Details

analyze5.0ms (0.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	25%	25%	4
62.5%	12.5%	25%	5
68.7%	6.2%	25%	6
71.8%	3.1%	25%	7
73.4%	1.6%	25%	8
74.2%	0.8%	25%	9
74.6%	0.4%	25%	10
74.8%	0.2%	25%	11
74.9%	0.1%	25%	12
74.9%	0%	25.1%	13
74.9%	0%	25.1%	14

Compiler

Compiled 15 to 12 computations (20% saved)

sample850.0ms (43.1%)

Results

833.0ms	8256×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 30 to 24 computations (20% saved)

preprocess50.0ms (2.5%)

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)

simplify43.0ms (2.2%)

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)

prune3.0ms (0.2%)

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

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 65 to 50 computations (23.1% saved)

localize4.0ms (0.2%)

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 (0.2%)

Counts

2 → 24

Calls

6 calls:

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

rewrite36.0ms (1.8%)

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 expm1.f64 (log1p.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 +.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 expm1.f64 (log1p.f64 (fma.f64 x 9 -12)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.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 expm1.f64 (log1p.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 +.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 expm1.f64 (log1p.f64 (fma.f64 x 9 -12)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 x 9 -12)))))))

simplify35.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

631×	`fma-neg_binary64`
466×	`cancel-sign-sub-inv_binary64`
418×	`distribute-rgt-neg-in_binary64`
413×	`fma-def_binary64`
296×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	16	198
1	38	182
2	69	156
3	141	144
4	380	144
5	1208	144
6	2780	144
7	4663	144

Stop Event

1×	node limit

Counts

68 → 58

Calls

Call 1

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

prune58.0ms (3%)

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

Status	Error	Program
	0.1b	(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))
▶	0.1b	(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))
✓	0.1b	(fma.f64 x (fma.f64 x 9 -12) 3)
	6.9b	(fma.f64 x (cbrt.f64 (pow.f64 (fma.f64 x 9 -12) 3)) 3)

Compiler

Compiled 695 to 545 computations (21.6% saved)

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))
✓	0.2b	(*.f64 9 (pow.f64 x 2))

series4.0ms (0.2%)

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))
1.0ms	x	@	-inf	(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))
1.0ms	x	@	inf	(*.f64 9 (pow.f64 x 2))
1.0ms	x	@	inf	(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))

rewrite61.0ms (3.1%)

Algorithm

1×	batch-egg-rewrite

Rules

494×	`log-prod_binary64`
395×	`fma-def_binary64`
203×	`expm1-udef_binary64`
203×	`log1p-udef_binary64`
193×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	23
1	251	21
2	3178	19

Stop Event

1×	node limit

Counts

2 → 148

Calls

Call 1

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

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

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

simplify32.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

806×	`fma-def_binary64`
757×	`fma-neg_binary64`
415×	`distribute-rgt-neg-in_binary64`
350×	`cancel-sign-sub-inv_binary64`
293×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	11	48
1	27	44
2	52	40
3	121	36
4	331	36
5	1109	36
6	2423	36
7	4614	36

Stop Event

1×	node limit

Counts

154 → 155

Calls

Call 1

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

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

prune131.0ms (6.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	154	1	155
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	155	4	159

Error

0.0b

Counts

159 → 4

Alt Table

Status	Error	Program
	10.0b	(-.f64 (+.f64 3 (sqrt.f64 (.f64 (pow.f64 x 4) 81))) (.f64 12 x))
✓	0.1b	(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))
✓	0.1b	(fma.f64 x (fma.f64 x 9 -12) 3)
▶	6.9b	(fma.f64 x (cbrt.f64 (pow.f64 (fma.f64 x 9 -12) 3)) 3)

Compiler

Compiled 2958 to 1980 computations (33.1% saved)

localize11.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 x 9 -12)
✓	0.1b	(fma.f64 x (cbrt.f64 (pow.f64 (fma.f64 x 9 -12) 3)) 3)
✓	0.2b	(pow.f64 (fma.f64 x 9 -12) 3)
✓	7.2b	(cbrt.f64 (pow.f64 (fma.f64 x 9 -12) 3))

series6.0ms (0.3%)

