f64 (.f64 1/36 (pow.f64 x 2)) (.f64 1/60 (pow.f64 x 2))) x) (+.f64 (.f64 1/18 (pow.f64 x 3)) (.f64 1/120 (pow.f64 x 3))))) (+.f64 (.f64 (pow.f64 y 5) (+.f64 (.f64 -1/6 (pow.f64 x 3)) (.f64 -1/3 (pow.f64 x 3)))) (.f64 (pow.f64 y 3) (pow.f64 x 3))))
(fma.f64 (pow.f64 y 7) (fma.f64 (.f64 (.f64 x x) 2/45) x (.f64 (pow.f64 x 3) 23/360)) (fma.f64 (pow.f64 y 5) (.f64 (pow.f64 x 3) -1/2) (*.f64 (pow.f64 y 3) (pow.f64 x 3))))
(fma.f64 (pow.f64 y 7) (fma.f64 (pow.f64 x 3) 23/360 (.f64 (pow.f64 x 3) 2/45)) (fma.f64 (pow.f64 y 3) (pow.f64 x 3) (.f64 (pow.f64 y 5) (*.f64 (pow.f64 x 3) -1/2))))
(fma.f64 (pow.f64 y 7) (.f64 (pow.f64 x 3) 13/120) (.f64 (pow.f64 x 3) (+.f64 (pow.f64 y 3) (*.f64 (pow.f64 y 5) -1/2))))
(+.f64 (.f64 (pow.f64 y 7) (+.f64 (.f64 (+.f64 (.f64 1/36 (pow.f64 x 2)) (.f64 1/60 (pow.f64 x 2))) x) (+.f64 (.f64 1/18 (pow.f64 x 3)) (.f64 1/120 (pow.f64 x 3))))) (+.f64 (.f64 (pow.f64 y 5) (+.f64 (.f64 -1/6 (pow.f64 x 3)) (.f64 -1/3 (pow.f64 x 3)))) (+.f64 (.f64 (pow.f64 y 3) (pow.f64 x 3)) (.f64 (pow.f64 y 9) (+.f64 (.f64 -1/6 (.f64 (+.f64 (.f64 1/36 (pow.f64 x 2)) (.f64 1/60 (pow.f64 x 2))) x)) (+.f64 (.f64 -1/360 (pow.f64 x 3)) (+.f64 (.f64 (+.f64 (.f64 -1/2520 (pow.f64 x 2)) (.f64 -1/360 (pow.f64 x 2))) x) (.f64 -1/5040 (pow.f64 x 3)))))))))
(fma.f64 (pow.f64 y 7) (fma.f64 (.f64 (.f64 x x) 2/45) x (.f64 (pow.f64 x 3) 23/360)) (fma.f64 (pow.f64 y 5) (.f64 (pow.f64 x 3) -1/2) (fma.f64 (pow.f64 y 3) (pow.f64 x 3) (.f64 (pow.f64 y 9) (fma.f64 -1/6 (.f64 x (.f64 (.f64 x x) 2/45)) (fma.f64 -1/360 (pow.f64 x 3) (fma.f64 (.f64 (.f64 x x) -1/315) x (*.f64 -1/5040 (pow.f64 x 3)))))))))
(fma.f64 (pow.f64 y 7) (fma.f64 (pow.f64 x 3) 23/360 (.f64 (pow.f64 x 3) 2/45)) (fma.f64 (pow.f64 y 5) (.f64 (pow.f64 x 3) -1/2) (fma.f64 (pow.f64 y 3) (pow.f64 x 3) (.f64 (pow.f64 y 9) (fma.f64 -1/6 (.f64 (pow.f64 x 3) 2/45) (fma.f64 (pow.f64 x 3) -1/360 (fma.f64 -1/5040 (pow.f64 x 3) (*.f64 (pow.f64 x 3) -1/315))))))))
(fma.f64 (pow.f64 y 7) (.f64 (pow.f64 x 3) 13/120) (fma.f64 (pow.f64 y 9) (+.f64 (.f64 (pow.f64 x 3) -1/135) (fma.f64 -1/5040 (pow.f64 x 3) (.f64 (pow.f64 x 3) -1/168))) (.f64 (pow.f64 x 3) (+.f64 (pow.f64 y 3) (*.f64 (pow.f64 y 5) -1/2)))))
(fma.f64 (pow.f64 y 7) (.f64 (pow.f64 x 3) 13/120) (fma.f64 (pow.f64 y 9) (+.f64 (.f64 (pow.f64 x 3) -1/168) (.f64 x (.f64 (.f64 x x) -23/3024))) (.f64 (pow.f64 x 3) (+.f64 (pow.f64 y 3) (*.f64 (pow.f64 y 5) -1/2)))))
(*.f64 (pow.f64 (sin.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (sin.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (sin.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (sin.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (sin.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (sin.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (sin.f64 y) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (sin.f64 y) 3) (pow.f64 x 3))

localize35.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (*.f64 z (cos.f64 y)))
	0.1b	(*.f64 x (sin.f64 y))
	0.1b	(*.f64 z (cos.f64 y))
✓	0.2b	(pow.f64 (sqrt.f64 (*.f64 z (cos.f64 y))) 2)

Compiler

Compiled 43 to 14 computations (67.4% saved)

series19.0ms (0.2%)

Counts

2 → 16

Calls

12 calls:

Time	Variable		Point	Expression
4.0ms	z	@	0	(sqrt.f64 (*.f64 z (cos.f64 y)))
2.0ms	z	@	0	(pow.f64 (sqrt.f64 (*.f64 z (cos.f64 y))) 2)
2.0ms	z	@	-inf	(pow.f64 (sqrt.f64 (*.f64 z (cos.f64 y))) 2)
2.0ms	y	@	0	(pow.f64 (sqrt.f64 (*.f64 z (cos.f64 y))) 2)
1.0ms	z	@	inf	(pow.f64 (sqrt.f64 (*.f64 z (cos.f64 y))) 2)

rewrite84.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

613×	`pow1_binary64`
565×	`add-log-exp_binary64`
565×	`log1p-expm1-u_binary64`
565×	`expm1-log1p-u_binary64`
551×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	163	14
2	1592	14

Stop Event

1×	node limit

Counts

2 → 50

Calls

Call 1

Inputs
(pow.f64 (sqrt.f64 (*.f64 z (cos.f64 y))) 2)
(sqrt.f64 (*.f64 z (cos.f64 y)))

Outputs

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

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

simplify70.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

398×	`*-commutative_binary64`
389×	`distribute-rgt-in_binary64`
382×	`distribute-lft-in_binary64`
316×	`distribute-lft-out_binary64`
307×	`unswap-sqr_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	53	293
1	144	289
2	411	241
3	1786	214
4	5193	213

Stop Event

1×	node limit

Counts

66 → 64

Calls

Call 1

Inputs
z
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) z)) z)
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) z)) (+.f64 (.f64 (pow.f64 y 4) (-.f64 (+.f64 (.f64 1/16 z) (.f64 1/24 z)) (pow.f64 (.f64 -1/4 (sqrt.f64 z)) 2))) z))
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) z)) (+.f64 (.f64 -1/720 (.f64 (pow.f64 y 6) z)) (+.f64 (.f64 (pow.f64 y 4) (-.f64 (+.f64 (.f64 1/16 z) (.f64 1/24 z)) (pow.f64 (.f64 -1/4 (sqrt.f64 z)) 2))) z)))
(*.f64 z (cos.f64 y))
(*.f64 z (cos.f64 y))
(*.f64 z (cos.f64 y))
(*.f64 z (cos.f64 y))
(*.f64 z (cos.f64 y))
(*.f64 z (cos.f64 y))
(*.f64 z (cos.f64 y))
(*.f64 z (cos.f64 y))
(sqrt.f64 z)
(+.f64 (sqrt.f64 z) (.f64 -1/4 (.f64 (pow.f64 y 2) (sqrt.f64 z))))
(+.f64 (sqrt.f64 z) (+.f64 (.f64 1/2 (.f64 (.f64 (-.f64 (.f64 1/24 z) (pow.f64 (.f64 -1/4 (sqrt.f64 z)) 2)) (pow.f64 y 4)) (sqrt.f64 (/.f64 1 z)))) (.f64 -1/4 (*.f64 (pow.f64 y 2) (sqrt.f64 z)))))
(+.f64 (.f64 1/2 (.f64 (.f64 (pow.f64 y 6) (-.f64 (.f64 -1/720 z) (.f64 -1/4 (-.f64 (.f64 1/24 z) (pow.f64 (.f64 -1/4 (sqrt.f64 z)) 2))))) (sqrt.f64 (/.f64 1 z)))) (+.f64 (sqrt.f64 z) (+.f64 (.f64 1/2 (.f64 (.f64 (-.f64 (.f64 1/24 z) (pow.f64 (.f64 -1/4 (sqrt.f64 z)) 2)) (pow.f64 y 4)) (sqrt.f64 (/.f64 1 z)))) (.f64 -1/4 (.f64 (pow.f64 y 2) (sqrt.f64 z))))))

