Details

analyze4.0ms (0.1%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
0%	0%	100%	0%	0%	0%	0%	2
50%	50%	50%	0%	0%	0%	0%	3
75%	75%	25%	0%	0%	0%	0%	4
87.5%	87.5%	12.5%	0%	0%	0%	0%	5
93.8%	93.7%	6.2%	0%	0%	0%	0%	6
96.9%	96.8%	3.1%	0%	0%	0%	0%	7
98.4%	98.4%	1.6%	0%	0%	0%	0%	8
99.2%	99.2%	0.8%	0%	0%	0%	0%	9
99.6%	99.6%	0.4%	0%	0%	0%	0%	10
99.8%	99.8%	0.2%	0%	0%	0%	0%	11
99.9%	99.8%	0.1%	0%	0.1%	0%	0%	12

Compiler

Compiled 11 to 10 computations (9.1% saved)

sample1.7s (33.6%)

Results

1.7s	8252×	body	256	valid
1.0ms	3×	body	1024	valid
1.0ms	4×	body	256	infinite
0.0ms	1×	body	512	valid

Bogosity

preprocess42.0ms (0.8%)

Algorithm

2×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	5
1	15	5
2	16	5
0	1	1

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0

Outputs
0

Call 2

Inputs
(+.f64 (*.f64 (/.f64 841 108) x) (/.f64 4 29))

Outputs
(+.f64 (*.f64 (/.f64 841 108) x) (/.f64 4 29))
(fma.f64 841/108 x 4/29)

Compiler

Compiled 11 to 10 computations (9.1% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	5
1	15	5
2	16	5

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

Inputs
(+.f64 (*.f64 (/.f64 841 108) x) (/.f64 4 29))

Outputs
(+.f64 (*.f64 (/.f64 841 108) x) (/.f64 4 29))
(fma.f64 841/108 x 4/29)

eval1.0ms (0%)

Compiler: Compiled 14 to 12 computations (14.3% saved)

prune2.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.1b

Counts

3 → 2

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.1b	(+.f64 (*.f64 (/.f64 841 108) x) (/.f64 4 29))
▶	0.1b	(fma.f64 841/108 x 4/29)

Compiler

Compiled 15 to 13 computations (13.3% saved)

localize21.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (*.f64 (/.f64 841 108) x) (/.f64 4 29))
✓	0.2b	(*.f64 (/.f64 841 108) x)

Compiler

Compiled 26 to 23 computations (11.5% saved)

series3.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(*.f64 (/.f64 841 108) x)
1.0ms	x	@	-inf	(*.f64 (/.f64 841 108) x)
1.0ms	x	@	0	(*.f64 (/.f64 841 108) x)
0.0ms	x	@	inf	(+.f64 (*.f64 (/.f64 841 108) x) (/.f64 4 29))
0.0ms	x	@	0	(+.f64 (*.f64 (/.f64 841 108) x) (/.f64 4 29))

rewrite62.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

901×	`pow1_binary64`
858×	`add-log-exp_binary64`
858×	`log1p-expm1-u_binary64`
858×	`expm1-log1p-u_binary64`
849×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	9
1	218	9
2	2263	9

Stop Event

1×	node limit

Counts

2 → 43

Calls

Call 1

Inputs
(*.f64 (/.f64 841 108) x)
(+.f64 (*.f64 (/.f64 841 108) x) (/.f64 4 29))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (.f64 841/108 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 841/108 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 841/108 x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 841/108 x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 x 3) 594823321/1259712) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (.f64 (.f64 x x) 707281/11664))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 x) 841/108))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 x 3) 594823321/1259712))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 841/108 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 841/108 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 841/108 x)))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (fma.f64 841/108 x 4/29)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (.f64 (.f64 x x) 707281/11664) (fma.f64 841/108 x -4/29)) (/.f64 16/841 (fma.f64 841/108 x -4/29)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fma.f64 841/108 x 4/29) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (fma.f64 841/108 x 4/29))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (pow.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) 2) (cbrt.f64 (fma.f64 841/108 x 4/29)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (fma.f64 841/108 x 4/29)) (sqrt.f64 (fma.f64 841/108 x 4/29)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 64/24389 (.f64 (pow.f64 x 3) 594823321/1259712)) (/.f64 1 (+.f64 (.f64 (.f64 x x) 707281/11664) (-.f64 16/841 (.f64 x 29/27)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 (.f64 (.f64 x x) 707281/11664) -16/841) (/.f64 1 (fma.f64 841/108 x -4/29)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (.f64 (.f64 x x) 707281/11664) (-.f64 16/841 (.f64 x 29/27))) (+.f64 64/24389 (.f64 (pow.f64 x 3) 594823321/1259712))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 841/108 x -4/29) (+.f64 (.f64 (.f64 x x) 707281/11664) -16/841)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 64/24389 (.f64 (pow.f64 x 3) 594823321/1259712)) (+.f64 (.f64 (.f64 x x) 707281/11664) (-.f64 16/841 (.f64 x 29/27))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 64/24389 (.f64 (pow.f64 x 3) 594823321/1259712)) (+.f64 16/841 (-.f64 (.f64 (.f64 x x) 707281/11664) (.f64 x 29/27))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (.f64 (.f64 x x) 707281/11664) -16/841) (fma.f64 841/108 x -4/29))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 64/24389 (.f64 (pow.f64 x 3) 594823321/1259712))) (neg.f64 (+.f64 (.f64 (.f64 x x) 707281/11664) (-.f64 16/841 (.f64 x 29/27)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (.f64 (.f64 x x) 707281/11664) -16/841)) (neg.f64 (fma.f64 841/108 x -4/29)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 16/841 (.f64 (.f64 x x) 707281/11664)) (-.f64 4/29 (.f64 841/108 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 841/108 x 4/29) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 841/108 x 4/29) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 841/108 x 4/29) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 841/108 x 4/29)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 841/108 x 4/29) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 841/108 x 4/29)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 841/108 x 4/29)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 841/108 x 4/29)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 841/108 x 4/29)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x 841/108 4/29)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (.f64 841/108 x) 4/29)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (.f64 (.f64 x x) 707281/11664)) (cbrt.f64 (.f64 841/108 x)) 4/29)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (.f64 841/108 x)) (sqrt.f64 (.f64 841/108 x)) 4/29)))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 841/108 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 841/108 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 841/108 x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 841/108 x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 x 3) 594823321/1259712) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (*.f64 x x) 707281/11664))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 x) 841/108))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 x 3) 594823321/1259712))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 841/108 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 841/108 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 841/108 x)))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (fma.f64 841/108 x 4/29)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (*.f64 (*.f64 x x) 707281/11664) (fma.f64 841/108 x -4/29)) (/.f64 16/841 (fma.f64 841/108 x -4/29)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 841/108 x 4/29) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 841/108 x 4/29))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (pow.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) 2) (cbrt.f64 (fma.f64 841/108 x 4/29)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)) (sqrt.f64 (fma.f64 841/108 x 4/29)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 64/24389 (*.f64 (pow.f64 x 3) 594823321/1259712)) (/.f64 1 (+.f64 (*.f64 (*.f64 x x) 707281/11664) (-.f64 16/841 (*.f64 x 29/27)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (*.f64 (*.f64 x x) 707281/11664) -16/841) (/.f64 1 (fma.f64 841/108 x -4/29)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (*.f64 (*.f64 x x) 707281/11664) (-.f64 16/841 (*.f64 x 29/27))) (+.f64 64/24389 (*.f64 (pow.f64 x 3) 594823321/1259712))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 841/108 x -4/29) (+.f64 (*.f64 (*.f64 x x) 707281/11664) -16/841)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 64/24389 (*.f64 (pow.f64 x 3) 594823321/1259712)) (+.f64 (*.f64 (*.f64 x x) 707281/11664) (-.f64 16/841 (*.f64 x 29/27))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 64/24389 (*.f64 (pow.f64 x 3) 594823321/1259712)) (+.f64 16/841 (-.f64 (*.f64 (*.f64 x x) 707281/11664) (*.f64 x 29/27))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 (*.f64 x x) 707281/11664) -16/841) (fma.f64 841/108 x -4/29))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 64/24389 (*.f64 (pow.f64 x 3) 594823321/1259712))) (neg.f64 (+.f64 (*.f64 (*.f64 x x) 707281/11664) (-.f64 16/841 (*.f64 x 29/27)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (*.f64 (*.f64 x x) 707281/11664) -16/841)) (neg.f64 (fma.f64 841/108 x -4/29)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 16/841 (*.f64 (*.f64 x x) 707281/11664)) (-.f64 4/29 (*.f64 841/108 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 841/108 x 4/29) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 841/108 x 4/29) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 841/108 x 4/29) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 841/108 x 4/29)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 841/108 x 4/29) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 841/108 x 4/29)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 841/108 x 4/29)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 841/108 x 4/29)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 841/108 x 4/29)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x 841/108 4/29)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 841/108 x) 4/29)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 (*.f64 x x) 707281/11664)) (cbrt.f64 (*.f64 841/108 x)) 4/29)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 841/108 x)) (sqrt.f64 (*.f64 841/108 x)) 4/29)))))

simplify10.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	120
1	8	102
2	10	102

Stop Event

1×

saturated

Counts

67 → 46

Calls

Call 1

Inputs
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
4/29
(+.f64 4/29 (*.f64 841/108 x))
(+.f64 4/29 (*.f64 841/108 x))
(+.f64 4/29 (*.f64 841/108 x))
(*.f64 841/108 x)
(+.f64 4/29 (*.f64 841/108 x))
(+.f64 4/29 (*.f64 841/108 x))
(+.f64 4/29 (*.f64 841/108 x))
(*.f64 841/108 x)
(+.f64 4/29 (*.f64 841/108 x))
(+.f64 4/29 (*.f64 841/108 x))
(+.f64 4/29 (*.f64 841/108 x))

Outputs
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
4/29
(+.f64 4/29 (*.f64 841/108 x))
(+.f64 (*.f64 841/108 x) 4/29)
(fma.f64 841/108 x 4/29)
(+.f64 4/29 (*.f64 841/108 x))
(+.f64 (*.f64 841/108 x) 4/29)
(fma.f64 841/108 x 4/29)
(+.f64 4/29 (*.f64 841/108 x))
(+.f64 (*.f64 841/108 x) 4/29)
(fma.f64 841/108 x 4/29)
(*.f64 841/108 x)
(+.f64 4/29 (*.f64 841/108 x))
(+.f64 (*.f64 841/108 x) 4/29)
(fma.f64 841/108 x 4/29)
(+.f64 4/29 (*.f64 841/108 x))
(+.f64 (*.f64 841/108 x) 4/29)
(fma.f64 841/108 x 4/29)
(+.f64 4/29 (*.f64 841/108 x))
(+.f64 (*.f64 841/108 x) 4/29)
(fma.f64 841/108 x 4/29)
(*.f64 841/108 x)
(+.f64 4/29 (*.f64 841/108 x))
(+.f64 (*.f64 841/108 x) 4/29)
(fma.f64 841/108 x 4/29)
(+.f64 4/29 (*.f64 841/108 x))
(+.f64 (*.f64 841/108 x) 4/29)
(fma.f64 841/108 x 4/29)
(+.f64 4/29 (*.f64 841/108 x))
(+.f64 (*.f64 841/108 x) 4/29)
(fma.f64 841/108 x 4/29)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 841/108 x 4/29)

Compiler

Compiled 8 to 6 computations (25% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(fma.f64 841/108 x 4/29)
0.0ms	x	@	0	(fma.f64 841/108 x 4/29)
0.0ms	x	@	inf	(fma.f64 841/108 x 4/29)

rewrite58.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

434×	`pow1_binary64`
430×	`add-sqr-sqrt_binary64`
417×	`*-un-lft-identity_binary64`
407×	`add-log-exp_binary64`
407×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	5
1	102	5
2	1072	5

Stop Event

1×	node limit

Counts

1 → 24

Calls

Call 1

Inputs
(fma.f64 841/108 x 4/29)

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 4/29 (.f64 841/108 x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 841/108 x) 4/29)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (fma.f64 841/108 x 4/29))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (.f64 841/108 x) 1) 4/29)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (exp.f64 (fma.f64 841/108 x 4/29))))) (log.f64 (cbrt.f64 (exp.f64 (fma.f64 841/108 x 4/29)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (fma.f64 841/108 x 4/29)))) (log.f64 (sqrt.f64 (exp.f64 (fma.f64 841/108 x 4/29)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (fma.f64 841/108 x 4/29)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fma.f64 841/108 x 4/29) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (fma.f64 841/108 x 4/29))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (pow.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) 2) (cbrt.f64 (fma.f64 841/108 x 4/29)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (fma.f64 841/108 x 4/29)) (sqrt.f64 (fma.f64 841/108 x 4/29)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (.f64 841/108 x) 3) 64/24389) (fma.f64 (.f64 841/108 x) (.f64 841/108 x) (-.f64 16/841 (.f64 (.f64 841/108 x) 4/29))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 (.f64 841/108 x) (*.f64 841/108 x) -16/841) (fma.f64 841/108 x -4/29))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 841/108 x 4/29) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 841/108 x 4/29) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 841/108 x 4/29) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 841/108 x 4/29)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 841/108 x 4/29) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 841/108 x 4/29)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 841/108 x 4/29)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 841/108 x 4/29)))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 4/29 (*.f64 841/108 x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 841/108 x) 4/29)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (fma.f64 841/108 x 4/29))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 841/108 x) 1) 4/29)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (exp.f64 (fma.f64 841/108 x 4/29))))) (log.f64 (cbrt.f64 (exp.f64 (fma.f64 841/108 x 4/29)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (fma.f64 841/108 x 4/29)))) (log.f64 (sqrt.f64 (exp.f64 (fma.f64 841/108 x 4/29)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (fma.f64 841/108 x 4/29)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 841/108 x 4/29) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 841/108 x 4/29))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (pow.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) 2) (cbrt.f64 (fma.f64 841/108 x 4/29)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)) (sqrt.f64 (fma.f64 841/108 x 4/29)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 841/108 x) 3) 64/24389) (fma.f64 (*.f64 841/108 x) (*.f64 841/108 x) (-.f64 16/841 (*.f64 (*.f64 841/108 x) 4/29))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 (*.f64 841/108 x) (*.f64 841/108 x) -16/841) (fma.f64 841/108 x -4/29))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 841/108 x 4/29) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 841/108 x 4/29) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 841/108 x 4/29) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 841/108 x 4/29)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 841/108 x 4/29) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 841/108 x 4/29)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 841/108 x 4/29)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 841/108 x 4/29)))))))

simplify49.0ms (1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	72
1	8	54
2	10	54

Stop Event

1×

saturated

Counts

36 → 27

Calls

Call 1

Inputs
4/29
(+.f64 4/29 (*.f64 841/108 x))
(+.f64 4/29 (*.f64 841/108 x))
(+.f64 4/29 (*.f64 841/108 x))
(*.f64 841/108 x)
(+.f64 4/29 (*.f64 841/108 x))
(+.f64 4/29 (*.f64 841/108 x))
(+.f64 4/29 (*.f64 841/108 x))
(*.f64 841/108 x)
(+.f64 4/29 (*.f64 841/108 x))
(+.f64 4/29 (*.f64 841/108 x))
(+.f64 4/29 (*.f64 841/108 x))

Outputs
4/29
(+.f64 4/29 (*.f64 841/108 x))
(fma.f64 841/108 x 4/29)
(+.f64 4/29 (*.f64 841/108 x))
(fma.f64 841/108 x 4/29)
(+.f64 4/29 (*.f64 841/108 x))
(fma.f64 841/108 x 4/29)
(*.f64 841/108 x)
(+.f64 4/29 (*.f64 841/108 x))
(fma.f64 841/108 x 4/29)
(+.f64 4/29 (*.f64 841/108 x))
(fma.f64 841/108 x 4/29)
(+.f64 4/29 (*.f64 841/108 x))
(fma.f64 841/108 x 4/29)
(*.f64 841/108 x)
(+.f64 4/29 (*.f64 841/108 x))
(fma.f64 841/108 x 4/29)
(+.f64 4/29 (*.f64 841/108 x))
(fma.f64 841/108 x 4/29)
(+.f64 4/29 (*.f64 841/108 x))
(fma.f64 841/108 x 4/29)

eval21.0ms (0.4%)

Compiler: Compiled 691 to 562 computations (18.7% saved)

prune21.0ms (0.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	65	8	73
Fresh	0	0	0
Picked	1	0	1
Done	1	0	1
Total	67	8	75

Error

0.0b

Counts

75 → 8

Alt Table

Click to see full alt table

Status	Error	Program
▶	16.1b	(/.f64 (-.f64 16/841 (.f64 (.f64 x x) 707281/11664)) (-.f64 4/29 (*.f64 841/108 x)))
	33.0b	4/29
▶	20.9b	(/.f64 (+.f64 64/24389 (.f64 (pow.f64 x 3) 594823321/1259712)) (+.f64 (.f64 (.f64 x x) 707281/11664) (-.f64 16/841 (.f64 x 29/27))))
▶	16.6b	(/.f64 1 (/.f64 (fma.f64 841/108 x -4/29) (+.f64 (.f64 (.f64 x x) 707281/11664) -16/841)))
▶	0.1b	(+.f64 (*.f64 841/108 x) 4/29)
	0.7b	(+.f64 (pow.f64 (cbrt.f64 (*.f64 841/108 x)) 3) (/.f64 4 29))
▶	30.3b	(*.f64 841/108 x)
	28.7b	(+.f64 (pow.f64 (sqrt.f64 (*.f64 841/108 x)) 2) (/.f64 4 29))