Counts

3 → 36

Calls

9 calls:

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

rewrite43.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

706×	`pow1_binary64`
668×	`add-log-exp_binary64`
668×	`log1p-expm1-u_binary64`
668×	`expm1-log1p-u_binary64`
78×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	22
1	191	22
2	1825	22

Stop Event

1×	node limit

Counts

3 → 70

Calls

Call 1

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

Outputs

((#(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 (cbrt.f64 (fma.f64 x 9 -12)) (pow.f64 (pow.f64 (fma.f64 x 9 -12) 2) 1/3))))) (#(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 (pow.f64 (pow.f64 (fma.f64 x 9 -12) 2) 1/3) (cbrt.f64 (fma.f64 x 9 -12)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (fma.f64 x 9 -12))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (fma.f64 x 9 -12) 3/2) 1/3) (pow.f64 (pow.f64 (fma.f64 x 9 -12) 3/2) 1/3))))) (#(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 log1p.f64 (expm1.f64 (fma.f64 x 9 -12)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x 9 -12)))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.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 +.f64 (*.f64 (*.f64 x 9) (pow.f64 (fma.f64 x 9 -12) 2)) (*.f64 -12 (pow.f64 (fma.f64 x 9 -12) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (pow.f64 (fma.f64 x 9 -12) 2) (*.f64 x 9)) (*.f64 (pow.f64 (fma.f64 x 9 -12) 2) -12))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (fma.f64 x 9 -12) 3))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 x 9 -12) (pow.f64 (fma.f64 x 9 -12) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (fma.f64 x 9 -12) 3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (fma.f64 x 9 -12) 3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (fma.f64 x 9 -12) 2) (fma.f64 x 9 -12))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 x 9 -12)) 2) (*.f64 (cbrt.f64 (fma.f64 x 9 -12)) (pow.f64 (fma.f64 x 9 -12) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 x 9 -12)) (*.f64 (sqrt.f64 (fma.f64 x 9 -12)) (pow.f64 (fma.f64 x 9 -12) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (fma.f64 x 9 -12) 3/2) (pow.f64 (fma.f64 x 9 -12) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (fma.f64 x 9 -12)) 2) 3) (fma.f64 x 9 -12))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (fma.f64 x 9 -12)) 3) (pow.f64 (sqrt.f64 (fma.f64 x 9 -12)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (fma.f64 x 9 -12) 2) 1) (fma.f64 x 9 -12))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (fma.f64 x 9 -12) 2) (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 (*.f64 (pow.f64 (fma.f64 x 9 -12) 2) (sqrt.f64 (fma.f64 x 9 -12))) (sqrt.f64 (fma.f64 x 9 -12)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 x 9 -12) 6))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (fma.f64 x 9 -12) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (fma.f64 x 9 -12) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (fma.f64 x 9 -12) 3) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (fma.f64 x 9 -12) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (fma.f64 x 9 -12) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 3 (log.f64 (fma.f64 x 9 -12))))))))

((#(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 expm1.f64 (log1p.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)))))))

simplify36.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

622×	`fma-neg_binary64`
473×	`distribute-rgt-neg-in_binary64`
415×	`cancel-sign-sub-inv_binary64`
268×	`unswap-sqr_binary64`
256×	`fma-def_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	32	373
1	89	343
2	201	305
3	569	273
4	1693	270
5	3864	270

