Details

analyze279.0ms (4.3%)

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 (38.9%)

Results

1.1s	2131×	body	1024	valid
1.0s	5072×	body	256	valid
416.0ms	1049×	body	512	valid
3.0ms	4×	body	2048	valid

preprocess17.0ms (0.3%)

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)

simplify6.0ms (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

0.1b

Counts

3 → 1

Alt Table

Click to see full alt table

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

Compiler

Compiled 12 to 8 computations (33.3% saved)

localize11.0ms (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))
✓	0.1b	(*.f64 z (cos.f64 y))
✓	0.1b	(*.f64 x (sin.f64 y))

Compiler

Compiled 27 to 8 computations (70.4% saved)

series7.0ms (0.1%)

Counts

2 → 40

Calls

12 calls:

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

rewrite38.0ms (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 x (sin.f64 y))
(*.f64 z (cos.f64 y))

Outputs
((#(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 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 expm1.f64 (log1p.f64 (.f64 x (sin.f64 y))))))))
((#(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 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 expm1.f64 (log1p.f64 (.f64 z (cos.f64 y))))))))

Outputs

((#(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 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 expm1.f64 (log1p.f64 (*.f64 x (sin.f64 y))))))))

((#(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 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 expm1.f64 (log1p.f64 (*.f64 z (cos.f64 y))))))))

simplify101.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

1987×	`fma-def_binary64`
723×	`sqr-pow_binary64`
499×	`pow-sqr_binary64`
439×	`*-commutative_binary64`
375×	`cube-prod_binary64`

Iterations

Useful iterations: 8 (0.0ms)

Iter	Nodes	Cost
0	49	336
1	129	329
2	357	314
3	1202	313
4	1944	313
5	2853	313
6	2991	313
7	3208	313
8	3424	305
9	5378	305
10	5791	305
11	6299	305
12	6896	305
13	7603	305

Stop Event

1×	node limit

Counts

66 → 42

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 (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)
(*.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)))))

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

eval10.0ms (0.1%)

Compiler: Compiled 595 to 258 computations (56.6% saved)

prune13.0ms (0.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	34	8	42
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	34	9	43

Error

0.1b

Counts

43 → 9

Alt Table

Click to see full alt table

Status	Error	Program
▶	28.3b	(+.f64 (.f64 x (sin.f64 y)) (cbrt.f64 (.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 z 3))))
	30.8b	(+.f64 (+.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 z (cos.f64 y)))
▶	28.3b	(+.f64 (.f64 x (sin.f64 y)) (cbrt.f64 (pow.f64 (.f64 z (cos.f64 y)) 3)))
	29.6b	(+.f64 (pow.f64 (sqrt.f64 (.f64 x (sin.f64 y))) 2) (.f64 z (cos.f64 y)))
▶	31.4b	(+.f64 (.f64 x (sin.f64 y)) (pow.f64 (sqrt.f64 (.f64 z (cos.f64 y))) 2))
	23.8b	(+.f64 (.f64 y x) (.f64 z (cos.f64 y)))
▶	0.9b	(+.f64 (.f64 x (sin.f64 y)) (pow.f64 (cbrt.f64 (.f64 z (cos.f64 y))) 3))
✓	0.1b	(+.f64 (.f64 x (sin.f64 y)) (.f64 z (cos.f64 y)))
▶	15.2b	(+.f64 (*.f64 x (sin.f64 y)) z)

Compiler

Compiled 276 to 198 computations (28.3% saved)

localize17.0ms (0.3%)

Local error

Found 8 expressions with local error:

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

series14.0ms (0.2%)

Counts

2 → 24

Calls

12 calls:

Time	Variable		Point	Expression
4.0ms	y	@	0	(pow.f64 (cbrt.f64 (*.f64 z (cos.f64 y))) 3)
3.0ms	y	@	inf	(pow.f64 (cbrt.f64 (*.f64 z (cos.f64 y))) 3)
2.0ms	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)
1.0ms	z	@	0	(pow.f64 (cbrt.f64 (*.f64 z (cos.f64 y))) 3)

rewrite41.0ms (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
(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 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 expm1.f64 (log1p.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 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)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (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 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 expm1.f64 (log1p.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 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)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (cbrt.f64 (*.f64 z (cos.f64 y)))))))))

simplify106.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

696×	`associate-r_binary64`
686×	`associate-l_binary64`
551×	`fma-def_binary64`
423×	`distribute-rgt-out_binary64`
230×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	89	496
1	277	453
2	968	401
3	5741	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 (.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 (cbrt.f64 (/.f64 1 z)) (.f64 z -1/36) (.f64 1/36 (cbrt.f64 (.f64 z z)))) (fma.f64 z 1/18 (.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 z -1/24) -1/9))) (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 (.f64 z -1/24) (cbrt.f64 (/.f64 1 z))) (.f64 1/36 (cbrt.f64 (.f64 z z)))) (.f64 (.f64 z -1/24) -1/9)))) (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 (.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 z (.f64 (.f64 y y) -1/2) (fma.f64 (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)) (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)))) (fma.f64 z 1/18 (.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 (.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 (.f64 y y) (cbrt.f64 z)) (cbrt.f64 z)))
(fma.f64 (cbrt.f64 (/.f64 1 (.f64 z z))) (.f64 (.f64 z -1/72) (pow.f64 y 4)) (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 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 (.f64 y 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 (.f64 z -1/24) (pow.f64 y 4))) (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)))

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 18 to 6 computations (66.7% saved)

rewrite0.0ms (0%)

Counts: 0 → 0

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

0 → 0

Calls

Call 1

Inputs

Outputs

localize16.0ms (0.2%)

Local error

Found 8 expressions with local error:

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

Compiler

Compiled 43 to 14 computations (67.4% saved)

series8.0ms (0.1%)

Counts

2 → 16

Calls

12 calls:

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

rewrite38.0ms (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	1591	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 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 expm1.f64 (log1p.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 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)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 z (cos.f64 y)))))))))

simplify36.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

426×	`*-commutative_binary64`
398×	`distribute-rgt-in_binary64`
389×	`distribute-lft-in_binary64`
311×	`distribute-lft-out_binary64`
306×	`unswap-sqr_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	53	293
1	144	289
2	411	241
3	1770	214
4	5065	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)
(fma.f64 (.f64 y y) (.f64 z -1/2) z)
(.f64 z (fma.f64 -1/2 (.f64 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 -1/2 (.f64 y y)) (fma.f64 (pow.f64 y 4) (*.f64 z 1/24) z))
(.f64 z (+.f64 (.f64 (pow.f64 y 4) 1/24) (fma.f64 -1/2 (*.f64 y y) 1)))
(+.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 y (.f64 y (sqrt.f64 z))) (sqrt.f64 z))
(.f64 (sqrt.f64 z) (fma.f64 (.f64 y y) -1/4 1))
(.f64 (sqrt.f64 z) (fma.f64 (.f64 y -1/4) y 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 (.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 -1/4 (.f64 y (*.f64 y (sqrt.f64 z))) (sqrt.f64 z)))
(fma.f64 1/2 (.f64 (fma.f64 z 1/24 (.f64 z -1/16)) (.f64 (pow.f64 y 4) (sqrt.f64 (/.f64 1 z)))) (.f64 (sqrt.f64 z) (fma.f64 (*.f64 y y) -1/4 1)))
(fma.f64 1/2 (.f64 (pow.f64 y 4) (.f64 (.f64 z -1/48) (sqrt.f64 (/.f64 1 z)))) (.f64 (sqrt.f64 z) (fma.f64 (*.f64 y -1/4) y 1)))
(fma.f64 (fma.f64 (.f64 y y) -1/4 1) (sqrt.f64 z) (.f64 (.f64 z -1/48) (.f64 (sqrt.f64 (/.f64 1 z)) (*.f64 (pow.f64 y 4) 1/2))))
(+.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 (pow.f64 y 6) (.f64 (-.f64 (.f64 z -1/720) (.f64 -1/4 (-.f64 (.f64 z 1/24) (pow.f64 (.f64 -1/4 (sqrt.f64 z)) 2)))) (sqrt.f64 (/.f64 1 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))))))
(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)))) (+.f64 (.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 -1/4 (.f64 y (.f64 y (sqrt.f64 z))) (sqrt.f64 z))))
(fma.f64 (pow.f64 y 6) (.f64 (fma.f64 (fma.f64 z 1/24 (.f64 z -1/16)) 1/4 (.f64 z -1/720)) (.f64 1/2 (sqrt.f64 (/.f64 1 z)))) (fma.f64 1/2 (.f64 (fma.f64 z 1/24 (.f64 z -1/16)) (.f64 (pow.f64 y 4) (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 -1/4) y 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)))))
(+.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)))))

localize17.0ms (0.3%)

Local error

Found 8 expressions with local error:

New	Error	Program
	41.1b	(cbrt.f64 (pow.f64 (*.f64 z (cos.f64 y)) 3))
	0.1b	(pow.f64 (*.f64 z (cos.f64 y)) 3)
	0.1b	(*.f64 x (sin.f64 y))
	0.1b	(*.f64 z (cos.f64 y))
	0.1b	(*.f64 z (cos.f64 y))
	0.1b	(*.f64 x (sin.f64 y))
✓	0.1b	(pow.f64 (*.f64 z (cos.f64 y)) 3)
✓	41.1b	(cbrt.f64 (pow.f64 (*.f64 z (cos.f64 y)) 3))

Compiler

Compiled 44 to 17 computations (61.4% saved)

series99.0ms (1.5%)

Counts

2 → 48

Calls

12 calls:

Time	Variable		Point	Expression
89.0ms	z	@	inf	(pow.f64 (*.f64 z (cos.f64 y)) 3)
4.0ms	z	@	-inf	(cbrt.f64 (pow.f64 (*.f64 z (cos.f64 y)) 3))
2.0ms	y	@	0	(pow.f64 (*.f64 z (cos.f64 y)) 3)
1.0ms	z	@	-inf	(pow.f64 (*.f64 z (cos.f64 y)) 3)
1.0ms	y	@	-inf	(pow.f64 (*.f64 z (cos.f64 y)) 3)

rewrite42.0ms (0.6%)

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	1724	15

Stop Event

1×	node limit

Counts

2 → 54

Calls

Call 1

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

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

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

simplify53.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

588×	`distribute-rgt-out_binary64`
532×	`fma-def_binary64`
528×	`distribute-rgt-in_binary64`
522×	`distribute-lft-in_binary64`
415×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	71	618
1	205	592
2	751	558
3	3892	551
4	7090	551

