Details

analyze6.0ms (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%	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)

sample753.0ms (36.9%)

Results

741.0ms	8256×	body	128	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 30 to 24 computations (20% saved)

preprocess52.0ms (2.6%)

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 (2.1%)

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 (0.1%)

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

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)

rewrite35.0ms (1.7%)

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)))))))

simplify40.0ms (1.9%)

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)

prune43.0ms (2.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	55	3	58
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	55	5	60

Error

0.0b

Counts

60 → 5

Alt Table

Status	Error	Program
▶	0.1b	(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))
	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)
	53.3b	(fma.f64 x (pow.f64 (sqrt.f64 (fma.f64 x 9 -12)) 2) 3)
	0.8b	(pow.f64 (sqrt.f64 (fma.f64 x (fma.f64 x 9 -12) 3)) 2)

Compiler

Compiled 717 to 563 computations (21.5% 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))

series7.0ms (0.3%)

Counts

2 → 6

Calls

6 calls:

Time	Variable		Point	Expression
3.0ms	x	@	-inf	(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))
1.0ms	x	@	inf	(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))
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 9 (pow.f64 x 2))

rewrite61.0ms (3%)

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 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 (.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 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(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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(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 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) (-.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 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Outputs

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fma.f64 (*.f64 (cbrt.f64 (fma.f64 9 (*.f64 x x) (*.f64 x -12))) (cbrt.f64 (fma.f64 9 (*.f64 x x) (*.f64 x -12)))) (cbrt.f64 (fma.f64 9 (*.f64 x x) (*.f64 x -12))) 3)))) (#(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 (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))))))))

simplify35.0ms (1.7%)

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 (6.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	154	1	155
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	154	6	160

Error

Counts

160 → 6

Alt Table

Status	Error	Program
✓	0.1b	(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))
▶	0.1b	(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))
	8.8b	(-.f64 (+.f64 3 (sqrt.f64 (.f64 (pow.f64 x 4) 81))) (.f64 12 x))
✓	0.1b	(fma.f64 x (fma.f64 x 9 -12) 3)
	53.3b	(fma.f64 x (pow.f64 (sqrt.f64 (fma.f64 x 9 -12)) 2) 3)
	0.8b	(pow.f64 (sqrt.f64 (fma.f64 x (fma.f64 x 9 -12) 3)) 2)

Compiler

Compiled 3008 to 2020 computations (32.8% saved)

localize7.0ms (0.3%)

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)

series8.0ms (0.4%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	(.f64 (.f64 x 3) x)
1.0ms	x	@	inf	(-.f64 (.f64 (.f64 x 3) x) (*.f64 x 4))
1.0ms	x	@	-inf	(-.f64 (.f64 (.f64 x 3) x) (*.f64 x 4))
1.0ms	x	@	0	(.f64 (.f64 x 3) x)
1.0ms	x	@	-inf	(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))

rewrite75.0ms (3.7%)

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

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

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

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simplify40.0ms (2%)

Algorithm

1×	egg-herbie

Rules

694×	`fma-def_binary64`
441×	`fma-neg_binary64`
424×	`cancel-sign-sub-inv_binary64`
311×	`distribute-rgt-neg-in_binary64`
300×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	19	363
1	47	329
2	91	304
3	225	264
4	624	264
5	2025	264
6	4532	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 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))
(*.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 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 (.f64 x x) 9) (*.f64 -12 x)))
(+.f64 3 (fma.f64 (.f64 x x) 9 (.f64 x -12)))
(fma.f64 x -12 (fma.f64 x (*.f64 x 9) 3))
(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 (.f64 x x) 9) (*.f64 -12 x)))
(+.f64 3 (fma.f64 (.f64 x x) 9 (.f64 x -12)))
(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 9 (pow.f64 x 2)) (.f64 12 x))
(+.f64 (.f64 (.f64 x x) 9) (*.f64 -12 x))
(fma.f64 (.f64 x x) 9 (.f64 x -12))
(.f64 x (+.f64 (.f64 x 9) -12))
(*.f64 x (fma.f64 x 9 -12))
(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))
(+.f64 3 (+.f64 (.f64 (.f64 x x) 9) (*.f64 -12 x)))
(+.f64 3 (fma.f64 (.f64 x x) 9 (.f64 x -12)))
(fma.f64 x -12 (fma.f64 x (*.f64 x 9) 3))
(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 (.f64 x x) 9) (*.f64 -12 x)))
(+.f64 3 (fma.f64 (.f64 x x) 9 (.f64 x -12)))
(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 9 (pow.f64 x 2)) (.f64 12 x))
(+.f64 (.f64 (.f64 x x) 9) (*.f64 -12 x))
(fma.f64 (.f64 x x) 9 (.f64 x -12))
(.f64 x (+.f64 (.f64 x 9) -12))
(*.f64 x (fma.f64 x 9 -12))
(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))
(+.f64 3 (+.f64 (.f64 (.f64 x x) 9) (*.f64 -12 x)))
(+.f64 3 (fma.f64 (.f64 x x) 9 (.f64 x -12)))
(fma.f64 x -12 (fma.f64 x (*.f64 x 9) 3))
(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 (.f64 x x) 9) (*.f64 -12 x)))
(+.f64 3 (fma.f64 (.f64 x x) 9 (.f64 x -12)))
(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))
(+.f64 (.f64 3 (.f64 x x)) (*.f64 x -4))
(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))
(+.f64 (.f64 3 (.f64 x x)) (*.f64 x -4))
(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))
(+.f64 (.f64 3 (.f64 x x)) (*.f64 x -4))
(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))
(+.f64 (.f64 3 (.f64 x x)) (*.f64 x -4))
(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))
(+.f64 (.f64 3 (.f64 x x)) (*.f64 x -4))
(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))
(+.f64 (.f64 3 (.f64 x x)) (*.f64 x -4))
(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))
(+.f64 (.f64 3 (.f64 x x)) (*.f64 x -4))
(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))
(+.f64 (.f64 3 (.f64 x x)) (*.f64 x -4))
(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))
(+.f64 (.f64 3 (.f64 x x)) (*.f64 x -4))
(fma.f64 3 (.f64 x x) (.f64 x -4))
(.f64 x (-.f64 (.f64 3 x) 4))
(*.f64 x (fma.f64 3 x -4))