Compiler

Compiled 164 to 136 computations (17.1% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (*.f64 841/108 x) 4/29)
✓	0.2b	(*.f64 841/108 x)

Compiler

Compiled 12 to 9 computations (25% saved)

series2.0ms (0%)

Counts

2 → 12

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(*.f64 841/108 x)
0.0ms	x	@	inf	(*.f64 841/108 x)
0.0ms	x	@	inf	(+.f64 (*.f64 841/108 x) 4/29)
0.0ms	x	@	-inf	(+.f64 (*.f64 841/108 x) 4/29)
0.0ms	x	@	0	(+.f64 (*.f64 841/108 x) 4/29)

rewrite97.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

642×	`pow1_binary64`
606×	`add-log-exp_binary64`
606×	`log1p-expm1-u_binary64`
606×	`expm1-log1p-u_binary64`
597×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	133	9
2	1587	9

Stop Event

1×	node limit

Counts

2 → 43

Calls

Call 1

Inputs
(*.f64 841/108 x)
(+.f64 (*.f64 841/108 x) 4/29)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 841/108 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 841/108 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 841/108 x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 841/108 x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 x 3) 594823321/1259712) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 841/108 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 841/108) x))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 x 3) 594823321/1259712))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 841/108 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 841/108 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 841/108 x)))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (fma.f64 841/108 x 4/29)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 (*.f64 841/108 x) 2) (fma.f64 841/108 x -4/29)) (/.f64 16/841 (fma.f64 841/108 x -4/29)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 841/108 x 4/29) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 841/108 x 4/29))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (pow.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) 2) (cbrt.f64 (fma.f64 841/108 x 4/29)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)) (sqrt.f64 (fma.f64 841/108 x 4/29)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 64/24389 (*.f64 (pow.f64 x 3) 594823321/1259712)) (/.f64 1 (+.f64 (pow.f64 (*.f64 841/108 x) 2) (-.f64 16/841 (*.f64 x 29/27)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (*.f64 841/108 x) 2) -16/841) (/.f64 1 (fma.f64 841/108 x -4/29)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (*.f64 841/108 x) 2) (-.f64 16/841 (*.f64 x 29/27))) (+.f64 64/24389 (*.f64 (pow.f64 x 3) 594823321/1259712))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 841/108 x -4/29) (+.f64 (pow.f64 (*.f64 841/108 x) 2) -16/841)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 64/24389 (*.f64 (pow.f64 x 3) 594823321/1259712)) (+.f64 (pow.f64 (*.f64 841/108 x) 2) (-.f64 16/841 (*.f64 x 29/27))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 64/24389 (*.f64 (pow.f64 x 3) 594823321/1259712)) (+.f64 16/841 (-.f64 (pow.f64 (*.f64 841/108 x) 2) (*.f64 x 29/27))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 841/108 x) 2) -16/841) (fma.f64 841/108 x -4/29))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 64/24389 (*.f64 (pow.f64 x 3) 594823321/1259712))) (neg.f64 (+.f64 (pow.f64 (*.f64 841/108 x) 2) (-.f64 16/841 (*.f64 x 29/27)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (*.f64 841/108 x) 2) -16/841)) (neg.f64 (fma.f64 841/108 x -4/29)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 16/841 (pow.f64 (*.f64 841/108 x) 2)) (-.f64 4/29 (*.f64 841/108 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 841/108 x 4/29) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 841/108 x 4/29) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 841/108 x 4/29) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 841/108 x 4/29)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 841/108 x 4/29) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 841/108 x 4/29)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 841/108 x 4/29)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 841/108 x 4/29)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 841/108 x 4/29)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x 841/108 4/29)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 841/108 x) 4/29)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 841/108 x)) 2) (cbrt.f64 (*.f64 841/108 x)) 4/29)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 841/108 x)) (sqrt.f64 (*.f64 841/108 x)) 4/29)))))

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	72
1	8	54
2	10	54

Stop Event

1×

saturated

Counts

55 → 46

Calls

Call 1

Inputs
4/29
(+.f64 4/29 (*.f64 841/108 x))
(+.f64 4/29 (*.f64 841/108 x))
(+.f64 4/29 (*.f64 841/108 x))
(*.f64 841/108 x)
(+.f64 4/29 (*.f64 841/108 x))
(+.f64 4/29 (*.f64 841/108 x))
(+.f64 4/29 (*.f64 841/108 x))
(*.f64 841/108 x)
(+.f64 4/29 (*.f64 841/108 x))
(+.f64 4/29 (*.f64 841/108 x))
(+.f64 4/29 (*.f64 841/108 x))

Outputs
4/29
(+.f64 4/29 (*.f64 841/108 x))
(fma.f64 841/108 x 4/29)
(+.f64 4/29 (*.f64 841/108 x))
(fma.f64 841/108 x 4/29)
(+.f64 4/29 (*.f64 841/108 x))
(fma.f64 841/108 x 4/29)
(*.f64 841/108 x)
(+.f64 4/29 (*.f64 841/108 x))
(fma.f64 841/108 x 4/29)
(+.f64 4/29 (*.f64 841/108 x))
(fma.f64 841/108 x 4/29)
(+.f64 4/29 (*.f64 841/108 x))
(fma.f64 841/108 x 4/29)
(*.f64 841/108 x)
(+.f64 4/29 (*.f64 841/108 x))
(fma.f64 841/108 x 4/29)
(+.f64 4/29 (*.f64 841/108 x))
(fma.f64 841/108 x 4/29)
(+.f64 4/29 (*.f64 841/108 x))
(fma.f64 841/108 x 4/29)

localize16.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
	0.2b	(*.f64 841/108 x)

Compiler

Compiled 6 to 4 computations (33.3% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 4/29 (*.f64 841/108 x))
	0.2b	(*.f64 841/108 x)
✓	0.2b	(.f64 (.f64 x x) 707281/11664)
✓	15.1b	(/.f64 (-.f64 16/841 (.f64 (.f64 x x) 707281/11664)) (-.f64 4/29 (*.f64 841/108 x)))

Compiler

Compiled 42 to 27 computations (35.7% saved)

series4.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(/.f64 (-.f64 16/841 (.f64 (.f64 x x) 707281/11664)) (-.f64 4/29 (*.f64 841/108 x)))
1.0ms	x	@	inf	(/.f64 (-.f64 16/841 (.f64 (.f64 x x) 707281/11664)) (-.f64 4/29 (*.f64 841/108 x)))
1.0ms	x	@	inf	(.f64 (.f64 x x) 707281/11664)
0.0ms	x	@	0	(.f64 (.f64 x x) 707281/11664)
0.0ms	x	@	-inf	(/.f64 (-.f64 16/841 (.f64 (.f64 x x) 707281/11664)) (-.f64 4/29 (*.f64 841/108 x)))

rewrite177.0ms (3.4%)

Algorithm

1×	batch-egg-rewrite

Rules

623×	`log-prod_binary64`
548×	`prod-diff_binary64`
244×	`fma-def_binary64`
226×	`pow1/3_binary64`
226×	`expm1-udef_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	33
1	280	21
2	3803	17

Stop Event

1×	node limit

Counts

3 → 246

Calls

Call 1

Inputs
(/.f64 (-.f64 16/841 (.f64 (.f64 x x) 707281/11664)) (-.f64 4/29 (*.f64 841/108 x)))
(.f64 (.f64 x x) 707281/11664)
(-.f64 4/29 (*.f64 841/108 x))

Outputs

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(#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 x -841/108 4/29)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (fma.f64 x -841/108 4/29)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x -841/108 4/29)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 841/108 (neg.f64 x) 4/29)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 x -841/108) 4/29)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 x 841/108)) 2) (neg.f64 (cbrt.f64 (*.f64 x 841/108))) 4/29)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 x 841/108)) (neg.f64 (sqrt.f64 (*.f64 x 841/108))) 4/29)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -841/108 x 4/29)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (cbrt.f64 (*.f64 x -841/108)) (cbrt.f64 (*.f64 x -841/108))) (cbrt.f64 (*.f64 x -841/108)) 4/29)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 x -841/108)) (sqrt.f64 (*.f64 x -841/108)) 4/29)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1 (*.f64 x 841/108) 4/29)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 x) 841/108 4/29)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (sqrt.f64 (*.f64 x 841/108))) (sqrt.f64 (*.f64 x 841/108)) 4/29)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (pow.f64 (cbrt.f64 (*.f64 x 841/108)) 2)) (cbrt.f64 (*.f64 x 841/108)) 4/29)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 -841/108 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) 4/29)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 -841/108 (sqrt.f64 x)) (sqrt.f64 x) 4/29)))))

simplify196.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

1101×	`sqr-pow_binary64`
586×	`associate-l_binary64`
565×	`cube-prod_binary64`
559×	`fabs-mul_binary64`
528×	`pow-sqr_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	210
1	24	192
2	38	192
3	68	192
4	158	192
5	468	192
6	1691	192
7	2606	192
8	2770	192
9	2983	192
10	3203	192
11	3506	192
12	3906	192
13	4399	192
14	4967	192
15	5649	192
16	6486	192
17	6882	192
18	7170	192
19	7444	192
20	7520	192
21	7556	192

Stop Event

1×	node limit

Counts

282 → 255

Calls

Call 1

Inputs
4/29
(+.f64 4/29 (*.f64 841/108 x))
(+.f64 4/29 (*.f64 841/108 x))
(+.f64 4/29 (*.f64 841/108 x))
(*.f64 841/108 x)
(+.f64 4/29 (*.f64 841/108 x))
(+.f64 4/29 (*.f64 841/108 x))
(+.f64 4/29 (*.f64 841/108 x))
(*.f64 841/108 x)
(+.f64 4/29 (*.f64 841/108 x))
(+.f64 4/29 (*.f64 841/108 x))
(+.f64 4/29 (*.f64 841/108 x))
(*.f64 707281/11664 (pow.f64 x 2))
(*.f64 707281/11664 (pow.f64 x 2))
(*.f64 707281/11664 (pow.f64 x 2))
(*.f64 707281/11664 (pow.f64 x 2))
(*.f64 707281/11664 (pow.f64 x 2))
(*.f64 707281/11664 (pow.f64 x 2))
(*.f64 707281/11664 (pow.f64 x 2))
(*.f64 707281/11664 (pow.f64 x 2))
(*.f64 707281/11664 (pow.f64 x 2))
(*.f64 707281/11664 (pow.f64 x 2))
(*.f64 707281/11664 (pow.f64 x 2))
(*.f64 707281/11664 (pow.f64 x 2))
4/29
(+.f64 (*.f64 -841/108 x) 4/29)
(+.f64 (*.f64 -841/108 x) 4/29)
(+.f64 (*.f64 -841/108 x) 4/29)
(*.f64 -841/108 x)
(+.f64 4/29 (*.f64 -841/108 x))
(+.f64 4/29 (*.f64 -841/108 x))
(+.f64 4/29 (*.f64 -841/108 x))
(*.f64 -841/108 x)
(+.f64 4/29 (*.f64 -841/108 x))
(+.f64 4/29 (*.f64 -841/108 x))
(+.f64 4/29 (*.f64 -841/108 x))

Outputs
4/29
(+.f64 4/29 (*.f64 841/108 x))
(fma.f64 841/108 x 4/29)
(+.f64 4/29 (*.f64 841/108 x))
(fma.f64 841/108 x 4/29)
(+.f64 4/29 (*.f64 841/108 x))
(fma.f64 841/108 x 4/29)
(*.f64 841/108 x)
(+.f64 4/29 (*.f64 841/108 x))
(fma.f64 841/108 x 4/29)
(+.f64 4/29 (*.f64 841/108 x))
(fma.f64 841/108 x 4/29)
(+.f64 4/29 (*.f64 841/108 x))
(fma.f64 841/108 x 4/29)
(*.f64 841/108 x)
(+.f64 4/29 (*.f64 841/108 x))
(fma.f64 841/108 x 4/29)
(+.f64 4/29 (*.f64 841/108 x))
(fma.f64 841/108 x 4/29)
(+.f64 4/29 (*.f64 841/108 x))
(fma.f64 841/108 x 4/29)
(*.f64 707281/11664 (pow.f64 x 2))
(.f64 707281/11664 (.f64 x x))
(.f64 x (.f64 x 707281/11664))
(*.f64 707281/11664 (pow.f64 x 2))
(.f64 707281/11664 (.f64 x x))
(.f64 x (.f64 x 707281/11664))
(*.f64 707281/11664 (pow.f64 x 2))
(.f64 707281/11664 (.f64 x x))
(.f64 x (.f64 x 707281/11664))
(*.f64 707281/11664 (pow.f64 x 2))
(.f64 707281/11664 (.f64 x x))
(.f64 x (.f64 x 707281/11664))
(*.f64 707281/11664 (pow.f64 x 2))
(.f64 707281/11664 (.f64 x x))
(.f64 x (.f64 x 707281/11664))
(*.f64 707281/11664 (pow.f64 x 2))
(.f64 707281/11664 (.f64 x x))
(.f64 x (.f64 x 707281/11664))
(*.f64 707281/11664 (pow.f64 x 2))
(.f64 707281/11664 (.f64 x x))
(.f64 x (.f64 x 707281/11664))
(*.f64 707281/11664 (pow.f64 x 2))
(.f64 707281/11664 (.f64 x x))
(.f64 x (.f64 x 707281/11664))
(*.f64 707281/11664 (pow.f64 x 2))
(.f64 707281/11664 (.f64 x x))
(.f64 x (.f64 x 707281/11664))
(*.f64 707281/11664 (pow.f64 x 2))
(.f64 707281/11664 (.f64 x x))
(.f64 x (.f64 x 707281/11664))
(*.f64 707281/11664 (pow.f64 x 2))
(.f64 707281/11664 (.f64 x x))
(.f64 x (.f64 x 707281/11664))
(*.f64 707281/11664 (pow.f64 x 2))
(.f64 707281/11664 (.f64 x x))
(.f64 x (.f64 x 707281/11664))
4/29
(+.f64 (*.f64 -841/108 x) 4/29)
(fma.f64 -841/108 x 4/29)
(fma.f64 x -841/108 4/29)
(+.f64 (*.f64 -841/108 x) 4/29)
(fma.f64 -841/108 x 4/29)
(fma.f64 x -841/108 4/29)
(+.f64 (*.f64 -841/108 x) 4/29)
(fma.f64 -841/108 x 4/29)
(fma.f64 x -841/108 4/29)
(*.f64 -841/108 x)
(*.f64 x -841/108)
(+.f64 4/29 (*.f64 -841/108 x))
(fma.f64 -841/108 x 4/29)
(fma.f64 x -841/108 4/29)
(+.f64 4/29 (*.f64 -841/108 x))
(fma.f64 -841/108 x 4/29)
(fma.f64 x -841/108 4/29)
(+.f64 4/29 (*.f64 -841/108 x))
(fma.f64 -841/108 x 4/29)
(fma.f64 x -841/108 4/29)
(*.f64 -841/108 x)
(*.f64 x -841/108)
(+.f64 4/29 (*.f64 -841/108 x))
(fma.f64 -841/108 x 4/29)
(fma.f64 x -841/108 4/29)
(+.f64 4/29 (*.f64 -841/108 x))
(fma.f64 -841/108 x 4/29)
(fma.f64 x -841/108 4/29)
(+.f64 4/29 (*.f64 -841/108 x))
(fma.f64 -841/108 x 4/29)
(fma.f64 x -841/108 4/29)

localize19.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 841/108 x -4/29)
✓	0.2b	(/.f64 1 (/.f64 (fma.f64 841/108 x -4/29) (+.f64 (.f64 (.f64 x x) 707281/11664) -16/841)))
	0.2b	(.f64 (.f64 x x) 707281/11664)
✓	15.5b	(/.f64 (fma.f64 841/108 x -4/29) (+.f64 (.f64 (.f64 x x) 707281/11664) -16/841))

Compiler

Compiled 52 to 34 computations (34.6% saved)

series49.0ms (0.9%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
45.0ms	x	@	0	(/.f64 1 (/.f64 (fma.f64 841/108 x -4/29) (+.f64 (.f64 (.f64 x x) 707281/11664) -16/841)))
1.0ms	x	@	0	(/.f64 (fma.f64 841/108 x -4/29) (+.f64 (.f64 (.f64 x x) 707281/11664) -16/841))
1.0ms	x	@	inf	(/.f64 (fma.f64 841/108 x -4/29) (+.f64 (.f64 (.f64 x x) 707281/11664) -16/841))
0.0ms	x	@	inf	(/.f64 1 (/.f64 (fma.f64 841/108 x -4/29) (+.f64 (.f64 (.f64 x x) 707281/11664) -16/841)))
0.0ms	x	@	-inf	(/.f64 (fma.f64 841/108 x -4/29) (+.f64 (.f64 (.f64 x x) 707281/11664) -16/841))

rewrite134.0ms (2.6%)