Stop Event

1×	node limit

Counts

102 → 70

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

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 -1 (.f64 (cbrt.f64 -1) (*.f64 (cos.f64 y) z)))
(neg.f64 (.f64 (.f64 (cos.f64 y) z) (cbrt.f64 -1)))
(.f64 (.f64 (cos.f64 y) z) (neg.f64 (cbrt.f64 -1)))
(.f64 z (.f64 (cbrt.f64 -1) (neg.f64 (cos.f64 y))))
(.f64 (cos.f64 y) (.f64 z (neg.f64 (cbrt.f64 -1))))
(.f64 -1 (.f64 (cbrt.f64 -1) (*.f64 (cos.f64 y) z)))
(neg.f64 (.f64 (.f64 (cos.f64 y) z) (cbrt.f64 -1)))
(.f64 (.f64 (cos.f64 y) z) (neg.f64 (cbrt.f64 -1)))
(.f64 z (.f64 (cbrt.f64 -1) (neg.f64 (cos.f64 y))))
(.f64 (cos.f64 y) (.f64 z (neg.f64 (cbrt.f64 -1))))
(.f64 -1 (.f64 (cbrt.f64 -1) (*.f64 (cos.f64 y) z)))
(neg.f64 (.f64 (.f64 (cos.f64 y) z) (cbrt.f64 -1)))
(.f64 (.f64 (cos.f64 y) z) (neg.f64 (cbrt.f64 -1)))
(.f64 z (.f64 (cbrt.f64 -1) (neg.f64 (cos.f64 y))))
(.f64 (cos.f64 y) (.f64 z (neg.f64 (cbrt.f64 -1))))
(.f64 -1 (.f64 (cbrt.f64 -1) (*.f64 (cos.f64 y) z)))
(neg.f64 (.f64 (.f64 (cos.f64 y) z) (cbrt.f64 -1)))
(.f64 (.f64 (cos.f64 y) z) (neg.f64 (cbrt.f64 -1)))
(.f64 z (.f64 (cbrt.f64 -1) (neg.f64 (cos.f64 y))))
(.f64 (cos.f64 y) (.f64 z (neg.f64 (cbrt.f64 -1))))
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 (.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 (.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 (fma.f64 -1/2 (.f64 y y) (*.f64 -1/720 (pow.f64 y 6))) (fma.f64 1/24 (pow.f64 y 4) 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 (pow.f64 (cos.f64 y) 3) (pow.f64 z 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 z 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 z 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 z 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 z 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 z 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 z 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 z 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 z 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 z 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 z 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 z 3))
(pow.f64 z 3)
(+.f64 (.f64 (+.f64 (.f64 -1 (pow.f64 z 3)) (*.f64 -1/2 (pow.f64 z 3))) (pow.f64 y 2)) (pow.f64 z 3))
(fma.f64 (.f64 (pow.f64 z 3) -3/2) (.f64 y y) (pow.f64 z 3))
(fma.f64 (.f64 y y) (.f64 (pow.f64 z 3) -3/2) (pow.f64 z 3))
(fma.f64 (pow.f64 z 3) (.f64 (.f64 y y) -3/2) (pow.f64 z 3))
(.f64 (+.f64 (.f64 (*.f64 y y) -3/2) 1) (pow.f64 z 3))
(+.f64 (.f64 (+.f64 (.f64 -1 (pow.f64 z 3)) (.f64 -1/2 (pow.f64 z 3))) (pow.f64 y 2)) (+.f64 (pow.f64 z 3) (.f64 (pow.f64 y 4) (+.f64 (.f64 1/24 (pow.f64 z 3)) (+.f64 (.f64 1/2 (pow.f64 z 3)) (.f64 (+.f64 (.f64 1/4 (pow.f64 z 2)) (*.f64 1/12 (pow.f64 z 2))) z))))))
(+.f64 (fma.f64 (.f64 (pow.f64 z 3) -3/2) (.f64 y y) (pow.f64 z 3)) (.f64 (pow.f64 y 4) (fma.f64 1/24 (pow.f64 z 3) (fma.f64 1/2 (pow.f64 z 3) (.f64 z (.f64 (.f64 z z) 1/3))))))
(fma.f64 (.f64 y y) (.f64 (pow.f64 z 3) -3/2) (fma.f64 (pow.f64 y 4) (+.f64 (.f64 (pow.f64 z 3) 1/3) (.f64 (pow.f64 z 3) 13/24)) (pow.f64 z 3)))
(fma.f64 y (.f64 y (.f64 (pow.f64 z 3) -3/2)) (fma.f64 (pow.f64 y 4) (*.f64 (pow.f64 z 3) 7/8) (pow.f64 z 3)))
(fma.f64 (pow.f64 y 4) (.f64 (pow.f64 z 3) 7/8) (.f64 (+.f64 (.f64 (.f64 y y) -3/2) 1) (pow.f64 z 3)))
(+.f64 (.f64 (+.f64 (.f64 -1 (pow.f64 z 3)) (.f64 -1/2 (pow.f64 z 3))) (pow.f64 y 2)) (+.f64 (pow.f64 z 3) (+.f64 (.f64 (pow.f64 y 6) (+.f64 (.f64 (+.f64 (.f64 -1/360 (pow.f64 z 2)) (.f64 -1/24 (pow.f64 z 2))) z) (+.f64 (.f64 -1/720 (pow.f64 z 3)) (+.f64 (.f64 -1/2 (.f64 (+.f64 (.f64 1/4 (pow.f64 z 2)) (.f64 1/12 (pow.f64 z 2))) z)) (.f64 -1/24 (pow.f64 z 3)))))) (.f64 (pow.f64 y 4) (+.f64 (.f64 1/24 (pow.f64 z 3)) (+.f64 (.f64 1/2 (pow.f64 z 3)) (.f64 (+.f64 (.f64 1/4 (pow.f64 z 2)) (*.f64 1/12 (pow.f64 z 2))) z)))))))
(+.f64 (fma.f64 (.f64 (pow.f64 z 3) -3/2) (.f64 y y) (pow.f64 z 3)) (fma.f64 (pow.f64 y 6) (fma.f64 (.f64 (.f64 z z) -2/45) z (fma.f64 -1/720 (pow.f64 z 3) (fma.f64 -1/2 (.f64 z (.f64 (.f64 z z) 1/3)) (.f64 (pow.f64 z 3) -1/24)))) (.f64 (pow.f64 y 4) (fma.f64 1/24 (pow.f64 z 3) (fma.f64 1/2 (pow.f64 z 3) (.f64 z (.f64 (.f64 z z) 1/3)))))))
(+.f64 (fma.f64 (pow.f64 y 4) (+.f64 (.f64 (pow.f64 z 3) 1/3) (.f64 (pow.f64 z 3) 13/24)) (.f64 (pow.f64 y 6) (+.f64 (.f64 (pow.f64 z 3) -2/45) (fma.f64 -1/720 (pow.f64 z 3) (fma.f64 -1/2 (.f64 (pow.f64 z 3) 1/3) (.f64 (pow.f64 z 3) -1/24)))))) (fma.f64 (.f64 y y) (.f64 (pow.f64 z 3) -3/2) (pow.f64 z 3)))
(fma.f64 y (.f64 y (.f64 (pow.f64 z 3) -3/2)) (fma.f64 (pow.f64 y 4) (.f64 (pow.f64 z 3) 7/8) (fma.f64 (pow.f64 y 6) (+.f64 (fma.f64 (pow.f64 z 3) -1/24 (.f64 (pow.f64 z 3) -1/6)) (*.f64 (pow.f64 z 3) -11/240)) (pow.f64 z 3))))
(fma.f64 y (.f64 y (.f64 (pow.f64 z 3) -3/2)) (fma.f64 (pow.f64 y 4) (.f64 (pow.f64 z 3) 7/8) (fma.f64 (pow.f64 y 6) (+.f64 (.f64 z (.f64 (.f64 z z) -5/24)) (*.f64 (pow.f64 z 3) -11/240)) (pow.f64 z 3))))
(*.f64 (pow.f64 z 3) (pow.f64 (cos.f64 y) 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 z 3))
(*.f64 (pow.f64 z 3) (pow.f64 (cos.f64 y) 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 z 3))
(*.f64 (pow.f64 z 3) (pow.f64 (cos.f64 y) 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 z 3))
(*.f64 (pow.f64 z 3) (pow.f64 (cos.f64 y) 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 z 3))
(*.f64 (pow.f64 z 3) (pow.f64 (cos.f64 y) 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 z 3))
(*.f64 (pow.f64 z 3) (pow.f64 (cos.f64 y) 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 z 3))
(*.f64 (pow.f64 z 3) (pow.f64 (cos.f64 y) 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 z 3))
(*.f64 (pow.f64 z 3) (pow.f64 (cos.f64 y) 3))
(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 z 3))

localize35.0ms (0.5%)

Local error

Found 8 expressions with local error:

New	Error	Program
	41.1b	(cbrt.f64 (*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 z 3)))
	0.3b	(pow.f64 (cos.f64 y) 3)
	0.1b	(*.f64 x (sin.f64 y))
	0.1b	(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 z 3))
✓	0.1b	(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 z 3))
	0.1b	(*.f64 x (sin.f64 y))
✓	0.3b	(pow.f64 (cos.f64 y) 3)
✓	41.1b	(cbrt.f64 (*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 z 3)))

Compiler

Compiled 53 to 29 computations (45.3% saved)

series7.0ms (0.1%)

Counts

3 → 40

Calls

15 calls:

Time	Variable		Point	Expression
1.0ms	z	@	0	(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 z 3))
1.0ms	y	@	inf	(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 z 3))
1.0ms	y	@	inf	(pow.f64 (cos.f64 y) 3)
1.0ms	y	@	-inf	(pow.f64 (cos.f64 y) 3)
0.0ms	y	@	0	(*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 z 3))

rewrite126.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

776×	`pow1_binary64`
722×	`add-log-exp_binary64`
722×	`log1p-expm1-u_binary64`
722×	`expm1-log1p-u_binary64`
700×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	21
1	194	21
2	2045	21

Stop Event

1×	node limit

Counts

3 → 56

Calls

Call 1

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

Outputs

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

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

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

simplify92.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

643×	`distribute-rgt-in_binary64`
465×	`sub-neg_binary64`
415×	`distribute-lft-in_binary64`
369×	`fma-neg_binary64`
318×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	56	458
1	150	441
2	491	422
3	1931	416
4	3242	416
5	4043	416
6	5094	416
7	5263	416
8	5524	416
9	6734	416

Stop Event

1×	node limit

Counts

96 → 80

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 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 (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 -1 (.f64 (cbrt.f64 -1) (*.f64 (cos.f64 y) z)))
(.f64 -1 (.f64 (cbrt.f64 -1) (*.f64 (cos.f64 y) z)))
(.f64 -1 (.f64 (cbrt.f64 -1) (*.f64 (cos.f64 y) z)))
(.f64 -1 (.f64 (cbrt.f64 -1) (*.f64 (cos.f64 y) z)))
1
(+.f64 1 (*.f64 -3/2 (pow.f64 y 2)))
(+.f64 1 (+.f64 (.f64 7/8 (pow.f64 y 4)) (.f64 -3/2 (pow.f64 y 2))))
(+.f64 1 (+.f64 (.f64 -61/240 (pow.f64 y 6)) (+.f64 (.f64 7/8 (pow.f64 y 4)) (*.f64 -3/2 (pow.f64 y 2)))))
(pow.f64 z 3)
(+.f64 (.f64 -3/2 (.f64 (pow.f64 y 2) (pow.f64 z 3))) (pow.f64 z 3))
(+.f64 (.f64 -3/2 (.f64 (pow.f64 y 2) (pow.f64 z 3))) (+.f64 (.f64 7/8 (.f64 (pow.f64 y 4) (pow.f64 z 3))) (pow.f64 z 3)))
(+.f64 (.f64 -61/240 (.f64 (pow.f64 y 6) (pow.f64 z 3))) (+.f64 (.f64 -3/2 (.f64 (pow.f64 y 2) (pow.f64 z 3))) (+.f64 (.f64 7/8 (.f64 (pow.f64 y 4) (pow.f64 z 3))) (pow.f64 z 3))))
(*.f64 (pow.f64 z 3) (pow.f64 (cos.f64 y) 3))
(*.f64 (pow.f64 z 3) (pow.f64 (cos.f64 y) 3))
(*.f64 (pow.f64 z 3) (pow.f64 (cos.f64 y) 3))
(*.f64 (pow.f64 z 3) (pow.f64 (cos.f64 y) 3))
(*.f64 (pow.f64 z 3) (pow.f64 (cos.f64 y) 3))
(*.f64 (pow.f64 z 3) (pow.f64 (cos.f64 y) 3))
(*.f64 (pow.f64 z 3) (pow.f64 (cos.f64 y) 3))
(*.f64 (pow.f64 z 3) (pow.f64 (cos.f64 y) 3))