Outputs
z
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) z)) z)
(fma.f64 -1/2 (.f64 z (.f64 y y)) z)
(.f64 z (fma.f64 -1/2 (.f64 y y) 1))
(.f64 z (fma.f64 (.f64 -1/2 y) y 1))
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) z)) (+.f64 (.f64 (pow.f64 y 4) (-.f64 (+.f64 (.f64 1/16 z) (.f64 1/24 z)) (pow.f64 (.f64 -1/4 (sqrt.f64 z)) 2))) z))
(fma.f64 -1/2 (.f64 z (.f64 y y)) (fma.f64 (pow.f64 y 4) (-.f64 (.f64 z 5/48) (pow.f64 (.f64 -1/4 (sqrt.f64 z)) 2)) z))
(fma.f64 z (.f64 -1/2 (.f64 y y)) (fma.f64 (pow.f64 y 4) (fma.f64 z 5/48 (*.f64 z -1/16)) z))
(fma.f64 z (.f64 y (.f64 -1/2 y)) (fma.f64 (pow.f64 y 4) (*.f64 z 1/24) z))
(.f64 z (+.f64 (fma.f64 (.f64 -1/2 y) y 1) (*.f64 (pow.f64 y 4) 1/24)))
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) z)) (+.f64 (.f64 -1/720 (.f64 (pow.f64 y 6) z)) (+.f64 (.f64 (pow.f64 y 4) (-.f64 (+.f64 (.f64 1/16 z) (.f64 1/24 z)) (pow.f64 (.f64 -1/4 (sqrt.f64 z)) 2))) z)))
(fma.f64 -1/2 (.f64 z (.f64 y y)) (fma.f64 -1/720 (.f64 z (pow.f64 y 6)) (fma.f64 (pow.f64 y 4) (-.f64 (.f64 z 5/48) (pow.f64 (*.f64 -1/4 (sqrt.f64 z)) 2)) z)))
(fma.f64 z (fma.f64 -1/2 (.f64 y y) (.f64 -1/720 (pow.f64 y 6))) (fma.f64 (pow.f64 y 4) (fma.f64 z 5/48 (*.f64 z -1/16)) z))
(fma.f64 z (fma.f64 -1/2 (.f64 y y) (.f64 -1/720 (pow.f64 y 6))) (fma.f64 (pow.f64 y 4) (*.f64 z 1/24) z))
(*.f64 z (cos.f64 y))
(*.f64 z (cos.f64 y))
(*.f64 z (cos.f64 y))
(*.f64 z (cos.f64 y))
(*.f64 z (cos.f64 y))
(*.f64 z (cos.f64 y))
(*.f64 z (cos.f64 y))
(*.f64 z (cos.f64 y))
(sqrt.f64 z)
(+.f64 (sqrt.f64 z) (.f64 -1/4 (.f64 (pow.f64 y 2) (sqrt.f64 z))))
(+.f64 (sqrt.f64 z) (.f64 -1/4 (.f64 (*.f64 y y) (sqrt.f64 z))))
(fma.f64 -1/4 (.f64 (.f64 y y) (sqrt.f64 z)) (sqrt.f64 z))
(.f64 (sqrt.f64 z) (fma.f64 (.f64 y y) -1/4 1))
(+.f64 (sqrt.f64 z) (+.f64 (.f64 1/2 (.f64 (.f64 (-.f64 (.f64 1/24 z) (pow.f64 (.f64 -1/4 (sqrt.f64 z)) 2)) (pow.f64 y 4)) (sqrt.f64 (/.f64 1 z)))) (.f64 -1/4 (*.f64 (pow.f64 y 2) (sqrt.f64 z)))))
(+.f64 (sqrt.f64 z) (fma.f64 1/2 (.f64 (-.f64 (.f64 z 1/24) (pow.f64 (.f64 -1/4 (sqrt.f64 z)) 2)) (.f64 (pow.f64 y 4) (sqrt.f64 (/.f64 1 z)))) (.f64 -1/4 (.f64 (*.f64 y y) (sqrt.f64 z)))))
(+.f64 (fma.f64 -1/4 (.f64 (.f64 y y) (sqrt.f64 z)) (sqrt.f64 z)) (.f64 (-.f64 (.f64 z 1/24) (pow.f64 (.f64 -1/4 (sqrt.f64 z)) 2)) (.f64 (*.f64 (pow.f64 y 4) (sqrt.f64 (/.f64 1 z))) 1/2)))
(fma.f64 1/2 (.f64 (pow.f64 y 4) (.f64 (fma.f64 z 1/24 (.f64 z -1/16)) (sqrt.f64 (/.f64 1 z)))) (.f64 (sqrt.f64 z) (fma.f64 (*.f64 y y) -1/4 1)))
(fma.f64 (fma.f64 (.f64 y y) -1/4 1) (sqrt.f64 z) (.f64 (pow.f64 y 4) (.f64 (sqrt.f64 (/.f64 1 z)) (.f64 1/2 (*.f64 z -1/48)))))
(fma.f64 (fma.f64 (.f64 y y) -1/4 1) (sqrt.f64 z) (.f64 (sqrt.f64 (/.f64 1 z)) (.f64 (pow.f64 y 4) (.f64 1/2 (*.f64 z -1/48)))))
(+.f64 (.f64 1/2 (.f64 (.f64 (pow.f64 y 6) (-.f64 (.f64 -1/720 z) (.f64 -1/4 (-.f64 (.f64 1/24 z) (pow.f64 (.f64 -1/4 (sqrt.f64 z)) 2))))) (sqrt.f64 (/.f64 1 z)))) (+.f64 (sqrt.f64 z) (+.f64 (.f64 1/2 (.f64 (.f64 (-.f64 (.f64 1/24 z) (pow.f64 (.f64 -1/4 (sqrt.f64 z)) 2)) (pow.f64 y 4)) (sqrt.f64 (/.f64 1 z)))) (.f64 -1/4 (.f64 (pow.f64 y 2) (sqrt.f64 z))))))
(fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 z)) (.f64 (pow.f64 y 6) (+.f64 (.f64 z -1/720) (.f64 1/4 (-.f64 (.f64 z 1/24) (pow.f64 (.f64 -1/4 (sqrt.f64 z)) 2)))))) (+.f64 (sqrt.f64 z) (fma.f64 1/2 (.f64 (-.f64 (.f64 z 1/24) (pow.f64 (.f64 -1/4 (sqrt.f64 z)) 2)) (.f64 (pow.f64 y 4) (sqrt.f64 (/.f64 1 z)))) (.f64 -1/4 (.f64 (*.f64 y y) (sqrt.f64 z))))))
(+.f64 (fma.f64 -1/4 (.f64 (.f64 y y) (sqrt.f64 z)) (.f64 (-.f64 (.f64 z 1/24) (pow.f64 (.f64 -1/4 (sqrt.f64 z)) 2)) (.f64 (.f64 (pow.f64 y 4) (sqrt.f64 (/.f64 1 z))) 1/2))) (fma.f64 1/2 (.f64 (fma.f64 z -1/720 (.f64 (-.f64 (.f64 z 1/24) (pow.f64 (.f64 -1/4 (sqrt.f64 z)) 2)) 1/4)) (.f64 (pow.f64 y 6) (sqrt.f64 (/.f64 1 z)))) (sqrt.f64 z)))
(fma.f64 (pow.f64 y 6) (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 z)) (fma.f64 (fma.f64 z 1/24 (.f64 z -1/16)) 1/4 (.f64 z -1/720)))) (fma.f64 1/2 (.f64 (pow.f64 y 4) (.f64 (fma.f64 z 1/24 (.f64 z -1/16)) (sqrt.f64 (/.f64 1 z)))) (.f64 (sqrt.f64 z) (fma.f64 (*.f64 y y) -1/4 1))))
(+.f64 (.f64 (sqrt.f64 z) (fma.f64 (.f64 y y) -1/4 1)) (.f64 (.f64 1/2 (sqrt.f64 (/.f64 1 z))) (+.f64 (.f64 (pow.f64 y 6) (fma.f64 z -1/720 (.f64 -1/4 (.f64 z 1/48)))) (.f64 (pow.f64 y 4) (*.f64 z -1/48)))))

localize49.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 45 to 10 computations (77.8% saved)

series11.0ms (0.1%)