Algorithm

1×	batch-egg-rewrite

Rules

567×	`log-prod_binary64`
325×	`pow2_binary64`
313×	`pow-prod-down_binary64`
228×	`prod-diff_binary64`
226×	`expm1-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	38
1	283	35
2	3434	35

Stop Event

1×	node limit

Counts

3 → 127

Calls

Call 1

Inputs
(/.f64 (fma.f64 841/108 x -4/29) (+.f64 (.f64 (.f64 x x) 707281/11664) -16/841))
(/.f64 1 (/.f64 (fma.f64 841/108 x -4/29) (+.f64 (.f64 (.f64 x x) 707281/11664) -16/841)))
(fma.f64 841/108 x -4/29)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (fma.f64 841/108 x -4/29) (fma.f64 x (*.f64 x 707281/11664) -16/841)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (fma.f64 841/108 x -4/29) (fma.f64 x (*.f64 x 707281/11664) -16/841)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (fma.f64 841/108 x -4/29) (fma.f64 x (*.f64 x 707281/11664) -16/841))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (fma.f64 841/108 x -4/29) (fma.f64 x (*.f64 x 707281/11664) -16/841))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (fma.f64 841/108 x -4/29) (fma.f64 x (*.f64 x 707281/11664) -16/841))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (fma.f64 841/108 x -4/29) (fma.f64 x (*.f64 x 707281/11664) -16/841)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 841/108 x -4/29) (/.f64 1 (fma.f64 x (*.f64 x 707281/11664) -16/841)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (fma.f64 841/108 x -4/29) (fma.f64 x (*.f64 x 707281/11664) -16/841)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (fma.f64 841/108 x -4/29) (fma.f64 x (*.f64 x 707281/11664) -16/841)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (fma.f64 841/108 x -4/29) (fma.f64 x (*.f64 x 707281/11664) -16/841))) (pow.f64 (cbrt.f64 (/.f64 (fma.f64 841/108 x -4/29) (fma.f64 x (*.f64 x 707281/11664) -16/841))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 (fma.f64 841/108 x -4/29) (fma.f64 x (*.f64 x 707281/11664) -16/841))) 2) (cbrt.f64 (/.f64 (fma.f64 841/108 x -4/29) (fma.f64 x (*.f64 x 707281/11664) -16/841))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 841/108 x -4/29)) 2) (*.f64 (cbrt.f64 (fma.f64 841/108 x -4/29)) (/.f64 1 (fma.f64 x (*.f64 x 707281/11664) -16/841))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (fma.f64 841/108 x -4/29) (fma.f64 x (*.f64 x 707281/11664) -16/841))) (sqrt.f64 (/.f64 (fma.f64 841/108 x -4/29) (fma.f64 x (*.f64 x 707281/11664) -16/841))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 841/108 x -4/29)) (*.f64 (sqrt.f64 (fma.f64 841/108 x -4/29)) (/.f64 1 (fma.f64 x (*.f64 x 707281/11664) -16/841))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (fma.f64 841/108 x -4/29)) (/.f64 1 (neg.f64 (fma.f64 x (*.f64 x 707281/11664) -16/841))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (fma.f64 x (*.f64 x 707281/11664) -16/841)) (fma.f64 841/108 x -4/29))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (fma.f64 841/108 x -4/29)) 2) 1) (/.f64 (cbrt.f64 (fma.f64 841/108 x -4/29)) (fma.f64 x (*.f64 x 707281/11664) -16/841)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (fma.f64 841/108 x -4/29)) 1) (/.f64 (sqrt.f64 (fma.f64 841/108 x -4/29)) (fma.f64 x (*.f64 x 707281/11664) -16/841)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 x (*.f64 x 707281/11664) -16/841)) -2) (/.f64 (fma.f64 841/108 x -4/29) (cbrt.f64 (fma.f64 x (*.f64 x 707281/11664) -16/841))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (fma.f64 841/108 x -4/29)) 2) (pow.f64 (cbrt.f64 (fma.f64 x (*.f64 x 707281/11664) -16/841)) 2)) (cbrt.f64 (/.f64 (fma.f64 841/108 x -4/29) (fma.f64 x (*.f64 x 707281/11664) -16/841))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (fma.f64 841/108 x -4/29)) (pow.f64 (cbrt.f64 (fma.f64 x (*.f64 x 707281/11664) -16/841)) 2)) (/.f64 (sqrt.f64 (fma.f64 841/108 x -4/29)) (cbrt.f64 (fma.f64 x (*.f64 x 707281/11664) -16/841))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (fma.f64 x (*.f64 x 707281/11664) -16/841) -1/2) (/.f64 (fma.f64 841/108 x -4/29) (sqrt.f64 (fma.f64 x (*.f64 x 707281/11664) -16/841))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (fma.f64 841/108 x -4/29)) 2) (sqrt.f64 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((#(struct:change #<rule egg-rr> (2) ((x +.f64 -4/29 (*.f64 841/108 x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (fma.f64 841/108 x -4/29))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 841/108 x) -4/29)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 841/108 x) 1) -4/29)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (fma.f64 841/108 x -4/29))) 2)) (log.f64 (cbrt.f64 (exp.f64 (fma.f64 841/108 x -4/29)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (fma.f64 841/108 x -4/29)))) (log.f64 (sqrt.f64 (exp.f64 (fma.f64 841/108 x -4/29)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 841/108 x -4/29))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 841/108 x -4/29) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 841/108 x -4/29))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 841/108 x -4/29)) (pow.f64 (cbrt.f64 (fma.f64 841/108 x -4/29)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 841/108 x -4/29)) 2) (cbrt.f64 (fma.f64 841/108 x -4/29)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 841/108 x -4/29)) (sqrt.f64 (fma.f64 841/108 x -4/29)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 x (*.f64 x 707281/11664) -16/841) (fma.f64 841/108 x 4/29))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 841/108 x) 3) -64/24389) (fma.f64 x (*.f64 x 707281/11664) (-.f64 16/841 (*.f64 (*.f64 841/108 x) -4/29))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 841/108 x -4/29) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 841/108 x -4/29) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 841/108 x -4/29) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 841/108 x -4/29)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 841/108 x -4/29)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 841/108 x -4/29) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 841/108 x -4/29)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 841/108 x -4/29))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 841/108 x -4/29) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 841/108 x -4/29)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 841/108 x -4/29)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 841/108 x -4/29)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (fma.f64 841/108 x -4/29)) 1))))))

simplify64.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

784×	`fma-def_binary64`
751×	`distribute-neg-frac_binary64`
685×	`associate-r_binary64`
417×	`times-frac_binary64`
288×	`associate-/l/_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	45	309
1	113	289
2	264	285
3	678	279
4	1988	276
5	6902	276

Stop Event

1×	node limit

Counts

163 → 149

Calls

Call 1

Inputs
29/4
(+.f64 29/4 (*.f64 -707281/1728 x))
(+.f64 29/4 (+.f64 (.f64 17249876309/746496 (pow.f64 x 2)) (.f64 -707281/1728 x)))
(+.f64 29/4 (+.f64 (.f64 -420707233300201/322486272 (pow.f64 x 3)) (+.f64 (.f64 17249876309/746496 (pow.f64 x 2)) (*.f64 -707281/1728 x))))
(/.f64 108/841 x)
(-.f64 (.f64 108/841 (/.f64 1 x)) (.f64 46656/20511149 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (.f64 108/841 (/.f64 1 x)) (.f64 20155392/500246412961 (/.f64 1 (pow.f64 x 3)))) (*.f64 46656/20511149 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (.f64 108/841 (/.f64 1 x)) (.f64 20155392/500246412961 (/.f64 1 (pow.f64 x 3)))) (+.f64 (.f64 8707129344/12200509765705829 (/.f64 1 (pow.f64 x 4))) (.f64 46656/20511149 (/.f64 1 (pow.f64 x 2)))))
(/.f64 108/841 x)
(-.f64 (.f64 108/841 (/.f64 1 x)) (.f64 46656/20511149 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (.f64 108/841 (/.f64 1 x)) (.f64 20155392/500246412961 (/.f64 1 (pow.f64 x 3)))) (*.f64 46656/20511149 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (.f64 108/841 (/.f64 1 x)) (.f64 20155392/500246412961 (/.f64 1 (pow.f64 x 3)))) (+.f64 (.f64 8707129344/12200509765705829 (/.f64 1 (pow.f64 x 4))) (.f64 46656/20511149 (/.f64 1 (pow.f64 x 2)))))
4/29
(+.f64 4/29 (*.f64 841/108 x))
(+.f64 4/29 (*.f64 841/108 x))
(+.f64 4/29 (*.f64 841/108 x))
(*.f64 841/108 x)
(+.f64 4/29 (*.f64 841/108 x))
(+.f64 4/29 (*.f64 841/108 x))
(+.f64 4/29 (*.f64 841/108 x))
(*.f64 841/108 x)
(+.f64 4/29 (*.f64 841/108 x))
(+.f64 4/29 (*.f64 841/108 x))
(+.f64 4/29 (*.f64 841/108 x))
-4/29
(-.f64 (*.f64 841/108 x) 4/29)
(-.f64 (*.f64 841/108 x) 4/29)
(-.f64 (*.f64 841/108 x) 4/29)
(*.f64 841/108 x)
(-.f64 (*.f64 841/108 x) 4/29)
(-.f64 (*.f64 841/108 x) 4/29)
(-.f64 (*.f64 841/108 x) 4/29)
(*.f64 841/108 x)
(-.f64 (*.f64 841/108 x) 4/29)
(-.f64 (*.f64 841/108 x) 4/29)
(-.f64 (*.f64 841/108 x) 4/29)

Outputs
29/4
(+.f64 29/4 (*.f64 -707281/1728 x))
(fma.f64 -707281/1728 x 29/4)
(+.f64 29/4 (+.f64 (.f64 17249876309/746496 (pow.f64 x 2)) (.f64 -707281/1728 x)))
(+.f64 29/4 (fma.f64 17249876309/746496 (.f64 x x) (.f64 -707281/1728 x)))
(+.f64 29/4 (fma.f64 -707281/1728 x (.f64 17249876309/746496 (.f64 x x))))
(fma.f64 x (*.f64 x 17249876309/746496) (fma.f64 -707281/1728 x 29/4))
(fma.f64 x (fma.f64 x 17249876309/746496 -707281/1728) 29/4)
(+.f64 29/4 (+.f64 (.f64 -420707233300201/322486272 (pow.f64 x 3)) (+.f64 (.f64 17249876309/746496 (pow.f64 x 2)) (*.f64 -707281/1728 x))))
(+.f64 29/4 (fma.f64 -420707233300201/322486272 (pow.f64 x 3) (fma.f64 17249876309/746496 (.f64 x x) (.f64 -707281/1728 x))))
(+.f64 29/4 (fma.f64 -420707233300201/322486272 (pow.f64 x 3) (fma.f64 -707281/1728 x (.f64 17249876309/746496 (.f64 x x)))))
(fma.f64 -420707233300201/322486272 (pow.f64 x 3) (fma.f64 x (*.f64 x 17249876309/746496) (fma.f64 -707281/1728 x 29/4)))
(fma.f64 x (fma.f64 x 17249876309/746496 -707281/1728) (fma.f64 -420707233300201/322486272 (pow.f64 x 3) 29/4))
(fma.f64 x (fma.f64 x (fma.f64 x -420707233300201/322486272 17249876309/746496) -707281/1728) 29/4)
(/.f64 108/841 x)
(-.f64 (.f64 108/841 (/.f64 1 x)) (.f64 46656/20511149 (/.f64 1 (pow.f64 x 2))))
(-.f64 (/.f64 108/841 x) (/.f64 46656/20511149 (*.f64 x x)))
(+.f64 (/.f64 108/841 x) (/.f64 -46656/20511149 (*.f64 x x)))
(+.f64 (/.f64 108/841 x) (/.f64 (/.f64 -46656/20511149 x) x))
(-.f64 (+.f64 (.f64 108/841 (/.f64 1 x)) (.f64 20155392/500246412961 (/.f64 1 (pow.f64 x 3)))) (*.f64 46656/20511149 (/.f64 1 (pow.f64 x 2))))
(+.f64 (/.f64 108/841 x) (-.f64 (/.f64 20155392/500246412961 (pow.f64 x 3)) (/.f64 46656/20511149 (*.f64 x x))))
(+.f64 (+.f64 (/.f64 108/841 x) (/.f64 20155392/500246412961 (pow.f64 x 3))) (/.f64 -46656/20511149 (*.f64 x x)))
(+.f64 (/.f64 108/841 x) (+.f64 (/.f64 20155392/500246412961 (pow.f64 x 3)) (/.f64 (/.f64 -46656/20511149 x) x)))
(+.f64 (+.f64 (/.f64 108/841 x) (/.f64 (/.f64 -46656/20511149 x) x)) (/.f64 20155392/500246412961 (pow.f64 x 3)))
(-.f64 (+.f64 (.f64 108/841 (/.f64 1 x)) (.f64 20155392/500246412961 (/.f64 1 (pow.f64 x 3)))) (+.f64 (.f64 8707129344/12200509765705829 (/.f64 1 (pow.f64 x 4))) (.f64 46656/20511149 (/.f64 1 (pow.f64 x 2)))))
(-.f64 (+.f64 (/.f64 108/841 x) (/.f64 20155392/500246412961 (pow.f64 x 3))) (+.f64 (/.f64 46656/20511149 (*.f64 x x)) (/.f64 8707129344/12200509765705829 (pow.f64 x 4))))
(-.f64 (+.f64 (+.f64 (/.f64 108/841 x) (/.f64 20155392/500246412961 (pow.f64 x 3))) (/.f64 -46656/20511149 (*.f64 x x))) (/.f64 8707129344/12200509765705829 (pow.f64 x 4)))
(+.f64 (/.f64 20155392/500246412961 (pow.f64 x 3)) (+.f64 (/.f64 108/841 x) (-.f64 (/.f64 (/.f64 -46656/20511149 x) x) (/.f64 8707129344/12200509765705829 (pow.f64 x 4)))))
(+.f64 (/.f64 108/841 x) (+.f64 (/.f64 20155392/500246412961 (pow.f64 x 3)) (-.f64 (/.f64 (/.f64 -46656/20511149 x) x) (/.f64 8707129344/12200509765705829 (pow.f64 x 4)))))
(+.f64 (/.f64 108/841 x) (+.f64 (/.f64 20155392/500246412961 (pow.f64 x 3)) (+.f64 (/.f64 (/.f64 -46656/20511149 x) x) (/.f64 -8707129344/12200509765705829 (pow.f64 x 4)))))
(/.f64 108/841 x)
(-.f64 (.f64 108/841 (/.f64 1 x)) (.f64 46656/20511149 (/.f64 1 (pow.f64 x 2))))
(-.f64 (/.f64 108/841 x) (/.f64 46656/20511149 (*.f64 x x)))
(+.f64 (/.f64 108/841 x) (/.f64 -46656/20511149 (*.f64 x x)))
(+.f64 (/.f64 108/841 x) (/.f64 (/.f64 -46656/20511149 x) x))
(-.f64 (+.f64 (.f64 108/841 (/.f64 1 x)) (.f64 20155392/500246412961 (/.f64 1 (pow.f64 x 3)))) (*.f64 46656/20511149 (/.f64 1 (pow.f64 x 2))))
(+.f64 (/.f64 108/841 x) (-.f64 (/.f64 20155392/500246412961 (pow.f64 x 3)) (/.f64 46656/20511149 (*.f64 x x))))
(+.f64 (+.f64 (/.f64 108/841 x) (/.f64 20155392/500246412961 (pow.f64 x 3))) (/.f64 -46656/20511149 (*.f64 x x)))
(+.f64 (/.f64 108/841 x) (+.f64 (/.f64 20155392/500246412961 (pow.f64 x 3)) (/.f64 (/.f64 -46656/20511149 x) x)))
(+.f64 (+.f64 (/.f64 108/841 x) (/.f64 (/.f64 -46656/20511149 x) x)) (/.f64 20155392/500246412961 (pow.f64 x 3)))
(-.f64 (+.f64 (.f64 108/841 (/.f64 1 x)) (.f64 20155392/500246412961 (/.f64 1 (pow.f64 x 3)))) (+.f64 (.f64 8707129344/12200509765705829 (/.f64 1 (pow.f64 x 4))) (.f64 46656/20511149 (/.f64 1 (pow.f64 x 2)))))
(-.f64 (+.f64 (/.f64 108/841 x) (/.f64 20155392/500246412961 (pow.f64 x 3))) (+.f64 (/.f64 46656/20511149 (*.f64 x x)) (/.f64 8707129344/12200509765705829 (pow.f64 x 4))))
(-.f64 (+.f64 (+.f64 (/.f64 108/841 x) (/.f64 20155392/500246412961 (pow.f64 x 3))) (/.f64 -46656/20511149 (*.f64 x x))) (/.f64 8707129344/12200509765705829 (pow.f64 x 4)))
(+.f64 (/.f64 20155392/500246412961 (pow.f64 x 3)) (+.f64 (/.f64 108/841 x) (-.f64 (/.f64 (/.f64 -46656/20511149 x) x) (/.f64 8707129344/12200509765705829 (pow.f64 x 4)))))
(+.f64 (/.f64 108/841 x) (+.f64 (/.f64 20155392/500246412961 (pow.f64 x 3)) (-.f64 (/.f64 (/.f64 -46656/20511149 x) x) (/.f64 8707129344/12200509765705829 (pow.f64 x 4)))))
(+.f64 (/.f64 108/841 x) (+.f64 (/.f64 20155392/500246412961 (pow.f64 x 3)) (+.f64 (/.f64 (/.f64 -46656/20511149 x) x) (/.f64 -8707129344/12200509765705829 (pow.f64 x 4)))))
4/29
(+.f64 4/29 (*.f64 841/108 x))
(+.f64 4/29 (*.f64 x 841/108))
(fma.f64 x 841/108 4/29)
(+.f64 4/29 (*.f64 841/108 x))
(+.f64 4/29 (*.f64 x 841/108))
(fma.f64 x 841/108 4/29)
(+.f64 4/29 (*.f64 841/108 x))
(+.f64 4/29 (*.f64 x 841/108))
(fma.f64 x 841/108 4/29)
(*.f64 841/108 x)
(*.f64 x 841/108)
(+.f64 4/29 (*.f64 841/108 x))
(+.f64 4/29 (*.f64 x 841/108))
(fma.f64 x 841/108 4/29)
(+.f64 4/29 (*.f64 841/108 x))
(+.f64 4/29 (*.f64 x 841/108))
(fma.f64 x 841/108 4/29)
(+.f64 4/29 (*.f64 841/108 x))
(+.f64 4/29 (*.f64 x 841/108))
(fma.f64 x 841/108 4/29)
(*.f64 841/108 x)
(*.f64 x 841/108)
(+.f64 4/29 (*.f64 841/108 x))
(+.f64 4/29 (*.f64 x 841/108))
(fma.f64 x 841/108 4/29)
(+.f64 4/29 (*.f64 841/108 x))
(+.f64 4/29 (*.f64 x 841/108))
(fma.f64 x 841/108 4/29)
(+.f64 4/29 (*.f64 841/108 x))
(+.f64 4/29 (*.f64 x 841/108))
(fma.f64 x 841/108 4/29)
-4/29
(-.f64 (*.f64 841/108 x) 4/29)
(fma.f64 841/108 x -4/29)
(fma.f64 x 841/108 -4/29)
(-.f64 (*.f64 841/108 x) 4/29)
(fma.f64 841/108 x -4/29)
(fma.f64 x 841/108 -4/29)
(-.f64 (*.f64 841/108 x) 4/29)
(fma.f64 841/108 x -4/29)
(fma.f64 x 841/108 -4/29)
(*.f64 841/108 x)
(*.f64 x 841/108)
(-.f64 (*.f64 841/108 x) 4/29)
(fma.f64 841/108 x -4/29)
(fma.f64 x 841/108 -4/29)
(-.f64 (*.f64 841/108 x) 4/29)
(fma.f64 841/108 x -4/29)
(fma.f64 x 841/108 -4/29)
(-.f64 (*.f64 841/108 x) 4/29)
(fma.f64 841/108 x -4/29)
(fma.f64 x 841/108 -4/29)
(*.f64 841/108 x)
(*.f64 x 841/108)
(-.f64 (*.f64 841/108 x) 4/29)
(fma.f64 841/108 x -4/29)
(fma.f64 x 841/108 -4/29)
(-.f64 (*.f64 841/108 x) 4/29)
(fma.f64 841/108 x -4/29)
(fma.f64 x 841/108 -4/29)
(-.f64 (*.f64 841/108 x) 4/29)
(fma.f64 841/108 x -4/29)
(fma.f64 x 841/108 -4/29)