Stop Event

1×	node limit

Counts

106 → 95

Calls

Call 1

Inputs
-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)
-1728
(-.f64 (*.f64 3888 x) 1728)
(-.f64 (.f64 3888 x) (+.f64 1728 (.f64 2916 (pow.f64 x 2))))
(-.f64 (+.f64 (.f64 3888 x) (.f64 729 (pow.f64 x 3))) (+.f64 1728 (*.f64 2916 (pow.f64 x 2))))
(*.f64 729 (pow.f64 x 3))
(-.f64 (.f64 729 (pow.f64 x 3)) (.f64 2916 (pow.f64 x 2)))
(-.f64 (+.f64 (.f64 3888 x) (.f64 729 (pow.f64 x 3))) (*.f64 2916 (pow.f64 x 2)))
(-.f64 (+.f64 (.f64 3888 x) (.f64 729 (pow.f64 x 3))) (+.f64 1728 (*.f64 2916 (pow.f64 x 2))))
(*.f64 729 (pow.f64 x 3))
(-.f64 (.f64 729 (pow.f64 x 3)) (.f64 2916 (pow.f64 x 2)))
(-.f64 (+.f64 (.f64 3888 x) (.f64 729 (pow.f64 x 3))) (*.f64 2916 (pow.f64 x 2)))
(-.f64 (+.f64 (.f64 3888 x) (.f64 729 (pow.f64 x 3))) (+.f64 1728 (*.f64 2916 (pow.f64 x 2))))
3
(-.f64 3 (*.f64 12 x))
(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))
(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))
(*.f64 9 (pow.f64 x 2))
(-.f64 (.f64 9 (pow.f64 x 2)) (.f64 12 x))
(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))
(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))
(*.f64 9 (pow.f64 x 2))
(-.f64 (.f64 9 (pow.f64 x 2)) (.f64 12 x))
(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))
(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))

