Details

analyze178.0ms (5.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
18.7%	81.1%	0.1%	8
28.1%	71.8%	0.1%	9
34.3%	59.3%	6.4%	10
40.6%	51.3%	8.1%	11
48%	43.2%	8.8%	12

Compiler

Compiled 11 to 7 computations (36.4% saved)

sample1.4s (44.2%)

Results

1.2s	8256×	body	256	valid
167.0ms	1226×	body	256	invalid

preprocess104.0ms (3.3%)

Algorithm

2×	egg-herbie

Rules

869×	`fma-neg_binary64`
384×	`fma-def_binary64`
156×	`unsub-neg_binary64`
145×	`distribute-rgt-in_binary64`
108×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	40
1	31	32
2	73	32
3	176	32
4	317	32
5	656	32
6	1272	32
7	2021	32
8	2747	32
9	2910	32
10	2938	32
11	2938	32
0	3	3

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0
1
2

Outputs
0
1
2

Call 2

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

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

Compiler

Compiled 13 to 9 computations (30.8% saved)

simplify20.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

276×	`fma-def_binary64`
251×	`fma-neg_binary64`
71×	`cancel-sign-sub-inv_binary64`
55×	`distribute-rgt-in_binary64`
42×	`sub-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	11	8
2	24	8
3	52	8
4	100	8
5	171	8
6	281	8
7	481	8
8	875	8
9	1116	8
10	1216	8
11	1223	8

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

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

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

eval0.0ms (0%)

Compiler: Compiled 16 to 7 computations (56.3% saved)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.0b

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.0b	(+.f64 x (*.f64 (-.f64 y x) z))

Compiler

Compiled 10 to 6 computations (40% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(*.f64 (-.f64 y x) z)
✓	0.0b	(*.f64 (-.f64 y x) z)

Compiler

Compiled 21 to 6 computations (71.4% saved)

series4.0ms (0.1%)

Counts

1 → 24

Calls

9 calls:

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

rewrite91.0ms (2.9%)

Algorithm

1×	batch-egg-rewrite

Rules

725×	`pow1_binary64`
672×	`add-log-exp_binary64`
672×	`log1p-expm1-u_binary64`
672×	`expm1-log1p-u_binary64`
657×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	129	7
2	1780	7

Stop Event

1×	node limit

Counts

1 → 19

Calls

Call 1

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

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

Outputs

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

simplify32.0ms (1%)

Algorithm

1×	egg-herbie

Rules

217×	`fma-def_binary64`
132×	`fma-neg_binary64`
41×	`cancel-sign-sub-inv_binary64`
25×	`distribute-rgt-in_binary64`
25×	`sub-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	210
1	17	210
2	35	156
3	58	156
4	86	156
5	138	156
6	254	156
7	410	156
8	576	156
9	730	156
10	744	156

Stop Event

1×

saturated

Counts

43 → 25

Calls

Call 1

Inputs
(.f64 -1 (.f64 z x))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(*.f64 y z)
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(*.f64 y z)
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(*.f64 y z)
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(.f64 -1 (.f64 z x))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(.f64 -1 (.f64 z x))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))