localize32.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(.f64 (.f64 x x) 707281/11664)
✓	0.2b	(*.f64 (pow.f64 x 3) 594823321/1259712)
✓	0.6b	(*.f64 x 29/27)
✓	20.1b	(/.f64 (+.f64 64/24389 (.f64 (pow.f64 x 3) 594823321/1259712)) (+.f64 (.f64 (.f64 x x) 707281/11664) (-.f64 16/841 (.f64 x 29/27))))

Compiler

Compiled 69 to 49 computations (29% saved)

series6.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	(*.f64 (pow.f64 x 3) 594823321/1259712)
1.0ms	x	@	inf	(/.f64 (+.f64 64/24389 (.f64 (pow.f64 x 3) 594823321/1259712)) (+.f64 (.f64 (.f64 x x) 707281/11664) (-.f64 16/841 (.f64 x 29/27))))
1.0ms	x	@	0	(/.f64 (+.f64 64/24389 (.f64 (pow.f64 x 3) 594823321/1259712)) (+.f64 (.f64 (.f64 x x) 707281/11664) (-.f64 16/841 (.f64 x 29/27))))
1.0ms	x	@	-inf	(*.f64 (pow.f64 x 3) 594823321/1259712)
1.0ms	x	@	-inf	(/.f64 (+.f64 64/24389 (.f64 (pow.f64 x 3) 594823321/1259712)) (+.f64 (.f64 (.f64 x x) 707281/11664) (-.f64 16/841 (.f64 x 29/27))))

rewrite96.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

797×	`log-prod_binary64`
549×	`fma-def_binary64`
309×	`expm1-udef_binary64`
309×	`log1p-udef_binary64`
301×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	17	37
1	397	35
2	5110	33

Stop Event

1×	node limit

Counts

3 → 70

Calls

Call 1

Inputs
(/.f64 (+.f64 64/24389 (.f64 (pow.f64 x 3) 594823321/1259712)) (+.f64 (.f64 (.f64 x x) 707281/11664) (-.f64 16/841 (.f64 x 29/27))))
(*.f64 x 29/27)
(*.f64 (pow.f64 x 3) 594823321/1259712)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (fma.f64 (pow.f64 x 3) 594823321/1259712 64/24389) (fma.f64 x (*.f64 x 707281/11664) (fma.f64 x -29/27 16/841))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (/.f64 (fma.f64 (pow.f64 x 3) 594823321/1259712 64/24389) (fma.f64 x (*.f64 x 707281/11664) (fma.f64 x -29/27 16/841))))) (cbrt.f64 (exp.f64 (/.f64 (fma.f64 (pow.f64 x 3) 594823321/1259712 64/24389) (fma.f64 x (*.f64 x 707281/11664) (fma.f64 x -29/27 16/841))))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (fma.f64 (pow.f64 x 3) 594823321/1259712 64/24389) (fma.f64 x (*.f64 x 707281/11664) (fma.f64 x -29/27 16/841)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (fma.f64 (pow.f64 x 3) 594823321/1259712 64/24389) (fma.f64 x (*.f64 x 707281/11664) (fma.f64 x -29/27 16/841)))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (fma.f64 (pow.f64 x 3) 594823321/1259712 64/24389) (fma.f64 x (*.f64 x 707281/11664) (fma.f64 x -29/27 16/841)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (fma.f64 (pow.f64 x 3) 594823321/1259712 64/24389) (fma.f64 x (*.f64 x 707281/11664) (fma.f64 x -29/27 16/841))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 (pow.f64 x 3) 594823321/1259712 64/24389) (/.f64 1 (fma.f64 x (*.f64 x 707281/11664) (fma.f64 x -29/27 16/841))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (fma.f64 (pow.f64 x 3) 594823321/1259712 64/24389) (fma.f64 x (*.f64 x 707281/11664) (fma.f64 x -29/27 16/841))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (fma.f64 (pow.f64 x 3) 594823321/1259712 64/24389) (fma.f64 x (*.f64 x 707281/11664) (fma.f64 x -29/27 16/841))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (fma.f64 (pow.f64 x 3) 594823321/1259712 64/24389) (fma.f64 x (*.f64 x 707281/11664) (fma.f64 x -29/27 16/841)))) (pow.f64 (cbrt.f64 (/.f64 (fma.f64 (pow.f64 x 3) 594823321/1259712 64/24389) (fma.f64 x (*.f64 x 707281/11664) (fma.f64 x -29/27 16/841)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 (fma.f64 (pow.f64 x 3) 594823321/1259712 64/24389) (fma.f64 x (*.f64 x 707281/11664) (fma.f64 x -29/27 16/841)))) 2) (cbrt.f64 (/.f64 (fma.f64 (pow.f64 x 3) 594823321/1259712 64/24389) (fma.f64 x (*.f64 x 707281/11664) (fma.f64 x -29/27 16/841)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (fma.f64 (pow.f64 x 3) 594823321/1259712 64/24389) 2)) (*.f64 (cbrt.f64 (fma.f64 (pow.f64 x 3) 594823321/1259712 64/24389)) (/.f64 1 (fma.f64 x (*.f64 x 707281/11664) (fma.f64 x -29/27 16/841)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (fma.f64 (pow.f64 x 3) 594823321/1259712 64/24389) (fma.f64 x (*.f64 x 707281/11664) (fma.f64 x -29/27 16/841)))) (sqrt.f64 (/.f64 (fma.f64 (pow.f64 x 3) 594823321/1259712 64/24389) (fma.f64 x (*.f64 x 707281/11664) (fma.f64 x -29/27 16/841)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 (pow.f64 x 3) 594823321/1259712 64/24389)) (*.f64 (sqrt.f64 (fma.f64 (pow.f64 x 3) 594823321/1259712 64/24389)) (/.f64 1 (fma.f64 x (*.f64 x 707281/11664) (fma.f64 x -29/27 16/841)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (fma.f64 (pow.f64 x 3) 594823321/1259712 64/24389)) (/.f64 1 (neg.f64 (fma.f64 x (*.f64 x 707281/11664) (fma.f64 x -29/27 16/841)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (fma.f64 x (*.f64 x 707281/11664) (fma.f64 x -29/27 16/841))) (fma.f64 (pow.f64 x 3) 594823321/1259712 64/24389))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 (fma.f64 (pow.f64 x 3) 594823321/1259712 64/24389) 2)) 1) (/.f64 (cbrt.f64 (fma.f64 (pow.f64 x 3) 594823321/1259712 64/24389)) (fma.f64 x (*.f64 x 707281/11664) (fma.f64 x -29/27 16/841))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (fma.f64 (pow.f64 x 3) 594823321/1259712 64/24389)) 1) (/.f64 (sqrt.f64 (fma.f64 (pow.f64 x 3) 594823321/1259712 64/24389)) (fma.f64 x (*.f64 x 707281/11664) (fma.f64 x -29/27 16/841))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 (fma.f64 x (*.f64 x 707281/11664) (fma.f64 x -29/27 16/841))) 2)) (/.f64 (fma.f64 (pow.f64 x 3) 594823321/1259712 64/24389) (cbrt.f64 (fma.f64 x (*.f64 x 707281/11664) (fma.f64 x -29/27 16/841)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 (fma.f64 (pow.f64 x 3) 594823321/1259712 64/24389) 2)) (pow.f64 (cbrt.f64 (fma.f64 x (*.f64 x 707281/11664) (fma.f64 x -29/27 16/841))) 2)) (cbrt.f64 (/.f64 (fma.f64 (pow.f64 x 3) 594823321/1259712 64/24389) (fma.f64 x (*.f64 x 707281/11664) (fma.f64 x -29/27 16/841)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (fma.f64 (pow.f64 x 3) 594823321/1259712 64/24389)) (pow.f64 (cbrt.f64 (fma.f64 x (*.f64 x 707281/11664) (fma.f64 x -29/27 16/841))) 2)) (/.f64 (sqrt.f64 (fma.f64 (pow.f64 x 3) 594823321/1259712 64/24389)) (cbrt.f64 (fma.f64 x (*.f64 x 707281/11664) (fma.f64 x -29/27 16/841)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (hypot.f64 (sqrt.f64 (fma.f64 x -29/27 16/841)) (*.f64 x 841/108))) (/.f64 (fma.f64 (pow.f64 x 3) 594823321/1259712 64/24389) (hypot.f64 (sqrt.f64 (fma.f64 x -29/27 16/841)) (*.f64 x 841/108))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 (fma.f64 (pow.f64 x 3) 594823321/1259712 64/24389) 2)) (hypot.f64 (sqrt.f64 (fma.f64 x -29/27 16/841)) (*.f64 x 841/108))) (/.f64 (cbrt.f64 (fma.f64 (pow.f64 x 3) 594823321/1259712 64/24389)) (hypot.f64 (sqrt.f64 (fma.f64 x -29/27 16/841)) (*.f64 x 841/108))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (fma.f64 (pow.f64 x 3) 594823321/1259712 64/24389) (fma.f64 (pow.f64 x 6) 353814783205469041/1586874322944 (pow.f64 (fma.f64 x -29/27 16/841) 3))) (fma.f64 (fma.f64 x -29/27 16/841) (-.f64 (fma.f64 x -29/27 16/841) (pow.f64 (*.f64 x 841/108) 2)) (*.f64 (pow.f64 x 4) 500246412961/136048896)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (fma.f64 (pow.f64 x 3) 594823321/1259712 64/24389) (-.f64 (*.f64 (pow.f64 x 4) 500246412961/136048896) (pow.f64 (fma.f64 x -29/27 16/841) 2))) (-.f64 (pow.f64 (*.f64 x 841/108) 2) (fma.f64 x -29/27 16/841)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (fma.f64 (pow.f64 x 3) 594823321/1259712 64/24389) (fma.f64 x (*.f64 x 707281/11664) (fma.f64 x -29/27 16/841))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (fma.f64 (pow.f64 x 3) 594823321/1259712 64/24389) (fma.f64 x (*.f64 x 707281/11664) (fma.f64 x -29/27 16/841))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (fma.f64 (pow.f64 x 3) 594823321/1259712 64/24389) (fma.f64 x (*.f64 x 707281/11664) (fma.f64 x -29/27 16/841)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (fma.f64 (pow.f64 x 3) 594823321/1259712 64/24389) (fma.f64 x (*.f64 x 707281/11664) (fma.f64 x -29/27 16/841)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (fma.f64 x (*.f64 x 707281/11664) (fma.f64 x -29/27 16/841)) (fma.f64 (pow.f64 x 3) 594823321/1259712 64/24389)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (fma.f64 (pow.f64 x 3) 594823321/1259712 64/24389) (neg.f64 (fma.f64 x (*.f64 x 707281/11664) (fma.f64 x -29/27 16/841)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (fma.f64 (pow.f64 x 3) 594823321/1259712 64/24389) (fma.f64 x (*.f64 x 707281/11664) (fma.f64 x -29/27 16/841))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (fma.f64 (pow.f64 x 3) 594823321/1259712 64/24389) (fma.f64 x (*.f64 x 707281/11664) (fma.f64 x -29/27 16/841)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (fma.f64 (pow.f64 x 3) 594823321/1259712 64/24389) (fma.f64 x (*.f64 x 707281/11664) (fma.f64 x -29/27 16/841))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (fma.f64 (pow.f64 x 3) 594823321/1259712 64/24389) (fma.f64 x (*.f64 x 707281/11664) (fma.f64 x -29/27 16/841))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (fma.f64 (pow.f64 x 3) 594823321/1259712 64/24389) 3) (pow.f64 (fma.f64 x (*.f64 x 707281/11664) (fma.f64 x -29/27 16/841)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (fma.f64 (pow.f64 x 3) 594823321/1259712 64/24389) (fma.f64 x (*.f64 x 707281/11664) (fma.f64 x -29/27 16/841)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (fma.f64 (pow.f64 x 3) 594823321/1259712 64/24389) (fma.f64 x (*.f64 x 707281/11664) (fma.f64 x -29/27 16/841)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (fma.f64 (pow.f64 x 3) 594823321/1259712 64/24389) (fma.f64 x (*.f64 x 707281/11664) (fma.f64 x -29/27 16/841)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (fma.f64 (pow.f64 x 3) 594823321/1259712 64/24389) (fma.f64 x (*.f64 x 707281/11664) (fma.f64 x -29/27 16/841)))) 1))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 x 29/27))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (pow.f64 (exp.f64 29/27) x)) (cbrt.f64 (pow.f64 (exp.f64 29/27) x)))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 29/27) x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 29/27) x))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 29/27) x))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 x 29/27))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x 29/27) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x 29/27)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 x 29/27)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 x 3) 24389/19683) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (*.f64 x x) 841/729))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 29/27) x))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 x 29/27))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 x 3) 24389/19683))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x 29/27)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x 29/27)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x 29/27)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 x 29/27)) 1))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (pow.f64 x 3) 594823321/1259712))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (pow.f64 (exp.f64 594823321/1259712) (pow.f64 x 3))) (cbrt.f64 (pow.f64 (exp.f64 594823321/1259712) (pow.f64 x 3))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 594823321/1259712) (pow.f64 x 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 594823321/1259712) (pow.f64 x 3)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 594823321/1259712) (pow.f64 x 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 x 3) 594823321/1259712))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 x 3) 594823321/1259712) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x 841/108) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 594823321/1259712) (pow.f64 x 3/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 210457284365172120330305161/1999004627104432128 (pow.f64 (pow.f64 x 3) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 x 6) 353814783205469041/1586874322944))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 594823321/1259712) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (pow.f64 x 3) 594823321/1259712))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 210457284365172120330305161/1999004627104432128 (pow.f64 (pow.f64 x 3) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (pow.f64 x 3) 594823321/1259712)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (pow.f64 x 3) 594823321/1259712)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 3 (log.f64 (*.f64 x 841/108))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (*.f64 x 841/108))) 1))))))

simplify183.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

1274×	`sqr-pow_binary64`
666×	`pow-sqr_binary64`
529×	`cube-prod_binary64`
473×	`fabs-mul_binary64`
439×	`associate-l_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	204
1	24	186
2	43	186
3	67	186
4	122	186
5	337	186
6	1199	186
7	1882	186
8	1969	186
9	2102	186
10	2260	186
11	2500	186
12	2822	186
13	3243	186
14	3746	186
15	4347	186
16	5065	186
17	5386	186
18	5672	186
19	5896	186
20	6076	186
21	6160	186
22	7100	186