Outputs
-12
(-.f64 (*.f64 9 x) 12)
(fma.f64 9 x -12)
(-.f64 (*.f64 9 x) 12)
(fma.f64 9 x -12)
(-.f64 (*.f64 9 x) 12)
(fma.f64 9 x -12)
(*.f64 9 x)
(-.f64 (*.f64 9 x) 12)
(fma.f64 9 x -12)
(-.f64 (*.f64 9 x) 12)
(fma.f64 9 x -12)
(-.f64 (*.f64 9 x) 12)
(fma.f64 9 x -12)
(*.f64 9 x)
(-.f64 (*.f64 9 x) 12)
(fma.f64 9 x -12)
(-.f64 (*.f64 9 x) 12)
(fma.f64 9 x -12)
(-.f64 (*.f64 9 x) 12)
(fma.f64 9 x -12)
-1728
(-.f64 (*.f64 3888 x) 1728)
(fma.f64 3888 x -1728)
(fma.f64 x 3888 -1728)
(-.f64 (.f64 3888 x) (+.f64 1728 (.f64 2916 (pow.f64 x 2))))
(-.f64 (fma.f64 3888 x -1728) (.f64 2916 (.f64 x x)))
(+.f64 (fma.f64 x 3888 -1728) (.f64 (.f64 x x) -2916))
(fma.f64 x 3888 (fma.f64 (*.f64 x x) -2916 -1728))
(fma.f64 x (+.f64 3888 (*.f64 x -2916)) -1728)
(-.f64 (+.f64 (.f64 3888 x) (.f64 729 (pow.f64 x 3))) (+.f64 1728 (*.f64 2916 (pow.f64 x 2))))
(-.f64 (fma.f64 3888 x (.f64 729 (pow.f64 x 3))) (+.f64 1728 (.f64 2916 (*.f64 x x))))
(-.f64 (fma.f64 x 3888 (.f64 729 (pow.f64 x 3))) (fma.f64 2916 (.f64 x x) 1728))
(fma.f64 x 3888 (fma.f64 729 (pow.f64 x 3) (fma.f64 (*.f64 x x) -2916 -1728)))
(fma.f64 x 3888 (fma.f64 (*.f64 x x) (fma.f64 x 729 -2916) -1728))
(fma.f64 x (+.f64 3888 (*.f64 x (fma.f64 x 729 -2916))) -1728)
(*.f64 729 (pow.f64 x 3))
(-.f64 (.f64 729 (pow.f64 x 3)) (.f64 2916 (pow.f64 x 2)))
(+.f64 (.f64 729 (pow.f64 x 3)) (.f64 -2916 (*.f64 x x)))
(fma.f64 729 (pow.f64 x 3) (.f64 (.f64 x x) -2916))
(.f64 (.f64 x x) (-.f64 (*.f64 x 729) 2916))
(.f64 (.f64 x x) (fma.f64 x 729 -2916))
(-.f64 (+.f64 (.f64 3888 x) (.f64 729 (pow.f64 x 3))) (*.f64 2916 (pow.f64 x 2)))
(+.f64 (fma.f64 3888 x (.f64 729 (pow.f64 x 3))) (.f64 -2916 (*.f64 x x)))
(fma.f64 x 3888 (fma.f64 729 (pow.f64 x 3) (.f64 (.f64 x x) -2916)))
(fma.f64 x 3888 (.f64 (.f64 x x) (-.f64 (*.f64 x 729) 2916)))
(.f64 x (+.f64 3888 (.f64 x (fma.f64 x 729 -2916))))
(-.f64 (+.f64 (.f64 3888 x) (.f64 729 (pow.f64 x 3))) (+.f64 1728 (*.f64 2916 (pow.f64 x 2))))
(-.f64 (fma.f64 3888 x (.f64 729 (pow.f64 x 3))) (+.f64 1728 (.f64 2916 (*.f64 x x))))
(-.f64 (fma.f64 x 3888 (.f64 729 (pow.f64 x 3))) (fma.f64 2916 (.f64 x x) 1728))
(fma.f64 x 3888 (fma.f64 729 (pow.f64 x 3) (fma.f64 (*.f64 x x) -2916 -1728)))
(fma.f64 x 3888 (fma.f64 (*.f64 x x) (fma.f64 x 729 -2916) -1728))
(fma.f64 x (+.f64 3888 (*.f64 x (fma.f64 x 729 -2916))) -1728)
(*.f64 729 (pow.f64 x 3))
(-.f64 (.f64 729 (pow.f64 x 3)) (.f64 2916 (pow.f64 x 2)))
(+.f64 (.f64 729 (pow.f64 x 3)) (.f64 -2916 (*.f64 x x)))
(fma.f64 729 (pow.f64 x 3) (.f64 (.f64 x x) -2916))
(.f64 (.f64 x x) (-.f64 (*.f64 x 729) 2916))
(.f64 (.f64 x x) (fma.f64 x 729 -2916))
(-.f64 (+.f64 (.f64 3888 x) (.f64 729 (pow.f64 x 3))) (*.f64 2916 (pow.f64 x 2)))
(+.f64 (fma.f64 3888 x (.f64 729 (pow.f64 x 3))) (.f64 -2916 (*.f64 x x)))
(fma.f64 x 3888 (fma.f64 729 (pow.f64 x 3) (.f64 (.f64 x x) -2916)))
(fma.f64 x 3888 (.f64 (.f64 x x) (-.f64 (*.f64 x 729) 2916)))
(.f64 x (+.f64 3888 (.f64 x (fma.f64 x 729 -2916))))
(-.f64 (+.f64 (.f64 3888 x) (.f64 729 (pow.f64 x 3))) (+.f64 1728 (*.f64 2916 (pow.f64 x 2))))
(-.f64 (fma.f64 3888 x (.f64 729 (pow.f64 x 3))) (+.f64 1728 (.f64 2916 (*.f64 x x))))
(-.f64 (fma.f64 x 3888 (.f64 729 (pow.f64 x 3))) (fma.f64 2916 (.f64 x x) 1728))
(fma.f64 x 3888 (fma.f64 729 (pow.f64 x 3) (fma.f64 (*.f64 x x) -2916 -1728)))
(fma.f64 x 3888 (fma.f64 (*.f64 x x) (fma.f64 x 729 -2916) -1728))
(fma.f64 x (+.f64 3888 (*.f64 x (fma.f64 x 729 -2916))) -1728)
3
(-.f64 3 (*.f64 12 x))
(+.f64 3 (*.f64 -12 x))
(+.f64 3 (*.f64 x -12))
(fma.f64 x -12 3)
(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))
(+.f64 3 (+.f64 (.f64 9 (.f64 x x)) (*.f64 -12 x)))
(+.f64 3 (fma.f64 9 (.f64 x x) (.f64 x -12)))
(+.f64 3 (*.f64 x (fma.f64 9 x -12)))
(fma.f64 x (fma.f64 9 x -12) 3)
(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))
(+.f64 3 (+.f64 (.f64 9 (.f64 x x)) (*.f64 -12 x)))
(+.f64 3 (fma.f64 9 (.f64 x x) (.f64 x -12)))
(+.f64 3 (*.f64 x (fma.f64 9 x -12)))
(fma.f64 x (fma.f64 9 x -12) 3)
(*.f64 9 (pow.f64 x 2))
(.f64 9 (.f64 x x))
(-.f64 (.f64 9 (pow.f64 x 2)) (.f64 12 x))
(+.f64 (.f64 9 (.f64 x x)) (*.f64 -12 x))
(fma.f64 9 (.f64 x x) (.f64 x -12))
(*.f64 x (fma.f64 9 x -12))
(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))
(+.f64 3 (+.f64 (.f64 9 (.f64 x x)) (*.f64 -12 x)))
(+.f64 3 (fma.f64 9 (.f64 x x) (.f64 x -12)))
(+.f64 3 (*.f64 x (fma.f64 9 x -12)))
(fma.f64 x (fma.f64 9 x -12) 3)
(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))
(+.f64 3 (+.f64 (.f64 9 (.f64 x x)) (*.f64 -12 x)))
(+.f64 3 (fma.f64 9 (.f64 x x) (.f64 x -12)))
(+.f64 3 (*.f64 x (fma.f64 9 x -12)))
(fma.f64 x (fma.f64 9 x -12) 3)
(*.f64 9 (pow.f64 x 2))
(.f64 9 (.f64 x x))
(-.f64 (.f64 9 (pow.f64 x 2)) (.f64 12 x))
(+.f64 (.f64 9 (.f64 x x)) (*.f64 -12 x))
(fma.f64 9 (.f64 x x) (.f64 x -12))
(*.f64 x (fma.f64 9 x -12))
(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))
(+.f64 3 (+.f64 (.f64 9 (.f64 x x)) (*.f64 -12 x)))
(+.f64 3 (fma.f64 9 (.f64 x x) (.f64 x -12)))
(+.f64 3 (*.f64 x (fma.f64 9 x -12)))
(fma.f64 x (fma.f64 9 x -12) 3)
(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))
(+.f64 3 (+.f64 (.f64 9 (.f64 x x)) (*.f64 -12 x)))
(+.f64 3 (fma.f64 9 (.f64 x x) (.f64 x -12)))
(+.f64 3 (*.f64 x (fma.f64 9 x -12)))
(fma.f64 x (fma.f64 9 x -12) 3)

