Details

analyze6.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	37.5%	12.5%	4
62.5%	18.7%	18.8%	5
68.7%	9.4%	21.9%	6
71.8%	4.7%	23.5%	7
73.4%	2.3%	24.3%	8
74.2%	1.2%	24.6%	9
74.6%	0.6%	24.8%	10
74.8%	0.3%	24.9%	11
74.9%	0.1%	25%	12
74.9%	0.1%	25.1%	13
74.9%	0%	25.1%	14

Compiler

Compiled 15 to 12 computations (20% saved)

sample875.0ms (25.9%)

Results

862.0ms	8256×	body	128	valid
0.0ms	2×	body	128	invalid

preprocess57.0ms (1.7%)

Algorithm

2×	egg-herbie

Rules

972×	`fma-def_binary64`
722×	`fma-neg_binary64`
154×	`cancel-sign-sub-inv_binary64`
107×	`distribute-rgt-in_binary64`
80×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	19
1	33	14
2	76	12
3	182	12
4	377	9
5	542	9
6	869	9
7	1535	9
8	2446	9
9	2827	9
10	2939	9
11	3065	9
12	3071	9
13	3071	9
0	1	1

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0

Outputs
0

Call 2

Inputs
(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))

Outputs
(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))
(.f64 3 (+.f64 (fma.f64 (.f64 3 x) x (neg.f64 (*.f64 x 4))) 1))
(fma.f64 3 (.f64 x (-.f64 (.f64 3 x) 4)) 3)
(*.f64 3 (fma.f64 x (fma.f64 3 x -4) 1))
(fma.f64 (*.f64 x x) 9 (fma.f64 x -12 3))
(fma.f64 x (fma.f64 x 9 -12) 3)

Compiler

Compiled 14 to 11 computations (21.4% saved)

simplify45.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

972×	`fma-def_binary64`
722×	`fma-neg_binary64`
154×	`cancel-sign-sub-inv_binary64`
107×	`distribute-rgt-in_binary64`
80×	`associate-l_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	11	19
1	33	14
2	76	12
3	182	12
4	377	9
5	542	9
6	869	9
7	1535	9
8	2446	9
9	2827	9
10	2939	9
11	3065	9
12	3071	9
13	3071	9

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

Inputs
(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))

Outputs
(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))
(.f64 3 (+.f64 (fma.f64 (.f64 3 x) x (neg.f64 (*.f64 x 4))) 1))
(fma.f64 3 (.f64 x (-.f64 (.f64 3 x) 4)) 3)
(*.f64 3 (fma.f64 x (fma.f64 3 x -4) 1))
(fma.f64 (*.f64 x x) 9 (fma.f64 x -12 3))
(fma.f64 x (fma.f64 x 9 -12) 3)

eval1.0ms (0%)

Compiler: Compiled 21 to 16 computations (23.8% saved)

prune2.0ms (0.1%)

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

0.0b

Counts

3 → 2

Alt Table

Click to see full alt table

Status	Error	Program
	0.1b	(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))
▶	0.1b	(fma.f64 x (fma.f64 x 9 -12) 3)

Compiler

Compiled 44 to 34 computations (22.7% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x 9 -12)
✓	0.1b	(fma.f64 x (fma.f64 x 9 -12) 3)

series3.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(fma.f64 x (fma.f64 x 9 -12) 3)
1.0ms	x	@	-inf	(fma.f64 x (fma.f64 x 9 -12) 3)
0.0ms	x	@	inf	(fma.f64 x (fma.f64 x 9 -12) 3)
0.0ms	x	@	-inf	(fma.f64 x 9 -12)
0.0ms	x	@	inf	(fma.f64 x 9 -12)

rewrite34.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

607×	`pow1_binary64`
568×	`add-log-exp_binary64`
568×	`log1p-expm1-u_binary64`
568×	`expm1-log1p-u_binary64`
66×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	14
1	142	14
2	1495	14

Stop Event

1×	node limit

Counts

2 → 44

Calls

Call 1

Inputs
(fma.f64 x (fma.f64 x 9 -12) 3)
(fma.f64 x 9 -12)

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 3 (.f64 x (fma.f64 x 9 -12)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 x (fma.f64 x 9 -12)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (.f64 x (fma.f64 x 9 -12)) 1) 3)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 x (fma.f64 x 9 -12) 3))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fma.f64 x (fma.f64 x 9 -12) 3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (fma.f64 x (fma.f64 x 9 -12) 3))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (fma.f64 x (fma.f64 x 9 -12) 3)) (pow.f64 (cbrt.f64 (fma.f64 x (fma.f64 x 9 -12) 3)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (fma.f64 x (fma.f64 x 9 -12) 3)) 2) (cbrt.f64 (fma.f64 x (fma.f64 x 9 -12) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (fma.f64 x (fma.f64 x 9 -12) 3)) (sqrt.f64 (fma.f64 x (fma.f64 x 9 -12) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (.f64 x (fma.f64 x 9 -12)) 3) 27) (+.f64 (.f64 (.f64 x (fma.f64 x 9 -12)) (.f64 x (fma.f64 x 9 -12))) (-.f64 9 (.f64 (.f64 x (fma.f64 x 9 -12)) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 (.f64 x (fma.f64 x 9 -12)) (.f64 x (fma.f64 x 9 -12))) 9) (-.f64 (*.f64 x (fma.f64 x 9 -12)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 x (fma.f64 x 9 -12) 3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x (fma.f64 x 9 -12) 3) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 x (fma.f64 x 9 -12) 3)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 x (fma.f64 x 9 -12) 3)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 x (fma.f64 x 9 -12) 3) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 x (fma.f64 x 9 -12) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 x (fma.f64 x 9 -12) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 x (fma.f64 x 9 -12) 3) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 x (fma.f64 x 9 -12) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 x (fma.f64 x 9 -12) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 x (fma.f64 x 9 -12) 3)))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 -12 (.f64 x 9))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 x 9) -12)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (.f64 x 9) 1) -12)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 x 9 -12))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fma.f64 x 9 -12) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (fma.f64 x 9 -12))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (fma.f64 x 9 -12)) (pow.f64 (cbrt.f64 (fma.f64 x 9 -12)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (fma.f64 x 9 -12)) 2) (cbrt.f64 (fma.f64 x 9 -12)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (fma.f64 x 9 -12)) (sqrt.f64 (fma.f64 x 9 -12)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (.f64 x 9) 3) -1728) (+.f64 (.f64 (.f64 x 9) (.f64 x 9)) (-.f64 144 (.f64 (.f64 x 9) -12))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 (.f64 x 9) (.f64 x 9)) 144) (-.f64 (*.f64 x 9) -12))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 x 9 -12) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x 9 -12) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 x 9 -12)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 x 9 -12)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 x 9 -12) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 x 9 -12)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 x 9 -12))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 x 9 -12) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 x 9 -12)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 x 9 -12)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 x 9 -12)))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 3 (*.f64 x (fma.f64 x 9 -12)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x (fma.f64 x 9 -12)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 x (fma.f64 x 9 -12)) 1) 3)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 x (fma.f64 x 9 -12) 3))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 x (fma.f64 x 9 -12) 3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 x (fma.f64 x 9 -12) 3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 x (fma.f64 x 9 -12) 3)) (pow.f64 (cbrt.f64 (fma.f64 x (fma.f64 x 9 -12) 3)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 x (fma.f64 x 9 -12) 3)) 2) (cbrt.f64 (fma.f64 x (fma.f64 x 9 -12) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 x (fma.f64 x 9 -12) 3)) (sqrt.f64 (fma.f64 x (fma.f64 x 9 -12) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 x (fma.f64 x 9 -12)) 3) 27) (+.f64 (*.f64 (*.f64 x (fma.f64 x 9 -12)) (*.f64 x (fma.f64 x 9 -12))) (-.f64 9 (*.f64 (*.f64 x (fma.f64 x 9 -12)) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 x (fma.f64 x 9 -12)) (*.f64 x (fma.f64 x 9 -12))) 9) (-.f64 (*.f64 x (fma.f64 x 9 -12)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 x (fma.f64 x 9 -12) 3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x (fma.f64 x 9 -12) 3) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 x (fma.f64 x 9 -12) 3)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 x (fma.f64 x 9 -12) 3)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 x (fma.f64 x 9 -12) 3) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 x (fma.f64 x 9 -12) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 x (fma.f64 x 9 -12) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 x (fma.f64 x 9 -12) 3) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 x (fma.f64 x 9 -12) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 x (fma.f64 x 9 -12) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 x (fma.f64 x 9 -12) 3)))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 -12 (*.f64 x 9))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x 9) -12)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 x 9) 1) -12)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 x 9 -12))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 x 9 -12) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 x 9 -12))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 x 9 -12)) (pow.f64 (cbrt.f64 (fma.f64 x 9 -12)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 x 9 -12)) 2) (cbrt.f64 (fma.f64 x 9 -12)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 x 9 -12)) (sqrt.f64 (fma.f64 x 9 -12)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 x 9) 3) -1728) (+.f64 (*.f64 (*.f64 x 9) (*.f64 x 9)) (-.f64 144 (*.f64 (*.f64 x 9) -12))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 x 9) (*.f64 x 9)) 144) (-.f64 (*.f64 x 9) -12))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 x 9 -12) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x 9 -12) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 x 9 -12)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 x 9 -12)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 x 9 -12) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 x 9 -12)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 x 9 -12))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 x 9 -12) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 x 9 -12)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 x 9 -12)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 x 9 -12)))))))