Stop Event

1×	node limit

Counts

106 → 77

Calls

Call 1

Inputs
4/29
(+.f64 4/29 (*.f64 841/108 x))
(+.f64 4/29 (*.f64 841/108 x))
(+.f64 4/29 (*.f64 841/108 x))
(*.f64 841/108 x)
(+.f64 4/29 (*.f64 841/108 x))
(+.f64 4/29 (*.f64 841/108 x))
(+.f64 4/29 (*.f64 841/108 x))
(*.f64 841/108 x)
(+.f64 4/29 (*.f64 841/108 x))
(+.f64 4/29 (*.f64 841/108 x))
(+.f64 4/29 (*.f64 841/108 x))
(*.f64 29/27 x)
(*.f64 29/27 x)
(*.f64 29/27 x)
(*.f64 29/27 x)
(*.f64 29/27 x)
(*.f64 29/27 x)
(*.f64 29/27 x)
(*.f64 29/27 x)
(*.f64 29/27 x)
(*.f64 29/27 x)
(*.f64 29/27 x)
(*.f64 29/27 x)
(*.f64 594823321/1259712 (pow.f64 x 3))
(*.f64 594823321/1259712 (pow.f64 x 3))
(*.f64 594823321/1259712 (pow.f64 x 3))
(*.f64 594823321/1259712 (pow.f64 x 3))
(*.f64 594823321/1259712 (pow.f64 x 3))
(*.f64 594823321/1259712 (pow.f64 x 3))
(*.f64 594823321/1259712 (pow.f64 x 3))
(*.f64 594823321/1259712 (pow.f64 x 3))
(*.f64 594823321/1259712 (pow.f64 x 3))
(*.f64 594823321/1259712 (pow.f64 x 3))
(*.f64 594823321/1259712 (pow.f64 x 3))
(*.f64 594823321/1259712 (pow.f64 x 3))

Outputs
4/29
(+.f64 4/29 (*.f64 841/108 x))
(fma.f64 841/108 x 4/29)
(+.f64 4/29 (*.f64 841/108 x))
(fma.f64 841/108 x 4/29)
(+.f64 4/29 (*.f64 841/108 x))
(fma.f64 841/108 x 4/29)
(*.f64 841/108 x)
(+.f64 4/29 (*.f64 841/108 x))
(fma.f64 841/108 x 4/29)
(+.f64 4/29 (*.f64 841/108 x))
(fma.f64 841/108 x 4/29)
(+.f64 4/29 (*.f64 841/108 x))
(fma.f64 841/108 x 4/29)
(*.f64 841/108 x)
(+.f64 4/29 (*.f64 841/108 x))
(fma.f64 841/108 x 4/29)
(+.f64 4/29 (*.f64 841/108 x))
(fma.f64 841/108 x 4/29)
(+.f64 4/29 (*.f64 841/108 x))
(fma.f64 841/108 x 4/29)
(*.f64 29/27 x)
(*.f64 x 29/27)
(*.f64 29/27 x)
(*.f64 x 29/27)
(*.f64 29/27 x)
(*.f64 x 29/27)
(*.f64 29/27 x)
(*.f64 x 29/27)
(*.f64 29/27 x)
(*.f64 x 29/27)
(*.f64 29/27 x)
(*.f64 x 29/27)
(*.f64 29/27 x)
(*.f64 x 29/27)
(*.f64 29/27 x)
(*.f64 x 29/27)
(*.f64 29/27 x)
(*.f64 x 29/27)
(*.f64 29/27 x)
(*.f64 x 29/27)
(*.f64 29/27 x)
(*.f64 x 29/27)
(*.f64 29/27 x)
(*.f64 x 29/27)
(*.f64 594823321/1259712 (pow.f64 x 3))
(*.f64 594823321/1259712 (pow.f64 x 3))
(*.f64 594823321/1259712 (pow.f64 x 3))
(*.f64 594823321/1259712 (pow.f64 x 3))
(*.f64 594823321/1259712 (pow.f64 x 3))
(*.f64 594823321/1259712 (pow.f64 x 3))
(*.f64 594823321/1259712 (pow.f64 x 3))
(*.f64 594823321/1259712 (pow.f64 x 3))
(*.f64 594823321/1259712 (pow.f64 x 3))
(*.f64 594823321/1259712 (pow.f64 x 3))
(*.f64 594823321/1259712 (pow.f64 x 3))
(*.f64 594823321/1259712 (pow.f64 x 3))

eval444.0ms (8.6%)

Compiler: Compiled 16452 to 12770 computations (22.4% saved)

prune102.0ms (2%)

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	580	5	585
Fresh	3	0	3
Picked	0	1	1
Done	1	3	4
Total	584	9	593

Error

Counts

593 → 9

Alt Table

Click to see full alt table

Status	Error	Program
▶	28.6b	(fma.f64 (sqrt.f64 x) (sqrt.f64 (*.f64 x 707281/11664)) 4/29)
✓	16.1b	(/.f64 (-.f64 16/841 (.f64 (.f64 x x) 707281/11664)) (-.f64 4/29 (*.f64 841/108 x)))
✓	0.1b	(+.f64 (*.f64 841/108 x) 4/29)
▶	30.3b	(/.f64 1 (/.f64 108/841 x))
▶	30.9b	(pow.f64 (cbrt.f64 (*.f64 841/108 x)) 3)
✓	30.3b	(*.f64 841/108 x)
✓	20.9b	(/.f64 (+.f64 64/24389 (.f64 (pow.f64 x 3) 594823321/1259712)) (+.f64 (.f64 (.f64 x x) 707281/11664) (-.f64 16/841 (.f64 x 29/27))))
▶	46.5b	(/.f64 (-.f64 16/841 (.f64 (.f64 x x) 707281/11664)) (*.f64 x -841/108))
	33.0b	4/29

Compiler

Compiled 80 to 64 computations (20% saved)

localize12.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 108/841 x)
✓	0.3b	(/.f64 1 (/.f64 108/841 x))

Compiler

Compiled 12 to 9 computations (25% saved)

series5.0ms (0.1%)

Counts

2 → 12

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(/.f64 1 (/.f64 108/841 x))
1.0ms	x	@	0	(/.f64 108/841 x)
1.0ms	x	@	inf	(/.f64 108/841 x)
1.0ms	x	@	-inf	(/.f64 108/841 x)
1.0ms	x	@	0	(/.f64 1 (/.f64 108/841 x))

rewrite75.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

552×	`pow1_binary64`
520×	`add-log-exp_binary64`
520×	`log1p-expm1-u_binary64`
520×	`expm1-log1p-u_binary64`
510×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	129	8
2	1501	8

Stop Event

1×	node limit

Counts

2 → 46

Calls

Call 1

Inputs
(/.f64 1 (/.f64 108/841 x))
(/.f64 108/841 x)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 x 841/108)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 x 841/108))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x 841/108)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x 841/108) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 x 841/108)) (pow.f64 (cbrt.f64 (*.f64 x 841/108)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 x 841/108)) 2) (cbrt.f64 (*.f64 x 841/108)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 x 841/108)) (sqrt.f64 (*.f64 x 841/108)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 1 (/.f64 -108/841 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 841/108 x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 841/108 (pow.f64 (/.f64 1 x) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 108/841 x)) 2) -1) (pow.f64 (cbrt.f64 (/.f64 108/841 x)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (/.f64 108/841 x)) -1) (pow.f64 (sqrt.f64 (/.f64 108/841 x)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -841/108 (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 841/108 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 841/108 (sqrt.f64 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 108/841 x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x 841/108) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x 841/108) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x 841/108)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 x 841/108)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 707281/11664 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 841/108) x))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x 841/108) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x 841/108)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x 841/108)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x 841/108)))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 108/841 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 108/841 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 108/841 (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 108/841 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 108/841 x)) (pow.f64 (cbrt.f64 (/.f64 108/841 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 108/841 x)) 2) (cbrt.f64 (/.f64 108/841 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 108/841 x)) (sqrt.f64 (/.f64 108/841 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -108/841 (/.f64 1 (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 x) 108/841)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 108/841 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x 841/108) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 108/841 x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 108/841 x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 108/841 x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 11664/707281 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 108/841 x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 108/841 x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 108/841 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 108/841 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 108/841 x)))))))

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	48
1	5	48

Stop Event

1×

saturated

Counts

58 → 46

Calls

Call 1

Inputs
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)

Outputs
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 16/841 (.f64 (.f64 x x) 707281/11664))
✓	0.2b	(*.f64 x -841/108)
	0.2b	(.f64 (.f64 x x) 707281/11664)
✓	15.3b	(/.f64 (-.f64 16/841 (.f64 (.f64 x x) 707281/11664)) (*.f64 x -841/108))

Compiler

Compiled 34 to 20 computations (41.2% saved)

series3.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(/.f64 (-.f64 16/841 (.f64 (.f64 x x) 707281/11664)) (*.f64 x -841/108))
1.0ms	x	@	inf	(/.f64 (-.f64 16/841 (.f64 (.f64 x x) 707281/11664)) (*.f64 x -841/108))
0.0ms	x	@	-inf	(/.f64 (-.f64 16/841 (.f64 (.f64 x x) 707281/11664)) (*.f64 x -841/108))
0.0ms	x	@	0	(*.f64 x -841/108)
0.0ms	x	@	inf	(-.f64 16/841 (.f64 (.f64 x x) 707281/11664))

rewrite116.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

546×	`log-prod_binary64`
341×	`prod-diff_binary64`
285×	`pow-prod-down_binary64`
268×	`pow2_binary64`
196×	`pow-unpow_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	30
1	231	30
2	3279	22

Stop Event

1×	node limit

Counts

3 → 239

Calls

Call 1

Inputs
(/.f64 (-.f64 16/841 (.f64 (.f64 x x) 707281/11664)) (*.f64 x -841/108))
(*.f64 x -841/108)
(-.f64 16/841 (.f64 (.f64 x x) 707281/11664))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (/.f64 -1728/707281 x) (*.f64 x -841/108)) (fma.f64 (neg.f64 x) -841/108 (*.f64 x -841/108)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (/.f64 -1728/707281 x) (*.f64 x -841/108)) (fma.f64 (*.f64 x -841/108) 1 (*.f64 x -841/108)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (/.f64 -1728/707281 x) (*.f64 x -841/108)) (fma.f64 (neg.f64 (cbrt.f64 (*.f64 x -841/108))) (cbrt.f64 (*.f64 (*.f64 x x) 707281/11664)) (*.f64 x -841/108)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (/.f64 -1728/707281 x) (*.f64 x -841/108)) (fma.f64 841/108 x (*.f64 x -841/108)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (/.f64 -1728/707281 x) (*.f64 x -841/108)) (fma.f64 (neg.f64 (/.f64 (*.f64 x x) -841/108)) (/.f64 707281/11664 x) (*.f64 x -841/108)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (/.f64 -1728/707281 x) (*.f64 x -841/108)) (fma.f64 (neg.f64 (/.f64 707281/11664 x)) (/.f64 (*.f64 x x) -841/108) (*.f64 x -841/108)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (/.f64 -1728/707281 x) (*.f64 x -841/108)) (fma.f64 (neg.f64 (/.f64 (*.f64 x -841/108) -841/108)) (/.f64 (*.f64 x -841/108) x) (*.f64 x -841/108)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (/.f64 -1728/707281 x) (*.f64 x -841/108)) (fma.f64 (neg.f64 (/.f64 (*.f64 x -841/108) x)) (/.f64 (*.f64 x -841/108) -841/108) (*.f64 x -841/108)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (/.f64 -1728/707281 x) (*.f64 x -841/108)) (fma.f64 (neg.f64 (/.f64 707281/11664 (sqrt.f64 (*.f64 x -841/108)))) (/.f64 (*.f64 x x) (sqrt.f64 (*.f64 x -841/108))) (*.f64 x -841/108)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (/.f64 -1728/707281 x) (*.f64 x -841/108)) (fma.f64 (neg.f64 (/.f64 (*.f64 x x) (sqrt.f64 (*.f64 x -841/108)))) (/.f64 707281/11664 (sqrt.f64 (*.f64 x -841/108))) (*.f64 x -841/108)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (/.f64 -1728/707281 x) (*.f64 x -841/108)) (fma.f64 (neg.f64 (sqrt.f64 (*.f64 x -841/108))) (sqrt.f64 (*.f64 x -841/108)) (*.f64 x -841/108)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (/.f64 -1728/707281 x) (*.f64 x -841/108)) (fma.f64 -1 (*.f64 x -841/108) (*.f64 x -841/108)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (/.f64 -1728/707281 x) (*.f64 x -841/108)) (fma.f64 (neg.f64 (cbrt.f64 (*.f64 (*.f64 x x) 707281/11664))) (cbrt.f64 (*.f64 x -841/108)) (*.f64 x -841/108)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 -1728/707281 x) (*.f64 x -841/108))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (+.f64 (/.f64 -1728/707281 x) (*.f64 x -841/108)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 16/841 (/.f64 -108/841 x) (neg.f64 (*.f64 (/.f64 (*.f64 x x) (*.f64 x -841/108)) 707281/11664))) (fma.f64 (neg.f64 (/.f64 (*.f64 x x) (*.f64 x -841/108))) 707281/11664 (*.f64 (/.f64 (*.f64 x x) (*.f64 x -841/108)) 707281/11664)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 1 (/.f64 -1728/707281 x) (neg.f64 (*.f64 (/.f64 (*.f64 x x) (*.f64 x -841/108)) 707281/11664))) (fma.f64 (neg.f64 (/.f64 (*.f64 x x) (*.f64 x -841/108))) 707281/11664 (*.f64 (/.f64 (*.f64 x x) (*.f64 x -841/108)) 707281/11664)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (pow.f64 (cbrt.f64 (/.f64 -1728/707281 x)) 2) (cbrt.f64 (/.f64 -1728/707281 x)) (neg.f64 (*.f64 (/.f64 (*.f64 x x) (*.f64 x -841/108)) 707281/11664))) (fma.f64 (neg.f64 (/.f64 (*.f64 x x) (*.f64 x -841/108))) 707281/11664 (*.f64 (/.f64 (*.f64 x x) (*.f64 x -841/108)) 707281/11664)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (sqrt.f64 (/.f64 -1728/707281 x)) (sqrt.f64 (/.f64 -1728/707281 x)) (neg.f64 (*.f64 (/.f64 (*.f64 x x) (*.f64 x -841/108)) 707281/11664))) (fma.f64 (neg.f64 (/.f64 (*.f64 x x) (*.f64 x -841/108))) 707281/11664 (*.f64 (/.f64 (*.f64 x x) (*.f64 x -841/108)) 707281/11664)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 16/841 (/.f64 -108/841 x) (neg.f64 (*.f64 (/.f64 -108/841 x) (*.f64 (*.f64 x x) 707281/11664)))) (fma.f64 (neg.f64 (/.f64 -108/841 x)) (*.f64 (*.f64 x x) 707281/11664) (*.f64 (/.f64 -108/841 x) (*.f64 (*.f64 x x) 707281/11664))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 1 (/.f64 -1728/707281 x) (neg.f64 (*.f64 (/.f64 -108/841 x) (*.f64 (*.f64 x x) 707281/11664)))) (fma.f64 (neg.f64 (/.f64 -108/841 x)) (*.f64 (*.f64 x x) 707281/11664) (*.f64 (/.f64 -108/841 x) (*.f64 (*.f64 x x) 707281/11664))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (pow.f64 (cbrt.f64 (/.f64 -1728/707281 x)) 2) (cbrt.f64 (/.f64 -1728/707281 x)) (neg.f64 (*.f64 (/.f64 -108/841 x) (*.f64 (*.f64 x x) 707281/11664)))) (fma.f64 (neg.f64 (/.f64 -108/841 x)) (*.f64 (*.f64 x x) 707281/11664) (*.f64 (/.f64 -108/841 x) (*.f64 (*.f64 x x) 707281/11664))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (sqrt.f64 (/.f64 -1728/707281 x)) (sqrt.f64 (/.f64 -1728/707281 x)) (neg.f64 (*.f64 (/.f64 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(#(struct:change #<rule egg-rr> (2) ((x fma.f64 x (*.f64 x 707281/11664) 16/841)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x (*.f64 -841/108 (*.f64 x -841/108)) 16/841)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x (neg.f64 (*.f64 x 707281/11664)) 16/841)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x x) 707281/11664 16/841)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x x) -707281/11664 16/841)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 707281/11664 (*.f64 x x) 16/841)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 707281/11664 (*.f64 x (neg.f64 x)) 16/841)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 x x) 707281/11664) 1 16/841)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -841/108 (*.f64 x (*.f64 x -841/108)) 16/841)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x -841/108) (*.f64 x -841/108) 16/841)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 (*.f64 x x) 707281/11664) 16/841)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 (*.f64 x x) 707281/11664)) (pow.f64 (cbrt.f64 (*.f64 x -841/108)) 4) 16/841)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 x -841/108)) 4) (cbrt.f64 (*.f64 (*.f64 x x) 707281/11664)) 16/841)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 x -841/108)) 4) (neg.f64 (cbrt.f64 (*.f64 (*.f64 x x) 707281/11664))) 16/841)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) (*.f64 x 707281/11664)) 16/841)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (cbrt.f64 x) x) (*.f64 (pow.f64 (cbrt.f64 x) 2) 707281/11664) 16/841)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 x -841/108)) (pow.f64 (*.f64 x -841/108) 3/2) 16/841)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (*.f64 x 707281/11664)) 16/841)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x (neg.f64 x)) 707281/11664 16/841)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x 707281/11664) x 16/841)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (*.f64 x -841/108) 3/2) (sqrt.f64 (*.f64 x -841/108)) 16/841)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1 (*.f64 (*.f64 x x) 707281/11664) 16/841)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 x) (*.f64 x 707281/11664) 16/841)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 x -841/108) -841/108) x 16/841)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -707281/11664 (*.f64 x x) 16/841)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (pow.f64 (cbrt.f64 (*.f64 x -841/108)) 4)) (cbrt.f64 (*.f64 (*.f64 x x) 707281/11664)) 16/841)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 x -841/108) x) -841/108 16/841)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 x -841/108)) 5) (cbrt.f64 (*.f64 x -841/108)) 16/841)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 707281/11664 (*.f64 (cbrt.f64 x) x)) (pow.f64 (cbrt.f64 x) 2) 16/841)))))

simplify66.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

627×	`times-frac_binary64`
598×	`associate-l_binary64`
570×	`associate-/l/_binary64`
471×	`fma-neg_binary64`
427×	`associate-/r*_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	237
1	39	219
2	63	219
3	118	219
4	275	219
5	811	219
6	2704	219
7	7471	219