Outputs
z
(+.f64 (.f64 -1/2 (.f64 (pow.f64 y 2) z)) z)
(fma.f64 -1/2 (.f64 z (.f64 y y)) z)
(fma.f64 (.f64 -1/2 (.f64 y y)) z 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 z (.f64 1/24 (.f64 (pow.f64 y 4) z))))
(fma.f64 -1/2 (.f64 z (.f64 y y)) (+.f64 z (.f64 1/24 (.f64 z (pow.f64 y 4)))))
(fma.f64 -1/2 (.f64 z (.f64 y y)) (fma.f64 1/24 (*.f64 z (pow.f64 y 4)) z))
(.f64 z (+.f64 (.f64 1/24 (pow.f64 y 4)) (fma.f64 -1/2 (*.f64 y y) 1)))
(.f64 z (+.f64 (.f64 y (*.f64 -1/2 y)) (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 z (.f64 y y)) (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 (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 (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 (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 z (cos.f64 y))
(.f64 -1 (.f64 (cbrt.f64 -1) (*.f64 (cos.f64 y) z)))
(neg.f64 (.f64 (.f64 z (cos.f64 y)) (cbrt.f64 -1)))
(.f64 (.f64 z (cos.f64 y)) (neg.f64 (cbrt.f64 -1)))
(.f64 z (.f64 (cos.f64 y) (neg.f64 (cbrt.f64 -1))))
(.f64 -1 (.f64 (cbrt.f64 -1) (*.f64 (cos.f64 y) z)))
(neg.f64 (.f64 (.f64 z (cos.f64 y)) (cbrt.f64 -1)))
(.f64 (.f64 z (cos.f64 y)) (neg.f64 (cbrt.f64 -1)))
(.f64 z (.f64 (cos.f64 y) (neg.f64 (cbrt.f64 -1))))
(.f64 -1 (.f64 (cbrt.f64 -1) (*.f64 (cos.f64 y) z)))
(neg.f64 (.f64 (.f64 z (cos.f64 y)) (cbrt.f64 -1)))
(.f64 (.f64 z (cos.f64 y)) (neg.f64 (cbrt.f64 -1)))
(.f64 z (.f64 (cos.f64 y) (neg.f64 (cbrt.f64 -1))))
(.f64 -1 (.f64 (cbrt.f64 -1) (*.f64 (cos.f64 y) z)))
(neg.f64 (.f64 (.f64 z (cos.f64 y)) (cbrt.f64 -1)))
(.f64 (.f64 z (cos.f64 y)) (neg.f64 (cbrt.f64 -1)))
(.f64 z (.f64 (cos.f64 y) (neg.f64 (cbrt.f64 -1))))
1
(+.f64 1 (*.f64 -3/2 (pow.f64 y 2)))
(+.f64 1 (.f64 (.f64 y y) -3/2))
(fma.f64 (*.f64 y y) -3/2 1)
(fma.f64 y (*.f64 y -3/2) 1)
(+.f64 1 (+.f64 (.f64 7/8 (pow.f64 y 4)) (.f64 -3/2 (pow.f64 y 2))))
(+.f64 1 (fma.f64 7/8 (pow.f64 y 4) (.f64 (.f64 y y) -3/2)))
(+.f64 1 (fma.f64 (pow.f64 y 4) 7/8 (.f64 y (.f64 y -3/2))))
(fma.f64 y (*.f64 y -3/2) (fma.f64 (pow.f64 y 4) 7/8 1))
(+.f64 1 (+.f64 (.f64 -61/240 (pow.f64 y 6)) (+.f64 (.f64 7/8 (pow.f64 y 4)) (*.f64 -3/2 (pow.f64 y 2)))))
(+.f64 1 (fma.f64 -61/240 (pow.f64 y 6) (fma.f64 7/8 (pow.f64 y 4) (.f64 (.f64 y y) -3/2))))
(+.f64 1 (fma.f64 (pow.f64 y 6) -61/240 (fma.f64 (pow.f64 y 4) 7/8 (.f64 y (.f64 y -3/2)))))
(fma.f64 (pow.f64 y 6) -61/240 (fma.f64 y (*.f64 y -3/2) (fma.f64 (pow.f64 y 4) 7/8 1)))
(pow.f64 z 3)
(+.f64 (.f64 -3/2 (.f64 (pow.f64 y 2) (pow.f64 z 3))) (pow.f64 z 3))
(fma.f64 -3/2 (.f64 (.f64 y y) (pow.f64 z 3)) (pow.f64 z 3))
(.f64 (fma.f64 (.f64 y y) -3/2 1) (pow.f64 z 3))
(.f64 (pow.f64 z 3) (fma.f64 y (.f64 y -3/2) 1))
(+.f64 (.f64 -3/2 (.f64 (pow.f64 y 2) (pow.f64 z 3))) (+.f64 (.f64 7/8 (.f64 (pow.f64 y 4) (pow.f64 z 3))) (pow.f64 z 3)))
(fma.f64 -3/2 (.f64 (.f64 y y) (pow.f64 z 3)) (fma.f64 7/8 (*.f64 (pow.f64 y 4) (pow.f64 z 3)) (pow.f64 z 3)))
(+.f64 (pow.f64 z 3) (.f64 (pow.f64 z 3) (fma.f64 (pow.f64 y 4) 7/8 (.f64 y (*.f64 y -3/2)))))
(.f64 (pow.f64 z 3) (fma.f64 y (.f64 y -3/2) (fma.f64 (pow.f64 y 4) 7/8 1)))
(+.f64 (.f64 -61/240 (.f64 (pow.f64 y 6) (pow.f64 z 3))) (+.f64 (.f64 -3/2 (.f64 (pow.f64 y 2) (pow.f64 z 3))) (+.f64 (.f64 7/8 (.f64 (pow.f64 y 4) (pow.f64 z 3))) (pow.f64 z 3))))
(fma.f64 -61/240 (.f64 (pow.f64 y 6) (pow.f64 z 3)) (fma.f64 -3/2 (.f64 (.f64 y y) (pow.f64 z 3)) (fma.f64 7/8 (.f64 (pow.f64 y 4) (pow.f64 z 3)) (pow.f64 z 3))))
(fma.f64 -61/240 (.f64 (pow.f64 y 6) (pow.f64 z 3)) (+.f64 (pow.f64 z 3) (.f64 (pow.f64 z 3) (fma.f64 (pow.f64 y 4) 7/8 (.f64 y (.f64 y -3/2))))))
(+.f64 (pow.f64 z 3) (.f64 (pow.f64 z 3) (fma.f64 y (.f64 y -3/2) (fma.f64 (pow.f64 y 4) 7/8 (*.f64 (pow.f64 y 6) -61/240)))))
(.f64 (pow.f64 z 3) (fma.f64 (pow.f64 y 6) -61/240 (fma.f64 y (.f64 y -3/2) (fma.f64 (pow.f64 y 4) 7/8 1))))
(*.f64 (pow.f64 z 3) (pow.f64 (cos.f64 y) 3))
(*.f64 (pow.f64 z 3) (pow.f64 (cos.f64 y) 3))
(*.f64 (pow.f64 z 3) (pow.f64 (cos.f64 y) 3))
(*.f64 (pow.f64 z 3) (pow.f64 (cos.f64 y) 3))
(*.f64 (pow.f64 z 3) (pow.f64 (cos.f64 y) 3))
(*.f64 (pow.f64 z 3) (pow.f64 (cos.f64 y) 3))
(*.f64 (pow.f64 z 3) (pow.f64 (cos.f64 y) 3))
(*.f64 (pow.f64 z 3) (pow.f64 (cos.f64 y) 3))

eval196.0ms (3%)

Compiler: Compiled 8152 to 3750 computations (54% saved)

prune72.0ms (1.1%)

Pruning

14 alts after pruning (10 fresh and 4 done)

	Pruned	Kept	Total
New	444	9	453
Fresh	2	1	3
Picked	1	0	1
Done	1	4	5
Total	448	14	462

Error

0.1b

Counts

462 → 14

Alt Table

Click to see full alt table

Status	Error	Program
	31.8b	(+.f64 (.f64 x (sin.f64 y)) (pow.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (.f64 z (cos.f64 y)))) 3) 2))
✓	15.2b	(+.f64 (*.f64 x (sin.f64 y)) z)
	24.3b	(+.f64 (.f64 y x) (pow.f64 (cbrt.f64 (.f64 z (cos.f64 y))) 3))
▶	0.9b	(+.f64 (.f64 x (sin.f64 y)) (.f64 (pow.f64 (cbrt.f64 z) 2) (*.f64 (cbrt.f64 z) (cos.f64 y))))
	36.3b	(+.f64 (pow.f64 (sqrt.f64 (*.f64 x (sin.f64 y))) 2) z)
▶	44.4b	(+.f64 (.f64 y x) (cbrt.f64 (pow.f64 (.f64 z (cos.f64 y)) 3)))
✓	28.3b	(+.f64 (.f64 x (sin.f64 y)) (cbrt.f64 (pow.f64 (.f64 z (cos.f64 y)) 3)))
✓	31.4b	(+.f64 (.f64 x (sin.f64 y)) (pow.f64 (sqrt.f64 (.f64 z (cos.f64 y))) 2))
	23.8b	(+.f64 (.f64 y x) (.f64 z (cos.f64 y)))
▶	30.8b	(+.f64 (*.f64 y x) z)
▶	31.9b	(+.f64 (+.f64 (.f64 y x) (.f64 -1/6 (*.f64 (pow.f64 y 3) x))) z)
✓	0.1b	(+.f64 (.f64 x (sin.f64 y)) (.f64 z (cos.f64 y)))
▶	32.0b	(+.f64 (+.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))))) z)
	32.2b	(+.f64 (.f64 x (sin.f64 y)) (.f64 (*.f64 (cos.f64 y) (sqrt.f64 z)) (sqrt.f64 z)))

Compiler

Compiled 369 to 258 computations (30.1% saved)

localize19.0ms (0.3%)

Local error

Found 8 expressions with local error:

New	Error	Program
	0.5b	(pow.f64 (cbrt.f64 z) 2)
	0.3b	(.f64 (pow.f64 (cbrt.f64 z) 2) (.f64 (cbrt.f64 z) (cos.f64 y)))
	0.1b	(*.f64 (cbrt.f64 z) (cos.f64 y))
	0.1b	(*.f64 x (sin.f64 y))
✓	0.1b	(*.f64 (cbrt.f64 z) (cos.f64 y))
✓	0.3b	(.f64 (pow.f64 (cbrt.f64 z) 2) (.f64 (cbrt.f64 z) (cos.f64 y)))
✓	0.5b	(pow.f64 (cbrt.f64 z) 2)
✓	0.6b	(cbrt.f64 z)

Compiler

Compiled 51 to 18 computations (64.7% saved)

series10.0ms (0.2%)

Counts

4 → 36

Calls

18 calls:

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

rewrite55.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

4 → 63

Calls

Call 1

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

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

simplify113.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

839×	`unswap-sqr_binary64`
756×	`distribute-rgt-out_binary64`
657×	`associate-+l+_binary64`
556×	`sqr-pow_binary64`
462×	`*-commutative_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	43	338
1	118	332
2	376	318
3	1377	314
4	2398	310
5	3986	310
6	5133	310
7	5581	310
8	5746	310
9	5961	310
10	6266	310
11	6626	310
12	7063	310
13	7811	310

Stop Event

1×	node limit

Counts

99 → 81

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

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

localize6.0ms (0.1%)

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

localize18.0ms (0.3%)

Local error

Found 6 expressions with local error:

New	Error	Program
	6.7b	(+.f64 (.f64 y x) (.f64 -1/6 (*.f64 (pow.f64 y 3) x)))
	4.5b	(*.f64 (pow.f64 y 3) x)
	0.1b	(.f64 -1/6 (.f64 (pow.f64 y 3) x))
✓	0.1b	(.f64 -1/6 (.f64 (pow.f64 y 3) x))
✓	4.5b	(*.f64 (pow.f64 y 3) x)
✓	6.7b	(+.f64 (.f64 y x) (.f64 -1/6 (*.f64 (pow.f64 y 3) x)))

Compiler

Compiled 50 to 29 computations (42% saved)

series9.0ms (0.1%)

Counts

3 → 15

Calls

18 calls:

Time	Variable		Point	Expression
2.0ms	y	@	-inf	(+.f64 (.f64 y x) (.f64 -1/6 (*.f64 (pow.f64 y 3) x)))
1.0ms	x	@	0	(+.f64 (.f64 y x) (.f64 -1/6 (*.f64 (pow.f64 y 3) x)))
1.0ms	x	@	inf	(+.f64 (.f64 y x) (.f64 -1/6 (*.f64 (pow.f64 y 3) x)))
1.0ms	y	@	inf	(+.f64 (.f64 y x) (.f64 -1/6 (*.f64 (pow.f64 y 3) x)))
1.0ms	y	@	0	(+.f64 (.f64 y x) (.f64 -1/6 (*.f64 (pow.f64 y 3) x)))

rewrite53.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

525×	`log-prod_binary64`
382×	`fma-def_binary64`
381×	`exp-prod_binary64`
355×	`pow-prod-down_binary64`
267×	`pow2_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	31
1	221	30
2	2774	28

Stop Event

1×	node limit

Counts

3 → 131

Calls

Call 1

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

Outputs

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egg-rr> (2) ((x fma.f64 (*.f64 -1/6 x) (pow.f64 y 3) (*.f64 y x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 -1/6 (pow.f64 (*.f64 y (cbrt.f64 x)) 2)) (*.f64 y (cbrt.f64 x)) (*.f64 y x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 -1/6 (*.f64 (sqrt.f64 x) (pow.f64 y 3/2))) (*.f64 (sqrt.f64 x) (pow.f64 y 3/2)) (*.f64 y x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 -1/6 (pow.f64 y 3)) 1) x (*.f64 y x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 -1/6 (pow.f64 y 3)) (cbrt.f64 (*.f64 x x))) (cbrt.f64 x) (*.f64 y x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 -1/6 (pow.f64 y 3)) (sqrt.f64 x)) (sqrt.f64 x) (*.f64 y x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 y (cbrt.f64 (*.f64 x x))) (cbrt.f64 x) (*.f64 (*.f64 -1/6 x) (pow.f64 y 3)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 y (sqrt.f64 x)) (sqrt.f64 x) (*.f64 (*.f64 -1/6 x) (pow.f64 y 3)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x (pow.f64 (cbrt.f64 y) 2)) (cbrt.f64 y) (*.f64 (*.f64 -1/6 x) (pow.f64 y 3)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x (sqrt.f64 y)) (sqrt.f64 y) (*.f64 (*.f64 -1/6 x) (pow.f64 y 3)))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 x (pow.f64 y 3)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) (pow.f64 y 3))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 x) (pow.f64 y 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 x) (pow.f64 y 3)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 x) (pow.f64 y 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 x (pow.f64 y 3)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (pow.f64 y 3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 y (cbrt.f64 x)) 6) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 y (cbrt.f64 x)) 9) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 y (cbrt.f64 x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 x) (pow.f64 y 3/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (*.f64 x (pow.f64 y 3))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 (*.f64 y x)) y) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 y (sqrt.f64 (*.f64 y x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 x (pow.f64 y 3)))) 2)) (cbrt.f64 (log.f64 (*.f64 x (pow.f64 y 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 x (pow.f64 y 3))))) (sqrt.f64 (log.f64 (*.f64 x (pow.f64 y 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 y (cbrt.f64 x)) 6))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 x) (pow.f64 y 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 x (pow.f64 y 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 y (cbrt.f64 x)) 9))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x (pow.f64 y 3))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x (pow.f64 y 3))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 x (pow.f64 y 3))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 y (cbrt.f64 x)) 9)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 y (cbrt.f64 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (sqrt.f64 x) (pow.f64 y 3/2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 x (pow.f64 y 3))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x (pow.f64 y 3))))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (*.f64 -1/6 x) (pow.f64 y 3)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 -1/6) (*.f64 x (pow.f64 y 3)))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 -1/6) (*.f64 x (pow.f64 y 3))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 -1/6) (*.f64 x (pow.f64 y 3))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 -1/6) (*.f64 x (pow.f64 y 3))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (*.f64 -1/6 x) (pow.f64 y 3)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (*.f64 -1/6 x) (pow.f64 y 3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (*.f64 y (cbrt.f64 x)) 6) 1/36) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (*.f64 y (cbrt.f64 x)) (cbrt.f64 -1/6)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (*.f64 -1/6 x) (pow.f64 y 3))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (*.f64 y (cbrt.f64 x)) 9) -1/216) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (*.f64 (*.f64 -1/6 x) (pow.f64 y 3))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 (*.f64 -1/6 x) (pow.f64 y 3)))) 2)) (cbrt.f64 (log.f64 (*.f64 (*.f64 -1/6 x) (pow.f64 y 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 (*.f64 -1/6 x) (pow.f64 y 3))))) (sqrt.f64 (log.f64 (*.f64 (*.f64 -1/6 x) (pow.f64 y 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 (*.f64 y (cbrt.f64 x)) 6) 1/36))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 -1/6) (*.f64 x (pow.f64 y 3))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (*.f64 -1/6 x) (pow.f64 y 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (*.f64 y (cbrt.f64 x)) 9) -1/216))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (*.f64 -1/6 x) (pow.f64 y 3))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (*.f64 -1/6 x) (pow.f64 y 3))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (*.f64 -1/6 x) (pow.f64 y 3))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (*.f64 y (cbrt.f64 x)) (cbrt.f64 -1/6))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (*.f64 -1/6 x) (pow.f64 y 3)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 (*.f64 y (cbrt.f64 x)) 9) -1/216)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 -1/6 x) (pow.f64 y 3))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 -1/6 x) (pow.f64 y 3))) 3) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (*.f64 -1/6 x) (pow.f64 y 3))))))))

simplify77.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

1442×	`fma-def_binary64`
1091×	`fma-neg_binary64`
480×	`unswap-sqr_binary64`
445×	`distribute-rgt-neg-in_binary64`
297×	`unsub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	156
1	45	156
2	129	156
3	443	156
4	1371	156
5	2300	156
6	4184	156
7	5284	156
8	6626	156
9	6941	156
10	7108	156
11	7315	156