Outputs
(.f64 -1 (.f64 z x))
(neg.f64 (*.f64 z x))
(*.f64 x (neg.f64 z))
(*.f64 z (neg.f64 x))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(fma.f64 y z (neg.f64 (*.f64 z x)))
(-.f64 (.f64 z y) (.f64 z x))
(*.f64 z (-.f64 y x))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(fma.f64 y z (neg.f64 (*.f64 z x)))
(-.f64 (.f64 z y) (.f64 z x))
(*.f64 z (-.f64 y x))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(fma.f64 y z (neg.f64 (*.f64 z x)))
(-.f64 (.f64 z y) (.f64 z x))
(*.f64 z (-.f64 y x))
(*.f64 y z)
(*.f64 z y)
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(fma.f64 y z (neg.f64 (*.f64 z x)))
(-.f64 (.f64 z y) (.f64 z x))
(*.f64 z (-.f64 y x))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(fma.f64 y z (neg.f64 (*.f64 z x)))
(-.f64 (.f64 z y) (.f64 z x))
(*.f64 z (-.f64 y x))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(fma.f64 y z (neg.f64 (*.f64 z x)))
(-.f64 (.f64 z y) (.f64 z x))
(*.f64 z (-.f64 y x))
(*.f64 y z)
(*.f64 z y)
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(fma.f64 y z (neg.f64 (*.f64 z x)))
(-.f64 (.f64 z y) (.f64 z x))
(*.f64 z (-.f64 y x))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(fma.f64 y z (neg.f64 (*.f64 z x)))
(-.f64 (.f64 z y) (.f64 z x))
(*.f64 z (-.f64 y x))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(fma.f64 y z (neg.f64 (*.f64 z x)))
(-.f64 (.f64 z y) (.f64 z x))
(*.f64 z (-.f64 y x))
(*.f64 y z)
(*.f64 z y)
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(fma.f64 y z (neg.f64 (*.f64 z x)))
(-.f64 (.f64 z y) (.f64 z x))
(*.f64 z (-.f64 y x))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(fma.f64 y z (neg.f64 (*.f64 z x)))
(-.f64 (.f64 z y) (.f64 z x))
(*.f64 z (-.f64 y x))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(fma.f64 y z (neg.f64 (*.f64 z x)))
(-.f64 (.f64 z y) (.f64 z x))
(*.f64 z (-.f64 y x))
(.f64 -1 (.f64 z x))
(neg.f64 (*.f64 z x))
(*.f64 x (neg.f64 z))
(*.f64 z (neg.f64 x))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(fma.f64 y z (neg.f64 (*.f64 z x)))
(-.f64 (.f64 z y) (.f64 z x))
(*.f64 z (-.f64 y x))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(fma.f64 y z (neg.f64 (*.f64 z x)))
(-.f64 (.f64 z y) (.f64 z x))
(*.f64 z (-.f64 y x))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(fma.f64 y z (neg.f64 (*.f64 z x)))
(-.f64 (.f64 z y) (.f64 z x))
(*.f64 z (-.f64 y x))
(.f64 -1 (.f64 z x))
(neg.f64 (*.f64 z x))
(*.f64 x (neg.f64 z))
(*.f64 z (neg.f64 x))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(fma.f64 y z (neg.f64 (*.f64 z x)))
(-.f64 (.f64 z y) (.f64 z x))
(*.f64 z (-.f64 y x))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(fma.f64 y z (neg.f64 (*.f64 z x)))
(-.f64 (.f64 z y) (.f64 z x))
(*.f64 z (-.f64 y x))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(fma.f64 y z (neg.f64 (*.f64 z x)))
(-.f64 (.f64 z y) (.f64 z x))
(*.f64 z (-.f64 y x))

eval4.0ms (0.1%)

Compiler: Compiled 265 to 111 computations (58.1% saved)

prune10.0ms (0.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	22	3	25
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	22	4	26

Error

0.0b

Counts

26 → 4

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.0b	(+.f64 x (+.f64 (.f64 y z) (.f64 (neg.f64 x) z)))
▶	15.0b	(+.f64 x (*.f64 y z))
▶	21.1b	(+.f64 x (*.f64 z (neg.f64 x)))
✓	0.0b	(+.f64 x (*.f64 (-.f64 y x) z))

Compiler

Compiled 40 to 25 computations (37.5% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(+.f64 x (*.f64 z (neg.f64 x)))
✓	0.0b	(+.f64 x (*.f64 z (neg.f64 x)))

Compiler

Compiled 17 to 6 computations (64.7% saved)

series3.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(+.f64 x (*.f64 z (neg.f64 x)))
1.0ms	x	@	0	(+.f64 x (*.f64 z (neg.f64 x)))
0.0ms	z	@	0	(+.f64 x (*.f64 z (neg.f64 x)))
0.0ms	z	@	inf	(+.f64 x (*.f64 z (neg.f64 x)))
0.0ms	x	@	-inf	(+.f64 x (*.f64 z (neg.f64 x)))

rewrite37.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

618×	`pow1_binary64`
575×	`add-log-exp_binary64`
574×	`log1p-expm1-u_binary64`
574×	`expm1-log1p-u_binary64`
562×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	134	5
2	2002	5

Stop Event

1×	node limit

Counts

1 → 38

Calls

Call 1

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

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

Outputs

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

simplify15.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

171×	`fma-def_binary64`
66×	`fma-neg_binary64`
26×	`associate-l_binary64`
24×	`distribute-rgt-in_binary64`
23×	`associate-r_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	181
1	34	160
2	69	160
3	133	160
4	213	160
5	348	160
6	545	160
7	562	160