simplify71.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

532×	`associate-l_binary64`
494×	`fma-def_binary64`
434×	`unswap-sqr_binary64`
370×	`sqr-pow_binary64`
327×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	16	180
1	35	168
2	56	156
3	88	144
4	192	144
5	531	144
6	1764	144
7	3092	144
8	3297	144
9	3509	144
10	3729	144
11	4037	144
12	4437	144
13	4947	144

Stop Event

1×	node limit

Counts

68 → 58

Calls

Call 1

Inputs
3
(+.f64 (*.f64 -12 x) 3)
(+.f64 (.f64 -12 x) (+.f64 3 (.f64 9 (pow.f64 x 2))))
(+.f64 (.f64 -12 x) (+.f64 3 (.f64 9 (pow.f64 x 2))))
(*.f64 9 (pow.f64 x 2))
(+.f64 (.f64 -12 x) (.f64 9 (pow.f64 x 2)))
(+.f64 (.f64 -12 x) (+.f64 3 (.f64 9 (pow.f64 x 2))))
(+.f64 (.f64 -12 x) (+.f64 3 (.f64 9 (pow.f64 x 2))))
(*.f64 9 (pow.f64 x 2))
(+.f64 (.f64 -12 x) (.f64 9 (pow.f64 x 2)))
(+.f64 (.f64 -12 x) (+.f64 3 (.f64 9 (pow.f64 x 2))))
(+.f64 (.f64 -12 x) (+.f64 3 (.f64 9 (pow.f64 x 2))))
-12
(-.f64 (*.f64 9 x) 12)
(-.f64 (*.f64 9 x) 12)
(-.f64 (*.f64 9 x) 12)
(*.f64 9 x)
(-.f64 (*.f64 9 x) 12)
(-.f64 (*.f64 9 x) 12)
(-.f64 (*.f64 9 x) 12)
(*.f64 9 x)
(-.f64 (*.f64 9 x) 12)
(-.f64 (*.f64 9 x) 12)
(-.f64 (*.f64 9 x) 12)

Outputs
3
(+.f64 (*.f64 -12 x) 3)
(fma.f64 -12 x 3)
(+.f64 (.f64 -12 x) (+.f64 3 (.f64 9 (pow.f64 x 2))))
(+.f64 (fma.f64 -12 x 3) (.f64 9 (.f64 x x)))
(fma.f64 -12 x (fma.f64 9 (*.f64 x x) 3))
(+.f64 3 (*.f64 x (fma.f64 x 9 -12)))
(fma.f64 x (fma.f64 x 9 -12) 3)
(+.f64 (.f64 -12 x) (+.f64 3 (.f64 9 (pow.f64 x 2))))
(+.f64 (fma.f64 -12 x 3) (.f64 9 (.f64 x x)))
(fma.f64 -12 x (fma.f64 9 (*.f64 x x) 3))
(+.f64 3 (*.f64 x (fma.f64 x 9 -12)))
(fma.f64 x (fma.f64 x 9 -12) 3)
(*.f64 9 (pow.f64 x 2))
(.f64 9 (.f64 x x))
(.f64 x (.f64 x 9))
(+.f64 (.f64 -12 x) (.f64 9 (pow.f64 x 2)))
(fma.f64 -12 x (.f64 9 (.f64 x x)))
(fma.f64 9 (.f64 x x) (.f64 -12 x))
(*.f64 x (fma.f64 x 9 -12))
(+.f64 (.f64 -12 x) (+.f64 3 (.f64 9 (pow.f64 x 2))))
(+.f64 (fma.f64 -12 x 3) (.f64 9 (.f64 x x)))
(fma.f64 -12 x (fma.f64 9 (*.f64 x x) 3))
(+.f64 3 (*.f64 x (fma.f64 x 9 -12)))
(fma.f64 x (fma.f64 x 9 -12) 3)
(+.f64 (.f64 -12 x) (+.f64 3 (.f64 9 (pow.f64 x 2))))
(+.f64 (fma.f64 -12 x 3) (.f64 9 (.f64 x x)))
(fma.f64 -12 x (fma.f64 9 (*.f64 x x) 3))
(+.f64 3 (*.f64 x (fma.f64 x 9 -12)))
(fma.f64 x (fma.f64 x 9 -12) 3)
(*.f64 9 (pow.f64 x 2))
(.f64 9 (.f64 x x))
(.f64 x (.f64 x 9))
(+.f64 (.f64 -12 x) (.f64 9 (pow.f64 x 2)))
(fma.f64 -12 x (.f64 9 (.f64 x x)))
(fma.f64 9 (.f64 x x) (.f64 -12 x))
(*.f64 x (fma.f64 x 9 -12))
(+.f64 (.f64 -12 x) (+.f64 3 (.f64 9 (pow.f64 x 2))))
(+.f64 (fma.f64 -12 x 3) (.f64 9 (.f64 x x)))
(fma.f64 -12 x (fma.f64 9 (*.f64 x x) 3))
(+.f64 3 (*.f64 x (fma.f64 x 9 -12)))
(fma.f64 x (fma.f64 x 9 -12) 3)
(+.f64 (.f64 -12 x) (+.f64 3 (.f64 9 (pow.f64 x 2))))
(+.f64 (fma.f64 -12 x 3) (.f64 9 (.f64 x x)))
(fma.f64 -12 x (fma.f64 9 (*.f64 x x) 3))
(+.f64 3 (*.f64 x (fma.f64 x 9 -12)))
(fma.f64 x (fma.f64 x 9 -12) 3)
-12
(-.f64 (*.f64 9 x) 12)
(fma.f64 9 x -12)
(fma.f64 x 9 -12)
(-.f64 (*.f64 9 x) 12)
(fma.f64 9 x -12)
(fma.f64 x 9 -12)
(-.f64 (*.f64 9 x) 12)
(fma.f64 9 x -12)
(fma.f64 x 9 -12)
(*.f64 9 x)
(*.f64 x 9)
(-.f64 (*.f64 9 x) 12)
(fma.f64 9 x -12)
(fma.f64 x 9 -12)
(-.f64 (*.f64 9 x) 12)
(fma.f64 9 x -12)
(fma.f64 x 9 -12)
(-.f64 (*.f64 9 x) 12)
(fma.f64 9 x -12)
(fma.f64 x 9 -12)
(*.f64 9 x)
(*.f64 x 9)
(-.f64 (*.f64 9 x) 12)
(fma.f64 9 x -12)
(fma.f64 x 9 -12)
(-.f64 (*.f64 9 x) 12)
(fma.f64 9 x -12)
(fma.f64 x 9 -12)
(-.f64 (*.f64 9 x) 12)
(fma.f64 9 x -12)
(fma.f64 x 9 -12)

eval25.0ms (0.7%)

Compiler: Compiled 613 to 479 computations (21.9% saved)

prune62.0ms (1.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	56	2	58
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	56	4	60

Error

0.0b

Counts

60 → 4

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.1b	(+.f64 (.f64 -12 x) (+.f64 3 (.f64 9 (pow.f64 x 2))))
	0.1b	(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))
✓	0.1b	(fma.f64 x (fma.f64 x 9 -12) 3)
	17.8b	(/.f64 (+.f64 (pow.f64 (.f64 x (fma.f64 x 9 -12)) 3) 27) (+.f64 (.f64 (.f64 x (fma.f64 x 9 -12)) (.f64 x (fma.f64 x 9 -12))) (-.f64 9 (.f64 (.f64 x (fma.f64 x 9 -12)) 3))))