Stop Event

1×	node limit

Counts

146 → 136

Calls

Call 1

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

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

localize15.0ms (0.2%)

Local error

Found 8 expressions with local error:

New	Error	Program
	41.1b	(cbrt.f64 (pow.f64 (*.f64 z (cos.f64 y)) 3))
	0.1b	(pow.f64 (*.f64 z (cos.f64 y)) 3)
	0.1b	(*.f64 z (cos.f64 y))
	0.0b	(+.f64 (.f64 y x) (cbrt.f64 (pow.f64 (.f64 z (cos.f64 y)) 3)))
✓	0.0b	(+.f64 (.f64 y x) (cbrt.f64 (pow.f64 (.f64 z (cos.f64 y)) 3)))
	0.1b	(*.f64 z (cos.f64 y))
	0.1b	(pow.f64 (*.f64 z (cos.f64 y)) 3)
	41.1b	(cbrt.f64 (pow.f64 (*.f64 z (cos.f64 y)) 3))

Compiler

Compiled 40 to 16 computations (60% saved)

series3.0ms (0%)

Counts

1 → 36

Calls

9 calls:

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

rewrite85.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

521×	`log-prod_binary64`
377×	`pow-prod-down_binary64`
375×	`exp-prod_binary64`
339×	`fma-def_binary64`
272×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	10
1	239	10
2	2808	10

Stop Event

1×	node limit

Counts

1 → 75

Calls

Call 1

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

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

simplify60.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

970×	`fma-def_binary64`
587×	`neg-mul-1_binary64`
584×	`neg-sub0_binary64`
477×	`distribute-lft-out_binary64`
362×	`*-commutative_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	31	354
1	74	352
2	185	351
3	478	349
4	1365	346
5	3041	346
6	4368	346
7	4868	346
8	7195	346

Stop Event

1×	node limit

Counts

111 → 92

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 -1 (.f64 (cbrt.f64 -1) (*.f64 (cos.f64 y) z)))
(+.f64 (.f64 y x) (.f64 -1 (.f64 (cbrt.f64 -1) (.f64 (cos.f64 y) z))))
(+.f64 (.f64 y x) (.f64 -1 (.f64 (cbrt.f64 -1) (.f64 (cos.f64 y) z))))
(+.f64 (.f64 y x) (.f64 -1 (.f64 (cbrt.f64 -1) (.f64 (cos.f64 y) z))))

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

localize53.0ms (0.8%)

Local error

Found 8 expressions with local error:

New	Error	Program
	1.2b	(*.f64 (pow.f64 y 7) x)
	0.5b	(.f64 -1/5040 (.f64 (pow.f64 y 7) x))
	0.1b	(.f64 -1/6 (.f64 (pow.f64 y 3) x))
	0.1b	(.f64 1/120 (.f64 (pow.f64 y 5) x))
✓	3.8b	(*.f64 (pow.f64 y 5) x)
	4.5b	(*.f64 (pow.f64 y 3) x)
✓	6.7b	(+.f64 (.f64 y x) (+.f64 (.f64 -1/5040 (.f64 (pow.f64 y 7) x)) (.f64 -1/6 (*.f64 (pow.f64 y 3) x))))
✓	23.6b	(+.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)))))

Compiler

Compiled 150 to 100 computations (33.3% saved)

series17.0ms (0.3%)

Counts

3 → 39

Calls

18 calls:

Time	Variable		Point	Expression
7.0ms	x	@	0	(+.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)))))
3.0ms	x	@	inf	(+.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)))))
1.0ms	x	@	-inf	(+.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)))))
1.0ms	y	@	inf	(+.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)))))
1.0ms	y	@	0	(*.f64 (pow.f64 y 5) x)

rewrite86.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

423×	`expm1-udef_binary64`
423×	`log1p-udef_binary64`
247×	`add-sqr-sqrt_binary64`
235×	`add-log-exp_binary64`
235×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	65
1	505	63
2	6635	63

Stop Event

1×	node limit

Counts

3 → 94

Calls

Call 1

Inputs

(+.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 (*.f64 y x) (+.f64 (*.f64 -1/5040 (*.f64 (pow.f64 y 7) x)) (*.f64 -1/6 (*.f64 (pow.f64 y 3) x))))

(*.f64 (pow.f64 y 5) x)

Outputs

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(neg.f64 (+.f64 (pow.f64 (*.f64 y x) 3) (pow.f64 (*.f64 x (+.f64 (*.f64 -1/5040 (pow.f64 y 7)) (*.f64 -1/6 (pow.f64 y 3)))) 3))) (neg.f64 (+.f64 (pow.f64 (*.f64 y x) 2) (*.f64 (*.f64 x (+.f64 (*.f64 -1/5040 (pow.f64 y 7)) (*.f64 -1/6 (pow.f64 y 3)))) (-.f64 (*.f64 x (+.f64 (*.f64 -1/5040 (pow.f64 y 7)) (*.f64 -1/6 (pow.f64 y 3)))) (*.f64 y x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 y x) 2) (pow.f64 (*.f64 x (+.f64 (*.f64 -1/5040 (pow.f64 y 7)) (*.f64 -1/6 (pow.f64 y 3)))) 2))) (neg.f64 (-.f64 (*.f64 y x) (*.f64 x (+.f64 (*.f64 -1/5040 (pow.f64 y 7)) (*.f64 -1/6 (pow.f64 y 3)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 x (+.f64 y (*.f64 -1/5040 (pow.f64 y 7)))) 3) (pow.f64 (*.f64 (pow.f64 y 3) (*.f64 x -1/6)) 3)) (+.f64 (*.f64 (*.f64 x (+.f64 y (*.f64 -1/5040 (pow.f64 y 7)))) (*.f64 x (+.f64 y (*.f64 -1/5040 (pow.f64 y 7))))) (-.f64 (*.f64 (*.f64 (*.f64 x x) (pow.f64 y 6)) 1/36) (*.f64 (*.f64 x (+.f64 y (*.f64 -1/5040 (pow.f64 y 7)))) (*.f64 (pow.f64 y 3) (*.f64 x -1/6))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (*.f64 x (+.f64 (*.f64 -1/5040 (pow.f64 y 7)) (*.f64 -1/6 (pow.f64 y 3)))) 2) (pow.f64 (*.f64 y x) 2)) (-.f64 (*.f64 x (+.f64 (*.f64 -1/5040 (pow.f64 y 7)) (*.f64 -1/6 (pow.f64 y 3)))) (*.f64 y x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 x (+.f64 y (*.f64 -1/5040 (pow.f64 y 7)))) (*.f64 x (+.f64 y (*.f64 -1/5040 (pow.f64 y 7))))) (*.f64 (*.f64 (*.f64 x x) (pow.f64 y 6)) 1/36)) (-.f64 (*.f64 x (+.f64 y (*.f64 -1/5040 (pow.f64 y 7)))) (*.f64 (pow.f64 y 3) (*.f64 x -1/6))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 y x (*.f64 x (+.f64 (*.f64 -1/5040 (pow.f64 y 7)) (*.f64 -1/6 (pow.f64 y 3))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 y x (*.f64 x (+.f64 (*.f64 -1/5040 (pow.f64 y 7)) (*.f64 -1/6 (pow.f64 y 3)))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 y x (*.f64 x (+.f64 (*.f64 -1/5040 (pow.f64 y 7)) (*.f64 -1/6 (pow.f64 y 3)))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 y x (*.f64 x (+.f64 (*.f64 -1/5040 (pow.f64 y 7)) (*.f64 -1/6 (pow.f64 y 3))))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 y x (*.f64 x (+.f64 (*.f64 -1/5040 (pow.f64 y 7)) (*.f64 -1/6 (pow.f64 y 3))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 y x (*.f64 x (+.f64 (*.f64 -1/5040 (pow.f64 y 7)) (*.f64 -1/6 (pow.f64 y 3)))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 y x (*.f64 x (+.f64 (*.f64 -1/5040 (pow.f64 y 7)) (*.f64 -1/6 (pow.f64 y 3))))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 y x (*.f64 x (+.f64 (*.f64 -1/5040 (pow.f64 y 7)) (*.f64 -1/6 (pow.f64 y 3))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 y x (*.f64 x (+.f64 (*.f64 -1/5040 (pow.f64 y 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7)) (*.f64 -1/6 (pow.f64 y 3)))) (*.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)) (*.f64 x (+.f64 (*.f64 -1/5040 (pow.f64 y 7)) (*.f64 -1/6 (pow.f64 y 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 x (+.f64 (*.f64 -1/5040 (pow.f64 y 7)) (*.f64 -1/6 (pow.f64 y 3))))) 2) (cbrt.f64 (*.f64 x (+.f64 (*.f64 -1/5040 (pow.f64 y 7)) (*.f64 -1/6 (pow.f64 y 3))))) (*.f64 y x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 y x)) (sqrt.f64 (*.f64 y x)) (*.f64 x (+.f64 (*.f64 -1/5040 (pow.f64 y 7)) (*.f64 -1/6 (pow.f64 y 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 x (+.f64 (*.f64 -1/5040 (pow.f64 y 7)) (*.f64 -1/6 (pow.f64 y 3))))) (sqrt.f64 (*.f64 x (+.f64 (*.f64 -1/5040 (pow.f64 y 7)) (*.f64 -1/6 (pow.f64 y 3))))) (*.f64 y x))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 y 5) x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 y 5) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (pow.f64 y 5) x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (pow.f64 y 5) x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 x) (pow.f64 y 5/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (*.f64 x x) (pow.f64 y 10)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 x) (pow.f64 y 5)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (pow.f64 y 5) x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (pow.f64 y 5) x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (pow.f64 y 5) 3) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 x 3) (pow.f64 (pow.f64 y 5) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (pow.f64 y 5) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (pow.f64 y 5) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 y 5) x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (pow.f64 y 5) x)))))))

simplify70.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

772×	`unsub-neg_binary64`
485×	`associate-l_binary64`
396×	`distribute-rgt-in_binary64`
369×	`sub-neg_binary64`
367×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	53	804
1	148	737
2	469	720
3	1796	720
4	3962	720
5	5550	720
6	7096	720