Stop Event

1×

saturated

Counts

62 → 45

Calls

Call 1

Inputs
(.f64 (+.f64 (.f64 -1 z) 1) x)
(.f64 (+.f64 (.f64 -1 z) 1) x)
(.f64 (+.f64 (.f64 -1 z) 1) x)
(.f64 (+.f64 (.f64 -1 z) 1) x)
(.f64 (+.f64 (.f64 -1 z) 1) x)
(.f64 (+.f64 (.f64 -1 z) 1) x)
(.f64 (+.f64 (.f64 -1 z) 1) x)
(.f64 (+.f64 (.f64 -1 z) 1) x)
(.f64 -1 (.f64 (-.f64 z 1) x))
(.f64 -1 (.f64 (-.f64 z 1) x))
(.f64 -1 (.f64 (-.f64 z 1) x))
(.f64 -1 (.f64 (-.f64 z 1) x))
x
(+.f64 (.f64 -1 (.f64 z x)) x)
(+.f64 (.f64 -1 (.f64 z x)) x)
(+.f64 (.f64 -1 (.f64 z x)) x)
(.f64 -1 (.f64 z x))
(+.f64 (.f64 -1 (.f64 z x)) x)
(+.f64 (.f64 -1 (.f64 z x)) x)
(+.f64 (.f64 -1 (.f64 z x)) x)
(.f64 -1 (.f64 z x))
(+.f64 (.f64 -1 (.f64 z x)) x)
(+.f64 (.f64 -1 (.f64 z x)) x)
(+.f64 (.f64 -1 (.f64 z x)) x)

Outputs
(.f64 (+.f64 (.f64 -1 z) 1) x)
(*.f64 (fma.f64 -1 z 1) x)
(fma.f64 (neg.f64 z) x x)
(.f64 (+.f64 (.f64 -1 z) 1) x)
(*.f64 (fma.f64 -1 z 1) x)
(fma.f64 (neg.f64 z) x x)
(.f64 (+.f64 (.f64 -1 z) 1) x)
(*.f64 (fma.f64 -1 z 1) x)
(fma.f64 (neg.f64 z) x x)
(.f64 (+.f64 (.f64 -1 z) 1) x)
(*.f64 (fma.f64 -1 z 1) x)
(fma.f64 (neg.f64 z) x x)
(.f64 (+.f64 (.f64 -1 z) 1) x)
(*.f64 (fma.f64 -1 z 1) x)
(fma.f64 (neg.f64 z) x x)
(.f64 (+.f64 (.f64 -1 z) 1) x)
(*.f64 (fma.f64 -1 z 1) x)
(fma.f64 (neg.f64 z) x x)
(.f64 (+.f64 (.f64 -1 z) 1) x)
(*.f64 (fma.f64 -1 z 1) x)
(fma.f64 (neg.f64 z) x x)
(.f64 (+.f64 (.f64 -1 z) 1) x)
(*.f64 (fma.f64 -1 z 1) x)
(fma.f64 (neg.f64 z) x x)
(.f64 -1 (.f64 (-.f64 z 1) x))
(*.f64 (fma.f64 -1 z 1) x)
(fma.f64 (neg.f64 z) x x)
(.f64 -1 (.f64 (-.f64 z 1) x))
(*.f64 (fma.f64 -1 z 1) x)
(fma.f64 (neg.f64 z) x x)
(.f64 -1 (.f64 (-.f64 z 1) x))
(*.f64 (fma.f64 -1 z 1) x)
(fma.f64 (neg.f64 z) x x)
(.f64 -1 (.f64 (-.f64 z 1) x))
(*.f64 (fma.f64 -1 z 1) x)
(fma.f64 (neg.f64 z) x x)
x
(+.f64 (.f64 -1 (.f64 z x)) x)
(*.f64 (fma.f64 -1 z 1) x)
(fma.f64 (neg.f64 z) x x)
(+.f64 (.f64 -1 (.f64 z x)) x)
(*.f64 (fma.f64 -1 z 1) x)
(fma.f64 (neg.f64 z) x x)
(+.f64 (.f64 -1 (.f64 z x)) x)
(*.f64 (fma.f64 -1 z 1) x)
(fma.f64 (neg.f64 z) x x)
(.f64 -1 (.f64 z x))
(*.f64 (neg.f64 z) x)
(*.f64 z (neg.f64 x))
(+.f64 (.f64 -1 (.f64 z x)) x)
(*.f64 (fma.f64 -1 z 1) x)
(fma.f64 (neg.f64 z) x x)
(+.f64 (.f64 -1 (.f64 z x)) x)
(*.f64 (fma.f64 -1 z 1) x)
(fma.f64 (neg.f64 z) x x)
(+.f64 (.f64 -1 (.f64 z x)) x)
(*.f64 (fma.f64 -1 z 1) x)
(fma.f64 (neg.f64 z) x x)
(.f64 -1 (.f64 z x))
(*.f64 (neg.f64 z) x)
(*.f64 z (neg.f64 x))
(+.f64 (.f64 -1 (.f64 z x)) x)
(*.f64 (fma.f64 -1 z 1) x)
(fma.f64 (neg.f64 z) x x)
(+.f64 (.f64 -1 (.f64 z x)) x)
(*.f64 (fma.f64 -1 z 1) x)
(fma.f64 (neg.f64 z) x x)
(+.f64 (.f64 -1 (.f64 z x)) x)
(*.f64 (fma.f64 -1 z 1) x)
(fma.f64 (neg.f64 z) x x)

localize5.0ms (0.2%)