prune82.0ms (4.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	122	0	122
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	122	4	126

Error

0.0b

Counts

126 → 4

Alt Table

Status	Error	Program
▶	10.0b	(-.f64 (+.f64 3 (sqrt.f64 (.f64 (pow.f64 x 4) 81))) (.f64 12 x))
✓	0.1b	(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))
✓	0.1b	(fma.f64 x (fma.f64 x 9 -12) 3)
✓	6.9b	(fma.f64 x (cbrt.f64 (pow.f64 (fma.f64 x 9 -12) 3)) 3)

Compiler

Compiled 1607 to 1294 computations (19.5% saved)

localize9.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 3 (sqrt.f64 (.f64 (pow.f64 x 4) 81))) (.f64 12 x))
✓	0.1b	(*.f64 (pow.f64 x 4) 81)
✓	19.7b	(sqrt.f64 (*.f64 (pow.f64 x 4) 81))

series7.0ms (0.4%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(*.f64 (pow.f64 x 4) 81)
1.0ms	x	@	-inf	(*.f64 (pow.f64 x 4) 81)
1.0ms	x	@	0	(*.f64 (pow.f64 x 4) 81)
1.0ms	x	@	0	(sqrt.f64 (*.f64 (pow.f64 x 4) 81))
1.0ms	x	@	inf	(-.f64 (+.f64 3 (sqrt.f64 (.f64 (pow.f64 x 4) 81))) (.f64 12 x))

rewrite64.0ms (3.2%)

Algorithm

1×	batch-egg-rewrite

Rules

440×	`fma-def_binary64`
239×	`fma-neg_binary64`
222×	`expm1-udef_binary64`
222×	`log1p-udef_binary64`
130×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	34
1	276	28
2	3501	26

Stop Event

1×	node limit

Counts

3 → 165

Calls

Call 1

Inputs
(sqrt.f64 (*.f64 (pow.f64 x 4) 81))
(*.f64 (pow.f64 x 4) 81)
(-.f64 (+.f64 3 (sqrt.f64 (.f64 (pow.f64 x 4) 81))) (.f64 12 x))