Stop Event

1×	node limit

Counts

133 → 114

Calls

Call 1

Inputs
(*.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 -1/5040 (.f64 (pow.f64 y 7) x))
(+.f64 (.f64 1/120 (.f64 (pow.f64 y 5) x)) (.f64 -1/5040 (.f64 (pow.f64 y 7) x)))
(+.f64 (.f64 1/120 (.f64 (pow.f64 y 5) x)) (+.f64 (.f64 -1/5040 (.f64 (pow.f64 y 7) x)) (.f64 -1/6 (.f64 (pow.f64 y 3) x))))
(.f64 -1/5040 (.f64 (pow.f64 y 7) x))
(+.f64 (.f64 1/120 (.f64 (pow.f64 y 5) x)) (.f64 -1/5040 (.f64 (pow.f64 y 7) x)))
(+.f64 (.f64 1/120 (.f64 (pow.f64 y 5) x)) (+.f64 (.f64 -1/5040 (.f64 (pow.f64 y 7) x)) (.f64 -1/6 (.f64 (pow.f64 y 3) x))))
(.f64 (+.f64 (.f64 -1/6 (pow.f64 y 3)) (+.f64 y (+.f64 (.f64 1/120 (pow.f64 y 5)) (.f64 -1/5040 (pow.f64 y 7))))) x)
(.f64 (+.f64 (.f64 -1/6 (pow.f64 y 3)) (+.f64 y (+.f64 (.f64 1/120 (pow.f64 y 5)) (.f64 -1/5040 (pow.f64 y 7))))) x)
(.f64 (+.f64 (.f64 -1/6 (pow.f64 y 3)) (+.f64 y (+.f64 (.f64 1/120 (pow.f64 y 5)) (.f64 -1/5040 (pow.f64 y 7))))) x)
(.f64 (+.f64 (.f64 -1/6 (pow.f64 y 3)) (+.f64 y (+.f64 (.f64 1/120 (pow.f64 y 5)) (.f64 -1/5040 (pow.f64 y 7))))) x)
(.f64 (+.f64 (.f64 -1/6 (pow.f64 y 3)) (+.f64 (.f64 1/120 (pow.f64 y 5)) (+.f64 y (.f64 -1/5040 (pow.f64 y 7))))) x)
(.f64 (+.f64 (.f64 -1/6 (pow.f64 y 3)) (+.f64 (.f64 1/120 (pow.f64 y 5)) (+.f64 y (.f64 -1/5040 (pow.f64 y 7))))) x)
(.f64 (+.f64 (.f64 -1/6 (pow.f64 y 3)) (+.f64 (.f64 1/120 (pow.f64 y 5)) (+.f64 y (.f64 -1/5040 (pow.f64 y 7))))) x)
(.f64 (+.f64 (.f64 -1/6 (pow.f64 y 3)) (+.f64 (.f64 1/120 (pow.f64 y 5)) (+.f64 y (.f64 -1/5040 (pow.f64 y 7))))) x)
(.f64 -1 (.f64 (+.f64 (.f64 1/5040 (pow.f64 y 7)) (+.f64 (.f64 -1/120 (pow.f64 y 5)) (+.f64 (.f64 -1 y) (.f64 1/6 (pow.f64 y 3))))) x))
(.f64 -1 (.f64 (+.f64 (.f64 1/5040 (pow.f64 y 7)) (+.f64 (.f64 -1/120 (pow.f64 y 5)) (+.f64 (.f64 -1 y) (.f64 1/6 (pow.f64 y 3))))) x))
(.f64 -1 (.f64 (+.f64 (.f64 1/5040 (pow.f64 y 7)) (+.f64 (.f64 -1/120 (pow.f64 y 5)) (+.f64 (.f64 -1 y) (.f64 1/6 (pow.f64 y 3))))) x))
(.f64 -1 (.f64 (+.f64 (.f64 1/5040 (pow.f64 y 7)) (+.f64 (.f64 -1/120 (pow.f64 y 5)) (+.f64 (.f64 -1 y) (.f64 1/6 (pow.f64 y 3))))) x))
(*.f64 y x)
(+.f64 (.f64 y x) (.f64 -1/6 (*.f64 (pow.f64 y 3) x)))
(.f64 -1/5040 (.f64 (pow.f64 y 7) x))
(+.f64 (.f64 -1/5040 (.f64 (pow.f64 y 7) x)) (.f64 -1/6 (.f64 (pow.f64 y 3) x)))
(.f64 -1/5040 (.f64 (pow.f64 y 7) x))
(+.f64 (.f64 -1/5040 (.f64 (pow.f64 y 7) x)) (.f64 -1/6 (.f64 (pow.f64 y 3) x)))
(.f64 (+.f64 (.f64 -1/6 (pow.f64 y 3)) (+.f64 y (*.f64 -1/5040 (pow.f64 y 7)))) x)
(.f64 (+.f64 (.f64 -1/6 (pow.f64 y 3)) (+.f64 y (*.f64 -1/5040 (pow.f64 y 7)))) x)
(.f64 (+.f64 (.f64 -1/6 (pow.f64 y 3)) (+.f64 y (*.f64 -1/5040 (pow.f64 y 7)))) x)
(.f64 (+.f64 (.f64 -1/6 (pow.f64 y 3)) (+.f64 y (*.f64 -1/5040 (pow.f64 y 7)))) x)
(.f64 (+.f64 (.f64 -1/6 (pow.f64 y 3)) (+.f64 y (*.f64 -1/5040 (pow.f64 y 7)))) x)
(.f64 (+.f64 (.f64 -1/6 (pow.f64 y 3)) (+.f64 y (*.f64 -1/5040 (pow.f64 y 7)))) x)
(.f64 (+.f64 (.f64 -1/6 (pow.f64 y 3)) (+.f64 y (*.f64 -1/5040 (pow.f64 y 7)))) x)
(.f64 (+.f64 (.f64 -1/6 (pow.f64 y 3)) (+.f64 y (*.f64 -1/5040 (pow.f64 y 7)))) x)
(.f64 -1 (.f64 (+.f64 (.f64 1/5040 (pow.f64 y 7)) (+.f64 (.f64 -1 y) (*.f64 1/6 (pow.f64 y 3)))) x))
(.f64 -1 (.f64 (+.f64 (.f64 1/5040 (pow.f64 y 7)) (+.f64 (.f64 -1 y) (*.f64 1/6 (pow.f64 y 3)))) x))
(.f64 -1 (.f64 (+.f64 (.f64 1/5040 (pow.f64 y 7)) (+.f64 (.f64 -1 y) (*.f64 1/6 (pow.f64 y 3)))) x))
(.f64 -1 (.f64 (+.f64 (.f64 1/5040 (pow.f64 y 7)) (+.f64 (.f64 -1 y) (*.f64 1/6 (pow.f64 y 3)))) x))