Compiler

Compiled 132 to 104 computations (21.2% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 -12 x) (+.f64 3 (.f64 9 (pow.f64 x 2))))
✓	0.3b	(*.f64 9 (pow.f64 x 2))

series3.0ms (0.1%)

Counts

2 → 6

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(*.f64 9 (pow.f64 x 2))
1.0ms	x	@	inf	(*.f64 9 (pow.f64 x 2))
0.0ms	x	@	inf	(+.f64 (.f64 -12 x) (+.f64 3 (.f64 9 (pow.f64 x 2))))
0.0ms	x	@	0	(+.f64 (.f64 -12 x) (+.f64 3 (.f64 9 (pow.f64 x 2))))
0.0ms	x	@	-inf	(*.f64 9 (pow.f64 x 2))

rewrite51.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

479×	`log-prod_binary64`
408×	`fma-def_binary64`
228×	`fma-neg_binary64`
200×	`expm1-udef_binary64`
200×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	21
1	247	19
2	3065	19

Stop Event

1×	node limit

Counts

2 → 89

Calls

Call 1

Inputs
(*.f64 9 (pow.f64 x 2))
(+.f64 (.f64 -12 x) (+.f64 3 (.f64 9 (pow.f64 x 2))))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 9 (.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 x) x) 9)) (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 x) x) 9)))) (log.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 x) x) 9))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (pow.f64 (exp.f64 x) x) 9))) (log.f64 (sqrt.f64 (pow.f64 (pow.f64 (exp.f64 x) x) 9))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 9 (.f64 x x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 9 (.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 9 (.f64 x x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 x 3) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 (.f64 x x) 3) 729) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (.f64 (pow.f64 x 4) 81))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (pow.f64 (exp.f64 x) x) 9))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 9 (.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (.f64 x x) 3) 729))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 9 (.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 9 (.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 9 (.f64 x x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 9 (.f64 x x))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 x -12 (fma.f64 9 (.f64 x x) 3)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (.f64 (.f64 x x) 144) (-.f64 (.f64 x -12) (fma.f64 9 (.f64 x x) 3))) (/.f64 (pow.f64 (fma.f64 9 (.f64 x x) 3) 2) (-.f64 (.f64 x -12) (fma.f64 9 (.f64 x x) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fma.f64 x -12 (fma.f64 9 (.f64 x x) 3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (fma.f64 x -12 (fma.f64 9 (.f64 x x) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (fma.f64 x -12 (fma.f64 9 (.f64 x x) 3))) (pow.f64 (cbrt.f64 (fma.f64 x -12 (fma.f64 9 (.f64 x x) 3))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (fma.f64 x -12 (fma.f64 9 (.f64 x x) 3))) 2) (cbrt.f64 (fma.f64 x -12 (fma.f64 9 (.f64 x x) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (hypot.f64 (.f64 x 3) (sqrt.f64 (fma.f64 x -12 3))) (hypot.f64 (.f64 x 3) (sqrt.f64 (fma.f64 x -12 3))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fma.f64 (pow.f64 x 3) -1728 (pow.f64 (fma.f64 9 (.f64 x x) 3) 3)) (/.f64 1 (fma.f64 (fma.f64 9 (.f64 x x) 3) (-.f64 (fma.f64 9 (.f64 x x) 3) (.f64 x -12)) (.f64 (.f64 x x) 144))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 (.f64 (.f64 x x) 144) (pow.f64 (fma.f64 9 (.f64 x x) 3) 2)) (/.f64 1 (-.f64 (.f64 x -12) (fma.f64 9 (.f64 x x) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 (fma.f64 9 (.f64 x x) 3) (-.f64 (fma.f64 9 (.f64 x x) 3) (.f64 x -12)) (.f64 (.f64 x x) 144)) (fma.f64 (pow.f64 x 3) -1728 (pow.f64 (fma.f64 9 (.f64 x x) 3) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (.f64 x -12) (fma.f64 9 (.f64 x x) 3)) (-.f64 (.f64 (.f64 x x) 144) (pow.f64 (fma.f64 9 (.f64 x x) 3) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 (pow.f64 x 3) -1728 (pow.f64 (fma.f64 9 (.f64 x x) 3) 3)) (fma.f64 (fma.f64 9 (.f64 x x) 3) (-.f64 (fma.f64 9 (.f64 x x) 3) (.f64 x -12)) (.f64 (.f64 x x) 144)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 (pow.f64 x 3) -1728 (pow.f64 (fma.f64 9 (.f64 x x) 3) 3)) (+.f64 (pow.f64 (fma.f64 9 (.f64 x x) 3) 2) (-.f64 (.f64 (.f64 x x) 144) (.f64 x (.f64 -12 (fma.f64 9 (.f64 x x) 3))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 (.f64 x x) 144) (pow.f64 (fma.f64 9 (.f64 x x) 3) 2)) (-.f64 (.f64 x -12) (fma.f64 9 (.f64 x x) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (fma.f64 (pow.f64 x 3) -1728 (pow.f64 (fma.f64 9 (.f64 x x) 3) 3))) (neg.f64 (fma.f64 (fma.f64 9 (.f64 x x) 3) (-.f64 (fma.f64 9 (.f64 x x) 3) (.f64 x -12)) (.f64 (.f64 x x) 144))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (.f64 (.f64 x x) 144) (pow.f64 (fma.f64 9 (.f64 x x) 3) 2))) (neg.f64 (-.f64 (.f64 x -12) (fma.f64 9 (.f64 x x) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (fma.f64 x -12 3) 3) (.f64 (pow.f64 (.f64 x x) 3) 729)) (fma.f64 (fma.f64 x -12 3) (fma.f64 x -12 3) (-.f64 (.f64 (pow.f64 x 4) 81) (.f64 (fma.f64 x -12 3) (.f64 9 (.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (fma.f64 9 (.f64 x x) 3) 2) (.f64 (.f64 x x) 144)) (-.f64 (fma.f64 9 (.f64 x x) 3) (.f64 x -12)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 (fma.f64 x -12 3) (fma.f64 x -12 3)) (.f64 (pow.f64 x 4) 81)) (-.f64 (fma.f64 x -12 3) (.f64 9 (.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 x -12 (fma.f64 9 (.f64 x x) 3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x -12 (fma.f64 9 (.f64 x x) 3)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 x -12 (fma.f64 9 (.f64 x x) 3))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 (.f64 x 3) (sqrt.f64 (fma.f64 x -12 3))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 x -12 (fma.f64 9 (.f64 x x) 3)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 x -12 (fma.f64 9 (.f64 x x) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 x -12 (fma.f64 9 (.f64 x x) 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (pow.f64 (pow.f64 (exp.f64 x) x) 9) (exp.f64 (fma.f64 x -12 3))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (+.f64 1 (expm1.f64 (.f64 9 (.f64 x x)))) (exp.f64 (fma.f64 x -12 3))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (+.f64 1 (expm1.f64 (.f64 x -12))) (exp.f64 (fma.f64 9 (.f64 x x) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (pow.f64 (exp.f64 x) -12) (+.f64 1 (expm1.f64 (fma.f64 9 (.f64 x x) 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (+.f64 1 (expm1.f64 (.f64 x -12))) (+.f64 1 (expm1.f64 (fma.f64 9 (.f64 x x) 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (+.f64 1 (expm1.f64 (fma.f64 9 (.f64 x x) 3))) (pow.f64 (exp.f64 x) -12)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (exp.f64 (fma.f64 9 (.f64 x x) 3)) (+.f64 1 (expm1.f64 (.f64 x -12)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (+.f64 1 (expm1.f64 (fma.f64 9 (.f64 x x) 3))) (+.f64 1 (expm1.f64 (.f64 x -12)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (exp.f64 (fma.f64 x -12 3)) (+.f64 1 (expm1.f64 (.f64 9 (.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 x -12 (fma.f64 9 (.f64 x x) 3)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 x -12 (fma.f64 9 (.f64 x x) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 x -12 (fma.f64 9 (.f64 x x) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (fma.f64 x -12 (fma.f64 9 (.f64 x x) 3))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 9 (.f64 x x) (fma.f64 x -12 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x -12 (fma.f64 9 (.f64 x x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x (.f64 x 9) (fma.f64 x -12 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 x x) 9 (fma.f64 x -12 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 9 (.f64 x x)) 1 (fma.f64 x -12 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -12 x (fma.f64 9 (.f64 x x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 x -12) 1 (fma.f64 9 (.f64 x x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 9 (.f64 x x) 3) 1 (.f64 x -12))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (.f64 9 (.f64 x x)) (fma.f64 x -12 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (.f64 x -12) (fma.f64 9 (.f64 x x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 9 (.f64 x x) 3) (.f64 x -12))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 x -12 3) (.f64 9 (.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (.f64 x -12)) (cbrt.f64 (.f64 (.f64 x x) 144)) (fma.f64 9 (.f64 x x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (.f64 (.f64 x x) 144)) (cbrt.f64 (.f64 x -12)) (fma.f64 9 (.f64 x x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (.f64 x x)) (.f64 (cbrt.f64 x) -12) (fma.f64 9 (.f64 x x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x 4)) (.f64 (cbrt.f64 (.f64 x x)) 9) (fma.f64 x -12 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (.f64 9 (.f64 x x))) (cbrt.f64 (.f64 (pow.f64 x 4) 81)) (fma.f64 x -12 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (.f64 (pow.f64 x 4) 81)) (cbrt.f64 (.f64 9 (.f64 x x))) (fma.f64 x -12 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (fma.f64 9 (.f64 x x) 3)) (cbrt.f64 (pow.f64 (fma.f64 9 (.f64 x x) 3) 2)) (.f64 x -12))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 (fma.f64 9 (.f64 x x) 3) 2)) (cbrt.f64 (fma.f64 9 (.f64 x x) 3)) (.f64 x -12))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (.f64 x -12)) (sqrt.f64 (.f64 x -12)) (fma.f64 9 (.f64 x x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 x 3) (.f64 x 3) (fma.f64 x -12 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) -12) (fma.f64 9 (.f64 x x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (fma.f64 9 (.f64 x x) 3)) (sqrt.f64 (fma.f64 9 (.f64 x x) 3)) (.f64 x -12))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 (pow.f64 (.f64 x x) 3) 729 27) (/.f64 1 (fma.f64 (.f64 9 (.f64 x x)) (fma.f64 9 (.f64 x x) -3) 9)) (.f64 x -12))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 9 (.f64 (pow.f64 x 4) 81)) (/.f64 1 (+.f64 3 (.f64 -9 (.f64 x x)))) (.f64 x -12))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 x -12 3) 1 (.f64 9 (.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (cbrt.f64 (fma.f64 x -12 3)) (cbrt.f64 (fma.f64 x -12 3))) (cbrt.f64 (fma.f64 x -12 3)) (.f64 9 (.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (fma.f64 x -12 3)) (sqrt.f64 (fma.f64 x -12 3)) (.f64 9 (.