Counts

3 → 44

Calls

15 calls:

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

rewrite92.0ms (0.9%)

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 (.f64 z (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y)))
(*.f64 z (sqrt.f64 (cos.f64 y)))
(sqrt.f64 (cos.f64 y))

Outputs

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

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

simplify125.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

1013×	`fma-def_binary64`
950×	`distribute-rgt-out_binary64`
761×	`distribute-lft-out_binary64`
654×	`associate-l_binary64`
487×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	48	402
1	119	392
2	318	379
3	1042	374
4	4130	374
5	7361	374
6	7708	374
7	7938	374

Stop Event

1×	node limit

Counts

86 → 66

Calls

Call 1

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

eval169.0ms (1.7%)

Compiler: Compiled 8224 to 3415 computations (58.5% saved)

prune129.0ms (1.3%)

Pruning

28 alts after pruning (24 fresh and 4 done)

	Pruned	Kept	Total
New	458	13	471
Fresh	5	11	16
Picked	1	0	1
Done	2	4	6
Total	466	28	494

Error

0.0b

Counts

494 → 28

Alt Table

Click to see full alt table

Status	Error	Program
	14.3b	(+.f64 (pow.f64 (cbrt.f64 (*.f64 x (sin.f64 y))) 3) z)
	32.7b	(+.f64 (.f64 (.f64 x (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))) (*.f64 z (cos.f64 y)))
▶	52.9b	(*.f64 y x)
	14.3b	(+.f64 (.f64 (pow.f64 (cbrt.f64 (sin.f64 y)) 2) (.f64 (cbrt.f64 (sin.f64 y)) x)) z)
	23.3b	(+.f64 (.f64 y x) (pow.f64 (cbrt.f64 (.f64 z (cos.f64 y))) 3))
	39.6b	z
✓	29.9b	(+.f64 (cbrt.f64 (pow.f64 (*.f64 x (sin.f64 y)) 3)) z)
▶	27.1b	(+.f64 (.f64 y x) (.f64 (*.f64 z (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))))
	30.8b	(fma.f64 y x z)
	37.3b	(+.f64 (cbrt.f64 (*.f64 (pow.f64 (sin.f64 y) 3) (pow.f64 x 3))) z)
✓	30.8b	(+.f64 (*.f64 y x) z)
	38.0b	(+.f64 (.f64 (.f64 (sin.f64 y) (sqrt.f64 x)) (sqrt.f64 x)) z)
✓	31.9b	(+.f64 (.f64 x (sin.f64 y)) (pow.f64 (sqrt.f64 (.f64 z (cos.f64 y))) 2))
	1.0b	(+.f64 (.f64 x (sin.f64 y)) (pow.f64 (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 z)) 3))
	37.5b	(+.f64 (pow.f64 (sqrt.f64 (*.f64 x (sin.f64 y))) 2) z)
	14.3b	(+.f64 (.f64 (.f64 (sin.f64 y) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x)) z)
▶	42.6b	(+.f64 (.f64 y x) (pow.f64 (sqrt.f64 (.f64 z (cos.f64 y))) 2))
	0.9b	(+.f64 (.f64 x (sin.f64 y)) (.f64 (pow.f64 (cbrt.f64 z) 2) (*.f64 (cbrt.f64 z) (cos.f64 y))))
	39.3b	(+.f64 (.f64 (.f64 x (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))) z)
	31.9b	(+.f64 (.f64 x (sin.f64 y)) (.f64 (*.f64 (cos.f64 y) (sqrt.f64 z)) (sqrt.f64 z)))
	26.2b	(+.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 (pow.f64 (sin.f64 y) 3) (pow.f64 x 3)))) 3) (.f64 z (cos.f64 y)))
✓	0.2b	(+.f64 (.f64 x (sin.f64 y)) (.f64 z (cos.f64 y)))
	36.3b	(*.f64 (sin.f64 y) x)
▶	41.2b	(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) z)) z)
	41.0b	(-.f64 (+.f64 1 (fma.f64 y x z)) 1)
	22.7b	(+.f64 (.f64 y x) (.f64 z (cos.f64 y)))
	22.9b	(+.f64 (.f64 y x) (.f64 (pow.f64 (cbrt.f64 (cos.f64 y)) 2) (*.f64 (cbrt.f64 (cos.f64 y)) z)))
▶	0.5b	(+.f64 (.f64 x (sin.f64 y)) (.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (cos.f64 y))) 2) (.f64 (cbrt.f64 (cbrt.f64 (cos.f64 y))) (cbrt.f64 (cos.f64 y)))) (*.f64 (cbrt.f64 (cos.f64 y)) z)))

Compiler

Compiled 707 to 470 computations (33.5% saved)

localize53.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 103 to 25 computations (75.7% saved)

series84.0ms (0.8%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
60.0ms	y	@	inf	(cbrt.f64 (cbrt.f64 (cos.f64 y)))
16.0ms	y	@	-inf	(cbrt.f64 (cbrt.f64 (cos.f64 y)))
2.0ms	y	@	inf	(.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (cos.f64 y))) 2) (.f64 (cbrt.f64 (cbrt.f64 (cos.f64 y))) (cbrt.f64 (cos.f64 y))))
2.0ms	y	@	-inf	(.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (cos.f64 y))) 2) (.f64 (cbrt.f64 (cbrt.f64 (cos.f64 y))) (cbrt.f64 (cos.f64 y))))
1.0ms	y	@	0	(cbrt.f64 (cbrt.f64 (cos.f64 y)))

rewrite70.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

654×	`pow1_binary64`
606×	`add-log-exp_binary64`
606×	`log1p-expm1-u_binary64`
606×	`expm1-log1p-u_binary64`
589×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	29
1	181	25
2	1952	25

Stop Event

1×	node limit

Counts

3 → 51

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (cbrt.f64 (cbrt.f64 (cos.f64 y)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (cos.f64 y))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (cbrt.f64 (cbrt.f64 (cos.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (cbrt.f64 (cos.f64 y)))) (pow.f64 (cbrt.f64 (cbrt.f64 (cbrt.f64 (cos.f64 y)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (cbrt.f64 (cos.f64 y)))) 2) (cbrt.f64 (cbrt.f64 (cbrt.f64 (cos.f64 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (cos.f64 y)) 1/6) (pow.f64 (cbrt.f64 (cos.f64 y)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (cos.f64 y))) 4))) (sqrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (cbrt.f64 (cos.f64 y)))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (cbrt.f64 (cbrt.f64 (cos.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cos.f64 y) 1/6) 1/3) (pow.f64 (pow.f64 (cos.f64 y) 1/6) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cos.f64 y) 1/9)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (cos.f64 y)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (cbrt.f64 (cos.f64 y))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (cos.f64 y))) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (cbrt.f64 (cbrt.f64 (cos.f64 y)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (cbrt.f64 (cos.f64 y)) 1/6) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (cos.f64 y))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (cbrt.f64 (cbrt.f64 (cos.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (cbrt.f64 (cbrt.f64 (cos.f64 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (cbrt.f64 (cbrt.f64 (cos.f64 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (cbrt.f64 (cbrt.f64 (cos.f64 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (cbrt.f64 (cbrt.f64 (cos.f64 y)))))))))

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

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

simplify117.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

652×	`fma-def_binary64`
581×	`associate-l_binary64`
524×	`distribute-rgt-out_binary64`
461×	`unswap-sqr_binary64`
461×	`sqr-pow_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	52	492
1	126	486
2	293	476
3	885	474
4	3442	370
5	5580	370
6	6787	370
7	7259	370
8	7705	370