Outputs
(*.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 (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 (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 -1/5040 (.f64 (pow.f64 y 7) x))
(.f64 -1/5040 (.f64 x (pow.f64 y 7)))
(.f64 (pow.f64 y 7) (.f64 x -1/5040))
(.f64 x (.f64 -1/5040 (pow.f64 y 7)))
(+.f64 (.f64 1/120 (.f64 (pow.f64 y 5) x)) (.f64 -1/5040 (.f64 (pow.f64 y 7) x)))
(fma.f64 1/120 (.f64 x (pow.f64 y 5)) (.f64 -1/5040 (*.f64 x (pow.f64 y 7))))
(.f64 x (fma.f64 -1/5040 (pow.f64 y 7) (.f64 1/120 (pow.f64 y 5))))
(.f64 x (fma.f64 1/120 (pow.f64 y 5) (.f64 -1/5040 (pow.f64 y 7))))
(+.f64 (.f64 1/120 (.f64 (pow.f64 y 5) 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 -1/5040 (.f64 x (pow.f64 y 7)) (.f64 -1/6 (.f64 x (pow.f64 y 3)))))
(+.f64 (.f64 (pow.f64 y 3) (.f64 x -1/6)) (.f64 x (fma.f64 -1/5040 (pow.f64 y 7) (.f64 1/120 (pow.f64 y 5)))))
(.f64 x (fma.f64 -1/6 (pow.f64 y 3) (fma.f64 1/120 (pow.f64 y 5) (.f64 -1/5040 (pow.f64 y 7)))))
(.f64 -1/5040 (.f64 (pow.f64 y 7) x))
(.f64 -1/5040 (.f64 x (pow.f64 y 7)))
(.f64 (pow.f64 y 7) (.f64 x -1/5040))
(.f64 x (.f64 -1/5040 (pow.f64 y 7)))
(+.f64 (.f64 1/120 (.f64 (pow.f64 y 5) x)) (.f64 -1/5040 (.f64 (pow.f64 y 7) x)))
(fma.f64 1/120 (.f64 x (pow.f64 y 5)) (.f64 -1/5040 (*.f64 x (pow.f64 y 7))))
(.f64 x (fma.f64 -1/5040 (pow.f64 y 7) (.f64 1/120 (pow.f64 y 5))))
(.f64 x (fma.f64 1/120 (pow.f64 y 5) (.f64 -1/5040 (pow.f64 y 7))))
(+.f64 (.f64 1/120 (.f64 (pow.f64 y 5) 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 -1/5040 (.f64 x (pow.f64 y 7)) (.f64 -1/6 (.f64 x (pow.f64 y 3)))))
(+.f64 (.f64 (pow.f64 y 3) (.f64 x -1/6)) (.f64 x (fma.f64 -1/5040 (pow.f64 y 7) (.f64 1/120 (pow.f64 y 5)))))
(.f64 x (fma.f64 -1/6 (pow.f64 y 3) (fma.f64 1/120 (pow.f64 y 5) (.f64 -1/5040 (pow.f64 y 7)))))
(.f64 (+.f64 (.f64 -1/6 (pow.f64 y 3)) (+.f64 y (+.f64 (.f64 1/120 (pow.f64 y 5)) (.f64 -1/5040 (pow.f64 y 7))))) x)
(.f64 x (fma.f64 -1/6 (pow.f64 y 3) (+.f64 y (fma.f64 1/120 (pow.f64 y 5) (.f64 -1/5040 (pow.f64 y 7))))))
(*.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 (+.f64 (.f64 -1/6 (pow.f64 y 3)) (+.f64 y (+.f64 (.f64 1/120 (pow.f64 y 5)) (.f64 -1/5040 (pow.f64 y 7))))) x)
(.f64 x (fma.f64 -1/6 (pow.f64 y 3) (+.f64 y (fma.f64 1/120 (pow.f64 y 5) (.f64 -1/5040 (pow.f64 y 7))))))
(*.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 (+.f64 (.f64 -1/6 (pow.f64 y 3)) (+.f64 y (+.f64 (.f64 1/120 (pow.f64 y 5)) (.f64 -1/5040 (pow.f64 y 7))))) x)
(.f64 x (fma.f64 -1/6 (pow.f64 y 3) (+.f64 y (fma.f64 1/120 (pow.f64 y 5) (.f64 -1/5040 (pow.f64 y 7))))))
(*.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 (+.f64 (.f64 -1/6 (pow.f64 y 3)) (+.f64 y (+.f64 (.f64 1/120 (pow.f64 y 5)) (.f64 -1/5040 (pow.f64 y 7))))) x)
(.f64 x (fma.f64 -1/6 (pow.f64 y 3) (+.f64 y (fma.f64 1/120 (pow.f64 y 5) (.f64 -1/5040 (pow.f64 y 7))))))
(*.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 (+.f64 (.f64 -1/6 (pow.f64 y 3)) (+.f64 (.f64 1/120 (pow.f64 y 5)) (+.f64 y (.f64 -1/5040 (pow.f64 y 7))))) x)
(.f64 x (fma.f64 -1/6 (pow.f64 y 3) (+.f64 y (fma.f64 1/120 (pow.f64 y 5) (.f64 -1/5040 (pow.f64 y 7))))))
(*.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 (+.f64 (.f64 -1/6 (pow.f64 y 3)) (+.f64 (.f64 1/120 (pow.f64 y 5)) (+.f64 y (.f64 -1/5040 (pow.f64 y 7))))) x)
(.f64 x (fma.f64 -1/6 (pow.f64 y 3) (+.f64 y (fma.f64 1/120 (pow.f64 y 5) (.f64 -1/5040 (pow.f64 y 7))))))
(*.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 (+.f64 (.f64 -1/6 (pow.f64 y 3)) (+.f64 (.f64 1/120 (pow.f64 y 5)) (+.f64 y (.f64 -1/5040 (pow.f64 y 7))))) x)
(.f64 x (fma.f64 -1/6 (pow.f64 y 3) (+.f64 y (fma.f64 1/120 (pow.f64 y 5) (.f64 -1/5040 (pow.f64 y 7))))))
(*.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 (+.f64 (.f64 -1/6 (pow.f64 y 3)) (+.f64 (.f64 1/120 (pow.f64 y 5)) (+.f64 y (.f64 -1/5040 (pow.f64 y 7))))) x)
(.f64 x (fma.f64 -1/6 (pow.f64 y 3) (+.f64 y (fma.f64 1/120 (pow.f64 y 5) (.f64 -1/5040 (pow.f64 y 7))))))
(*.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 -1 (.f64 (+.f64 (.f64 1/5040 (pow.f64 y 7)) (+.f64 (.f64 -1/120 (pow.f64 y 5)) (+.f64 (.f64 -1 y) (.f64 1/6 (pow.f64 y 3))))) x))
(.f64 x (fma.f64 -1/6 (pow.f64 y 3) (+.f64 y (fma.f64 1/120 (pow.f64 y 5) (.f64 -1/5040 (pow.f64 y 7))))))
(*.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 -1 (.f64 (+.f64 (.f64 1/5040 (pow.f64 y 7)) (+.f64 (.f64 -1/120 (pow.f64 y 5)) (+.f64 (.f64 -1 y) (.f64 1/6 (pow.f64 y 3))))) x))
(.f64 x (fma.f64 -1/6 (pow.f64 y 3) (+.f64 y (fma.f64 1/120 (pow.f64 y 5) (.f64 -1/5040 (pow.f64 y 7))))))
(*.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 -1 (.f64 (+.f64 (.f64 1/5040 (pow.f64 y 7)) (+.f64 (.f64 -1/120 (pow.f64 y 5)) (+.f64 (.f64 -1 y) (.f64 1/6 (pow.f64 y 3))))) x))
(.f64 x (fma.f64 -1/6 (pow.f64 y 3) (+.f64 y (fma.f64 1/120 (pow.f64 y 5) (.f64 -1/5040 (pow.f64 y 7))))))
(*.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 -1 (.f64 (+.f64 (.f64 1/5040 (pow.f64 y 7)) (+.f64 (.f64 -1/120 (pow.f64 y 5)) (+.f64 (.f64 -1 y) (.f64 1/6 (pow.f64 y 3))))) x))
(.f64 x (fma.f64 -1/6 (pow.f64 y 3) (+.f64 y (fma.f64 1/120 (pow.f64 y 5) (.f64 -1/5040 (pow.f64 y 7))))))
(*.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 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 (fma.f64 -1/6 (pow.f64 y 3) y))
(.f64 -1/5040 (.f64 (pow.f64 y 7) x))
(.f64 -1/5040 (.f64 x (pow.f64 y 7)))
(.f64 (pow.f64 y 7) (.f64 x -1/5040))
(.f64 x (.f64 -1/5040 (pow.f64 y 7)))
(+.f64 (.f64 -1/5040 (.f64 (pow.f64 y 7) x)) (.f64 -1/6 (.f64 (pow.f64 y 3) x)))
(fma.f64 -1/5040 (.f64 x (pow.f64 y 7)) (.f64 -1/6 (*.f64 x (pow.f64 y 3))))
(.f64 x (+.f64 (.f64 -1/6 (pow.f64 y 3)) (*.f64 -1/5040 (pow.f64 y 7))))
(.f64 x (fma.f64 -1/6 (pow.f64 y 3) (.f64 -1/5040 (pow.f64 y 7))))
(.f64 -1/5040 (.f64 (pow.f64 y 7) x))
(.f64 -1/5040 (.f64 x (pow.f64 y 7)))
(.f64 (pow.f64 y 7) (.f64 x -1/5040))
(.f64 x (.f64 -1/5040 (pow.f64 y 7)))
(+.f64 (.f64 -1/5040 (.f64 (pow.f64 y 7) x)) (.f64 -1/6 (.f64 (pow.f64 y 3) x)))
(fma.f64 -1/5040 (.f64 x (pow.f64 y 7)) (.f64 -1/6 (*.f64 x (pow.f64 y 3))))
(.f64 x (+.f64 (.f64 -1/6 (pow.f64 y 3)) (*.f64 -1/5040 (pow.f64 y 7))))
(.f64 x (fma.f64 -1/6 (pow.f64 y 3) (.f64 -1/5040 (pow.f64 y 7))))
(.f64 (+.f64 (.f64 -1/6 (pow.f64 y 3)) (+.f64 y (*.f64 -1/5040 (pow.f64 y 7)))) x)
(.f64 x (fma.f64 -1/6 (pow.f64 y 3) (+.f64 y (.f64 -1/5040 (pow.f64 y 7)))))
(*.f64 x (fma.f64 -1/6 (pow.f64 y 3) (fma.f64 -1/5040 (pow.f64 y 7) y)))
(*.f64 x (fma.f64 -1/5040 (pow.f64 y 7) (fma.f64 -1/6 (pow.f64 y 3) y)))
(.f64 (+.f64 (.f64 -1/6 (pow.f64 y 3)) (+.f64 y (*.f64 -1/5040 (pow.f64 y 7)))) x)
(.f64 x (fma.f64 -1/6 (pow.f64 y 3) (+.f64 y (.f64 -1/5040 (pow.f64 y 7)))))
(*.f64 x (fma.f64 -1/6 (pow.f64 y 3) (fma.f64 -1/5040 (pow.f64 y 7) y)))
(*.f64 x (fma.f64 -1/5040 (pow.f64 y 7) (fma.f64 -1/6 (pow.f64 y 3) y)))
(.f64 (+.f64 (.f64 -1/6 (pow.f64 y 3)) (+.f64 y (*.f64 -1/5040 (pow.f64 y 7)))) x)
(.f64 x (fma.f64 -1/6 (pow.f64 y 3) (+.f64 y (.f64 -1/5040 (pow.f64 y 7)))))
(*.f64 x (fma.f64 -1/6 (pow.f64 y 3) (fma.f64 -1/5040 (pow.f64 y 7) y)))
(*.f64 x (fma.f64 -1/5040 (pow.f64 y 7) (fma.f64 -1/6 (pow.f64 y 3) y)))
(.f64 (+.f64 (.f64 -1/6 (pow.f64 y 3)) (+.f64 y (*.f64 -1/5040 (pow.f64 y 7)))) x)
(.f64 x (fma.f64 -1/6 (pow.f64 y 3) (+.f64 y (.f64 -1/5040 (pow.f64 y 7)))))
(*.f64 x (fma.f64 -1/6 (pow.f64 y 3) (fma.f64 -1/5040 (pow.f64 y 7) y)))
(*.f64 x (fma.f64 -1/5040 (pow.f64 y 7) (fma.f64 -1/6 (pow.f64 y 3) y)))
(.f64 (+.f64 (.f64 -1/6 (pow.f64 y 3)) (+.f64 y (*.f64 -1/5040 (pow.f64 y 7)))) x)
(.f64 x (fma.f64 -1/6 (pow.f64 y 3) (+.f64 y (.f64 -1/5040 (pow.f64 y 7)))))
(*.f64 x (fma.f64 -1/6 (pow.f64 y 3) (fma.f64 -1/5040 (pow.f64 y 7) y)))
(*.f64 x (fma.f64 -1/5040 (pow.f64 y 7) (fma.f64 -1/6 (pow.f64 y 3) y)))
(.f64 (+.f64 (.f64 -1/6 (pow.f64 y 3)) (+.f64 y (*.f64 -1/5040 (pow.f64 y 7)))) x)
(.f64 x (fma.f64 -1/6 (pow.f64 y 3) (+.f64 y (.f64 -1/5040 (pow.f64 y 7)))))
(*.f64 x (fma.f64 -1/6 (pow.f64 y 3) (fma.f64 -1/5040 (pow.f64 y 7) y)))
(*.f64 x (fma.f64 -1/5040 (pow.f64 y 7) (fma.f64 -1/6 (pow.f64 y 3) y)))
(.f64 (+.f64 (.f64 -1/6 (pow.f64 y 3)) (+.f64 y (*.f64 -1/5040 (pow.f64 y 7)))) x)
(.f64 x (fma.f64 -1/6 (pow.f64 y 3) (+.f64 y (.f64 -1/5040 (pow.f64 y 7)))))
(*.f64 x (fma.f64 -1/6 (pow.f64 y 3) (fma.f64 -1/5040 (pow.f64 y 7) y)))
(*.f64 x (fma.f64 -1/5040 (pow.f64 y 7) (fma.f64 -1/6 (pow.f64 y 3) y)))
(.f64 (+.f64 (.f64 -1/6 (pow.f64 y 3)) (+.f64 y (*.f64 -1/5040 (pow.f64 y 7)))) x)
(.f64 x (fma.f64 -1/6 (pow.f64 y 3) (+.f64 y (.f64 -1/5040 (pow.f64 y 7)))))
(*.f64 x (fma.f64 -1/6 (pow.f64 y 3) (fma.f64 -1/5040 (pow.f64 y 7) y)))
(*.f64 x (fma.f64 -1/5040 (pow.f64 y 7) (fma.f64 -1/6 (pow.f64 y 3) y)))
(.f64 -1 (.f64 (+.f64 (.f64 1/5040 (pow.f64 y 7)) (+.f64 (.f64 -1 y) (*.f64 1/6 (pow.f64 y 3)))) x))
(.f64 x (fma.f64 -1/6 (pow.f64 y 3) (+.f64 y (.f64 -1/5040 (pow.f64 y 7)))))
(*.f64 x (fma.f64 -1/6 (pow.f64 y 3) (fma.f64 -1/5040 (pow.f64 y 7) y)))
(*.f64 x (fma.f64 -1/5040 (pow.f64 y 7) (fma.f64 -1/6 (pow.f64 y 3) y)))
(.f64 -1 (.f64 (+.f64 (.f64 1/5040 (pow.f64 y 7)) (+.f64 (.f64 -1 y) (*.f64 1/6 (pow.f64 y 3)))) x))
(.f64 x (fma.f64 -1/6 (pow.f64 y 3) (+.f64 y (.f64 -1/5040 (pow.f64 y 7)))))
(*.f64 x (fma.f64 -1/6 (pow.f64 y 3) (fma.f64 -1/5040 (pow.f64 y 7) y)))
(*.f64 x (fma.f64 -1/5040 (pow.f64 y 7) (fma.f64 -1/6 (pow.f64 y 3) y)))
(.f64 -1 (.f64 (+.f64 (.f64 1/5040 (pow.f64 y 7)) (+.f64 (.f64 -1 y) (*.f64 1/6 (pow.f64 y 3)))) x))
(.f64 x (fma.f64 -1/6 (pow.f64 y 3) (+.f64 y (.f64 -1/5040 (pow.f64 y 7)))))
(*.f64 x (fma.f64 -1/6 (pow.f64 y 3) (fma.f64 -1/5040 (pow.f64 y 7) y)))
(*.f64 x (fma.f64 -1/5040 (pow.f64 y 7) (fma.f64 -1/6 (pow.f64 y 3) y)))
(.f64 -1 (.f64 (+.f64 (.f64 1/5040 (pow.f64 y 7)) (+.f64 (.f64 -1 y) (*.f64 1/6 (pow.f64 y 3)))) x))
(.f64 x (fma.f64 -1/6 (pow.f64 y 3) (+.f64 y (.f64 -1/5040 (pow.f64 y 7)))))
(*.f64 x (fma.f64 -1/6 (pow.f64 y 3) (fma.f64 -1/5040 (pow.f64 y 7) y)))
(*.f64 x (fma.f64 -1/5040 (pow.f64 y 7) (fma.f64 -1/6 (pow.f64 y 3) y)))

eval219.0ms (3.4%)

Compiler: Compiled 12229 to 6847 computations (44% saved)

prune91.0ms (1.4%)

Pruning

19 alts after pruning (12 fresh and 7 done)

	Pruned	Kept	Total
New	551	8	559
Fresh	1	4	5
Picked	1	0	1
Done	1	7	8
Total	554	19	573

Error

0.0b

Counts

573 → 19

Alt Table

Click to see full alt table

Status	Error	Program
	37.5b	(fma.f64 (cbrt.f64 (.f64 z z)) (.f64 (cbrt.f64 z) (cos.f64 y)) (*.f64 y x))
▶	53.1b	(*.f64 y x)
	31.8b	(+.f64 (.f64 x (sin.f64 y)) (pow.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (.f64 z (cos.f64 y)))) 3) 2))
✓	15.2b	(+.f64 (*.f64 x (sin.f64 y)) z)
	24.3b	(+.f64 (.f64 y x) (pow.f64 (cbrt.f64 (.f64 z (cos.f64 y))) 3))
✓	0.9b	(+.f64 (.f64 x (sin.f64 y)) (.f64 (pow.f64 (cbrt.f64 z) 2) (*.f64 (cbrt.f64 z) (cos.f64 y))))
▶	44.9b	(+.f64 (.f64 y x) (.f64 (*.f64 (cos.f64 y) (sqrt.f64 z)) (sqrt.f64 z)))
	24.7b	(*.f64 (cos.f64 y) z)
▶	36.3b	(+.f64 (pow.f64 (sqrt.f64 (*.f64 x (sin.f64 y))) 2) z)
✓	44.4b	(+.f64 (.f64 y x) (cbrt.f64 (pow.f64 (.f64 z (cos.f64 y)) 3)))
✓	28.3b	(+.f64 (.f64 x (sin.f64 y)) (cbrt.f64 (pow.f64 (.f64 z (cos.f64 y)) 3)))
✓	30.8b	(+.f64 (*.f64 y x) z)
✓	0.1b	(+.f64 (.f64 x (sin.f64 y)) (.f64 z (cos.f64 y)))
▶	1.3b	(+.f64 (.f64 x (sin.f64 y)) (.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 z)) 3) 2) (*.f64 (cbrt.f64 z) (cos.f64 y))))
	39.4b	z
	24.4b	(+.f64 (.f64 y x) (.f64 (pow.f64 (cbrt.f64 z) 2) (*.f64 (cbrt.f64 z) (cos.f64 y))))
	32.0b	(+.f64 (+.f64 (.f64 1/120 (.f64 (pow.f64 y 5) x)) (.f64 (+.f64 (.f64 -1/6 (pow.f64 y 3)) (+.f64 y (*.f64 -1/5040 (pow.f64 y 7)))) x)) z)
▶	32.2b	(+.f64 (.f64 x (sin.f64 y)) (.f64 (*.f64 (cos.f64 y) (sqrt.f64 z)) (sqrt.f64 z)))
✓	31.4b	(+.f64 (.f64 x (sin.f64 y)) (pow.f64 (sqrt.f64 (.f64 z (cos.f64 y))) 2))

Compiler

Compiled 435 to 302 computations (30.6% saved)

localize24.0ms (0.4%)

Local error

Found 8 expressions with local error:

New	Error	Program
	0.5b	(pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 z)) 3) 2)
	0.3b	(.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 z)) 3) 2) (.f64 (cbrt.f64 z) (cos.f64 y)))
	0.1b	(*.f64 (cbrt.f64 z) (cos.f64 y))
	0.1b	(*.f64 x (sin.f64 y))
✓	0.5b	(pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 z)) 3) 2)
	0.6b	(cbrt.f64 z)
✓	0.6b	(cbrt.f64 (cbrt.f64 z))
✓	0.7b	(pow.f64 (cbrt.f64 (cbrt.f64 z)) 3)

Compiler

Compiled 69 to 28 computations (59.4% saved)

series42.0ms (0.6%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
30.0ms	z	@	0	(pow.f64 (cbrt.f64 (cbrt.f64 z)) 3)
7.0ms	z	@	inf	(pow.f64 (cbrt.f64 (cbrt.f64 z)) 3)
2.0ms	z	@	-inf	(pow.f64 (cbrt.f64 (cbrt.f64 z)) 3)
1.0ms	z	@	-inf	(pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 z)) 3) 2)
1.0ms	z	@	0	(pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 z)) 3) 2)

rewrite43.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

528×	`pow1_binary64`
518×	`add-sqr-sqrt_binary64`
501×	`add-log-exp_binary64`
500×	`log1p-expm1-u_binary64`
500×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	171	14
2	1534	14