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 -12 (cbrt.f64 (.f64 x x))) (cbrt.f64 x) (fma.f64 9 (.f64 x x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 -12 (sqrt.f64 x)) (sqrt.f64 x) (fma.f64 9 (.f64 x x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 9 x) x (fma.f64 x -12 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 9 (cbrt.f64 (pow.f64 x 4))) (cbrt.f64 (.f64 x x)) (fma.f64 x -12 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 x -12 (fma.f64 9 (*.f64 x x) 3))))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 9 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 x) x) 9)) (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 x) x) 9)))) (log.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 x) x) 9))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (pow.f64 (exp.f64 x) x) 9))) (log.f64 (sqrt.f64 (pow.f64 (pow.f64 (exp.f64 x) x) 9))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 9 (*.f64 x x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 9 (*.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 9 (*.f64 x x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x 3) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (*.f64 x x) 3) 729) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 x 4) 81))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (pow.f64 (exp.f64 x) x) 9))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 9 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (*.f64 x x) 3) 729))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 9 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 9 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 9 (*.f64 x x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 9 (*.f64 x x))))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 x -12 (fma.f64 9 (*.f64 x x) 3)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (*.f64 (*.f64 x x) 144) (-.f64 (*.f64 x -12) (fma.f64 9 (*.f64 x x) 3))) (/.f64 (pow.f64 (fma.f64 9 (*.f64 x x) 3) 2) (-.f64 (*.f64 x -12) (fma.f64 9 (*.f64 x x) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 x -12 (fma.f64 9 (*.f64 x x) 3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 x -12 (fma.f64 9 (*.f64 x x) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 x -12 (fma.f64 9 (*.f64 x x) 3))) (pow.f64 (cbrt.f64 (fma.f64 x -12 (fma.f64 9 (*.f64 x x) 3))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 x -12 (fma.f64 9 (*.f64 x x) 3))) 2) (cbrt.f64 (fma.f64 x -12 (fma.f64 9 (*.f64 x x) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 (*.f64 x 3) (sqrt.f64 (fma.f64 x -12 3))) (hypot.f64 (*.f64 x 3) (sqrt.f64 (fma.f64 x -12 3))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 (pow.f64 x 3) -1728 (pow.f64 (fma.f64 9 (*.f64 x x) 3) 3)) (/.f64 1 (fma.f64 (fma.f64 9 (*.f64 x x) 3) (-.f64 (fma.f64 9 (*.f64 x x) 3) (*.f64 x -12)) (*.f64 (*.f64 x x) 144))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 (*.f64 x x) 144) (pow.f64 (fma.f64 9 (*.f64 x x) 3) 2)) (/.f64 1 (-.f64 (*.f64 x -12) (fma.f64 9 (*.f64 x x) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 (fma.f64 9 (*.f64 x x) 3) (-.f64 (fma.f64 9 (*.f64 x x) 3) (*.f64 x -12)) (*.f64 (*.f64 x x) 144)) (fma.f64 (pow.f64 x 3) -1728 (pow.f64 (fma.f64 9 (*.f64 x x) 3) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (*.f64 x -12) (fma.f64 9 (*.f64 x x) 3)) (-.f64 (*.f64 (*.f64 x x) 144) (pow.f64 (fma.f64 9 (*.f64 x x) 3) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 (pow.f64 x 3) -1728 (pow.f64 (fma.f64 9 (*.f64 x x) 3) 3)) (fma.f64 (fma.f64 9 (*.f64 x x) 3) (-.f64 (fma.f64 9 (*.f64 x x) 3) (*.f64 x -12)) (*.f64 (*.f64 x x) 144)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 (pow.f64 x 3) -1728 (pow.f64 (fma.f64 9 (*.f64 x x) 3) 3)) (+.f64 (pow.f64 (fma.f64 9 (*.f64 x x) 3) 2) (-.f64 (*.f64 (*.f64 x x) 144) (*.f64 x (*.f64 -12 (fma.f64 9 (*.f64 x x) 3))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 x x) 144) (pow.f64 (fma.f64 9 (*.f64 x x) 3) 2)) (-.f64 (*.f64 x -12) (fma.f64 9 (*.f64 x x) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (fma.f64 (pow.f64 x 3) -1728 (pow.f64 (fma.f64 9 (*.f64 x x) 3) 3))) (neg.f64 (fma.f64 (fma.f64 9 (*.f64 x x) 3) (-.f64 (fma.f64 9 (*.f64 x x) 3) (*.f64 x -12)) (*.f64 (*.f64 x x) 144))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (*.f64 (*.f64 x x) 144) (pow.f64 (fma.f64 9 (*.f64 x x) 3) 2))) (neg.f64 (-.f64 (*.f64 x -12) (fma.f64 9 (*.f64 x x) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (fma.f64 x -12 3) 3) (*.f64 (pow.f64 (*.f64 x x) 3) 729)) (fma.f64 (fma.f64 x -12 3) (fma.f64 x -12 3) (-.f64 (*.f64 (pow.f64 x 4) 81) (*.f64 (fma.f64 x -12 3) (*.f64 9 (*.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (fma.f64 9 (*.f64 x x) 3) 2) (*.f64 (*.f64 x x) 144)) (-.f64 (fma.f64 9 (*.f64 x x) 3) (*.f64 x -12)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (fma.f64 x -12 3) (fma.f64 x -12 3)) (*.f64 (pow.f64 x 4) 81)) (-.f64 (fma.f64 x -12 3) (*.f64 9 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 x -12 (fma.f64 9 (*.f64 x x) 3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x -12 (fma.f64 9 (*.f64 x x) 3)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 x -12 (fma.f64 9 (*.f64 x x) 3))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 (*.f64 x 3) (sqrt.f64 (fma.f64 x -12 3))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 x -12 (fma.f64 9 (*.f64 x x) 3)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 x -12 (fma.f64 9 (*.f64 x x) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 x -12 (fma.f64 9 (*.f64 x x) 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (pow.f64 (pow.f64 (exp.f64 x) x) 9) (exp.f64 (fma.f64 x -12 3))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (*.f64 9 (*.f64 x x)))) (exp.f64 (fma.f64 x -12 3))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (*.f64 x -12))) (exp.f64 (fma.f64 9 (*.f64 x x) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (pow.f64 (exp.f64 x) -12) (+.f64 1 (expm1.f64 (fma.f64 9 (*.f64 x x) 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (*.f64 x -12))) (+.f64 1 (expm1.f64 (fma.f64 9 (*.f64 x x) 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (fma.f64 9 (*.f64 x x) 3))) (pow.f64 (exp.f64 x) -12)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (fma.f64 9 (*.f64 x x) 3)) (+.f64 1 (expm1.f64 (*.f64 x -12)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (fma.f64 9 (*.f64 x x) 3))) (+.f64 1 (expm1.f64 (*.f64 x -12)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (fma.f64 x -12 3)) (+.f64 1 (expm1.f64 (*.f64 9 (*.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 x -12 (fma.f64 9 (*.f64 x x) 3)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 x -12 (fma.f64 9 (*.f64 x x) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 x -12 (fma.f64 9 (*.f64 x x) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (fma.f64 x -12 (fma.f64 9 (*.f64 x x) 3))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 9 (*.f64 x x) (fma.f64 x -12 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x -12 (fma.f64 9 (*.f64 x x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x (*.f64 x 9) (fma.f64 x -12 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x x) 9 (fma.f64 x -12 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 9 (*.f64 x x)) 1 (fma.f64 x -12 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -12 x (fma.f64 9 (*.f64 x x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x -12) 1 (fma.f64 9 (*.f64 x x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 9 (*.f64 x x) 3) 1 (*.f64 x -12))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 9 (*.f64 x x)) (fma.f64 x -12 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 x -12) (fma.f64 9 (*.f64 x x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 9 (*.f64 x x) 3) (*.f64 x -12))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 x -12 3) (*.f64 9 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 x -12)) (cbrt.f64 (*.f64 (*.f64 x x) 144)) (fma.f64 9 (*.f64 x x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 (*.f64 x x) 144)) (cbrt.f64 (*.f64 x -12)) (fma.f64 9 (*.f64 x x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 x x)) (*.f64 (cbrt.f64 x) -12) (fma.f64 9 (*.f64 x x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x 4)) (*.f64 (cbrt.f64 (*.f64 x x)) 9) (fma.f64 x -12 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 9 (*.f64 x x))) (cbrt.f64 (*.f64 (pow.f64 x 4) 81)) (fma.f64 x -12 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 (pow.f64 x 4) 81)) (cbrt.f64 (*.f64 9 (*.f64 x x))) (fma.f64 x -12 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (fma.f64 9 (*.f64 x x) 3)) (cbrt.f64 (pow.f64 (fma.f64 9 (*.f64 x x) 3) 2)) (*.f64 x -12))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 (fma.f64 9 (*.f64 x x) 3) 2)) (cbrt.f64 (fma.f64 9 (*.f64 x x) 3)) (*.f64 x -12))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 x -12)) (sqrt.f64 (*.f64 x -12)) (fma.f64 9 (*.f64 x x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x 3) (*.f64 x 3) (fma.f64 x -12 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) -12) (fma.f64 9 (*.f64 x x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (fma.f64 9 (*.f64 x x) 3)) (sqrt.f64 (fma.f64 9 (*.f64 x x) 3)) (*.f64 x -12))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 (pow.f64 (*.f64 x x) 3) 729 27) (/.f64 1 (fma.f64 (*.f64 9 (*.f64 x x)) (fma.f64 9 (*.f64 x x) -3) 9)) (*.f64 x -12))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 9 (*.f64 (pow.f64 x 4) 81)) (/.f64 1 (+.f64 3 (*.f64 -9 (*.f64 x x)))) (*.f64 x -12))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 x -12 3) 1 (*.f64 9 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (cbrt.f64 (fma.f64 x -12 3)) (cbrt.f64 (fma.f64 x -12 3))) (cbrt.f64 (fma.f64 x -12 3)) (*.f64 9 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (fma.f64 x -12 3)) (sqrt.f64 (fma.f64 x -12 3)) (*.f64 9 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 -12 (cbrt.f64 (*.f64 x x))) (cbrt.f64 x) (fma.f64 9 (*.f64 x x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 -12 (sqrt.f64 x)) (sqrt.f64 x) (fma.f64 9 (*.f64 x x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 9 x) x (fma.f64 x -12 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 9 (cbrt.f64 (pow.f64 x 4))) (cbrt.f64 (*.f64 x x)) (fma.f64 x -12 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 x -12 (fma.f64 9 (*.f64 x x) 3))))))))