Stop Event

1×	node limit

Counts

87 → 73

Calls

Call 1

Inputs
1
(+.f64 1 (*.f64 -1/18 (pow.f64 y 2)))
(+.f64 1 (+.f64 (.f64 -5/648 (pow.f64 y 4)) (.f64 -1/18 (pow.f64 y 2))))
(+.f64 1 (+.f64 (.f64 -347/174960 (pow.f64 y 6)) (+.f64 (.f64 -5/648 (pow.f64 y 4)) (*.f64 -1/18 (pow.f64 y 2)))))
(pow.f64 (cos.f64 y) 1/9)
(pow.f64 (cos.f64 y) 1/9)
(pow.f64 (cos.f64 y) 1/9)
(pow.f64 (cos.f64 y) 1/9)
(pow.f64 (cos.f64 y) 1/9)
(pow.f64 (cos.f64 y) 1/9)
(pow.f64 (cos.f64 y) 1/9)
(pow.f64 (cos.f64 y) 1/9)
1
(+.f64 1 (*.f64 -1/9 (pow.f64 y 2)))
(+.f64 1 (+.f64 (.f64 -1/9 (pow.f64 y 2)) (.f64 -1/81 (pow.f64 y 4))))
(+.f64 1 (+.f64 (.f64 -1/9 (pow.f64 y 2)) (+.f64 (.f64 -1/81 (pow.f64 y 4)) (*.f64 -34/10935 (pow.f64 y 6)))))
(pow.f64 (pow.f64 (cos.f64 y) 2) 1/9)
(pow.f64 (pow.f64 (cos.f64 y) 2) 1/9)
(pow.f64 (pow.f64 (cos.f64 y) 2) 1/9)
(pow.f64 (pow.f64 (cos.f64 y) 2) 1/9)
(pow.f64 (pow.f64 (cos.f64 y) 2) 1/9)
(pow.f64 (pow.f64 (cos.f64 y) 2) 1/9)
(pow.f64 (pow.f64 (cos.f64 y) 2) 1/9)
(pow.f64 (pow.f64 (cos.f64 y) 2) 1/9)
1
(+.f64 1 (*.f64 -1/3 (pow.f64 y 2)))
(+.f64 1 (+.f64 (.f64 -1/3 (pow.f64 y 2)) (.f64 -1/405 (pow.f64 y 6))))
(+.f64 1 (+.f64 (.f64 -1/1701 (pow.f64 y 8)) (+.f64 (.f64 -1/3 (pow.f64 y 2)) (*.f64 -1/405 (pow.f64 y 6)))))
(pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)
(pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)
(pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)
(pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)
(pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)
(pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)
(pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)
(pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)

Outputs
1
(+.f64 1 (*.f64 -1/18 (pow.f64 y 2)))
(+.f64 1 (.f64 -1/18 (.f64 y y)))
(fma.f64 -1/18 (*.f64 y y) 1)
(+.f64 1 (+.f64 (.f64 -5/648 (pow.f64 y 4)) (.f64 -1/18 (pow.f64 y 2))))
(+.f64 1 (fma.f64 -5/648 (pow.f64 y 4) (.f64 -1/18 (.f64 y y))))
(+.f64 (fma.f64 -1/18 (.f64 y y) 1) (.f64 -5/648 (pow.f64 y 4)))
(fma.f64 -1/18 (*.f64 y y) (fma.f64 -5/648 (pow.f64 y 4) 1))
(fma.f64 (.f64 y y) (fma.f64 y (.f64 y -5/648) -1/18) 1)
(+.f64 1 (+.f64 (.f64 -347/174960 (pow.f64 y 6)) (+.f64 (.f64 -5/648 (pow.f64 y 4)) (*.f64 -1/18 (pow.f64 y 2)))))
(+.f64 1 (fma.f64 -347/174960 (pow.f64 y 6) (fma.f64 -5/648 (pow.f64 y 4) (.f64 -1/18 (.f64 y y)))))
(+.f64 (fma.f64 -347/174960 (pow.f64 y 6) (.f64 -5/648 (pow.f64 y 4))) (fma.f64 -1/18 (.f64 y y) 1))
(fma.f64 -347/174960 (pow.f64 y 6) (fma.f64 -1/18 (*.f64 y y) (fma.f64 -5/648 (pow.f64 y 4) 1)))
(fma.f64 -1/18 (*.f64 y y) (fma.f64 -5/648 (pow.f64 y 4) (fma.f64 -347/174960 (pow.f64 y 6) 1)))
(fma.f64 (.f64 y y) (fma.f64 y (.f64 y -5/648) -1/18) (fma.f64 -347/174960 (pow.f64 y 6) 1))
(pow.f64 (cos.f64 y) 1/9)
(*.f64 (pow.f64 (cos.f64 y) 1/18) (pow.f64 (cos.f64 y) 1/18))
(pow.f64 (pow.f64 (cos.f64 y) 1/36) 4)
(pow.f64 (pow.f64 (cos.f64 y) 1/72) 8)
(pow.f64 (cos.f64 y) 1/9)
(*.f64 (pow.f64 (cos.f64 y) 1/18) (pow.f64 (cos.f64 y) 1/18))
(pow.f64 (pow.f64 (cos.f64 y) 1/36) 4)
(pow.f64 (pow.f64 (cos.f64 y) 1/72) 8)
(pow.f64 (cos.f64 y) 1/9)
(*.f64 (pow.f64 (cos.f64 y) 1/18) (pow.f64 (cos.f64 y) 1/18))
(pow.f64 (pow.f64 (cos.f64 y) 1/36) 4)
(pow.f64 (pow.f64 (cos.f64 y) 1/72) 8)
(pow.f64 (cos.f64 y) 1/9)
(*.f64 (pow.f64 (cos.f64 y) 1/18) (pow.f64 (cos.f64 y) 1/18))
(pow.f64 (pow.f64 (cos.f64 y) 1/36) 4)
(pow.f64 (pow.f64 (cos.f64 y) 1/72) 8)
(pow.f64 (cos.f64 y) 1/9)
(*.f64 (pow.f64 (cos.f64 y) 1/18) (pow.f64 (cos.f64 y) 1/18))
(pow.f64 (pow.f64 (cos.f64 y) 1/36) 4)
(pow.f64 (pow.f64 (cos.f64 y) 1/72) 8)
(pow.f64 (cos.f64 y) 1/9)
(*.f64 (pow.f64 (cos.f64 y) 1/18) (pow.f64 (cos.f64 y) 1/18))
(pow.f64 (pow.f64 (cos.f64 y) 1/36) 4)
(pow.f64 (pow.f64 (cos.f64 y) 1/72) 8)
(pow.f64 (cos.f64 y) 1/9)
(*.f64 (pow.f64 (cos.f64 y) 1/18) (pow.f64 (cos.f64 y) 1/18))
(pow.f64 (pow.f64 (cos.f64 y) 1/36) 4)
(pow.f64 (pow.f64 (cos.f64 y) 1/72) 8)
(pow.f64 (cos.f64 y) 1/9)
(*.f64 (pow.f64 (cos.f64 y) 1/18) (pow.f64 (cos.f64 y) 1/18))
(pow.f64 (pow.f64 (cos.f64 y) 1/36) 4)
(pow.f64 (pow.f64 (cos.f64 y) 1/72) 8)
1
(+.f64 1 (*.f64 -1/9 (pow.f64 y 2)))
(+.f64 1 (.f64 (.f64 y y) -1/9))
(fma.f64 (*.f64 y y) -1/9 1)
(fma.f64 y (*.f64 y -1/9) 1)
(+.f64 1 (+.f64 (.f64 -1/9 (pow.f64 y 2)) (.f64 -1/81 (pow.f64 y 4))))
(+.f64 1 (fma.f64 -1/9 (.f64 y y) (.f64 (pow.f64 y 4) -1/81)))
(+.f64 1 (fma.f64 (pow.f64 y 4) -1/81 (.f64 y (.f64 y -1/9))))
(fma.f64 (pow.f64 y 4) -1/81 (fma.f64 y (*.f64 y -1/9) 1))
(fma.f64 (.f64 y y) (fma.f64 y (.f64 y -1/81) -1/9) 1)
(fma.f64 y (*.f64 y -1/9) (fma.f64 (pow.f64 y 4) -1/81 1))
(+.f64 1 (+.f64 (.f64 -1/9 (pow.f64 y 2)) (+.f64 (.f64 -1/81 (pow.f64 y 4)) (*.f64 -34/10935 (pow.f64 y 6)))))
(+.f64 1 (fma.f64 -1/9 (.f64 y y) (fma.f64 -1/81 (pow.f64 y 4) (.f64 (pow.f64 y 6) -34/10935))))
(+.f64 (fma.f64 (.f64 y y) -1/9 1) (fma.f64 (pow.f64 y 4) -1/81 (.f64 (pow.f64 y 6) -34/10935)))
(+.f64 1 (fma.f64 y (.f64 y -1/9) (fma.f64 (pow.f64 y 4) -1/81 (.f64 (pow.f64 y 6) -34/10935))))
(fma.f64 y (*.f64 y -1/9) (fma.f64 (pow.f64 y 4) -1/81 (fma.f64 (pow.f64 y 6) -34/10935 1)))
(pow.f64 (pow.f64 (cos.f64 y) 2) 1/9)
(*.f64 (pow.f64 (pow.f64 (cos.f64 y) 2) 1/18) (pow.f64 (pow.f64 (cos.f64 y) 2) 1/18))
(pow.f64 (pow.f64 (pow.f64 (cos.f64 y) 2) 1/36) 4)
(pow.f64 (pow.f64 (pow.f64 (cos.f64 y) 2) 1/72) 8)
(pow.f64 (pow.f64 (cos.f64 y) 2) 1/9)
(*.f64 (pow.f64 (pow.f64 (cos.f64 y) 2) 1/18) (pow.f64 (pow.f64 (cos.f64 y) 2) 1/18))
(pow.f64 (pow.f64 (pow.f64 (cos.f64 y) 2) 1/36) 4)
(pow.f64 (pow.f64 (pow.f64 (cos.f64 y) 2) 1/72) 8)
(pow.f64 (pow.f64 (cos.f64 y) 2) 1/9)
(*.f64 (pow.f64 (pow.f64 (cos.f64 y) 2) 1/18) (pow.f64 (pow.f64 (cos.f64 y) 2) 1/18))
(pow.f64 (pow.f64 (pow.f64 (cos.f64 y) 2) 1/36) 4)
(pow.f64 (pow.f64 (pow.f64 (cos.f64 y) 2) 1/72) 8)
(pow.f64 (pow.f64 (cos.f64 y) 2) 1/9)
(*.f64 (pow.f64 (pow.f64 (cos.f64 y) 2) 1/18) (pow.f64 (pow.f64 (cos.f64 y) 2) 1/18))
(pow.f64 (pow.f64 (pow.f64 (cos.f64 y) 2) 1/36) 4)
(pow.f64 (pow.f64 (pow.f64 (cos.f64 y) 2) 1/72) 8)
(pow.f64 (pow.f64 (cos.f64 y) 2) 1/9)
(*.f64 (pow.f64 (pow.f64 (cos.f64 y) 2) 1/18) (pow.f64 (pow.f64 (cos.f64 y) 2) 1/18))
(pow.f64 (pow.f64 (pow.f64 (cos.f64 y) 2) 1/36) 4)
(pow.f64 (pow.f64 (pow.f64 (cos.f64 y) 2) 1/72) 8)
(pow.f64 (pow.f64 (cos.f64 y) 2) 1/9)
(*.f64 (pow.f64 (pow.f64 (cos.f64 y) 2) 1/18) (pow.f64 (pow.f64 (cos.f64 y) 2) 1/18))
(pow.f64 (pow.f64 (pow.f64 (cos.f64 y) 2) 1/36) 4)
(pow.f64 (pow.f64 (pow.f64 (cos.f64 y) 2) 1/72) 8)
(pow.f64 (pow.f64 (cos.f64 y) 2) 1/9)
(*.f64 (pow.f64 (pow.f64 (cos.f64 y) 2) 1/18) (pow.f64 (pow.f64 (cos.f64 y) 2) 1/18))
(pow.f64 (pow.f64 (pow.f64 (cos.f64 y) 2) 1/36) 4)
(pow.f64 (pow.f64 (pow.f64 (cos.f64 y) 2) 1/72) 8)
(pow.f64 (pow.f64 (cos.f64 y) 2) 1/9)
(*.f64 (pow.f64 (pow.f64 (cos.f64 y) 2) 1/18) (pow.f64 (pow.f64 (cos.f64 y) 2) 1/18))
(pow.f64 (pow.f64 (pow.f64 (cos.f64 y) 2) 1/36) 4)
(pow.f64 (pow.f64 (pow.f64 (cos.f64 y) 2) 1/72) 8)
1
(+.f64 1 (*.f64 -1/3 (pow.f64 y 2)))
(+.f64 1 (.f64 (.f64 y y) -1/3))
(fma.f64 (*.f64 y y) -1/3 1)
(fma.f64 y (*.f64 y -1/3) 1)
(+.f64 1 (+.f64 (.f64 -1/3 (pow.f64 y 2)) (.f64 -1/405 (pow.f64 y 6))))
(+.f64 1 (fma.f64 -1/3 (.f64 y y) (.f64 (pow.f64 y 6) -1/405)))
(+.f64 1 (fma.f64 (pow.f64 y 6) -1/405 (.f64 y (.f64 y -1/3))))
(fma.f64 (pow.f64 y 6) -1/405 (fma.f64 y (*.f64 y -1/3) 1))
(fma.f64 y (*.f64 y -1/3) (fma.f64 (pow.f64 y 6) -1/405 1))
(+.f64 1 (+.f64 (.f64 -1/1701 (pow.f64 y 8)) (+.f64 (.f64 -1/3 (pow.f64 y 2)) (*.f64 -1/405 (pow.f64 y 6)))))
(+.f64 1 (fma.f64 -1/1701 (pow.f64 y 8) (fma.f64 -1/3 (.f64 y y) (.f64 (pow.f64 y 6) -1/405))))
(+.f64 1 (fma.f64 -1/1701 (pow.f64 y 8) (fma.f64 (pow.f64 y 6) -1/405 (.f64 y (.f64 y -1/3)))))
(fma.f64 -1/1701 (pow.f64 y 8) (fma.f64 (pow.f64 y 6) -1/405 (fma.f64 y (*.f64 y -1/3) 1)))
(fma.f64 y (*.f64 y -1/3) (fma.f64 (pow.f64 y 6) -1/405 (fma.f64 -1/1701 (pow.f64 y 8) 1)))
(pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)
(cbrt.f64 (pow.f64 (cos.f64 y) 2))
(pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)
(cbrt.f64 (pow.f64 (cos.f64 y) 2))
(pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)
(cbrt.f64 (pow.f64 (cos.f64 y) 2))
(pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)
(cbrt.f64 (pow.f64 (cos.f64 y) 2))
(pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)
(cbrt.f64 (pow.f64 (cos.f64 y) 2))
(pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)
(cbrt.f64 (pow.f64 (cos.f64 y) 2))
(pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)
(cbrt.f64 (pow.f64 (cos.f64 y) 2))
(pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)
(cbrt.f64 (pow.f64 (cos.f64 y) 2))