Stop Event

1×	node limit

Counts

3 → 63

Calls

Call 1

Inputs
(pow.f64 (cbrt.f64 (cbrt.f64 z)) 3)
(cbrt.f64 (cbrt.f64 z))
(pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 z)) 3) 2)

Outputs

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

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

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

simplify98.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

828×	`sqr-pow_binary64`
676×	`unswap-sqr_binary64`
651×	`fma-def_binary64`
340×	`cube-prod_binary64`
335×	`associate-l_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	28	392
1	77	332
2	149	332
3	381	332
4	1397	288
5	2750	288
6	2948	288
7	3254	288
8	3682	288
9	4159	288
10	4791	288
11	5579	288
12	6530	288
13	7351	288

Stop Event

1×	node limit

Counts

99 → 74

Calls

Call 1

Inputs
(*.f64 (pow.f64 (pow.f64 1 4) 1/9) (pow.f64 z 1/3))
(*.f64 (pow.f64 (pow.f64 1 4) 1/9) (pow.f64 z 1/3))
(*.f64 (pow.f64 (pow.f64 1 4) 1/9) (pow.f64 z 1/3))
(*.f64 (pow.f64 (pow.f64 1 4) 1/9) (pow.f64 z 1/3))
(pow.f64 z 1/3)
(pow.f64 z 1/3)
(pow.f64 z 1/3)
(pow.f64 z 1/3)
(.f64 (pow.f64 (.f64 -1 z) 1/3) (*.f64 (pow.f64 1 1/9) (cbrt.f64 -1)))
(.f64 (pow.f64 (.f64 -1 z) 1/3) (*.f64 (pow.f64 1 1/9) (cbrt.f64 -1)))
(.f64 (pow.f64 (.f64 -1 z) 1/3) (*.f64 (pow.f64 1 1/9) (cbrt.f64 -1)))
(.f64 (pow.f64 (.f64 -1 z) 1/3) (*.f64 (pow.f64 1 1/9) (cbrt.f64 -1)))
(pow.f64 z 1/9)
(pow.f64 z 1/9)
(pow.f64 z 1/9)
(pow.f64 z 1/9)
(pow.f64 z 1/9)
(pow.f64 z 1/9)
(pow.f64 z 1/9)
(pow.f64 z 1/9)
(.f64 (pow.f64 (.f64 -1 z) 1/9) (pow.f64 (*.f64 1 (cbrt.f64 -1)) 1/3))
(.f64 (pow.f64 (.f64 -1 z) 1/9) (pow.f64 (*.f64 1 (cbrt.f64 -1)) 1/3))
(.f64 (pow.f64 (.f64 -1 z) 1/9) (pow.f64 (*.f64 1 (cbrt.f64 -1)) 1/3))
(.f64 (pow.f64 (.f64 -1 z) 1/9) (pow.f64 (*.f64 1 (cbrt.f64 -1)) 1/3))
(*.f64 (pow.f64 (pow.f64 1 4) 1/9) (pow.f64 (pow.f64 z 2) 1/3))
(*.f64 (pow.f64 (pow.f64 1 4) 1/9) (pow.f64 (pow.f64 z 2) 1/3))
(*.f64 (pow.f64 (pow.f64 1 4) 1/9) (pow.f64 (pow.f64 z 2) 1/3))
(*.f64 (pow.f64 (pow.f64 1 4) 1/9) (pow.f64 (pow.f64 z 2) 1/3))
(pow.f64 (pow.f64 z 2) 1/3)
(pow.f64 (pow.f64 z 2) 1/3)
(pow.f64 (pow.f64 z 2) 1/3)
(pow.f64 (pow.f64 z 2) 1/3)
(.f64 (pow.f64 (pow.f64 1 4) 1/9) (.f64 (pow.f64 (cbrt.f64 -1) 2) (pow.f64 (pow.f64 z 2) 1/3)))
(.f64 (pow.f64 (pow.f64 1 4) 1/9) (.f64 (pow.f64 (cbrt.f64 -1) 2) (pow.f64 (pow.f64 z 2) 1/3)))
(.f64 (pow.f64 (pow.f64 1 4) 1/9) (.f64 (pow.f64 (cbrt.f64 -1) 2) (pow.f64 (pow.f64 z 2) 1/3)))
(.f64 (pow.f64 (pow.f64 1 4) 1/9) (.f64 (pow.f64 (cbrt.f64 -1) 2) (pow.f64 (pow.f64 z 2) 1/3)))

Outputs
(*.f64 (pow.f64 (pow.f64 1 4) 1/9) (pow.f64 z 1/3))
(*.f64 1 (cbrt.f64 z))
(cbrt.f64 z)
(*.f64 (pow.f64 (pow.f64 1 4) 1/9) (pow.f64 z 1/3))
(*.f64 1 (cbrt.f64 z))
(cbrt.f64 z)
(*.f64 (pow.f64 (pow.f64 1 4) 1/9) (pow.f64 z 1/3))
(*.f64 1 (cbrt.f64 z))
(cbrt.f64 z)
(*.f64 (pow.f64 (pow.f64 1 4) 1/9) (pow.f64 z 1/3))
(*.f64 1 (cbrt.f64 z))
(cbrt.f64 z)
(pow.f64 z 1/3)
(*.f64 1 (cbrt.f64 z))
(cbrt.f64 z)
(pow.f64 z 1/3)
(*.f64 1 (cbrt.f64 z))
(cbrt.f64 z)
(pow.f64 z 1/3)
(*.f64 1 (cbrt.f64 z))
(cbrt.f64 z)
(pow.f64 z 1/3)
(*.f64 1 (cbrt.f64 z))
(cbrt.f64 z)
(.f64 (pow.f64 (.f64 -1 z) 1/3) (*.f64 (pow.f64 1 1/9) (cbrt.f64 -1)))
(*.f64 (cbrt.f64 (neg.f64 z)) (cbrt.f64 -1))
(.f64 (pow.f64 (.f64 -1 z) 1/3) (*.f64 (pow.f64 1 1/9) (cbrt.f64 -1)))
(*.f64 (cbrt.f64 (neg.f64 z)) (cbrt.f64 -1))
(.f64 (pow.f64 (.f64 -1 z) 1/3) (*.f64 (pow.f64 1 1/9) (cbrt.f64 -1)))
(*.f64 (cbrt.f64 (neg.f64 z)) (cbrt.f64 -1))
(.f64 (pow.f64 (.f64 -1 z) 1/3) (*.f64 (pow.f64 1 1/9) (cbrt.f64 -1)))
(*.f64 (cbrt.f64 (neg.f64 z)) (cbrt.f64 -1))
(pow.f64 z 1/9)
(*.f64 (pow.f64 z 1/18) (pow.f64 z 1/18))
(pow.f64 (pow.f64 z 1/36) 4)
(pow.f64 z 1/9)
(*.f64 (pow.f64 z 1/18) (pow.f64 z 1/18))
(pow.f64 (pow.f64 z 1/36) 4)
(pow.f64 z 1/9)
(*.f64 (pow.f64 z 1/18) (pow.f64 z 1/18))
(pow.f64 (pow.f64 z 1/36) 4)
(pow.f64 z 1/9)
(*.f64 (pow.f64 z 1/18) (pow.f64 z 1/18))
(pow.f64 (pow.f64 z 1/36) 4)
(pow.f64 z 1/9)
(*.f64 (pow.f64 z 1/18) (pow.f64 z 1/18))
(pow.f64 (pow.f64 z 1/36) 4)
(pow.f64 z 1/9)
(*.f64 (pow.f64 z 1/18) (pow.f64 z 1/18))
(pow.f64 (pow.f64 z 1/36) 4)
(pow.f64 z 1/9)
(*.f64 (pow.f64 z 1/18) (pow.f64 z 1/18))
(pow.f64 (pow.f64 z 1/36) 4)
(pow.f64 z 1/9)
(*.f64 (pow.f64 z 1/18) (pow.f64 z 1/18))
(pow.f64 (pow.f64 z 1/36) 4)
(.f64 (pow.f64 (.f64 -1 z) 1/9) (pow.f64 (*.f64 1 (cbrt.f64 -1)) 1/3))
(.f64 (.f64 (pow.f64 (neg.f64 z) 1/18) (pow.f64 (neg.f64 z) 1/18)) (cbrt.f64 (cbrt.f64 -1)))
(*.f64 (pow.f64 (pow.f64 (neg.f64 z) 1/36) 4) (cbrt.f64 (cbrt.f64 -1)))
(.f64 (pow.f64 (.f64 -1 z) 1/9) (pow.f64 (*.f64 1 (cbrt.f64 -1)) 1/3))
(.f64 (.f64 (pow.f64 (neg.f64 z) 1/18) (pow.f64 (neg.f64 z) 1/18)) (cbrt.f64 (cbrt.f64 -1)))
(*.f64 (pow.f64 (pow.f64 (neg.f64 z) 1/36) 4) (cbrt.f64 (cbrt.f64 -1)))
(.f64 (pow.f64 (.f64 -1 z) 1/9) (pow.f64 (*.f64 1 (cbrt.f64 -1)) 1/3))
(.f64 (.f64 (pow.f64 (neg.f64 z) 1/18) (pow.f64 (neg.f64 z) 1/18)) (cbrt.f64 (cbrt.f64 -1)))
(*.f64 (pow.f64 (pow.f64 (neg.f64 z) 1/36) 4) (cbrt.f64 (cbrt.f64 -1)))
(.f64 (pow.f64 (.f64 -1 z) 1/9) (pow.f64 (*.f64 1 (cbrt.f64 -1)) 1/3))
(.f64 (.f64 (pow.f64 (neg.f64 z) 1/18) (pow.f64 (neg.f64 z) 1/18)) (cbrt.f64 (cbrt.f64 -1)))
(*.f64 (pow.f64 (pow.f64 (neg.f64 z) 1/36) 4) (cbrt.f64 (cbrt.f64 -1)))
(*.f64 (pow.f64 (pow.f64 1 4) 1/9) (pow.f64 (pow.f64 z 2) 1/3))
(.f64 1 (cbrt.f64 (.f64 z z)))
(cbrt.f64 (*.f64 z z))
(*.f64 (pow.f64 (pow.f64 1 4) 1/9) (pow.f64 (pow.f64 z 2) 1/3))
(.f64 1 (cbrt.f64 (.f64 z z)))
(cbrt.f64 (*.f64 z z))
(*.f64 (pow.f64 (pow.f64 1 4) 1/9) (pow.f64 (pow.f64 z 2) 1/3))
(.f64 1 (cbrt.f64 (.f64 z z)))
(cbrt.f64 (*.f64 z z))
(*.f64 (pow.f64 (pow.f64 1 4) 1/9) (pow.f64 (pow.f64 z 2) 1/3))
(.f64 1 (cbrt.f64 (.f64 z z)))
(cbrt.f64 (*.f64 z z))
(pow.f64 (pow.f64 z 2) 1/3)
(.f64 1 (cbrt.f64 (.f64 z z)))
(cbrt.f64 (*.f64 z z))
(pow.f64 (pow.f64 z 2) 1/3)
(.f64 1 (cbrt.f64 (.f64 z z)))
(cbrt.f64 (*.f64 z z))
(pow.f64 (pow.f64 z 2) 1/3)
(.f64 1 (cbrt.f64 (.f64 z z)))
(cbrt.f64 (*.f64 z z))
(pow.f64 (pow.f64 z 2) 1/3)
(.f64 1 (cbrt.f64 (.f64 z z)))
(cbrt.f64 (*.f64 z z))
(.f64 (pow.f64 (pow.f64 1 4) 1/9) (.f64 (pow.f64 (cbrt.f64 -1) 2) (pow.f64 (pow.f64 z 2) 1/3)))
(.f64 1 (.f64 (cbrt.f64 (*.f64 z z)) (pow.f64 (cbrt.f64 -1) 2)))
(.f64 (cbrt.f64 (.f64 z z)) (pow.f64 (cbrt.f64 -1) 2))
(.f64 (pow.f64 (pow.f64 1 4) 1/9) (.f64 (pow.f64 (cbrt.f64 -1) 2) (pow.f64 (pow.f64 z 2) 1/3)))
(.f64 1 (.f64 (cbrt.f64 (*.f64 z z)) (pow.f64 (cbrt.f64 -1) 2)))
(.f64 (cbrt.f64 (.f64 z z)) (pow.f64 (cbrt.f64 -1) 2))
(.f64 (pow.f64 (pow.f64 1 4) 1/9) (.f64 (pow.f64 (cbrt.f64 -1) 2) (pow.f64 (pow.f64 z 2) 1/3)))
(.f64 1 (.f64 (cbrt.f64 (*.f64 z z)) (pow.f64 (cbrt.f64 -1) 2)))
(.f64 (cbrt.f64 (.f64 z z)) (pow.f64 (cbrt.f64 -1) 2))
(.f64 (pow.f64 (pow.f64 1 4) 1/9) (.f64 (pow.f64 (cbrt.f64 -1) 2) (pow.f64 (pow.f64 z 2) 1/3)))
(.f64 1 (.f64 (cbrt.f64 (*.f64 z z)) (pow.f64 (cbrt.f64 -1) 2)))
(.f64 (cbrt.f64 (.f64 z z)) (pow.f64 (cbrt.f64 -1) 2))

localize3.0ms (0%)