prune231.0ms (11.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	248	2	250
Fresh	2	1	3
Picked	0	1	1
Done	1	1	2
Total	251	5	256

Error

Counts

256 → 5

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 3 (*.f64 x (fma.f64 x 3 -4)) 3)
	0.1b	(.f64 3 (+.f64 (.f64 x (fma.f64 3 x -4)) 1))
	8.8b	(-.f64 (+.f64 3 (sqrt.f64 (.f64 (pow.f64 x 4) 81))) (.f64 12 x))
✓	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 5456 to 4225 computations (22.6% saved)

localize5.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series6.0ms (0.3%)

Counts

3 → 36

Calls

9 calls:

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

rewrite48.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

656×	`pow1_binary64`
609×	`add-log-exp_binary64`
609×	`log1p-expm1-u_binary64`
609×	`expm1-log1p-u_binary64`
70×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	25
1	143	25
2	1606	25

Stop Event

1×	node limit

Counts

3 → 60

Calls

Call 1

Inputs
(fma.f64 3 (*.f64 x (fma.f64 x 3 -4)) 3)
(*.f64 x (fma.f64 x 3 -4))
(fma.f64 x 3 -4)

Outputs

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

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

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

simplify37.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

703×	`fma-def_binary64`
441×	`fma-neg_binary64`
424×	`cancel-sign-sub-inv_binary64`
311×	`distribute-rgt-neg-in_binary64`
303×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	21	333
1	52	299
2	96	256
3	215	234
4	606	234
5	2014	234
6	4526	234

Stop Event

1×	node limit

Counts

96 → 79

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))
(*.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))
-4
(-.f64 (*.f64 3 x) 4)
(-.f64 (*.f64 3 x) 4)
(-.f64 (*.f64 3 x) 4)
(*.f64 3 x)
(-.f64 (*.f64 3 x) 4)
(-.f64 (*.f64 3 x) 4)
(-.f64 (*.f64 3 x) 4)
(*.f64 3 x)
(-.f64 (*.f64 3 x) 4)
(-.f64 (*.f64 3 x) 4)
(-.f64 (*.f64 3 x) 4)

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

prune72.0ms (3.5%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	79	0	79
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	79	5	84

Error

Counts

84 → 5

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 3 (*.f64 x (fma.f64 x 3 -4)) 3)
	0.1b	(.f64 3 (+.f64 (.f64 x (fma.f64 3 x -4)) 1))
	8.8b	(-.f64 (+.f64 3 (sqrt.f64 (.f64 (pow.f64 x 4) 81))) (.f64 12 x))
✓	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 1018 to 832 computations (18.3% saved)

regimes197.0ms (9.7%)

Accuracy

Total 0.1b remaining (80.2%)

Threshold costs 0.1b (80.2%)

Counts

57 → 1

Compiler

Compiled 2608 to 2041 computations (21.7% saved)

simplify2.0ms (0.1%)

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)

end91.0ms (4.4%)

Stop Event

1×

fuel

Compiler

Compiled 72 to 57 computations (20.8% saved)

Details

analyze6.0ms (0.3%)

sample753.0ms (36.9%)

preprocess52.0ms (2.6%)

simplify43.0ms (2.1%)

prune3.0ms (0.1%)

localize4.0ms (0.2%)

series3.0ms (0.2%)

rewrite35.0ms (1.7%)

simplify40.0ms (1.9%)

prune43.0ms (2.1%)

localize6.0ms (0.3%)

series7.0ms (0.3%)

rewrite61.0ms (3%)

simplify35.0ms (1.7%)

prune131.0ms (6.4%)

localize7.0ms (0.3%)

series8.0ms (0.4%)

rewrite75.0ms (3.7%)

simplify40.0ms (2%)

prune231.0ms (11.3%)

localize5.0ms (0.2%)

series6.0ms (0.3%)

rewrite48.0ms (2.4%)

simplify37.0ms (1.8%)

prune72.0ms (3.5%)

regimes197.0ms (9.7%)

simplify2.0ms (0.1%)

end91.0ms (4.4%)

Profiling