simplify63.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

545×	`associate-l_binary64`
434×	`unswap-sqr_binary64`
384×	`fma-def_binary64`
370×	`sqr-pow_binary64`
307×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	11	42
1	22	42
2	37	40
3	73	36
4	172	36
5	474	36
6	1712	36
7	2966	36
8	3170	36
9	3382	36
10	3602	36
11	3905	36
12	4305	36
13	4815	36

Stop Event

1×	node limit

Counts

95 → 96

Calls

Call 1

Inputs
3
(+.f64 (*.f64 -12 x) 3)
(*.f64 9 (pow.f64 x 2))
(+.f64 (.f64 -12 x) (.f64 9 (pow.f64 x 2)))
(*.f64 9 (pow.f64 x 2))
(+.f64 (.f64 -12 x) (.f64 9 (pow.f64 x 2)))

Outputs
3
(+.f64 (*.f64 -12 x) 3)
(fma.f64 -12 x 3)
(*.f64 9 (pow.f64 x 2))
(.f64 9 (.f64 x x))
(.f64 x (.f64 x 9))
(+.f64 (.f64 -12 x) (.f64 9 (pow.f64 x 2)))
(fma.f64 -12 x (.f64 9 (.f64 x x)))
(fma.f64 -12 x (.f64 x (.f64 x 9)))
(.f64 x (+.f64 -12 (.f64 x 9)))
(*.f64 x (fma.f64 x 9 -12))
(*.f64 9 (pow.f64 x 2))
(.f64 9 (.f64 x x))
(.f64 x (.f64 x 9))
(+.f64 (.f64 -12 x) (.f64 9 (pow.f64 x 2)))
(fma.f64 -12 x (.f64 9 (.f64 x x)))
(fma.f64 -12 x (.f64 x (.f64 x 9)))
(.f64 x (+.f64 -12 (.f64 x 9)))
(*.f64 x (fma.f64 x 9 -12))

eval38.0ms (1.1%)

Compiler: Compiled 1544 to 1020 computations (33.9% saved)

prune178.0ms (5.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	94	2	96
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	96	4	100

Error

0.0b

Counts

100 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.1b	(fma.f64 x (fma.f64 x 9 -12) 3)
▶	0.1b	(fma.f64 9 (*.f64 x x) (fma.f64 x -12 3))
	0.1b	(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))
	13.1b	(/.f64 (-.f64 (.f64 (fma.f64 x -12 3) (fma.f64 x -12 3)) (.f64 (pow.f64 x 4) 81)) (-.f64 (fma.f64 x -12 3) (.f64 9 (.f64 x x))))

Compiler

Compiled 110 to 84 computations (23.6% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x -12 3)
✓	0.1b	(fma.f64 9 (*.f64 x x) (fma.f64 x -12 3))

series2.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(fma.f64 9 (*.f64 x x) (fma.f64 x -12 3))
0.0ms	x	@	-inf	(fma.f64 9 (*.f64 x x) (fma.f64 x -12 3))
0.0ms	x	@	inf	(fma.f64 9 (*.f64 x x) (fma.f64 x -12 3))
0.0ms	x	@	-inf	(fma.f64 x -12 3)
0.0ms	x	@	0	(fma.f64 x -12 3)

rewrite36.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

670×	`pow1_binary64`
625×	`add-log-exp_binary64`
625×	`log1p-expm1-u_binary64`
625×	`expm1-log1p-u_binary64`
76×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	162	17
2	1711	17