Outputs

((#(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 *.f64 (*.f64 9 (*.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 9 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 9 (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x x) 9)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x x) (pow.f64 81 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (pow.f64 x 4) 81)) (cbrt.f64 (*.f64 9 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 9 (*.f64 x x))) (cbrt.f64 (*.f64 (pow.f64 x 4) 81)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x 3) (*.f64 x 3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (cbrt.f64 (*.f64 6561 (pow.f64 x 8)))) (sqrt.f64 (cbrt.f64 (*.f64 (pow.f64 x 4) 81))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 81 1/2) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (*.f64 9 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 6561 (pow.f64 x 8))) 1/2) (pow.f64 (cbrt.f64 (*.f64 (pow.f64 x 4) 81)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 x 4) 81) 1/2)))) (#(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 (pow.f64 (*.f64 (pow.f64 x 4) 81) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (*.f64 9 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (*.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 (pow.f64 (*.f64 (pow.f64 x 4) 81) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 9 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.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 (pow.f64 x 4) 81)) 1/2))))) (#(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 -.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 x 4) 81))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 x 4) 81) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 9 (*.f64 x x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 6561 (pow.f64 x 8)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (pow.f64 x 4) 81) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (pow.f64 x 4) 81)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 6561 (pow.f64 x 8)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 81) (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (pow.f64 x 4) 81))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (pow.f64 x 4) 81) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (pow.f64 x 4) 81)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (pow.f64 x 4) 81)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (pow.f64 x 4) 81)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 x 4) 81)) 1))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 9 (*.f64 x x)) (-.f64 3 (*.f64 x 12)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 9 (*.f64 x x)) (+.f64 3 (*.f64 x -12)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 3 (fma.f64 9 (*.f64 x x) (*.f64 x -12)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 3 (*.f64 (fma.f64 9 (*.f64 x x) (*.f64 x -12)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 9 (*.f64 x x) 3) (*.f64 x -12))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 9 (*.f64 x x) 3) (*.f64 (*.f64 x -12) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 x -12 (fma.f64 9 (*.f64 x x) 3)) (fma.f64 -12 x (*.f64 x 12)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 x -12 (fma.f64 9 (*.f64 x x) 3)) (fma.f64 (*.f64 x -12) 1 (*.f64 x 12)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 x -12 (fma.f64 9 (*.f64 x x) 3)) (fma.f64 (neg.f64 (cbrt.f64 (*.f64 x 12))) (pow.f64 (cbrt.f64 (*.f64 x 12)) 2) (*.f64 x 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(neg.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 (pow.f64 81 1/2) (*.f64 x x) (-.f64 3 (*.f64 x 12)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 81 1/2) (*.f64 x x) (+.f64 3 (*.f64 x -12)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 1 1/2) (*.f64 9 (*.f64 x x)) (-.f64 3 (*.f64 x 12)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 1 1/2) (*.f64 9 (*.f64 x x)) (+.f64 3 (*.f64 x -12)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 6561 (pow.f64 x 8))) 1/2) (pow.f64 (cbrt.f64 (*.f64 (pow.f64 x 4) 81)) 1/2) (-.f64 3 (*.f64 x 12)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 6561 (pow.f64 x 8))) 1/2) (pow.f64 (cbrt.f64 (*.f64 (pow.f64 x 4) 81)) 1/2) (+.f64 3 (*.f64 x -12)))))) (#(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 (fma.f64 x 3 (sqrt.f64 (*.f64 x 12))) (-.f64 (*.f64 x 3) (sqrt.f64 (*.f64 x 12))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (sqrt.f64 (fma.f64 9 (*.f64 x x) 3)) (sqrt.f64 (*.f64 x 12))) (-.f64 (sqrt.f64 (fma.f64 9 (*.f64 x x) 3)) (sqrt.f64 (*.f64 x 12))) (fma.f64 -12 x (*.f64 x 12)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (sqrt.f64 (fma.f64 9 (*.f64 x x) 3)) (sqrt.f64 (*.f64 x 12))) (-.f64 (sqrt.f64 (fma.f64 9 (*.f64 x x) 3)) (sqrt.f64 (*.f64 x 12))) (fma.f64 (*.f64 x -12) 1 (*.f64 x 12)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (sqrt.f64 (fma.f64 9 (*.f64 x x) 3)) (sqrt.f64 (*.f64 x 12))) (-.f64 (sqrt.f64 (fma.f64 9 (*.f64 x x) 3)) (sqrt.f64 (*.f64 x 12))) (fma.f64 (neg.f64 (cbrt.f64 (*.f64 x 12))) (pow.f64 (cbrt.f64 (*.f64 x 12)) 2) (*.f64 x 12)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (pow.f64 (cbrt.f64 (*.f64 x 12)) 2)) (cbrt.f64 (*.f64 x 12)) (fma.f64 9 (*.f64 x x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 -12 (pow.f64 (cbrt.f64 x) 2)) (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 expm1.f64 (log1p.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))))))