Stop Event

1×	node limit

Counts

275 → 251

Calls

Call 1

Inputs
(/.f64 -1728/707281 x)
(-.f64 (.f64 841/108 x) (.f64 1728/707281 (/.f64 1 x)))
(-.f64 (.f64 841/108 x) (.f64 1728/707281 (/.f64 1 x)))
(-.f64 (.f64 841/108 x) (.f64 1728/707281 (/.f64 1 x)))
(*.f64 841/108 x)
(-.f64 (.f64 841/108 x) (.f64 1728/707281 (/.f64 1 x)))
(-.f64 (.f64 841/108 x) (.f64 1728/707281 (/.f64 1 x)))
(-.f64 (.f64 841/108 x) (.f64 1728/707281 (/.f64 1 x)))
(*.f64 841/108 x)
(-.f64 (.f64 841/108 x) (.f64 1728/707281 (/.f64 1 x)))
(-.f64 (.f64 841/108 x) (.f64 1728/707281 (/.f64 1 x)))
(-.f64 (.f64 841/108 x) (.f64 1728/707281 (/.f64 1 x)))
(*.f64 -841/108 x)
(*.f64 -841/108 x)
(*.f64 -841/108 x)
(*.f64 -841/108 x)
(*.f64 -841/108 x)
(*.f64 -841/108 x)
(*.f64 -841/108 x)
(*.f64 -841/108 x)
(*.f64 -841/108 x)
(*.f64 -841/108 x)
(*.f64 -841/108 x)
(*.f64 -841/108 x)
16/841
(+.f64 (*.f64 -707281/11664 (pow.f64 x 2)) 16/841)
(+.f64 (*.f64 -707281/11664 (pow.f64 x 2)) 16/841)
(+.f64 (*.f64 -707281/11664 (pow.f64 x 2)) 16/841)
(*.f64 -707281/11664 (pow.f64 x 2))
(+.f64 (*.f64 -707281/11664 (pow.f64 x 2)) 16/841)
(+.f64 (*.f64 -707281/11664 (pow.f64 x 2)) 16/841)
(+.f64 (*.f64 -707281/11664 (pow.f64 x 2)) 16/841)
(*.f64 -707281/11664 (pow.f64 x 2))
(+.f64 (*.f64 -707281/11664 (pow.f64 x 2)) 16/841)
(+.f64 (*.f64 -707281/11664 (pow.f64 x 2)) 16/841)
(+.f64 (*.f64 -707281/11664 (pow.f64 x 2)) 16/841)

Outputs
(/.f64 -1728/707281 x)
(-.f64 (.f64 841/108 x) (.f64 1728/707281 (/.f64 1 x)))
(-.f64 (*.f64 x 841/108) (/.f64 1728/707281 x))
(fma.f64 x 841/108 (/.f64 -1728/707281 x))
(-.f64 (.f64 841/108 x) (.f64 1728/707281 (/.f64 1 x)))
(-.f64 (*.f64 x 841/108) (/.f64 1728/707281 x))
(fma.f64 x 841/108 (/.f64 -1728/707281 x))
(-.f64 (.f64 841/108 x) (.f64 1728/707281 (/.f64 1 x)))
(-.f64 (*.f64 x 841/108) (/.f64 1728/707281 x))
(fma.f64 x 841/108 (/.f64 -1728/707281 x))
(*.f64 841/108 x)
(*.f64 x 841/108)
(-.f64 (.f64 841/108 x) (.f64 1728/707281 (/.f64 1 x)))
(-.f64 (*.f64 x 841/108) (/.f64 1728/707281 x))
(fma.f64 x 841/108 (/.f64 -1728/707281 x))
(-.f64 (.f64 841/108 x) (.f64 1728/707281 (/.f64 1 x)))
(-.f64 (*.f64 x 841/108) (/.f64 1728/707281 x))
(fma.f64 x 841/108 (/.f64 -1728/707281 x))
(-.f64 (.f64 841/108 x) (.f64 1728/707281 (/.f64 1 x)))
(-.f64 (*.f64 x 841/108) (/.f64 1728/707281 x))
(fma.f64 x 841/108 (/.f64 -1728/707281 x))
(*.f64 841/108 x)
(*.f64 x 841/108)
(-.f64 (.f64 841/108 x) (.f64 1728/707281 (/.f64 1 x)))
(-.f64 (*.f64 x 841/108) (/.f64 1728/707281 x))
(fma.f64 x 841/108 (/.f64 -1728/707281 x))
(-.f64 (.f64 841/108 x) (.f64 1728/707281 (/.f64 1 x)))
(-.f64 (*.f64 x 841/108) (/.f64 1728/707281 x))
(fma.f64 x 841/108 (/.f64 -1728/707281 x))
(-.f64 (.f64 841/108 x) (.f64 1728/707281 (/.f64 1 x)))
(-.f64 (*.f64 x 841/108) (/.f64 1728/707281 x))
(fma.f64 x 841/108 (/.f64 -1728/707281 x))
(*.f64 -841/108 x)
(*.f64 x -841/108)
(*.f64 -841/108 x)
(*.f64 x -841/108)
(*.f64 -841/108 x)
(*.f64 x -841/108)
(*.f64 -841/108 x)
(*.f64 x -841/108)
(*.f64 -841/108 x)
(*.f64 x -841/108)
(*.f64 -841/108 x)
(*.f64 x -841/108)
(*.f64 -841/108 x)
(*.f64 x -841/108)
(*.f64 -841/108 x)
(*.f64 x -841/108)
(*.f64 -841/108 x)
(*.f64 x -841/108)
(*.f64 -841/108 x)
(*.f64 x -841/108)
(*.f64 -841/108 x)
(*.f64 x -841/108)
(*.f64 -841/108 x)
(*.f64 x -841/108)
16/841
(+.f64 (*.f64 -707281/11664 (pow.f64 x 2)) 16/841)
(fma.f64 -707281/11664 (*.f64 x x) 16/841)
(fma.f64 x (*.f64 x -707281/11664) 16/841)
(+.f64 (*.f64 -707281/11664 (pow.f64 x 2)) 16/841)
(fma.f64 -707281/11664 (*.f64 x x) 16/841)
(fma.f64 x (*.f64 x -707281/11664) 16/841)
(+.f64 (*.f64 -707281/11664 (pow.f64 x 2)) 16/841)
(fma.f64 -707281/11664 (*.f64 x x) 16/841)
(fma.f64 x (*.f64 x -707281/11664) 16/841)
(*.f64 -707281/11664 (pow.f64 x 2))
(.f64 -707281/11664 (.f64 x x))
(.f64 x (.f64 x -707281/11664))
(+.f64 (*.f64 -707281/11664 (pow.f64 x 2)) 16/841)
(fma.f64 -707281/11664 (*.f64 x x) 16/841)
(fma.f64 x (*.f64 x -707281/11664) 16/841)
(+.f64 (*.f64 -707281/11664 (pow.f64 x 2)) 16/841)
(fma.f64 -707281/11664 (*.f64 x x) 16/841)
(fma.f64 x (*.f64 x -707281/11664) 16/841)
(+.f64 (*.f64 -707281/11664 (pow.f64 x 2)) 16/841)
(fma.f64 -707281/11664 (*.f64 x x) 16/841)
(fma.f64 x (*.f64 x -707281/11664) 16/841)
(*.f64 -707281/11664 (pow.f64 x 2))
(.f64 -707281/11664 (.f64 x x))
(.f64 x (.f64 x -707281/11664))
(+.f64 (*.f64 -707281/11664 (pow.f64 x 2)) 16/841)
(fma.f64 -707281/11664 (*.f64 x x) 16/841)
(fma.f64 x (*.f64 x -707281/11664) 16/841)
(+.f64 (*.f64 -707281/11664 (pow.f64 x 2)) 16/841)
(fma.f64 -707281/11664 (*.f64 x x) 16/841)
(fma.f64 x (*.f64 x -707281/11664) 16/841)
(+.f64 (*.f64 -707281/11664 (pow.f64 x 2)) 16/841)
(fma.f64 -707281/11664 (*.f64 x x) 16/841)
(fma.f64 x (*.f64 x -707281/11664) 16/841)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.2b	(*.f64 841/108 x)
✓	0.6b	(cbrt.f64 (*.f64 841/108 x))
✓	0.8b	(pow.f64 (cbrt.f64 (*.f64 841/108 x)) 3)

Compiler

Compiled 17 to 13 computations (23.5% saved)

series6.0ms (0.1%)

Counts

2 → 0

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	x	@	0	(pow.f64 (cbrt.f64 (*.f64 841/108 x)) 3)
2.0ms	x	@	-inf	(pow.f64 (cbrt.f64 (*.f64 841/108 x)) 3)
1.0ms	x	@	inf	(pow.f64 (cbrt.f64 (*.f64 841/108 x)) 3)
1.0ms	x	@	-inf	(cbrt.f64 (*.f64 841/108 x))
0.0ms	x	@	0	(cbrt.f64 (*.f64 841/108 x))

rewrite53.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

522×	`pow1_binary64`
517×	`add-sqr-sqrt_binary64`
496×	`add-log-exp_binary64`
496×	`log1p-expm1-u_binary64`
496×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	149	10
2	1398	10

Stop Event

1×	node limit

Counts

2 → 49

Calls

Call 1

Inputs
(pow.f64 (cbrt.f64 (*.f64 841/108 x)) 3)
(cbrt.f64 (*.f64 841/108 x))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 841/108 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 841/108 x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x 841/108)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 841/108 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 841/108 x)) (pow.f64 (cbrt.f64 (*.f64 841/108 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 841/108 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 841/108 x)) 2) (cbrt.f64 (*.f64 841/108 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) 841/108))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 841/108 x))) 2) (*.f64 (cbrt.f64 (cbrt.f64 (*.f64 841/108 x))) (pow.f64 (cbrt.f64 (*.f64 841/108 x)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 841/108) (*.f64 (cbrt.f64 x) (pow.f64 (cbrt.f64 (*.f64 841/108 x)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) 841/108))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 841/108 x) 1/6) (*.f64 (pow.f64 (*.f64 841/108 x) 1/6) (pow.f64 (cbrt.f64 (*.f64 841/108 x)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 841/108 x)) (sqrt.f64 (*.f64 841/108 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 841/108 x))) 2) 3) (cbrt.f64 (*.f64 841/108 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 841/108) 3) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (*.f64 841/108 x) 1/6) 3) (pow.f64 (pow.f64 (*.f64 841/108 x) 1/6) 3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 841/108 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 841/108 (sqrt.f64 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (cbrt.f64 (*.f64 841/108 x)) 2) 1) (cbrt.f64 (*.f64 841/108 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (cbrt.f64 (*.f64 841/108 x)) 2) (pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 841/108 x))) 2)) (cbrt.f64 (cbrt.f64 (*.f64 841/108 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (cbrt.f64 (*.f64 841/108 x)) 2) (cbrt.f64 841/108)) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (cbrt.f64 (*.f64 841/108 x)) 2) (pow.f64 (*.f64 841/108 x) 1/6)) (pow.f64 (*.f64 841/108 x) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 841/108 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 841/108) x))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 841/108 x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 841/108 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 841/108 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 841/108 x)))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (cbrt.f64 (*.f64 841/108 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 841/108 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (cbrt.f64 (*.f64 841/108 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 x) (cbrt.f64 841/108))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (*.f64 841/108 x))) (pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 841/108 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (*.f64 841/108 x))) (pow.f64 (pow.f64 (cbrt.f64 (*.f64 841/108 x)) 2) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 841/108 x))) 2) (cbrt.f64 (cbrt.f64 (*.f64 841/108 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 841/108) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 841/108 x) 1/6) (pow.f64 (*.f64 841/108 x) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 841/108 x)) 2) 1/3) (cbrt.f64 (cbrt.f64 (*.f64 841/108 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (cbrt.f64 (*.f64 841/108 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (*.f64 841/108 x)) 1/3) (pow.f64 (sqrt.f64 (*.f64 841/108 x)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 841/108 x) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 841/108 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 841/108 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 841/108 x) 1/6) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (cbrt.f64 (*.f64 841/108 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (cbrt.f64 (*.f64 841/108 x))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (cbrt.f64 (*.f64 841/108 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (cbrt.f64 (*.f64 841/108 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (cbrt.f64 (*.f64 841/108 x))))))))

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

49 → 49

Calls

Call 1

Inputs

Outputs

localize12.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (*.f64 x 707281/11664))
✓	0.1b	(fma.f64 (sqrt.f64 x) (sqrt.f64 (*.f64 x 707281/11664)) 4/29)
✓	0.2b	(*.f64 x 707281/11664)

Compiler

Compiled 21 to 14 computations (33.3% saved)

series7.0ms (0.1%)

Counts

3 → 13

Calls

9 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	(fma.f64 (sqrt.f64 x) (sqrt.f64 (*.f64 x 707281/11664)) 4/29)
1.0ms	x	@	inf	(fma.f64 (sqrt.f64 x) (sqrt.f64 (*.f64 x 707281/11664)) 4/29)
1.0ms	x	@	0	(fma.f64 (sqrt.f64 x) (sqrt.f64 (*.f64 x 707281/11664)) 4/29)
1.0ms	x	@	0	(*.f64 x 707281/11664)
0.0ms	x	@	inf	(sqrt.f64 (*.f64 x 707281/11664))

rewrite67.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

678×	`pow1_binary64`
634×	`add-log-exp_binary64`
634×	`log1p-expm1-u_binary64`
634×	`expm1-log1p-u_binary64`
619×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	22
1	163	17
2	1762	17