Stop Event

1×	node limit

Counts

2 → 45

Calls

Call 1

Inputs
(fma.f64 9 (*.f64 x x) (fma.f64 x -12 3))
(fma.f64 x -12 3)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 x -12 3) (*.f64 9 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 9 (*.f64 x x)) (fma.f64 x -12 3))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 9 (*.f64 x x)) 1) (fma.f64 x -12 3))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (*.f64 9 (*.f64 x x)) (*.f64 x -12)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 9 (*.f64 x x) (fma.f64 x -12 3)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 9 (*.f64 x x) (fma.f64 x -12 3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 9 (*.f64 x x) (fma.f64 x -12 3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 9 (*.f64 x x) (fma.f64 x -12 3))) (pow.f64 (cbrt.f64 (fma.f64 9 (*.f64 x x) (fma.f64 x -12 3))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 9 (*.f64 x x) (fma.f64 x -12 3))) 2) (cbrt.f64 (fma.f64 9 (*.f64 x x) (fma.f64 x -12 3))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 9 (*.f64 x x) (fma.f64 x -12 3))) (sqrt.f64 (fma.f64 9 (*.f64 x x) (fma.f64 x -12 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 9 (*.f64 x x)) 3) (pow.f64 (fma.f64 x -12 3) 3)) (+.f64 (*.f64 (*.f64 9 (*.f64 x x)) (*.f64 9 (*.f64 x x))) (-.f64 (pow.f64 (fma.f64 x -12 3) 2) (*.f64 (*.f64 9 (*.f64 x x)) (fma.f64 x -12 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 9 (*.f64 x x)) (*.f64 9 (*.f64 x x))) (pow.f64 (fma.f64 x -12 3) 2)) (-.f64 (*.f64 9 (*.f64 x x)) (fma.f64 x -12 3)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 9 (*.f64 x x) (fma.f64 x -12 3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 9 (*.f64 x x) (fma.f64 x -12 3)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 9 (*.f64 x x) (fma.f64 x -12 3))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 9 (*.f64 x x) (fma.f64 x -12 3))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 9 (*.f64 x x) (fma.f64 x -12 3)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 9 (*.f64 x x) (fma.f64 x -12 3))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 9 (*.f64 x x) (fma.f64 x -12 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 9 (*.f64 x x) (fma.f64 x -12 3)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 9 (*.f64 x x) (fma.f64 x -12 3))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 9 (*.f64 x x) (fma.f64 x -12 3))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 9 (*.f64 x x) (fma.f64 x -12 3))))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 3 (*.f64 x -12))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x -12) 3)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 x -12) 1) 3)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 x -12 3))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 x -12 3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 x -12 3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 x -12 3)) (pow.f64 (cbrt.f64 (fma.f64 x -12 3)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 x -12 3)) 2) (cbrt.f64 (fma.f64 x -12 3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 x -12 3)) (sqrt.f64 (fma.f64 x -12 3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 x -12) 3) 27) (+.f64 (*.f64 (*.f64 x -12) (*.f64 x -12)) (-.f64 9 (*.f64 (*.f64 x -12) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 x -12) (*.f64 x -12)) 9) (-.f64 (*.f64 x -12) 3))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 x -12 3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x -12 3) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 x -12 3)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 x -12 3)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 x -12 3) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 x -12 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 x -12 3))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 x -12 3) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 x -12 3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 x -12 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 x -12 3)))))))

simplify66.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

534×	`associate-l_binary64`
513×	`fma-def_binary64`
434×	`unswap-sqr_binary64`
370×	`sqr-pow_binary64`
319×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	14	180
1	28	168
2	49	166
3	93	144
4	204	144
5	517	144
6	1763	144
7	3096	144
8	3302	144
9	3515	144
10	3735	144
11	4043	144
12	4443	144
13	4953	144

Stop Event

1×	node limit

Counts

69 → 56

Calls

Call 1

Inputs
3
(+.f64 (*.f64 -12 x) 3)
(+.f64 (.f64 -12 x) (+.f64 3 (.f64 9 (pow.f64 x 2))))
(+.f64 (.f64 -12 x) (+.f64 3 (.f64 9 (pow.f64 x 2))))
(*.f64 9 (pow.f64 x 2))
(+.f64 (.f64 -12 x) (.f64 9 (pow.f64 x 2)))
(+.f64 (.f64 -12 x) (+.f64 3 (.f64 9 (pow.f64 x 2))))
(+.f64 (.f64 -12 x) (+.f64 3 (.f64 9 (pow.f64 x 2))))
(*.f64 9 (pow.f64 x 2))
(+.f64 (.f64 -12 x) (.f64 9 (pow.f64 x 2)))
(+.f64 (.f64 -12 x) (+.f64 3 (.f64 9 (pow.f64 x 2))))
(+.f64 (.f64 -12 x) (+.f64 3 (.f64 9 (pow.f64 x 2))))
3
(+.f64 (*.f64 -12 x) 3)
(+.f64 (*.f64 -12 x) 3)
(+.f64 (*.f64 -12 x) 3)
(*.f64 -12 x)
(+.f64 3 (*.f64 -12 x))
(+.f64 3 (*.f64 -12 x))
(+.f64 3 (*.f64 -12 x))
(*.f64 -12 x)
(+.f64 3 (*.f64 -12 x))
(+.f64 3 (*.f64 -12 x))
(+.f64 3 (*.f64 -12 x))

Outputs
3
(+.f64 (*.f64 -12 x) 3)
(fma.f64 -12 x 3)
(+.f64 (.f64 -12 x) (+.f64 3 (.f64 9 (pow.f64 x 2))))
(+.f64 (fma.f64 -12 x 3) (.f64 9 (.f64 x x)))
(fma.f64 -12 x (fma.f64 9 (*.f64 x x) 3))
(fma.f64 x (fma.f64 x 9 -12) 3)
(+.f64 (.f64 -12 x) (+.f64 3 (.f64 9 (pow.f64 x 2))))
(+.f64 (fma.f64 -12 x 3) (.f64 9 (.f64 x x)))
(fma.f64 -12 x (fma.f64 9 (*.f64 x x) 3))
(fma.f64 x (fma.f64 x 9 -12) 3)
(*.f64 9 (pow.f64 x 2))
(.f64 9 (.f64 x x))
(.f64 x (.f64 x 9))
(+.f64 (.f64 -12 x) (.f64 9 (pow.f64 x 2)))
(fma.f64 -12 x (.f64 9 (.f64 x x)))
(fma.f64 9 (.f64 x x) (.f64 -12 x))
(.f64 x (+.f64 (.f64 x 9) -12))
(*.f64 x (fma.f64 x 9 -12))
(+.f64 (.f64 -12 x) (+.f64 3 (.f64 9 (pow.f64 x 2))))
(+.f64 (fma.f64 -12 x 3) (.f64 9 (.f64 x x)))
(fma.f64 -12 x (fma.f64 9 (*.f64 x x) 3))
(fma.f64 x (fma.f64 x 9 -12) 3)
(+.f64 (.f64 -12 x) (+.f64 3 (.f64 9 (pow.f64 x 2))))
(+.f64 (fma.f64 -12 x 3) (.f64 9 (.f64 x x)))
(fma.f64 -12 x (fma.f64 9 (*.f64 x x) 3))
(fma.f64 x (fma.f64 x 9 -12) 3)
(*.f64 9 (pow.f64 x 2))
(.f64 9 (.f64 x x))
(.f64 x (.f64 x 9))
(+.f64 (.f64 -12 x) (.f64 9 (pow.f64 x 2)))
(fma.f64 -12 x (.f64 9 (.f64 x x)))
(fma.f64 9 (.f64 x x) (.f64 -12 x))
(.f64 x (+.f64 (.f64 x 9) -12))
(*.f64 x (fma.f64 x 9 -12))
(+.f64 (.f64 -12 x) (+.f64 3 (.f64 9 (pow.f64 x 2))))
(+.f64 (fma.f64 -12 x 3) (.f64 9 (.f64 x x)))
(fma.f64 -12 x (fma.f64 9 (*.f64 x x) 3))
(fma.f64 x (fma.f64 x 9 -12) 3)
(+.f64 (.f64 -12 x) (+.f64 3 (.f64 9 (pow.f64 x 2))))
(+.f64 (fma.f64 -12 x 3) (.f64 9 (.f64 x x)))
(fma.f64 -12 x (fma.f64 9 (*.f64 x x) 3))
(fma.f64 x (fma.f64 x 9 -12) 3)
3
(+.f64 (*.f64 -12 x) 3)
(fma.f64 -12 x 3)
(+.f64 (*.f64 -12 x) 3)
(fma.f64 -12 x 3)
(+.f64 (*.f64 -12 x) 3)
(fma.f64 -12 x 3)
(*.f64 -12 x)
(+.f64 3 (*.f64 -12 x))
(fma.f64 -12 x 3)
(+.f64 3 (*.f64 -12 x))
(fma.f64 -12 x 3)
(+.f64 3 (*.f64 -12 x))
(fma.f64 -12 x 3)
(*.f64 -12 x)
(+.f64 3 (*.f64 -12 x))
(fma.f64 -12 x 3)
(+.f64 3 (*.f64 -12 x))
(fma.f64 -12 x 3)
(+.f64 3 (*.f64 -12 x))
(fma.f64 -12 x 3)

eval17.0ms (0.5%)