localize4.0ms (0%)

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

localize14.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 -1/2 (.f64 (pow.f64 y 2) z))
	0.0b	(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) z)) z)
	6.3b	(*.f64 (pow.f64 y 2) z)

Compiler

Compiled 31 to 21 computations (32.3% saved)

series2.0ms (0%)

Counts

1 → 0

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	y	@	0	(.f64 -1/2 (.f64 (pow.f64 y 2) z))
0.0ms	y	@	inf	(.f64 -1/2 (.f64 (pow.f64 y 2) z))
0.0ms	z	@	0	(.f64 -1/2 (.f64 (pow.f64 y 2) z))
0.0ms	y	@	-inf	(.f64 -1/2 (.f64 (pow.f64 y 2) z))
0.0ms	z	@	inf	(.f64 -1/2 (.f64 (pow.f64 y 2) z))

rewrite50.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

690×	`pow1_binary64`
636×	`add-log-exp_binary64`
636×	`log1p-expm1-u_binary64`
636×	`expm1-log1p-u_binary64`
623×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	165	10
2	1791	10

Stop Event

1×	node limit

Counts

1 → 11

Calls

Call 1

Inputs
(.f64 -1/2 (.f64 (pow.f64 y 2) z))

Outputs

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

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

11 → 11

Calls

Call 1

Inputs

Outputs

localize17.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(sqrt.f64 (*.f64 z (cos.f64 y)))
	0.1b	(*.f64 z (cos.f64 y))
	0.2b	(pow.f64 (sqrt.f64 (*.f64 z (cos.f64 y))) 2)

Compiler

Compiled 39 to 13 computations (66.7% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 41 to 9 computations (78% saved)

series5.0ms (0%)

Counts

1 → 36

Calls

9 calls:

Time	Variable		Point	Expression
2.0ms	x	@	0	(+.f64 (.f64 y x) (.f64 (*.f64 z (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))))
0.0ms	y	@	0	(+.f64 (.f64 y x) (.f64 (*.f64 z (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))))
0.0ms	y	@	inf	(+.f64 (.f64 y x) (.f64 (*.f64 z (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))))
0.0ms	z	@	-inf	(+.f64 (.f64 y x) (.f64 (*.f64 z (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))))
0.0ms	y	@	-inf	(+.f64 (.f64 y x) (.f64 (*.f64 z (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))))

rewrite74.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

555×	`log-prod_binary64`
416×	`pow-prod-down_binary64`
391×	`exp-prod_binary64`
375×	`fma-def_binary64`
275×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	10
1	209	10
2	2795	10