Stop Event

1×	node limit

Counts

3 → 59

Calls

Call 1

Inputs
(*.f64 x 707281/11664)
(fma.f64 (sqrt.f64 x) (sqrt.f64 (*.f64 x 707281/11664)) 4/29)
(sqrt.f64 (*.f64 x 707281/11664))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 x 707281/11664)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x 707281/11664) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 x) 841/108) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (*.f64 x x) 500246412961/136048896) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x 707281/11664) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x 707281/11664)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (*.f64 x x) 500246412961/136048896))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 x) 707281/11664))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x 707281/11664) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x 707281/11664)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x 707281/11664)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x 707281/11664)))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 4/29 (*.f64 x 841/108))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x 841/108) 4/29)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 x 841/108) 1) 4/29)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (+.f64 4/29 (*.f64 x 841/108))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 4/29 (*.f64 x 841/108)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 4/29 (*.f64 x 841/108)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 4/29 (*.f64 x 841/108))) (pow.f64 (cbrt.f64 (+.f64 4/29 (*.f64 x 841/108))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 4/29 (*.f64 x 841/108))) 2) (cbrt.f64 (+.f64 4/29 (*.f64 x 841/108))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 4/29 (*.f64 x 841/108))) (sqrt.f64 (+.f64 4/29 (*.f64 x 841/108))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 x 841/108) 3) 64/24389) (+.f64 (*.f64 (*.f64 x 841/108) (*.f64 x 841/108)) (-.f64 16/841 (*.f64 (*.f64 x 841/108) 4/29))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 x 841/108) (*.f64 x 841/108)) 16/841) (-.f64 (*.f64 x 841/108) 4/29))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 4/29 (*.f64 x 841/108)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 4/29 (*.f64 x 841/108)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 4/29 (*.f64 x 841/108))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 4/29 (*.f64 x 841/108))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 4/29 (*.f64 x 841/108)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 4/29 (*.f64 x 841/108))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 4/29 (*.f64 x 841/108)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 4/29 (*.f64 x 841/108))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 4/29 (*.f64 x 841/108))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 4/29 (*.f64 x 841/108))))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 (sqrt.f64 x) 841/108)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) 841/108)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (pow.f64 707281/11664 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 x) 841/108) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 (sqrt.f64 x) 841/108))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 x) (*.f64 (cbrt.f64 (sqrt.f64 x)) 841/108))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (sqrt.f64 x) 841/108)) (cbrt.f64 (*.f64 x 707281/11664)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 x 707281/11664)) (cbrt.f64 (*.f64 (sqrt.f64 x) 841/108)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x 1/4) (*.f64 (pow.f64 x 1/4) 841/108))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 x 707281/11664) 1/4) (pow.f64 (*.f64 x 707281/11664) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 841/108 (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (*.f64 x 707281/11664)) 2)) (sqrt.f64 (cbrt.f64 (*.f64 x 707281/11664))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 707281/11664 1/2) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (*.f64 (sqrt.f64 x) 841/108))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 x 707281/11664)) 2) 1/2) (pow.f64 (cbrt.f64 (*.f64 x 707281/11664)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x 707281/11664) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 x) 841/108) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x 707281/11664) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 x) 841/108)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x 707281/11664) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (*.f64 (sqrt.f64 x) 841/108))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (sqrt.f64 x)) 841/108))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x 707281/11664) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 x) 841/108)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 x) 841/108)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (sqrt.f64 x) 841/108)))))))

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	49
1	6	49

Stop Event

1×

saturated

Counts

72 → 61

Calls

Call 1

Inputs
(*.f64 707281/11664 x)
(*.f64 707281/11664 x)
(*.f64 707281/11664 x)
(*.f64 707281/11664 x)
(*.f64 707281/11664 x)
(*.f64 707281/11664 x)
(*.f64 707281/11664 x)
(*.f64 707281/11664 x)
(*.f64 707281/11664 x)
(*.f64 707281/11664 x)
(*.f64 707281/11664 x)
(*.f64 707281/11664 x)
4/29

Outputs
(*.f64 707281/11664 x)
(*.f64 707281/11664 x)
(*.f64 707281/11664 x)
(*.f64 707281/11664 x)
(*.f64 707281/11664 x)
(*.f64 707281/11664 x)
(*.f64 707281/11664 x)
(*.f64 707281/11664 x)
(*.f64 707281/11664 x)
(*.f64 707281/11664 x)
(*.f64 707281/11664 x)
(*.f64 707281/11664 x)
4/29

eval191.0ms (3.7%)

Compiler: Compiled 8128 to 5990 computations (26.3% saved)

prune64.0ms (1.2%)

Pruning

10 alts after pruning (4 fresh and 6 done)

	Pruned	Kept	Total
New	433	3	436
Fresh	0	1	1
Picked	1	0	1
Done	1	6	7
Total	435	10	445

Error

Counts

445 → 10

Alt Table

Click to see full alt table

Status	Error	Program
✓	30.3b	(/.f64 1 (/.f64 108/841 x))
▶	30.5b	(*.f64 (pow.f64 (cbrt.f64 841/108) 3) x)
▶	46.3b	(/.f64 (.f64 x (.f64 x -707281/11664)) (*.f64 x -841/108))
✓	16.1b	(/.f64 (-.f64 16/841 (.f64 (.f64 x x) 707281/11664)) (-.f64 4/29 (*.f64 841/108 x)))
✓	0.1b	(+.f64 (*.f64 841/108 x) 4/29)
▶	30.4b	(/.f64 1 (*.f64 (/.f64 1 x) 108/841))
✓	30.3b	(*.f64 841/108 x)
✓	20.9b	(/.f64 (+.f64 64/24389 (.f64 (pow.f64 x 3) 594823321/1259712)) (+.f64 (.f64 (.f64 x x) 707281/11664) (-.f64 16/841 (.f64 x 29/27))))
✓	46.5b	(/.f64 (-.f64 16/841 (.f64 (.f64 x x) 707281/11664)) (*.f64 x -841/108))
	33.0b	4/29

Compiler

Compiled 89 to 71 computations (20.2% saved)

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (pow.f64 (cbrt.f64 841/108) 3) x)
✓	1.0b	(pow.f64 (cbrt.f64 841/108) 3)

Compiler

Compiled 16 to 14 computations (12.5% saved)

series1.0ms (0%)

Counts

2 → 12

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(*.f64 (pow.f64 (cbrt.f64 841/108) 3) x)
0.0ms	x	@	inf	(*.f64 (pow.f64 (cbrt.f64 841/108) 3) x)
0.0ms	x	@	-inf	(*.f64 (pow.f64 (cbrt.f64 841/108) 3) x)

rewrite49.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

505×	`pow1_binary64`
499×	`add-sqr-sqrt_binary64`
478×	`add-log-exp_binary64`
478×	`log1p-expm1-u_binary64`
478×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	5
1	149	5
2	1340	5

Stop Event

1×	node limit

Counts

2 → 12

Calls

Call 1

Inputs
(pow.f64 (cbrt.f64 841/108) 3)
(*.f64 (pow.f64 (cbrt.f64 841/108) 3) x)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x . 841/108)))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 841/108 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 841/108 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 841/108 x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 841/108 x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 841/108 x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 841/108 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 x) 841/108))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 841/108 x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 841/108 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 841/108 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 841/108 x)))))))

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	48
1	5	48

Stop Event

1×

saturated

Counts

24 → 13

Calls

Call 1

Inputs
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)

Outputs
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 1 (*.f64 (/.f64 1 x) 108/841))
✓	0.3b	(*.f64 (/.f64 1 x) 108/841)

Compiler

Compiled 19 to 15 computations (21.1% saved)

series2.0ms (0%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(*.f64 (/.f64 1 x) 108/841)
0.0ms	x	@	-inf	(*.f64 (/.f64 1 x) 108/841)
0.0ms	x	@	-inf	(/.f64 1 (*.f64 (/.f64 1 x) 108/841))
0.0ms	x	@	inf	(*.f64 (/.f64 1 x) 108/841)
0.0ms	x	@	0	(/.f64 1 (*.f64 (/.f64 1 x) 108/841))

rewrite57.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

620×	`pow1_binary64`
577×	`add-log-exp_binary64`
577×	`log1p-expm1-u_binary64`
577×	`expm1-log1p-u_binary64`
564×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	146	8
2	1715	8

Stop Event

1×	node limit

Counts

2 → 43

Calls

Call 1

Inputs
(*.f64 (/.f64 1 x) 108/841)
(/.f64 1 (*.f64 (/.f64 1 x) 108/841))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 108/841 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (*.f64 x 841/108))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 1 x) 841/108)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 108/841 x)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 108/841 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (cbrt.f64 (/.f64 108/841 x)) 2) (cbrt.f64 (*.f64 x 841/108)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (/.f64 108/841 x)) (sqrt.f64 (*.f64 x 841/108)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 -108/841 x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -108/841 (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 108/841 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 108/841 (sqrt.f64 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 108/841 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 108/841 x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 108/841 x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 108/841 x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 11664/707281 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 108/841 x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 108/841 x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 108/841 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 108/841 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 108/841 x)))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 x 841/108)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 x 841/108))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x 841/108)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x 841/108) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 x 841/108)) (pow.f64 (cbrt.f64 (*.f64 x 841/108)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 x 841/108)) 2) (cbrt.f64 (*.f64 x 841/108)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 x 841/108)) (sqrt.f64 (*.f64 x 841/108)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 1 (/.f64 -108/841 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 841/108 x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 108/841 x)) 2) -1) (pow.f64 (cbrt.f64 (/.f64 108/841 x)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (/.f64 108/841 x)) -1) (pow.f64 (sqrt.f64 (/.f64 108/841 x)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 108/841 x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x 841/108) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x 841/108) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x 841/108)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 x 841/108)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (*.f64 x x) 11664/707281))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (*.f64 x 841/108)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x 841/108) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x 841/108)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x 841/108)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x 841/108)))))))

simplify10.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	96
1	7	96

Stop Event

1×

saturated

Counts

67 → 43

Calls

Call 1

Inputs
(/.f64 108/841 x)
(/.f64 108/841 x)
(/.f64 108/841 x)
(/.f64 108/841 x)
(/.f64 108/841 x)
(/.f64 108/841 x)
(/.f64 108/841 x)
(/.f64 108/841 x)
(/.f64 108/841 x)
(/.f64 108/841 x)
(/.f64 108/841 x)
(/.f64 108/841 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)

Outputs
(/.f64 108/841 x)
(/.f64 108/841 x)
(/.f64 108/841 x)
(/.f64 108/841 x)
(/.f64 108/841 x)
(/.f64 108/841 x)
(/.f64 108/841 x)
(/.f64 108/841 x)
(/.f64 108/841 x)
(/.f64 108/841 x)
(/.f64 108/841 x)
(/.f64 108/841 x)
(*.f64 841/108 x)
(*.f64 x 841/108)
(*.f64 841/108 x)
(*.f64 x 841/108)
(*.f64 841/108 x)
(*.f64 x 841/108)
(*.f64 841/108 x)
(*.f64 x 841/108)
(*.f64 841/108 x)
(*.f64 x 841/108)
(*.f64 841/108 x)
(*.f64 x 841/108)
(*.f64 841/108 x)
(*.f64 x 841/108)
(*.f64 841/108 x)
(*.f64 x 841/108)
(*.f64 841/108 x)
(*.f64 x 841/108)
(*.f64 841/108 x)
(*.f64 x 841/108)
(*.f64 841/108 x)
(*.f64 x 841/108)
(*.f64 841/108 x)
(*.f64 x 841/108)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 x (.f64 x -707281/11664))
	0.2b	(*.f64 x -841/108)
✓	0.2b	(*.f64 x -707281/11664)
✓	27.8b	(/.f64 (.f64 x (.f64 x -707281/11664)) (*.f64 x -841/108))

Compiler

Compiled 24 to 16 computations (33.3% saved)

series6.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
3.0ms	x	@	inf	(/.f64 (.f64 x (.f64 x -707281/11664)) (*.f64 x -841/108))
0.0ms	x	@	0	(*.f64 x -707281/11664)
0.0ms	x	@	inf	(.f64 x (.f64 x -707281/11664))
0.0ms	x	@	0	(.f64 x (.f64 x -707281/11664))
0.0ms	x	@	0	(/.f64 (.f64 x (.f64 x -707281/11664)) (*.f64 x -841/108))

rewrite74.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

959×	`pow1_binary64`
907×	`add-log-exp_binary64`
907×	`log1p-expm1-u_binary64`
907×	`expm1-log1p-u_binary64`
105×	`times-frac_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	24
1	175	15
2	2510	15

Stop Event

1×	node limit

Counts

3 → 95

Calls

Call 1

Inputs
(/.f64 (.f64 x (.f64 x -707281/11664)) (*.f64 x -841/108))
(*.f64 x -707281/11664)
(.f64 x (.f64 x -707281/11664))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 x 841/108))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (*.f64 x -841/108))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x 841/108)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (*.f64 (*.f64 x -707281/11664) (/.f64 -108/841 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x -707281/11664) -108/841)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x -707281/11664) (*.f64 x (/.f64 -108/841 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x (*.f64 x -707281/11664)) (/.f64 -108/841 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -841/108 (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 x 841/108))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x x) (*.f64 -707281/11664 (/.f64 -108/841 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 x 841/108)) (pow.f64 (cbrt.f64 (*.f64 x 841/108)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 x 841/108)) 2) (cbrt.f64 (*.f64 x 841/108)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 x (*.f64 x -707281/11664))) 2) (*.f64 (cbrt.f64 (*.f64 x (*.f64 x -707281/11664))) (/.f64 -108/841 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 x -841/108)) 2) (neg.f64 (cbrt.f64 (*.f64 x -841/108))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 x 841/108)) (sqrt.f64 (*.f64 x 841/108)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x (sqrt.f64 -707281/11664)) (*.f64 (*.f64 x (sqrt.f64 -707281/11664)) (/.f64 -108/841 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 x -841/108)) (neg.f64 (sqrt.f64 (*.f64 x -841/108))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 x -841/108) 2) (/.f64 108/841 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x 841/108) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 -108/841 x) (*.f64 x (*.f64 x -707281/11664)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 x -707281/11664) 1) -108/841)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 x -707281/11664) 1) (/.f64 x (*.f64 x -841/108)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 841/108 x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (*.f64 x -841/108))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 x) -841/108)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 x) (/.f64 (*.f64 x (*.f64 x -707281/11664)) -841/108))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x 1) (/.f64 (*.f64 x -707281/11664) (*.f64 x -841/108)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 x -707281/11664) x) (/.f64 x -841/108))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x -841/108) (/.f64 (*.f64 x -707281/11664) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 x x) x) 841/108)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (*.f64 x (*.f64 x -707281/11664))) 2) x) (/.f64 (cbrt.f64 (*.f64 x (*.f64 x -707281/11664))) -841/108))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 x (sqrt.f64 -707281/11664)) x) (/.f64 (*.f64 x (sqrt.f64 -707281/11664)) -841/108))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 x (sqrt.f64 -707281/11664)) -841/108) (/.f64 (*.f64 x (sqrt.f64 -707281/11664)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -108/841 (/.f64 (*.f64 x -707281/11664) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 x x) -841/108) (/.f64 -707281/11664 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (*.f64 x (*.f64 x -707281/11664))) 2) -841/108) (/.f64 (cbrt.f64 (*.f64 x (*.f64 x -707281/11664))) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (*.f64 x -841/108)) (*.f64 x -707281/11664))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 x x) 1) (/.f64 -707281/11664 (*.f64 x -841/108)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (*.f64 x (*.f64 x -707281/11664))) 2) 1) (/.f64 (cbrt.f64 (*.f64 x (*.f64 x -707281/11664))) (*.f64 x -841/108)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 x (sqrt.f64 -707281/11664)) 1) (/.f64 (*.f64 x (sqrt.f64 -707281/11664)) (*.f64 x -841/108)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (pow.f64 (cbrt.f64 (*.f64 x -841/108)) 2)) (/.f64 (*.f64 x -707281/11664) (cbrt.f64 (*.f64 x -841/108))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 x -707281/11664) (pow.f64 (cbrt.f64 (*.f64 x -841/108)) 2)) (/.f64 x (cbrt.f64 (*.f64 x -841/108))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 (*.f64 x -841/108)) 2)) (/.f64 (*.f64 x (*.f64 x -707281/11664)) (cbrt.f64 (*.f64 x -841/108))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 x x) (pow.f64 (cbrt.f64 (*.f64 x -841/108)) 2)) (/.f64 -707281/11664 (cbrt.f64 (*.f64 x -841/108))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (*.f64 x (*.f64 x -707281/11664))) 2) (pow.f64 (cbrt.f64 (*.f64 x -841/108)) 2)) (cbrt.f64 (*.f64 x 841/108)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 x (sqrt.f64 -707281/11664)) (pow.f64 (cbrt.f64 (*.f64 x -841/108)) 2)) (/.f64 (*.f64 x (sqrt.f64 -707281/11664)) (cbrt.f64 (*.f64 x -841/108))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (sqrt.f64 (*.f64 x -841/108))) (/.f64 (*.f64 x -707281/11664) (sqrt.f64 (*.f64 x -841/108))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 x -707281/11664) (sqrt.f64 (*.f64 x -841/108))) (/.f64 x (sqrt.f64 (*.f64 x -841/108))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 (*.f64 x -841/108))) (/.f64 (*.f64 x (*.f64 x -707281/11664)) (sqrt.f64 (*.f64 x -841/108))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 x x) (sqrt.f64 (*.f64 x -841/108))) (/.f64 -707281/11664 (sqrt.f64 (*.f64 x -841/108))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (*.f64 x (*.f64 x -707281/11664))) 2) (sqrt.f64 (*.f64 x -841/108))) (/.f64 (cbrt.f64 (*.f64 x (*.f64 x -707281/11664))) (sqrt.f64 (*.f64 x -841/108))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (sqrt.f64 (*.f64 x -841/108))) (sqrt.f64 (*.f64 x -841/108)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (pow.f64 (cbrt.f64 (*.f64 x -841/108)) 2)) (cbrt.f64 (*.f64 x -841/108)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x 841/108) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x 841/108)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 x 841/108)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x 841/108) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 108/841 x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (*.f64 x -841/108))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (*.f64 x (*.f64 x -707281/11664)) (*.f64 x 841/108)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (*.f64 x x) 11664/707281))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (*.f64 x 841/108)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 x 841/108))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (/.f64 1 (pow.f64 (exp.f64 -841/108) x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x 841/108) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (*.f64 x (*.f64 x -707281/11664)) 3) (pow.f64 (*.f64 x -841/108) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x 841/108)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x 841/108)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x 841/108)))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 x -707281/11664))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x -707281/11664) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x -707281/11664) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x -707281/11664)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 x -707281/11664)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 x -707281/11664) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 x) -707281/11664))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 x -707281/11664))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x -707281/11664) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x -707281/11664)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x -707281/11664)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x -707281/11664)))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 x (*.f64 x -707281/11664)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (*.f64 x -707281/11664)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x (*.f64 x -707281/11664)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x (*.f64 x -707281/11664))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (sqrt.f64 -707281/11664)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 x (*.f64 x -707281/11664)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 x) (*.f64 x -707281/11664)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 x (*.f64 x -707281/11664)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x (*.f64 x -707281/11664)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 x 3) (pow.f64 (*.f64 x -707281/11664) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (*.f64 x -707281/11664) 3) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x (*.f64 x -707281/11664))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x (*.f64 x -707281/11664))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x (*.f64 x -707281/11664))))))))

simplify178.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

1101×	`sqr-pow_binary64`
565×	`cube-prod_binary64`
556×	`fabs-mul_binary64`
528×	`pow-sqr_binary64`
513×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	180
1	17	180
2	26	180
3	49	180
4	119	180
5	372	180
6	1435	180
7	2320	180
8	2484	180
9	2697	180
10	2917	180
11	3221	180
12	3621	180
13	4112	180
14	4678	180
15	5362	180
16	6197	180
17	6591	180
18	6877	180
19	7153	180
20	7227	180
21	7263	180