Compiler: Compiled 715 to 477 computations (33.3% saved)

prune67.0ms (2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	56	0	56
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	56	4	60

Error

0.0b

Counts

60 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.1b	(fma.f64 x (fma.f64 x 9 -12) 3)
✓	0.1b	(fma.f64 9 (*.f64 x x) (fma.f64 x -12 3))
▶	0.1b	(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))
	13.1b	(/.f64 (-.f64 (.f64 (fma.f64 x -12 3) (fma.f64 x -12 3)) (.f64 (pow.f64 x 4) 81)) (-.f64 (fma.f64 x -12 3) (.f64 9 (.f64 x x))))

Compiler

Compiled 100 to 77 computations (23% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 (.f64 x 3) x) (*.f64 x 4))
✓	0.1b	(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))
✓	0.2b	(.f64 (.f64 x 3) x)

series4.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))
1.0ms	x	@	0	(.f64 (.f64 x 3) x)
0.0ms	x	@	inf	(.f64 (.f64 x 3) x)
0.0ms	x	@	inf	(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))
0.0ms	x	@	inf	(-.f64 (.f64 (.f64 x 3) x) (*.f64 x 4))

rewrite71.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

707×	`fma-def_binary64`
400×	`fma-neg_binary64`
206×	`log1p-udef_binary64`
204×	`expm1-udef_binary64`
190×	`egg-rr`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	39
1	256	31
2	3352	27

Stop Event

1×	node limit

Counts

3 → 235

Calls

Call 1

Inputs
(.f64 (.f64 x 3) x)
(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))
(-.f64 (.f64 (.f64 x 3) x) (*.f64 x 4))

Outputs

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

simplify87.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

599×	`sqr-pow_binary64`
386×	`cube-prod_binary64`
323×	`fabs-mul_binary64`
301×	`fma-def_binary64`
274×	`pow-sqr_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	17	327
1	36	315
2	64	304
3	135	264
4	316	264
5	839	264
6	1310	264
7	1776	264
8	1885	264
9	2019	264
10	2188	264
11	2433	264
12	2746	264
13	3118	264
14	3572	264
15	4155	264
16	4863	264

Stop Event

1×	node limit

Counts

271 → 250

Calls

Call 1

Inputs
(*.f64 3 (pow.f64 x 2))
(*.f64 3 (pow.f64 x 2))
(*.f64 3 (pow.f64 x 2))
(*.f64 3 (pow.f64 x 2))
(*.f64 3 (pow.f64 x 2))
(*.f64 3 (pow.f64 x 2))
(*.f64 3 (pow.f64 x 2))
(*.f64 3 (pow.f64 x 2))
(*.f64 3 (pow.f64 x 2))
(*.f64 3 (pow.f64 x 2))
(*.f64 3 (pow.f64 x 2))
(*.f64 3 (pow.f64 x 2))
3
(+.f64 (*.f64 -12 x) 3)
(+.f64 (.f64 -12 x) (+.f64 3 (.f64 9 (pow.f64 x 2))))
(+.f64 (.f64 -12 x) (+.f64 3 (.f64 9 (pow.f64 x 2))))
(*.f64 9 (pow.f64 x 2))
(+.f64 (.f64 -12 x) (.f64 9 (pow.f64 x 2)))
(+.f64 (.f64 -12 x) (+.f64 3 (.f64 9 (pow.f64 x 2))))
(+.f64 (.f64 -12 x) (+.f64 3 (.f64 9 (pow.f64 x 2))))
(*.f64 9 (pow.f64 x 2))
(+.f64 (.f64 -12 x) (.f64 9 (pow.f64 x 2)))
(+.f64 (.f64 -12 x) (+.f64 3 (.f64 9 (pow.f64 x 2))))
(+.f64 (.f64 -12 x) (+.f64 3 (.f64 9 (pow.f64 x 2))))
(*.f64 -4 x)
(+.f64 (.f64 3 (pow.f64 x 2)) (.f64 -4 x))
(+.f64 (.f64 3 (pow.f64 x 2)) (.f64 -4 x))
(+.f64 (.f64 3 (pow.f64 x 2)) (.f64 -4 x))
(*.f64 3 (pow.f64 x 2))
(+.f64 (.f64 3 (pow.f64 x 2)) (.f64 -4 x))
(+.f64 (.f64 3 (pow.f64 x 2)) (.f64 -4 x))
(+.f64 (.f64 3 (pow.f64 x 2)) (.f64 -4 x))
(*.f64 3 (pow.f64 x 2))
(+.f64 (.f64 3 (pow.f64 x 2)) (.f64 -4 x))
(+.f64 (.f64 3 (pow.f64 x 2)) (.f64 -4 x))
(+.f64 (.f64 3 (pow.f64 x 2)) (.f64 -4 x))