simplify36.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

631×	`fma-neg_binary64`
474×	`associate-l_binary64`
463×	`cancel-sign-sub-inv_binary64`
405×	`fma-def_binary64`
342×	`unswap-sqr_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	17	312
1	40	296
2	80	280
3	198	258
4	572	258
5	2046	258
6	4175	258

Stop Event

1×	node limit

Counts

201 → 174

Calls

Call 1

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

Outputs
(*.f64 9 (pow.f64 x 2))
(.f64 9 (.f64 x x))
(*.f64 9 (pow.f64 x 2))
(.f64 9 (.f64 x x))
(*.f64 9 (pow.f64 x 2))
(.f64 9 (.f64 x x))
(*.f64 9 (pow.f64 x 2))
(.f64 9 (.f64 x x))
(*.f64 9 (pow.f64 x 2))
(.f64 9 (.f64 x x))
(*.f64 9 (pow.f64 x 2))
(.f64 9 (.f64 x x))
(*.f64 9 (pow.f64 x 2))
(.f64 9 (.f64 x x))
(*.f64 9 (pow.f64 x 2))
(.f64 9 (.f64 x x))
(*.f64 9 (pow.f64 x 2))
(.f64 9 (.f64 x x))
(*.f64 9 (pow.f64 x 2))
(.f64 9 (.f64 x x))
(*.f64 9 (pow.f64 x 2))
(.f64 9 (.f64 x x))
(*.f64 9 (pow.f64 x 2))
(.f64 9 (.f64 x x))
(*.f64 81 (pow.f64 x 4))
(*.f64 81 (pow.f64 x 4))
(*.f64 81 (pow.f64 x 4))
(*.f64 81 (pow.f64 x 4))
(*.f64 81 (pow.f64 x 4))
(*.f64 81 (pow.f64 x 4))
(*.f64 81 (pow.f64 x 4))
(*.f64 81 (pow.f64 x 4))
(*.f64 81 (pow.f64 x 4))
(*.f64 81 (pow.f64 x 4))
(*.f64 81 (pow.f64 x 4))
(*.f64 81 (pow.f64 x 4))
3
(-.f64 3 (*.f64 12 x))
(+.f64 3 (*.f64 -12 x))
(-.f64 3 (*.f64 x 12))
(fma.f64 x -12 3)
(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))
(+.f64 3 (+.f64 (.f64 9 (.f64 x x)) (*.f64 -12 x)))
(+.f64 (fma.f64 9 (.f64 x x) 3) (.f64 x -12))
(fma.f64 9 (*.f64 x x) (fma.f64 x -12 3))
(fma.f64 x (fma.f64 9 x -12) 3)
(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))
(+.f64 3 (+.f64 (.f64 9 (.f64 x x)) (*.f64 -12 x)))
(+.f64 (fma.f64 9 (.f64 x x) 3) (.f64 x -12))
(fma.f64 9 (*.f64 x x) (fma.f64 x -12 3))
(fma.f64 x (fma.f64 9 x -12) 3)
(*.f64 9 (pow.f64 x 2))
(.f64 9 (.f64 x x))
(-.f64 (.f64 9 (pow.f64 x 2)) (.f64 12 x))
(+.f64 (.f64 9 (.f64 x x)) (*.f64 -12 x))
(fma.f64 9 (.f64 x x) (.f64 x -12))
(.f64 x (-.f64 (.f64 9 x) 12))
(*.f64 x (fma.f64 9 x -12))
(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))
(+.f64 3 (+.f64 (.f64 9 (.f64 x x)) (*.f64 -12 x)))
(+.f64 (fma.f64 9 (.f64 x x) 3) (.f64 x -12))
(fma.f64 9 (*.f64 x x) (fma.f64 x -12 3))
(fma.f64 x (fma.f64 9 x -12) 3)
(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))
(+.f64 3 (+.f64 (.f64 9 (.f64 x x)) (*.f64 -12 x)))
(+.f64 (fma.f64 9 (.f64 x x) 3) (.f64 x -12))
(fma.f64 9 (*.f64 x x) (fma.f64 x -12 3))
(fma.f64 x (fma.f64 9 x -12) 3)
(*.f64 9 (pow.f64 x 2))
(.f64 9 (.f64 x x))
(-.f64 (.f64 9 (pow.f64 x 2)) (.f64 12 x))
(+.f64 (.f64 9 (.f64 x x)) (*.f64 -12 x))
(fma.f64 9 (.f64 x x) (.f64 x -12))
(.f64 x (-.f64 (.f64 9 x) 12))
(*.f64 x (fma.f64 9 x -12))
(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))
(+.f64 3 (+.f64 (.f64 9 (.f64 x x)) (*.f64 -12 x)))
(+.f64 (fma.f64 9 (.f64 x x) 3) (.f64 x -12))
(fma.f64 9 (*.f64 x x) (fma.f64 x -12 3))
(fma.f64 x (fma.f64 9 x -12) 3)
(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))
(+.f64 3 (+.f64 (.f64 9 (.f64 x x)) (*.f64 -12 x)))
(+.f64 (fma.f64 9 (.f64 x x) 3) (.f64 x -12))
(fma.f64 9 (*.f64 x x) (fma.f64 x -12 3))
(fma.f64 x (fma.f64 9 x -12) 3)