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

localize114.0ms (3.6%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(+.f64 (.f64 y z) (.f64 (neg.f64 x) z))
✓	0.0b	(+.f64 (.f64 y z) (.f64 (neg.f64 x) z))

Compiler

Compiled 33 to 8 computations (75.8% saved)

series4.0ms (0.1%)

Counts

1 → 36

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	z	@	0	(+.f64 (.f64 y z) (.f64 (neg.f64 x) z))
1.0ms	z	@	inf	(+.f64 (.f64 y z) (.f64 (neg.f64 x) z))
1.0ms	y	@	0	(+.f64 (.f64 y z) (.f64 (neg.f64 x) z))
0.0ms	z	@	-inf	(+.f64 (.f64 y z) (.f64 (neg.f64 x) z))
0.0ms	y	@	inf	(+.f64 (.f64 y z) (.f64 (neg.f64 x) z))

rewrite45.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

835×	`pow1_binary64`
773×	`add-log-exp_binary64`
772×	`log1p-expm1-u_binary64`
772×	`expm1-log1p-u_binary64`
756×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	9
1	176	7
2	2561	7

Stop Event

1×	node limit

Counts

1 → 44

Calls

Call 1

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

Outputs

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

simplify121.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

146×	`fma-def_binary64`
108×	`fma-neg_binary64`
32×	`unsub-neg_binary64`
30×	`cancel-sign-sub-inv_binary64`
27×	`associate-r_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	330
1	46	240
2	102	240
3	179	240
4	315	240
5	497	240
6	611	240
7	652	240

Stop Event

1×

saturated

Counts

80 → 52

Calls

Call 1

Inputs
(.f64 -1 (.f64 z x))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(*.f64 y z)
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(*.f64 y z)
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(.f64 z (+.f64 y (.f64 -1 x)))
(.f64 z (+.f64 y (.f64 -1 x)))
(.f64 z (+.f64 y (.f64 -1 x)))
(.f64 z (+.f64 y (.f64 -1 x)))
(.f64 z (+.f64 y (.f64 -1 x)))
(.f64 z (+.f64 y (.f64 -1 x)))
(.f64 z (+.f64 y (.f64 -1 x)))
(.f64 z (+.f64 y (.f64 -1 x)))
(.f64 -1 (.f64 z (+.f64 (*.f64 -1 y) x)))
(.f64 -1 (.f64 z (+.f64 (*.f64 -1 y) x)))
(.f64 -1 (.f64 z (+.f64 (*.f64 -1 y) x)))
(.f64 -1 (.f64 z (+.f64 (*.f64 -1 y) x)))
(*.f64 y z)
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(.f64 -1 (.f64 z x))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(.f64 -1 (.f64 z x))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))