Outputs
(*.f64 3 (pow.f64 x 2))
(.f64 3 (.f64 x x))
(*.f64 3 (pow.f64 x 2))
(.f64 3 (.f64 x x))
(*.f64 3 (pow.f64 x 2))
(.f64 3 (.f64 x x))
(*.f64 3 (pow.f64 x 2))
(.f64 3 (.f64 x x))
(*.f64 3 (pow.f64 x 2))
(.f64 3 (.f64 x x))
(*.f64 3 (pow.f64 x 2))
(.f64 3 (.f64 x x))
(*.f64 3 (pow.f64 x 2))
(.f64 3 (.f64 x x))
(*.f64 3 (pow.f64 x 2))
(.f64 3 (.f64 x x))
(*.f64 3 (pow.f64 x 2))
(.f64 3 (.f64 x x))
(*.f64 3 (pow.f64 x 2))
(.f64 3 (.f64 x x))
(*.f64 3 (pow.f64 x 2))
(.f64 3 (.f64 x x))
(*.f64 3 (pow.f64 x 2))
(.f64 3 (.f64 x x))
3
(+.f64 (*.f64 -12 x) 3)
(fma.f64 -12 x 3)
(fma.f64 x -12 3)
(+.f64 (.f64 -12 x) (+.f64 3 (.f64 9 (pow.f64 x 2))))
(+.f64 (fma.f64 -12 x 3) (.f64 (.f64 x x) 9))
(fma.f64 x -12 (fma.f64 (*.f64 x x) 9 3))
(fma.f64 x -12 (fma.f64 x (*.f64 x 9) 3))
(fma.f64 x (fma.f64 x 9 -12) 3)
(+.f64 (.f64 -12 x) (+.f64 3 (.f64 9 (pow.f64 x 2))))
(+.f64 (fma.f64 -12 x 3) (.f64 (.f64 x x) 9))
(fma.f64 x -12 (fma.f64 (*.f64 x x) 9 3))
(fma.f64 x -12 (fma.f64 x (*.f64 x 9) 3))
(fma.f64 x (fma.f64 x 9 -12) 3)
(*.f64 9 (pow.f64 x 2))
(.f64 (.f64 x x) 9)
(.f64 x (.f64 x 9))
(+.f64 (.f64 -12 x) (.f64 9 (pow.f64 x 2)))
(fma.f64 -12 x (.f64 (.f64 x x) 9))
(fma.f64 x -12 (.f64 x (.f64 x 9)))
(.f64 x (+.f64 -12 (.f64 x 9)))
(*.f64 x (fma.f64 x 9 -12))
(+.f64 (.f64 -12 x) (+.f64 3 (.f64 9 (pow.f64 x 2))))
(+.f64 (fma.f64 -12 x 3) (.f64 (.f64 x x) 9))
(fma.f64 x -12 (fma.f64 (*.f64 x x) 9 3))
(fma.f64 x -12 (fma.f64 x (*.f64 x 9) 3))
(fma.f64 x (fma.f64 x 9 -12) 3)
(+.f64 (.f64 -12 x) (+.f64 3 (.f64 9 (pow.f64 x 2))))
(+.f64 (fma.f64 -12 x 3) (.f64 (.f64 x x) 9))
(fma.f64 x -12 (fma.f64 (*.f64 x x) 9 3))
(fma.f64 x -12 (fma.f64 x (*.f64 x 9) 3))
(fma.f64 x (fma.f64 x 9 -12) 3)
(*.f64 9 (pow.f64 x 2))
(.f64 (.f64 x x) 9)
(.f64 x (.f64 x 9))
(+.f64 (.f64 -12 x) (.f64 9 (pow.f64 x 2)))
(fma.f64 -12 x (.f64 (.f64 x x) 9))
(fma.f64 x -12 (.f64 x (.f64 x 9)))
(.f64 x (+.f64 -12 (.f64 x 9)))
(*.f64 x (fma.f64 x 9 -12))
(+.f64 (.f64 -12 x) (+.f64 3 (.f64 9 (pow.f64 x 2))))
(+.f64 (fma.f64 -12 x 3) (.f64 (.f64 x x) 9))
(fma.f64 x -12 (fma.f64 (*.f64 x x) 9 3))
(fma.f64 x -12 (fma.f64 x (*.f64 x 9) 3))
(fma.f64 x (fma.f64 x 9 -12) 3)
(+.f64 (.f64 -12 x) (+.f64 3 (.f64 9 (pow.f64 x 2))))
(+.f64 (fma.f64 -12 x 3) (.f64 (.f64 x x) 9))
(fma.f64 x -12 (fma.f64 (*.f64 x x) 9 3))
(fma.f64 x -12 (fma.f64 x (*.f64 x 9) 3))
(fma.f64 x (fma.f64 x 9 -12) 3)
(*.f64 -4 x)
(*.f64 x -4)
(+.f64 (.f64 3 (pow.f64 x 2)) (.f64 -4 x))
(fma.f64 3 (.f64 x x) (.f64 x -4))
(.f64 x (+.f64 (.f64 3 x) -4))
(*.f64 x (fma.f64 3 x -4))
(+.f64 (.f64 3 (pow.f64 x 2)) (.f64 -4 x))
(fma.f64 3 (.f64 x x) (.f64 x -4))
(.f64 x (+.f64 (.f64 3 x) -4))
(*.f64 x (fma.f64 3 x -4))
(+.f64 (.f64 3 (pow.f64 x 2)) (.f64 -4 x))
(fma.f64 3 (.f64 x x) (.f64 x -4))
(.f64 x (+.f64 (.f64 3 x) -4))
(*.f64 x (fma.f64 3 x -4))
(*.f64 3 (pow.f64 x 2))
(.f64 3 (.f64 x x))
(+.f64 (.f64 3 (pow.f64 x 2)) (.f64 -4 x))
(fma.f64 3 (.f64 x x) (.f64 x -4))
(.f64 x (+.f64 (.f64 3 x) -4))
(*.f64 x (fma.f64 3 x -4))
(+.f64 (.f64 3 (pow.f64 x 2)) (.f64 -4 x))
(fma.f64 3 (.f64 x x) (.f64 x -4))
(.f64 x (+.f64 (.f64 3 x) -4))
(*.f64 x (fma.f64 3 x -4))
(+.f64 (.f64 3 (pow.f64 x 2)) (.f64 -4 x))
(fma.f64 3 (.f64 x x) (.f64 x -4))
(.f64 x (+.f64 (.f64 3 x) -4))
(*.f64 x (fma.f64 3 x -4))
(*.f64 3 (pow.f64 x 2))
(.f64 3 (.f64 x x))
(+.f64 (.f64 3 (pow.f64 x 2)) (.f64 -4 x))
(fma.f64 3 (.f64 x x) (.f64 x -4))
(.f64 x (+.f64 (.f64 3 x) -4))
(*.f64 x (fma.f64 3 x -4))
(+.f64 (.f64 3 (pow.f64 x 2)) (.f64 -4 x))
(fma.f64 3 (.f64 x x) (.f64 x -4))
(.f64 x (+.f64 (.f64 3 x) -4))
(*.f64 x (fma.f64 3 x -4))
(+.f64 (.f64 3 (pow.f64 x 2)) (.f64 -4 x))
(fma.f64 3 (.f64 x x) (.f64 x -4))
(.f64 x (+.f64 (.f64 3 x) -4))
(*.f64 x (fma.f64 3 x -4))

eval111.0ms (3.3%)

Compiler: Compiled 5366 to 4152 computations (22.6% saved)

prune1.3s (39.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	250	0	250
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	250	4	254

Error

0.0b

Counts

254 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.1b	(fma.f64 x (fma.f64 x 9 -12) 3)
✓	0.1b	(fma.f64 9 (*.f64 x x) (fma.f64 x -12 3))
✓	0.1b	(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))
	13.1b	(/.f64 (-.f64 (.f64 (fma.f64 x -12 3) (fma.f64 x -12 3)) (.f64 (pow.f64 x 4) 81)) (-.f64 (fma.f64 x -12 3) (.f64 9 (.f64 x x))))

Compiler

Compiled 59 to 45 computations (23.7% saved)

regimes22.0ms (0.6%)

Accuracy

Total -17.8b remaining (-21670.3%)

Threshold costs -17.8b (-21670.3%)

Counts

6 → 1

Calls

Call 1

Inputs
(fma.f64 9 (*.f64 x x) (fma.f64 x -12 3))
(/.f64 (-.f64 (.f64 (fma.f64 x -12 3) (fma.f64 x -12 3)) (.f64 (pow.f64 x 4) 81)) (-.f64 (fma.f64 x -12 3) (.f64 9 (.f64 x x))))
(+.f64 (.f64 -12 x) (+.f64 3 (.f64 9 (pow.f64 x 2))))
(/.f64 (+.f64 (pow.f64 (.f64 x (fma.f64 x 9 -12)) 3) 27) (+.f64 (.f64 (.f64 x (fma.f64 x 9 -12)) (.f64 x (fma.f64 x 9 -12))) (-.f64 9 (.f64 (.f64 x (fma.f64 x 9 -12)) 3))))
(fma.f64 x (fma.f64 x 9 -12) 3)
(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))

Outputs
(fma.f64 x (fma.f64 x 9 -12) 3)

Results

Time	Error	Segments	Branch
5.0ms	0.1b	1	`x`
3.0ms	0.1b	1	`(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))`
3.0ms	0.1b	1	`(+.f64 (-.f64 (.f64 (.f64 x 3) x) (*.f64 x 4)) 1)`
5.0ms	0.1b	1	`(-.f64 (.f64 (.f64 x 3) x) (*.f64 x 4))`

Compiler

Compiled 140 to 105 computations (25% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9

Stop Event

1×

saturated

Calls

Call 1

Inputs
(fma.f64 x (fma.f64 x 9 -12) 3)

Outputs
(fma.f64 x (fma.f64 x 9 -12) 3)

end14.0ms (0.4%)

Stop Event

1×

fuel

Compiler

Compiled 16 to 12 computations (25% saved)

Details

analyze6.0ms (0.2%)

sample875.0ms (25.9%)

preprocess57.0ms (1.7%)

simplify45.0ms (1.3%)

eval1.0ms (0%)

prune2.0ms (0.1%)

localize4.0ms (0.1%)

series3.0ms (0.1%)

rewrite34.0ms (1%)

simplify71.0ms (2.1%)

eval25.0ms (0.7%)

prune62.0ms (1.8%)

localize8.0ms (0.2%)

series3.0ms (0.1%)

rewrite51.0ms (1.5%)

simplify63.0ms (1.9%)

eval38.0ms (1.1%)

prune178.0ms (5.3%)

localize6.0ms (0.2%)

series2.0ms (0.1%)

rewrite36.0ms (1.1%)

simplify66.0ms (1.9%)

eval17.0ms (0.5%)

prune67.0ms (2%)

localize7.0ms (0.2%)

series4.0ms (0.1%)

rewrite71.0ms (2.1%)

simplify87.0ms (2.6%)

eval111.0ms (3.3%)

prune1.3s (39.6%)

regimes22.0ms (0.6%)

simplify6.0ms (0.2%)

end14.0ms (0.4%)

Profiling