prune125.0ms (6.3%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	174	0	174
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	174	4	178

Error

0.0b

Counts

178 → 4

Alt Table

Status	Error	Program
✓	10.0b	(-.f64 (+.f64 3 (sqrt.f64 (.f64 (pow.f64 x 4) 81))) (.f64 12 x))
✓	0.1b	(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))
✓	0.1b	(fma.f64 x (fma.f64 x 9 -12) 3)
✓	6.9b	(fma.f64 x (cbrt.f64 (pow.f64 (fma.f64 x 9 -12) 3)) 3)

Compiler

Compiled 3191 to 2238 computations (29.9% saved)

regimes165.0ms (8.4%)

Accuracy

Total 0.1b remaining (79%)

Threshold costs 0.1b (79%)

Counts

48 → 1

Compiler

Compiled 2084 to 1597 computations (23.4% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`+-commutative_binary64`
1×	`*-rgt-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	11
1	16	11

Stop Event

1×

saturated

Calls

Call 1

Inputs
(fma.f64 x (+.f64 (.f64 (.f64 x 9) 1) -12) 3)

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

end64.0ms (3.2%)

Stop Event

1×

done

Compiler

Compiled 62 to 50 computations (19.4% saved)

Details

analyze5.0ms (0.3%)

sample850.0ms (43.1%)

preprocess50.0ms (2.5%)

simplify43.0ms (2.2%)

prune3.0ms (0.2%)

localize4.0ms (0.2%)

series3.0ms (0.2%)

rewrite36.0ms (1.8%)

simplify35.0ms (1.8%)

prune58.0ms (3%)

localize6.0ms (0.3%)

series4.0ms (0.2%)

rewrite61.0ms (3.1%)

simplify32.0ms (1.6%)

prune131.0ms (6.6%)

localize11.0ms (0.5%)

series6.0ms (0.3%)

rewrite43.0ms (2.2%)

simplify36.0ms (1.8%)

prune82.0ms (4.2%)

localize9.0ms (0.4%)

series7.0ms (0.4%)

rewrite64.0ms (3.2%)

simplify36.0ms (1.8%)

prune125.0ms (6.3%)

regimes165.0ms (8.4%)

simplify2.0ms (0.1%)

end64.0ms (3.2%)

Profiling