Stop Event

1×	node limit

Counts

1 → 80

Calls

Call 1

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

Outputs

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

simplify215.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	26	326
1	58	324
2	133	323
3	356	321
4	1215	318
5	2715	318
6	3881	318
7	3962	318
8	4085	318
9	4240	318
10	4504	318
11	4761	318
12	5118	318
13	5492	318
14	5985	318
15	6572	318
16	7288	318
17	7616	318
18	7880	318

Stop Event

1×	node limit

Counts

116 → 93

Calls

Call 1

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

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

eval256.0ms (2.6%)

Compiler: Compiled 12055 to 4358 computations (63.8% saved)

prune259.0ms (2.6%)

Pruning

30 alts after pruning (23 fresh and 7 done)

	Pruned	Kept	Total
New	574	11	585
Fresh	7	12	19
Picked	0	1	1
Done	2	6	8
Total	583	30	613

Error

0.0b

Counts

613 → 30

Alt Table

Click to see full alt table

Status	Error	Program
	14.3b	(+.f64 (pow.f64 (cbrt.f64 (*.f64 x (sin.f64 y))) 3) z)
	32.7b	(+.f64 (.f64 (.f64 x (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))) (*.f64 z (cos.f64 y)))
	22.9b	(+.f64 (.f64 y x) (.f64 (pow.f64 (cbrt.f64 (cos.f64 y)) 2) (*.f64 (cbrt.f64 (cos.f64 y)) z)))
✓	52.9b	(*.f64 y x)
	14.3b	(+.f64 (.f64 (pow.f64 (cbrt.f64 (sin.f64 y)) 2) (.f64 (cbrt.f64 (sin.f64 y)) x)) z)
	37.1b	(fma.f64 (cbrt.f64 (.f64 z z)) (.f64 (cbrt.f64 z) (cos.f64 y)) (*.f64 y x))
	39.6b	z
	23.3b	(+.f64 (.f64 y x) (pow.f64 (cbrt.f64 (.f64 z (cos.f64 y))) 3))
✓	27.1b	(+.f64 (.f64 y x) (.f64 (*.f64 z (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))))
	62.5b	(.f64 y (.f64 y (*.f64 z -1/2)))
✓	29.9b	(+.f64 (cbrt.f64 (pow.f64 (*.f64 x (sin.f64 y)) 3)) z)
	37.3b	(+.f64 (cbrt.f64 (*.f64 (pow.f64 (sin.f64 y) 3) (pow.f64 x 3))) z)
✓	30.8b	(+.f64 (*.f64 y x) z)
	38.0b	(+.f64 (.f64 (.f64 (sin.f64 y) (sqrt.f64 x)) (sqrt.f64 x)) z)
✓	31.9b	(+.f64 (.f64 x (sin.f64 y)) (pow.f64 (sqrt.f64 (.f64 z (cos.f64 y))) 2))
	41.1b	(+.f64 (.f64 -1/2 (+.f64 0 (.f64 y (*.f64 y z)))) z)
	1.0b	(+.f64 (.f64 x (sin.f64 y)) (pow.f64 (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 z)) 3))
	37.5b	(+.f64 (pow.f64 (sqrt.f64 (*.f64 x (sin.f64 y))) 2) z)
	14.3b	(+.f64 (.f64 (.f64 (sin.f64 y) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x)) z)
✓	42.6b	(+.f64 (.f64 y x) (pow.f64 (sqrt.f64 (.f64 z (cos.f64 y))) 2))
	0.9b	(+.f64 (.f64 x (sin.f64 y)) (.f64 (pow.f64 (cbrt.f64 z) 2) (*.f64 (cbrt.f64 z) (cos.f64 y))))
	43.5b	(+.f64 (.f64 y x) (.f64 (*.f64 (cos.f64 y) (sqrt.f64 z)) (sqrt.f64 z)))
	39.3b	(+.f64 (.f64 (.f64 x (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))) z)
	26.7b	(*.f64 (cos.f64 y) z)
	26.2b	(+.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 (pow.f64 (sin.f64 y) 3) (pow.f64 x 3)))) 3) (.f64 z (cos.f64 y)))
	41.2b	(.f64 z (+.f64 1 (.f64 (*.f64 y y) -1/2)))
✓	0.2b	(+.f64 (.f64 x (sin.f64 y)) (.f64 z (cos.f64 y)))
	36.3b	(*.f64 (sin.f64 y) x)
	41.1b	(+.f64 (-.f64 (+.f64 1 (.f64 z (.f64 (*.f64 -1/2 y) y))) 1) z)
	0.3b	(+.f64 (.f64 x (sin.f64 y)) (.f64 (sqrt.f64 (.f64 (cos.f64 y) (cbrt.f64 (cos.f64 y)))) (.f64 (cbrt.f64 (cos.f64 y)) z)))

Compiler

Compiled 404 to 274 computations (32.2% saved)

regimes287.0ms (2.9%)

Counts

53 → 1

Calls

Call 1

Inputs
z
z
(*.f64 y x)
(+.f64 (*.f64 y x) z)
(.f64 y (.f64 y (*.f64 z -1/2)))
(.f64 z (+.f64 1 (.f64 (*.f64 y y) -1/2)))
(+.f64 (.f64 -1/2 (+.f64 0 (.f64 y (*.f64 y z)))) z)
(+.f64 (-.f64 (+.f64 1 (.f64 z (.f64 (*.f64 -1/2 y) y))) 1) z)
(*.f64 (cos.f64 y) z)
(fma.f64 y x z)
(fma.f64 y x z)
(*.f64 (sin.f64 y) x)
(+.f64 (*.f64 x (sin.f64 y)) z)
(-.f64 (+.f64 1 (fma.f64 y x z)) 1)
(+.f64 (.f64 y x) (.f64 z (cos.f64 y)))
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) z)) z)
(+.f64 (.f64 x (sin.f64 y)) (.f64 z (cos.f64 y)))
(+.f64 (.f64 x (sin.f64 y)) (+.f64 (.f64 -1/2 (*.f64 (pow.f64 y 2) z)) z))
(+.f64 (pow.f64 (cbrt.f64 (*.f64 x (sin.f64 y))) 3) z)
(+.f64 (cbrt.f64 (pow.f64 (*.f64 x (sin.f64 y)) 3)) z)
(+.f64 (pow.f64 (sqrt.f64 (*.f64 x (sin.f64 y))) 2) z)
(+.f64 (.f64 (.f64 (sin.f64 y) (sqrt.f64 x)) (sqrt.f64 x)) z)
(+.f64 (.f64 y x) (pow.f64 (cbrt.f64 (.f64 z (cos.f64 y))) 3))
(+.f64 (.f64 y x) (pow.f64 (sqrt.f64 (.f64 z (cos.f64 y))) 2))
(+.f64 (.f64 y x) (pow.f64 (cbrt.f64 (.f64 z (cos.f64 y))) 3))
(+.f64 (.f64 y x) (.f64 (*.f64 (cos.f64 y) (sqrt.f64 z)) (sqrt.f64 z)))
(+.f64 (.f64 (.f64 x (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))) z)
(+.f64 (cbrt.f64 (*.f64 (pow.f64 (sin.f64 y) 3) (pow.f64 x 3))) z)
(+.f64 (.f64 (.f64 (sin.f64 y) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x)) z)
(+.f64 (cbrt.f64 (pow.f64 (.f64 x (sin.f64 y)) 3)) (.f64 z (cos.f64 y)))
(+.f64 (.f64 x (sin.f64 y)) (pow.f64 (sqrt.f64 (.f64 z (cos.f64 y))) 2))
(+.f64 (pow.f64 (sqrt.f64 (.f64 x (sin.f64 y))) 2) (.f64 z (cos.f64 y)))
(+.f64 (pow.f64 (cbrt.f64 (.f64 x (sin.f64 y))) 3) (.f64 z (cos.f64 y)))
(+.f64 (.f64 x (sin.f64 y)) (pow.f64 (cbrt.f64 (.f64 z (cos.f64 y))) 3))
(fma.f64 (cbrt.f64 (.f64 z z)) (.f64 (cbrt.f64 z) (cos.f64 y)) (*.f64 y x))
(+.f64 (.f64 y x) (.f64 (*.f64 z (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))))
(+.f64 (.f64 x (sin.f64 y)) (.f64 (*.f64 (cos.f64 y) (sqrt.f64 z)) (sqrt.f64 z)))
(+.f64 (.f64 (pow.f64 (cbrt.f64 (sin.f64 y)) 2) (.f64 (cbrt.f64 (sin.f64 y)) x)) z)
(+.f64 (pow.f64 (.f64 (sqrt.f64 (sin.f64 y)) (sqrt.f64 x)) 2) (.f64 z (cos.f64 y)))
(+.f64 (.f64 x (sin.f64 y)) (pow.f64 (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 z)) 3))
(+.f64 (pow.f64 (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 x)) 3) (.f64 z (cos.f64 y)))
(+.f64 (.f64 (.f64 x (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))) (*.f64 z (cos.f64 y)))
(+.f64 (.f64 x (sin.f64 y)) (.f64 (*.f64 z (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))))
(+.f64 (cbrt.f64 (.f64 (pow.f64 (sin.f64 y) 3) (pow.f64 x 3))) (.f64 z (cos.f64 y)))
(+.f64 (.f64 y x) (.f64 (pow.f64 (cbrt.f64 (cos.f64 y)) 2) (*.f64 (cbrt.f64 (cos.f64 y)) z)))
(+.f64 (.f64 x (sin.f64 y)) (.f64 (pow.f64 (cbrt.f64 z) 2) (*.f64 (cbrt.f64 z) (cos.f64 y))))
(+.f64 (.f64 y x) (.f64 (pow.f64 (cbrt.f64 (cos.f64 y)) 2) (*.f64 (cbrt.f64 (cos.f64 y)) z)))
(+.f64 (pow.f64 (pow.f64 (pow.f64 (.f64 x (sin.f64 y)) 1/4) 2) 2) (.f64 z (cos.f64 y)))
(+.f64 (.f64 x (sin.f64 y)) (.f64 (pow.f64 (cbrt.f64 z) 2) (*.f64 (cbrt.f64 z) (cos.f64 y))))
(+.f64 (.f64 x (sin.f64 y)) (.f64 (pow.f64 (cbrt.f64 (cos.f64 y)) 2) (*.f64 (cbrt.f64 (cos.f64 y)) z)))
(+.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 (pow.f64 (sin.f64 y) 3) (pow.f64 x 3)))) 3) (.f64 z (cos.f64 y)))
(+.f64 (.f64 x (sin.f64 y)) (.f64 (sqrt.f64 (.f64 (cos.f64 y) (cbrt.f64 (cos.f64 y)))) (.f64 (cbrt.f64 (cos.f64 y)) z)))
(+.f64 (.f64 x (sin.f64 y)) (.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (cos.f64 y))) 2) (.f64 (cbrt.f64 (cbrt.f64 (cos.f64 y))) (cbrt.f64 (cos.f64 y)))) (*.f64 (cbrt.f64 (cos.f64 y)) z)))