Stop Event

1×	node limit

Counts

131 → 99

Calls

Call 1

Inputs
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 -707281/11664 x)
(*.f64 -707281/11664 x)
(*.f64 -707281/11664 x)
(*.f64 -707281/11664 x)
(*.f64 -707281/11664 x)
(*.f64 -707281/11664 x)
(*.f64 -707281/11664 x)
(*.f64 -707281/11664 x)
(*.f64 -707281/11664 x)
(*.f64 -707281/11664 x)
(*.f64 -707281/11664 x)
(*.f64 -707281/11664 x)
(*.f64 -707281/11664 (pow.f64 x 2))
(*.f64 -707281/11664 (pow.f64 x 2))
(*.f64 -707281/11664 (pow.f64 x 2))
(*.f64 -707281/11664 (pow.f64 x 2))
(*.f64 -707281/11664 (pow.f64 x 2))
(*.f64 -707281/11664 (pow.f64 x 2))
(*.f64 -707281/11664 (pow.f64 x 2))
(*.f64 -707281/11664 (pow.f64 x 2))
(*.f64 -707281/11664 (pow.f64 x 2))
(*.f64 -707281/11664 (pow.f64 x 2))
(*.f64 -707281/11664 (pow.f64 x 2))
(*.f64 -707281/11664 (pow.f64 x 2))

Outputs
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 841/108 x)
(*.f64 -707281/11664 x)
(*.f64 x -707281/11664)
(*.f64 -707281/11664 x)
(*.f64 x -707281/11664)
(*.f64 -707281/11664 x)
(*.f64 x -707281/11664)
(*.f64 -707281/11664 x)
(*.f64 x -707281/11664)
(*.f64 -707281/11664 x)
(*.f64 x -707281/11664)
(*.f64 -707281/11664 x)
(*.f64 x -707281/11664)
(*.f64 -707281/11664 x)
(*.f64 x -707281/11664)
(*.f64 -707281/11664 x)
(*.f64 x -707281/11664)
(*.f64 -707281/11664 x)
(*.f64 x -707281/11664)
(*.f64 -707281/11664 x)
(*.f64 x -707281/11664)
(*.f64 -707281/11664 x)
(*.f64 x -707281/11664)
(*.f64 -707281/11664 x)
(*.f64 x -707281/11664)
(*.f64 -707281/11664 (pow.f64 x 2))
(.f64 -707281/11664 (.f64 x x))
(.f64 x (.f64 x -707281/11664))
(*.f64 -707281/11664 (pow.f64 x 2))
(.f64 -707281/11664 (.f64 x x))
(.f64 x (.f64 x -707281/11664))
(*.f64 -707281/11664 (pow.f64 x 2))
(.f64 -707281/11664 (.f64 x x))
(.f64 x (.f64 x -707281/11664))
(*.f64 -707281/11664 (pow.f64 x 2))
(.f64 -707281/11664 (.f64 x x))
(.f64 x (.f64 x -707281/11664))
(*.f64 -707281/11664 (pow.f64 x 2))
(.f64 -707281/11664 (.f64 x x))
(.f64 x (.f64 x -707281/11664))
(*.f64 -707281/11664 (pow.f64 x 2))
(.f64 -707281/11664 (.f64 x x))
(.f64 x (.f64 x -707281/11664))
(*.f64 -707281/11664 (pow.f64 x 2))
(.f64 -707281/11664 (.f64 x x))
(.f64 x (.f64 x -707281/11664))
(*.f64 -707281/11664 (pow.f64 x 2))
(.f64 -707281/11664 (.f64 x x))
(.f64 x (.f64 x -707281/11664))
(*.f64 -707281/11664 (pow.f64 x 2))
(.f64 -707281/11664 (.f64 x x))
(.f64 x (.f64 x -707281/11664))
(*.f64 -707281/11664 (pow.f64 x 2))
(.f64 -707281/11664 (.f64 x x))
(.f64 x (.f64 x -707281/11664))
(*.f64 -707281/11664 (pow.f64 x 2))
(.f64 -707281/11664 (.f64 x x))
(.f64 x (.f64 x -707281/11664))
(*.f64 -707281/11664 (pow.f64 x 2))
(.f64 -707281/11664 (.f64 x x))
(.f64 x (.f64 x -707281/11664))

eval85.0ms (1.6%)

Compiler: Compiled 1963 to 1476 computations (24.8% saved)

prune31.0ms (0.6%)

Pruning

12 alts after pruning (5 fresh and 7 done)

	Pruned	Kept	Total
New	190	4	194
Fresh	0	1	1
Picked	0	1	1
Done	2	6	8
Total	192	12	204

Error

Counts

204 → 12

Alt Table

Click to see full alt table

Status	Error	Program
	30.4b	(.f64 (.f64 x -707281/11664) -108/841)
✓	16.1b	(/.f64 (-.f64 16/841 (.f64 (.f64 x x) 707281/11664)) (-.f64 4/29 (*.f64 841/108 x)))
	46.1b	(.f64 (/.f64 (.f64 x x) -841/108) (/.f64 -707281/11664 x))
✓	30.3b	(/.f64 1 (/.f64 108/841 x))
	30.4b	(.f64 (/.f64 (.f64 x -707281/11664) x) (/.f64 x -841/108))
✓	20.9b	(/.f64 (+.f64 64/24389 (.f64 (pow.f64 x 3) 594823321/1259712)) (+.f64 (.f64 (.f64 x x) 707281/11664) (-.f64 16/841 (.f64 x 29/27))))
✓	46.3b	(/.f64 (.f64 x (.f64 x -707281/11664)) (*.f64 x -841/108))
✓	0.1b	(+.f64 (*.f64 841/108 x) 4/29)
✓	30.4b	(/.f64 1 (*.f64 (/.f64 1 x) 108/841))
✓	30.3b	(*.f64 841/108 x)
	30.3b	(.f64 (/.f64 x 1) (/.f64 (.f64 x -707281/11664) (*.f64 x -841/108)))
	33.0b	4/29

Compiler

Compiled 108 to 84 computations (22.2% saved)

regimes64.0ms (1.2%)

Counts

22 → 1

Calls

Call 1

Inputs
4/29
4/29
(*.f64 841/108 x)
(.f64 (.f64 x -707281/11664) -108/841)
(/.f64 1 (/.f64 108/841 x))
(+.f64 (*.f64 841/108 x) 4/29)
(/.f64 1 (*.f64 (/.f64 1 x) 108/841))
(.f64 (/.f64 (.f64 x x) -841/108) (/.f64 -707281/11664 x))
(.f64 (/.f64 (.f64 x -707281/11664) x) (/.f64 x -841/108))
(/.f64 (.f64 x (.f64 x -707281/11664)) (*.f64 x -841/108))
(+.f64 (*.f64 (/.f64 841 108) x) (/.f64 4 29))
(.f64 (/.f64 x 1) (/.f64 (.f64 x -707281/11664) (*.f64 x -841/108)))
(/.f64 (-.f64 16/841 (.f64 (.f64 x x) 707281/11664)) (*.f64 x -841/108))
(/.f64 (-.f64 16/841 (.f64 (.f64 x x) 707281/11664)) (-.f64 4/29 (*.f64 841/108 x)))
(fma.f64 841/108 x 4/29)
(/.f64 1 (/.f64 (fma.f64 841/108 x -4/29) (+.f64 (.f64 (.f64 x x) 707281/11664) -16/841)))
(/.f64 (+.f64 64/24389 (.f64 (pow.f64 x 3) 594823321/1259712)) (+.f64 (.f64 (.f64 x x) 707281/11664) (-.f64 16/841 (.f64 x 29/27))))
(*.f64 (pow.f64 (cbrt.f64 841/108) 3) x)
(pow.f64 (cbrt.f64 (*.f64 841/108 x)) 3)
(+.f64 (pow.f64 (cbrt.f64 (*.f64 841/108 x)) 3) (/.f64 4 29))
(+.f64 (pow.f64 (sqrt.f64 (*.f64 841/108 x)) 2) (/.f64 4 29))
(fma.f64 (sqrt.f64 x) (sqrt.f64 (*.f64 x 707281/11664)) 4/29)

Outputs
(fma.f64 841/108 x 4/29)

Calls

5 calls:

19.0ms	x
12.0ms	(*.f64 (/.f64 841 108) x)
12.0ms	(*.f64 (/.f64 841 108) x)
7.0ms	(+.f64 (*.f64 (/.f64 841 108) x) (/.f64 4 29))
7.0ms	(+.f64 (*.f64 (/.f64 841 108) x) (/.f64 4 29))

Results

Error	Segments	Branch
0.1b	1	`x`
0.1b	1	`(+.f64 (*.f64 (/.f64 841 108) x) (/.f64 4 29))`
0.1b	1	`(+.f64 (*.f64 (/.f64 841 108) x) (/.f64 4 29))`
0.1b	1	`(*.f64 (/.f64 841 108) x)`
0.1b	1	`(*.f64 (/.f64 841 108) x)`

Compiler

Compiled 210 to 163 computations (22.4% saved)

regimes40.0ms (0.8%)

Counts

14 → 1

Calls

Call 1

Inputs
4/29
4/29
(*.f64 841/108 x)
(.f64 (.f64 x -707281/11664) -108/841)
(/.f64 1 (/.f64 108/841 x))
(+.f64 (*.f64 841/108 x) 4/29)
(/.f64 1 (*.f64 (/.f64 1 x) 108/841))
(.f64 (/.f64 (.f64 x x) -841/108) (/.f64 -707281/11664 x))
(.f64 (/.f64 (.f64 x -707281/11664) x) (/.f64 x -841/108))
(/.f64 (.f64 x (.f64 x -707281/11664)) (*.f64 x -841/108))
(+.f64 (*.f64 (/.f64 841 108) x) (/.f64 4 29))
(.f64 (/.f64 x 1) (/.f64 (.f64 x -707281/11664) (*.f64 x -841/108)))
(/.f64 (-.f64 16/841 (.f64 (.f64 x x) 707281/11664)) (*.f64 x -841/108))
(/.f64 (-.f64 16/841 (.f64 (.f64 x x) 707281/11664)) (-.f64 4/29 (*.f64 841/108 x)))

Outputs
(+.f64 (*.f64 841/108 x) 4/29)

Calls

5 calls:

9.0ms	(*.f64 (/.f64 841 108) x)
8.0ms	(*.f64 (/.f64 841 108) x)
7.0ms	x
6.0ms	(+.f64 (*.f64 (/.f64 841 108) x) (/.f64 4 29))
5.0ms	(+.f64 (*.f64 (/.f64 841 108) x) (/.f64 4 29))

Results

Error	Segments	Branch
0.1b	1	`x`
0.1b	1	`(+.f64 (*.f64 (/.f64 841 108) x) (/.f64 4 29))`
0.1b	1	`(+.f64 (*.f64 (/.f64 841 108) x) (/.f64 4 29))`
0.1b	1	`(*.f64 (/.f64 841 108) x)`
0.1b	1	`(*.f64 (/.f64 841 108) x)`

Compiler

Compiled 133 to 102 computations (23.3% saved)

regimes26.0ms (0.5%)

Counts

5 → 3

Calls

Call 1

Inputs
4/29
4/29
(*.f64 841/108 x)
(.f64 (.f64 x -707281/11664) -108/841)
(/.f64 1 (/.f64 108/841 x))

Outputs
(*.f64 841/108 x)
4/29
(*.f64 841/108 x)

Calls

1 calls:

25.0ms

Results

Error	Segments	Branch
1.6b	3	`x`

Compiler

Compiled 18 to 14 computations (22.2% saved)

bsearch35.0ms (0.7%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
17.0ms	2.2078869502073876e-9	2318408269.198578
18.0ms	-2.9621526934651756	-0.0018559628785769838

Compiler

Compiled 14 to 12 computations (14.3% saved)

regimes5.0ms (0.1%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0.0b (-0%)

Counts

2 → 1

Calls

Call 1

Inputs
4/29
4/29

Outputs
4/29

Calls

1 calls:

3.0ms

Results

Error	Segments	Branch
33.0b	1	`x`

Compiler

Compiled 5 to 4 computations (20% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	34
1	16	34

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(fma.f64 841/108 x 4/29)
(+.f64 (*.f64 841/108 x) 4/29)
(if (<=.f64 x -3335087441626069/1125899906842624) (.f64 841/108 x) (if (<=.f64 x 1334585770447955/604462909807314587353088) 4/29 (.f64 841/108 x)))
4/29

Outputs
(fma.f64 841/108 x 4/29)
(+.f64 (*.f64 841/108 x) 4/29)
(+.f64 4/29 (*.f64 841/108 x))
(if (<=.f64 x -3335087441626069/1125899906842624) (.f64 841/108 x) (if (<=.f64 x 1334585770447955/604462909807314587353088) 4/29 (.f64 841/108 x)))
4/29

Compiler

Compiled 29 to 23 computations (20.7% saved)

soundness10.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	5
1	15	5
2	16	5

Stop Event

1×

saturated

Compiler

Compiled 31 to 27 computations (12.9% saved)

end32.0ms (0.6%)

Compiler: Compiled 26 to 20 computations (23.1% saved)

Details

analyze4.0ms (0.1%)

sample1.7s (33.6%)

preprocess42.0ms (0.8%)

simplify7.0ms (0.1%)

eval1.0ms (0%)

prune2.0ms (0%)

localize21.0ms (0.4%)

series3.0ms (0.1%)

rewrite62.0ms (1.2%)

simplify10.0ms (0.2%)

localize4.0ms (0.1%)

series1.0ms (0%)

rewrite58.0ms (1.1%)

simplify49.0ms (1%)

eval21.0ms (0.4%)

prune21.0ms (0.4%)

localize5.0ms (0.1%)

series2.0ms (0%)

rewrite97.0ms (1.9%)

simplify9.0ms (0.2%)

localize16.0ms (0.3%)

localize16.0ms (0.3%)

series4.0ms (0.1%)

rewrite177.0ms (3.4%)

simplify196.0ms (3.8%)

localize19.0ms (0.4%)

series49.0ms (0.9%)

rewrite134.0ms (2.6%)

simplify64.0ms (1.2%)

localize32.0ms (0.6%)

series6.0ms (0.1%)

rewrite96.0ms (1.9%)

simplify183.0ms (3.6%)

eval444.0ms (8.6%)

prune102.0ms (2%)

localize12.0ms (0.2%)

series5.0ms (0.1%)

rewrite75.0ms (1.5%)

simplify9.0ms (0.2%)

localize14.0ms (0.3%)

series3.0ms (0.1%)

rewrite116.0ms (2.2%)

simplify66.0ms (1.3%)

localize11.0ms (0.2%)

series6.0ms (0.1%)

rewrite53.0ms (1%)

simplify8.0ms (0.1%)

localize12.0ms (0.2%)

series7.0ms (0.1%)

rewrite67.0ms (1.3%)

simplify9.0ms (0.2%)

eval191.0ms (3.7%)

prune64.0ms (1.2%)

localize10.0ms (0.2%)

series1.0ms (0%)

rewrite49.0ms (0.9%)

simplify8.0ms (0.2%)

localize9.0ms (0.2%)

series2.0ms (0%)

rewrite57.0ms (1.1%)

simplify10.0ms (0.2%)

localize11.0ms (0.2%)

series6.0ms (0.1%)

rewrite74.0ms (1.4%)

simplify178.0ms (3.5%)

eval85.0ms (1.6%)

prune31.0ms (0.6%)

regimes64.0ms (1.2%)

regimes40.0ms (0.8%)

regimes26.0ms (0.5%)

bsearch35.0ms (0.7%)

regimes5.0ms (0.1%)

simplify5.0ms (0.1%)

soundness10.0ms (0.2%)

end32.0ms (0.6%)

Profiling