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

localize19.0ms (0.3%)

Local error

Found 6 expressions with local error:

New	Error	Program
	6.4b	(sqrt.f64 (*.f64 x (sin.f64 y)))
	0.2b	(pow.f64 (sqrt.f64 (*.f64 x (sin.f64 y))) 2)
	0.1b	(*.f64 x (sin.f64 y))
	0.1b	(*.f64 x (sin.f64 y))
✓	0.2b	(pow.f64 (sqrt.f64 (*.f64 x (sin.f64 y))) 2)
✓	6.4b	(sqrt.f64 (*.f64 x (sin.f64 y)))

Compiler

Compiled 34 to 12 computations (64.7% saved)

series9.0ms (0.1%)

Counts

2 → 16

Calls

12 calls:

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

rewrite43.0ms (0.7%)

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	1591	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 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 expm1.f64 (log1p.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 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 expm1.f64 (log1p.f64 (*.f64 x (sin.f64 y))))))))

simplify7.0ms (0.1%)

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)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(.f64 (.f64 (cos.f64 y) (sqrt.f64 z)) (sqrt.f64 z))
	0.1b	(*.f64 (cos.f64 y) (sqrt.f64 z))
✓	0.1b	(*.f64 (cos.f64 y) (sqrt.f64 z))
✓	0.2b	(.f64 (.f64 (cos.f64 y) (sqrt.f64 z)) (sqrt.f64 z))

Compiler

Compiled 38 to 9 computations (76.3% saved)

series6.0ms (0.1%)

Counts

2 → 36

Calls

12 calls:

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

rewrite42.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

2 → 22

Calls

Call 1

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

Outputs

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

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

simplify44.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

805×	`fma-def_binary64`
597×	`fma-neg_binary64`
568×	`unsub-neg_binary64`
485×	`cancel-sign-sub-inv_binary64`
454×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	43	340
1	110	331
2	320	314
3	1024	306
4	2393	306
5	3197	306
6	5070	306

Stop Event

1×	node limit

Counts

58 → 41

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

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

localize25.0ms (0.4%)

Local error

Found 6 expressions with local error:

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

Compiler

Compiled 42 to 10 computations (76.2% saved)

rewrite0.0ms (0%)

Counts: 0 → 0

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

0 → 0

Calls

Call 1

Inputs

Outputs

eval68.0ms (1.1%)

Compiler: Compiled 4955 to 1997 computations (59.7% saved)

prune98.0ms (1.5%)

Pruning

24 alts after pruning (12 fresh and 12 done)

	Pruned	Kept	Total
New	282	5	287
Fresh	0	7	7
Picked	0	1	1
Done	0	11	11
Total	282	24	306

Error

0.0b

Counts

306 → 24

Alt Table

Click to see full alt table

Status	Error	Program
	37.5b	(fma.f64 (cbrt.f64 (.f64 z z)) (.f64 (cbrt.f64 z) (cos.f64 y)) (*.f64 y x))
✓	53.1b	(*.f64 y x)
	15.7b	(+.f64 (.f64 (cbrt.f64 (.f64 x (sin.f64 y))) (pow.f64 (cbrt.f64 (*.f64 x (sin.f64 y))) 2)) z)
✓	0.1b	(+.f64 (.f64 x (sin.f64 y)) (.f64 z (cos.f64 y)))
	39.5b	(+.f64 (.f64 (.f64 (sin.f64 y) (sqrt.f64 x)) (sqrt.f64 x)) z)
	39.4b	z
	31.8b	(+.f64 (.f64 x (sin.f64 y)) (pow.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (.f64 z (cos.f64 y)))) 3) 2))
	15.6b	(+.f64 (.f64 (.f64 (sin.f64 y) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x)) z)
✓	15.2b	(+.f64 (*.f64 x (sin.f64 y)) z)
	24.3b	(+.f64 (.f64 y x) (pow.f64 (cbrt.f64 (.f64 z (cos.f64 y))) 3))
✓	0.9b	(+.f64 (.f64 x (sin.f64 y)) (.f64 (pow.f64 (cbrt.f64 z) 2) (*.f64 (cbrt.f64 z) (cos.f64 y))))
✓	44.9b	(+.f64 (.f64 y x) (.f64 (*.f64 (cos.f64 y) (sqrt.f64 z)) (sqrt.f64 z)))
	24.7b	(*.f64 (cos.f64 y) z)
✓	36.3b	(+.f64 (pow.f64 (sqrt.f64 (*.f64 x (sin.f64 y))) 2) z)
✓	44.4b	(+.f64 (.f64 y x) (cbrt.f64 (pow.f64 (.f64 z (cos.f64 y)) 3)))
✓	28.3b	(+.f64 (.f64 x (sin.f64 y)) (cbrt.f64 (pow.f64 (.f64 z (cos.f64 y)) 3)))
✓	30.8b	(+.f64 (*.f64 y x) z)
	36.4b	(+.f64 (.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))))) z)
✓	1.3b	(+.f64 (.f64 x (sin.f64 y)) (.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 z)) 3) 2) (*.f64 (cbrt.f64 z) (cos.f64 y))))
	40.6b	(+.f64 (.f64 (.f64 x (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))) z)
	24.4b	(+.f64 (.f64 y x) (.f64 (pow.f64 (cbrt.f64 z) 2) (*.f64 (cbrt.f64 z) (cos.f64 y))))
	32.0b	(+.f64 (+.f64 (.f64 1/120 (.f64 (pow.f64 y 5) x)) (.f64 (+.f64 (.f64 -1/6 (pow.f64 y 3)) (+.f64 y (*.f64 -1/5040 (pow.f64 y 7)))) x)) z)
✓	32.2b	(+.f64 (.f64 x (sin.f64 y)) (.f64 (*.f64 (cos.f64 y) (sqrt.f64 z)) (sqrt.f64 z)))
✓	31.4b	(+.f64 (.f64 x (sin.f64 y)) (pow.f64 (sqrt.f64 (.f64 z (cos.f64 y))) 2))

Compiler

Compiled 348 to 231 computations (33.6% saved)

regimes68.0ms (1%)

Counts

24 → 1

Calls

Call 1

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

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

Calls

4 calls:

26.0ms	y
13.0ms	(+.f64 (.f64 x (sin.f64 y)) (.f64 z (cos.f64 y)))
12.0ms	z
11.0ms	x

Results

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

Compiler

Compiled 303 to 121 computations (60.1% saved)

regimes48.0ms (0.7%)

Counts

5 → 3

Calls

Call 1

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

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

Calls

3 calls:

16.0ms	z
15.0ms	x
15.0ms	y

Results

Error	Segments	Branch
6.9b	3	`x`
10.3b	4	`y`
7.0b	3	`z`

Compiler

Compiled 34 to 19 computations (44.1% saved)

bsearch181.0ms (2.8%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
84.0ms	2.864802210685416e-125	4.4285123489338425e-116
97.0ms	-6.068695247515499e+30	-2.3564920836118957e+20

Compiler

Compiled 18 to 13 computations (27.8% saved)

regimes37.0ms (0.6%)

Counts

4 → 3

Calls

Call 1

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

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

Calls

3 calls:

14.0ms	y
13.0ms	x
10.0ms	z

Results

Error	Segments	Branch
19.2b	3	`x`
15.2b	3	`y`
18.8b	3	`z`

Compiler

Compiled 28 to 16 computations (42.9% saved)

bsearch88.0ms (1.4%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
35.0ms	2387346450.22095	752707377563.393
53.0ms	-901.760773367421	-1.0491666815934236e-10

Compiler

Compiled 18 to 13 computations (27.8% saved)

regimes15.0ms (0.2%)

Counts

3 → 1

Calls

Call 1

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

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

Calls

3 calls:

8.0ms	z
3.0ms	y
3.0ms	x

Results

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

Compiler

Compiled 24 to 14 computations (41.7% saved)

regimes66.0ms (1%)

Accuracy

Total -27.5b remaining (-78.8%)

Threshold costs -27.5b (-78.8%)

Counts

2 → 5

Calls

Call 1

Inputs
z
(*.f64 y x)

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

Calls

3 calls:

44.0ms	z
13.0ms	x
8.0ms	y

Results

Error	Segments	Branch
35.0b	5	`x`
37.9b	3	`y`
35.1b	3	`z`

Compiler

Compiled 19 to 13 computations (31.6% saved)

bsearch261.0ms (4%)

Algorithm

4×	binary-search

Steps

Time	Left	Right
64.0ms	8.650410171542639e+76	1.0410926397721233e+77
78.0ms	-9.883103112724682e+97	-1.072544978006888e+94
58.0ms	-7.202556039975565e+190	-4.841713462073088e+190
60.0ms	-1.1823230536834126e+221	-6.642619667446766e+220

Compiler

Compiled 18 to 13 computations (27.8% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	127
1	44	127

Stop Event

1×

saturated

Calls

Call 1

Inputs
(+.f64 (.f64 x (sin.f64 y)) (.f64 z (cos.f64 y)))
(if (<=.f64 x -6068695247515498718551053697024) (+.f64 (.f64 x (sin.f64 y)) z) (if (<=.f64 x 341155706335039/11908525658859223294760121268437066290850060053501019099651935423375594096449911575776314174894302258147533153997065059263030913083222523904) (.f64 (cos.f64 y) z) (+.f64 (*.f64 x (sin.f64 y)) z)))
(if (<=.f64 y -3965985823159031/4398046511104) (.f64 (cos.f64 y) z) (if (<=.f64 y 2503314191386883/1048576) (+.f64 (.f64 y x) z) (*.f64 (cos.f64 y) z)))
(+.f64 (*.f64 y x) z)
(if (<=.f64 x -118232305368341256331012252254786283463978329030352334790805060172114184229277243767986474979399912609633210755793769001357920160399183331481011704924432788108430978745913748145275131161163700519264121370390441889613479936) (.f64 y x) (if (<=.f64 x -72025560399755645438321156391233924483984303214329782683749460163862477303986610804978642874550380261219247639025948863482461742441581790963427653614968024493192683206405472364080811357503488) z (if (<=.f64 x -98831031127246823318241765547704889224886246794375846615278096913456701770303634821844738334785536) (.f64 y x) (if (<=.f64 x 86504101715426392994505572727059545674992736074727618007941472008404429963264) z (*.f64 y x)))))
z

Outputs
(+.f64 (.f64 x (sin.f64 y)) (.f64 z (cos.f64 y)))
(if (<=.f64 x -6068695247515498718551053697024) (+.f64 (.f64 x (sin.f64 y)) z) (if (<=.f64 x 341155706335039/11908525658859223294760121268437066290850060053501019099651935423375594096449911575776314174894302258147533153997065059263030913083222523904) (.f64 (cos.f64 y) z) (+.f64 (*.f64 x (sin.f64 y)) z)))
(if (<=.f64 x -6068695247515498718551053697024) (+.f64 (.f64 x (sin.f64 y)) z) (if (<=.f64 x 341155706335039/11908525658859223294760121268437066290850060053501019099651935423375594096449911575776314174894302258147533153997065059263030913083222523904) (.f64 z (cos.f64 y)) (+.f64 (*.f64 x (sin.f64 y)) z)))
(if (<=.f64 y -3965985823159031/4398046511104) (.f64 (cos.f64 y) z) (if (<=.f64 y 2503314191386883/1048576) (+.f64 (.f64 y x) z) (*.f64 (cos.f64 y) z)))
(if (<=.f64 y -3965985823159031/4398046511104) (.f64 z (cos.f64 y)) (if (<=.f64 y 2503314191386883/1048576) (+.f64 z (.f64 x y)) (*.f64 z (cos.f64 y))))
(+.f64 (*.f64 y x) z)
(+.f64 z (*.f64 x y))
(if (<=.f64 x -118232305368341256331012252254786283463978329030352334790805060172114184229277243767986474979399912609633210755793769001357920160399183331481011704924432788108430978745913748145275131161163700519264121370390441889613479936) (.f64 y x) (if (<=.f64 x -72025560399755645438321156391233924483984303214329782683749460163862477303986610804978642874550380261219247639025948863482461742441581790963427653614968024493192683206405472364080811357503488) z (if (<=.f64 x -98831031127246823318241765547704889224886246794375846615278096913456701770303634821844738334785536) (.f64 y x) (if (<=.f64 x 86504101715426392994505572727059545674992736074727618007941472008404429963264) z (*.f64 y x)))))
(if (<=.f64 x -118232305368341256331012252254786283463978329030352334790805060172114184229277243767986474979399912609633210755793769001357920160399183331481011704924432788108430978745913748145275131161163700519264121370390441889613479936) (.f64 x y) (if (<=.f64 x -72025560399755645438321156391233924483984303214329782683749460163862477303986610804978642874550380261219247639025948863482461742441581790963427653614968024493192683206405472364080811357503488) z (if (<=.f64 x -98831031127246823318241765547704889224886246794375846615278096913456701770303634821844738334785536) (.f64 x y) (if (<=.f64 x 86504101715426392994505572727059545674992736074727618007941472008404429963264) z (*.f64 x y)))))
z

end51.0ms (0.8%)

Stop Event

1×

fuel

Compiler

Compiled 195 to 94 computations (51.8% saved)