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

Calls

4 calls:

77.0ms	z
65.0ms	y
44.0ms	(+.f64 (.f64 x (sin.f64 y)) (.f64 z (cos.f64 y)))
43.0ms	x

Results

Error	Segments	Branch
0.2b	1	`x`
0.2b	1	`y`
0.2b	1	`z`
0.2b	1	`(+.f64 (.f64 x (sin.f64 y)) (.f64 z (cos.f64 y)))`

Compiler

Compiled 608 to 226 computations (62.8% saved)

regimes366.0ms (3.7%)

Counts

16 → 5

Calls

Call 1

Inputs
z
z
(*.f64 y x)
(+.f64 (*.f64 y x) z)
(.f64 y (.f64 y (*.f64 z -1/2)))
(.f64 z (+.f64 1 (.f64 (*.f64 y y) -1/2)))
(+.f64 (.f64 -1/2 (+.f64 0 (.f64 y (*.f64 y z)))) z)
(+.f64 (-.f64 (+.f64 1 (.f64 z (.f64 (*.f64 -1/2 y) y))) 1) z)
(*.f64 (cos.f64 y) z)
(fma.f64 y x z)
(fma.f64 y x z)
(*.f64 (sin.f64 y) x)
(+.f64 (*.f64 x (sin.f64 y)) z)
(-.f64 (+.f64 1 (fma.f64 y x z)) 1)
(+.f64 (.f64 y x) (.f64 z (cos.f64 y)))
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) z)) z)

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

Calls

3 calls:

165.0ms	y
119.0ms	z
75.0ms	x

Results

Error	Segments	Branch
7.2b	3	`x`
10.5b	5	`y`
7.0b	5	`z`

Compiler

Compiled 112 to 59 computations (47.3% saved)

bsearch475.0ms (4.8%)

Algorithm

4×	binary-search

Steps

Time	Left	Right
122.0ms	6.1808399442153046e+47	1.5470975288538274e+56
122.0ms	-9.071300668515432e-14	-1.1576661129978958e-20
140.0ms	-6.1218348465704036e+41	-5.001972212645505e+39
91.0ms	-8.069696018579312e+196	-1.2582800421291595e+194

Compiler

Compiled 18 to 13 computations (27.8% saved)

regimes240.0ms (2.4%)

Counts

12 → 7

Calls

Call 1

Inputs
z
z
(*.f64 y x)
(+.f64 (*.f64 y x) z)
(.f64 y (.f64 y (*.f64 z -1/2)))
(.f64 z (+.f64 1 (.f64 (*.f64 y y) -1/2)))
(+.f64 (.f64 -1/2 (+.f64 0 (.f64 y (*.f64 y z)))) z)
(+.f64 (-.f64 (+.f64 1 (.f64 z (.f64 (*.f64 -1/2 y) y))) 1) z)
(*.f64 (cos.f64 y) z)
(fma.f64 y x z)
(fma.f64 y x z)
(*.f64 (sin.f64 y) x)

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

Calls

3 calls:

91.0ms	y
75.0ms	z
70.0ms	x

Results

Error	Segments	Branch
13.7b	3	`x`
11.1b	7	`y`
14.3b	5	`z`

Compiler

Compiled 81 to 45 computations (44.4% saved)

bsearch633.0ms (6.4%)

Algorithm

6×	binary-search

Steps

Time	Left	Right
68.0ms	0.08839147709823608	6.904028969813479
46.0ms	-10604636.769083364	-5.025292739923839e-8
141.0ms	-7.58325743152806e+89	-2.0759025492798803e+86
134.0ms	-1.6551753127859233e+187	-1.3670252685500282e+187
117.0ms	-7.73123433079739e+213	-4.010715378716946e+212
127.0ms	-4.467235781468881e+269	-2.0671629876694233e+263

Compiler

Compiled 18 to 13 computations (27.8% saved)

regimes179.0ms (1.8%)

Counts

11 → 3

Calls

Call 1

Inputs
z
z
(*.f64 y x)
(+.f64 (*.f64 y x) z)
(.f64 y (.f64 y (*.f64 z -1/2)))
(.f64 z (+.f64 1 (.f64 (*.f64 y y) -1/2)))
(+.f64 (.f64 -1/2 (+.f64 0 (.f64 y (*.f64 y z)))) z)
(+.f64 (-.f64 (+.f64 1 (.f64 z (.f64 (*.f64 -1/2 y) y))) 1) z)
(*.f64 (cos.f64 y) z)
(fma.f64 y x z)
(fma.f64 y x z)

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

Calls

3 calls:

126.0ms	y
27.0ms	x
22.0ms	z

Results

Error	Segments	Branch
20.8b	3	`x`
17.4b	3	`y`
20.6b	3	`z`

Compiler

Compiled 77 to 43 computations (44.2% saved)

bsearch116.0ms (1.2%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
75.0ms	9.789299162384845e-16	0.00012028864921560288
41.0ms	-6.22550385717427e+34	-1.0562257270902327e+29

Compiler

Compiled 18 to 13 computations (27.8% saved)

regimes22.0ms (0.2%)

Counts

8 → 1

Calls

Call 1

Inputs
z
z
(*.f64 y x)
(+.f64 (*.f64 y x) z)
(.f64 y (.f64 y (*.f64 z -1/2)))
(.f64 z (+.f64 1 (.f64 (*.f64 y y) -1/2)))
(+.f64 (.f64 -1/2 (+.f64 0 (.f64 y (*.f64 y z)))) z)
(+.f64 (-.f64 (+.f64 1 (.f64 z (.f64 (*.f64 -1/2 y) y))) 1) z)

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

Calls

3 calls:

7.0ms	z
5.0ms	x
5.0ms	y

Results

Error	Segments	Branch
30.8b	1	`x`
30.8b	1	`y`
30.8b	1	`z`

Compiler

Compiled 65 to 40 computations (38.5% saved)

regimes33.0ms (0.3%)

Counts

3 → 3

Calls

Call 1

Inputs
z
z
(*.f64 y x)

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

Calls

3 calls:

14.0ms	z
14.0ms	x
4.0ms	y

Results

Error	Segments	Branch
35.2b	3	`x`
39.6b	1	`y`
35.9b	3	`z`

Compiler

Compiled 20 to 13 computations (35% saved)

bsearch198.0ms (2%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
57.0ms	3.840291792634429e+77	4.09667594258213e+77
141.0ms	-1.1660026554212445e+118	-3.447416757579016e+117

Compiler

Compiled 18 to 13 computations (27.8% saved)

regimes10.0ms (0.1%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0.0b (-0%)

Counts

2 → 1

Calls

Call 1

Inputs
z
z

Outputs
z

Calls

3 calls:

3.0ms	z
3.0ms	y
3.0ms	x

Results

Error	Segments	Branch
39.6b	1	`x`
39.6b	1	`y`
39.6b	1	`z`

Compiler

Compiled 17 to 12 computations (29.4% saved)

simplify46.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	213
1	63	213

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(+.f64 (.f64 x (sin.f64 y)) (.f64 z (cos.f64 y)))
(if (<=.f64 z -80696960185793117418418492977943268870327980530031957292705086622062209663580833948103109400334086037599137240729993820671848948351896946650531956240498468189405212503048376602193895137110378151936) (.f64 (cos.f64 y) z) (if (<=.f64 z -612183484657040359748470836321241335332864) (+.f64 (.f64 x (sin.f64 y)) z) (if (<=.f64 z -7187024835808954/79228162514264337593543950336) (.f64 (cos.f64 y) z) (if (<=.f64 z 618083994421530457890804952986795969439573475328) (+.f64 (.f64 x (sin.f64 y)) z) (*.f64 (cos.f64 y) z)))))
(if (<=.f64 y -446723578146888114905140502667146732167601747351298119695531847089882952548351902617787805633893631460850862461808944845057217030705896779865475445174598980258804229209968375653309685925463450623550841136980775993004810489436698548930166270757722892775689647464013365248) (.f64 (sin.f64 y) x) (if (<=.f64 y -7731234330797390218459609206827994840741265724685444951773957676317046720286916913926377078902197716610308268486969771806984420191009229451277907086238106523464731719125073814660069823715934527296640503825882415104) (.f64 (cos.f64 y) z) (if (<=.f64 y -16551753127859232648373331454702849988017578769505670130453150669975857257508069702555482865846186819758165656356366190825881307899974270540330659143572912015832896776043317328714305372160) (.f64 (sin.f64 y) x) (if (<=.f64 y -758325743152806013951705039971629235505177337563619300967984824736736194982359030959177728) (.f64 (cos.f64 y) z) (if (<=.f64 y -45546568109172152/4294967296) (.f64 (sin.f64 y) x) (if (<=.f64 y 1630534956328320000/18446744073709551616) (+.f64 (.f64 y x) z) (*.f64 (sin.f64 y) x)))))))
(if (<=.f64 y -62255038571742699602444550194331648) (.f64 (cos.f64 y) z) (if (<=.f64 y 4963764383604341/5070602400912917605986812821504) (+.f64 (.f64 y x) z) (*.f64 (cos.f64 y) z)))
(+.f64 (*.f64 y x) z)
(if (<=.f64 x -11660026554212444966310322289247636812736516650732823046703759746481582299734702514426936352305076677752168269922435072) (.f64 y x) (if (<=.f64 x 384029179263442900427246529109638289548696076289593884072852399416155970732032) z (.f64 y x)))
z

Outputs
(+.f64 (.f64 x (sin.f64 y)) (.f64 z (cos.f64 y)))
(+.f64 (.f64 z (cos.f64 y)) (.f64 x (sin.f64 y)))
(if (<=.f64 z -80696960185793117418418492977943268870327980530031957292705086622062209663580833948103109400334086037599137240729993820671848948351896946650531956240498468189405212503048376602193895137110378151936) (.f64 (cos.f64 y) z) (if (<=.f64 z -612183484657040359748470836321241335332864) (+.f64 (.f64 x (sin.f64 y)) z) (if (<=.f64 z -7187024835808954/79228162514264337593543950336) (.f64 (cos.f64 y) z) (if (<=.f64 z 618083994421530457890804952986795969439573475328) (+.f64 (.f64 x (sin.f64 y)) z) (*.f64 (cos.f64 y) z)))))
(if (<=.f64 z -80696960185793117418418492977943268870327980530031957292705086622062209663580833948103109400334086037599137240729993820671848948351896946650531956240498468189405212503048376602193895137110378151936) (.f64 z (cos.f64 y)) (if (<=.f64 z -612183484657040359748470836321241335332864) (+.f64 z (.f64 x (sin.f64 y))) (if (<=.f64 z -3593512417904477/39614081257132168796771975168) (.f64 z (cos.f64 y)) (if (<=.f64 z 618083994421530457890804952986795969439573475328) (+.f64 z (.f64 x (sin.f64 y))) (*.f64 z (cos.f64 y))))))
(if (<=.f64 y -446723578146888114905140502667146732167601747351298119695531847089882952548351902617787805633893631460850862461808944845057217030705896779865475445174598980258804229209968375653309685925463450623550841136980775993004810489436698548930166270757722892775689647464013365248) (.f64 (sin.f64 y) x) (if (<=.f64 y -7731234330797390218459609206827994840741265724685444951773957676317046720286916913926377078902197716610308268486969771806984420191009229451277907086238106523464731719125073814660069823715934527296640503825882415104) (.f64 (cos.f64 y) z) (if (<=.f64 y -16551753127859232648373331454702849988017578769505670130453150669975857257508069702555482865846186819758165656356366190825881307899974270540330659143572912015832896776043317328714305372160) (.f64 (sin.f64 y) x) (if (<=.f64 y -758325743152806013951705039971629235505177337563619300967984824736736194982359030959177728) (.f64 (cos.f64 y) z) (if (<=.f64 y -45546568109172152/4294967296) (.f64 (sin.f64 y) x) (if (<=.f64 y 1630534956328320000/18446744073709551616) (+.f64 (.f64 y x) z) (*.f64 (sin.f64 y) x)))))))
(if (<=.f64 y -446723578146888114905140502667146732167601747351298119695531847089882952548351902617787805633893631460850862461808944845057217030705896779865475445174598980258804229209968375653309685925463450623550841136980775993004810489436698548930166270757722892775689647464013365248) (.f64 x (sin.f64 y)) (if (<=.f64 y -7731234330797390218459609206827994840741265724685444951773957676317046720286916913926377078902197716610308268486969771806984420191009229451277907086238106523464731719125073814660069823715934527296640503825882415104) (.f64 z (cos.f64 y)) (if (<=.f64 y -16551753127859232648373331454702849988017578769505670130453150669975857257508069702555482865846186819758165656356366190825881307899974270540330659143572912015832896776043317328714305372160) (.f64 x (sin.f64 y)) (if (<=.f64 y -758325743152806013951705039971629235505177337563619300967984824736736194982359030959177728) (.f64 z (cos.f64 y)) (if (<=.f64 y -5693321013646519/536870912) (.f64 x (sin.f64 y)) (if (<=.f64 y 1592319293289375/18014398509481984) (+.f64 z (.f64 x y)) (*.f64 x (sin.f64 y))))))))
(if (<=.f64 y -62255038571742699602444550194331648) (.f64 (cos.f64 y) z) (if (<=.f64 y 4963764383604341/5070602400912917605986812821504) (+.f64 (.f64 y x) z) (*.f64 (cos.f64 y) z)))
(if (<=.f64 y -62255038571742699602444550194331648) (.f64 z (cos.f64 y)) (if (<=.f64 y 4963764383604341/5070602400912917605986812821504) (+.f64 z (.f64 x y)) (*.f64 z (cos.f64 y))))
(+.f64 (*.f64 y x) z)
(+.f64 z (*.f64 x y))
(if (<=.f64 x -11660026554212444966310322289247636812736516650732823046703759746481582299734702514426936352305076677752168269922435072) (.f64 y x) (if (<=.f64 x 384029179263442900427246529109638289548696076289593884072852399416155970732032) z (.f64 y x)))
(if (<=.f64 x -11660026554212444966310322289247636812736516650732823046703759746481582299734702514426936352305076677752168269922435072) (.f64 x y) (if (<=.f64 x 384029179263442900427246529109638289548696076289593884072852399416155970732032) z (.f64 x y)))
z

Compiler

Compiled 165 to 86 computations (47.9% saved)

soundness0.0ms (0%)

end82.0ms (0.8%)

Compiler: Compiled 147 to 53 computations (63.9% saved)