Outputs
(.f64 -1 (.f64 z x))
(neg.f64 (*.f64 z x))
(*.f64 x (neg.f64 z))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(fma.f64 y z (neg.f64 (*.f64 z x)))
(*.f64 z (-.f64 y x))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(fma.f64 y z (neg.f64 (*.f64 z x)))
(*.f64 z (-.f64 y x))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(fma.f64 y z (neg.f64 (*.f64 z x)))
(*.f64 z (-.f64 y x))
(*.f64 y z)
(*.f64 z y)
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(fma.f64 y z (neg.f64 (*.f64 z x)))
(*.f64 z (-.f64 y x))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(fma.f64 y z (neg.f64 (*.f64 z x)))
(*.f64 z (-.f64 y x))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(fma.f64 y z (neg.f64 (*.f64 z x)))
(*.f64 z (-.f64 y x))
(*.f64 y z)
(*.f64 z y)
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(fma.f64 y z (neg.f64 (*.f64 z x)))
(*.f64 z (-.f64 y x))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(fma.f64 y z (neg.f64 (*.f64 z x)))
(*.f64 z (-.f64 y x))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(fma.f64 y z (neg.f64 (*.f64 z x)))
(*.f64 z (-.f64 y x))
(.f64 z (+.f64 y (.f64 -1 x)))
(fma.f64 y z (neg.f64 (*.f64 z x)))
(*.f64 z (-.f64 y x))
(.f64 z (+.f64 y (.f64 -1 x)))
(fma.f64 y z (neg.f64 (*.f64 z x)))
(*.f64 z (-.f64 y x))
(.f64 z (+.f64 y (.f64 -1 x)))
(fma.f64 y z (neg.f64 (*.f64 z x)))
(*.f64 z (-.f64 y x))
(.f64 z (+.f64 y (.f64 -1 x)))
(fma.f64 y z (neg.f64 (*.f64 z x)))
(*.f64 z (-.f64 y x))
(.f64 z (+.f64 y (.f64 -1 x)))
(fma.f64 y z (neg.f64 (*.f64 z x)))
(*.f64 z (-.f64 y x))
(.f64 z (+.f64 y (.f64 -1 x)))
(fma.f64 y z (neg.f64 (*.f64 z x)))
(*.f64 z (-.f64 y x))
(.f64 z (+.f64 y (.f64 -1 x)))
(fma.f64 y z (neg.f64 (*.f64 z x)))
(*.f64 z (-.f64 y x))
(.f64 z (+.f64 y (.f64 -1 x)))
(fma.f64 y z (neg.f64 (*.f64 z x)))
(*.f64 z (-.f64 y x))
(.f64 -1 (.f64 z (+.f64 (*.f64 -1 y) x)))
(fma.f64 y z (neg.f64 (*.f64 z x)))
(*.f64 z (-.f64 y x))
(.f64 -1 (.f64 z (+.f64 (*.f64 -1 y) x)))
(fma.f64 y z (neg.f64 (*.f64 z x)))
(*.f64 z (-.f64 y x))
(.f64 -1 (.f64 z (+.f64 (*.f64 -1 y) x)))
(fma.f64 y z (neg.f64 (*.f64 z x)))
(*.f64 z (-.f64 y x))
(.f64 -1 (.f64 z (+.f64 (*.f64 -1 y) x)))
(fma.f64 y z (neg.f64 (*.f64 z x)))
(*.f64 z (-.f64 y x))
(*.f64 y z)
(*.f64 z y)
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(fma.f64 y z (neg.f64 (*.f64 z x)))
(*.f64 z (-.f64 y x))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(fma.f64 y z (neg.f64 (*.f64 z x)))
(*.f64 z (-.f64 y x))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(fma.f64 y z (neg.f64 (*.f64 z x)))
(*.f64 z (-.f64 y x))
(.f64 -1 (.f64 z x))
(neg.f64 (*.f64 z x))
(*.f64 x (neg.f64 z))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(fma.f64 y z (neg.f64 (*.f64 z x)))
(*.f64 z (-.f64 y x))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(fma.f64 y z (neg.f64 (*.f64 z x)))
(*.f64 z (-.f64 y x))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(fma.f64 y z (neg.f64 (*.f64 z x)))
(*.f64 z (-.f64 y x))
(.f64 -1 (.f64 z x))
(neg.f64 (*.f64 z x))
(*.f64 x (neg.f64 z))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(fma.f64 y z (neg.f64 (*.f64 z x)))
(*.f64 z (-.f64 y x))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(fma.f64 y z (neg.f64 (*.f64 z x)))
(*.f64 z (-.f64 y x))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(fma.f64 y z (neg.f64 (*.f64 z x)))
(*.f64 z (-.f64 y x))

eval16.0ms (0.5%)

Compiler: Compiled 1178 to 413 computations (64.9% saved)

prune18.0ms (0.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	93	4	97
Fresh	0	0	0
Picked	1	0	1
Done	1	2	3
Total	95	6	101

Error

0.0b

Counts

101 → 6

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.0b	(+.f64 x (-.f64 (.f64 y z) (.f64 z x)))
✓	15.0b	(+.f64 x (*.f64 y z))
▶	21.1b	(-.f64 x (*.f64 x z))
▶	48.1b	(*.f64 z (neg.f64 x))
	35.4b	x
✓	0.0b	(+.f64 x (*.f64 (-.f64 y x) z))

Compiler

Compiled 49 to 31 computations (36.7% saved)

localize5.0ms (0.1%)

Compiler: Compiled 11 to 5 computations (54.5% saved)

localize19.0ms (0.6%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(-.f64 x (*.f64 x z))
✓	0.0b	(-.f64 x (*.f64 x z))

Compiler

Compiled 13 to 5 computations (61.5% saved)

series2.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(-.f64 x (*.f64 x z))
0.0ms	z	@	-inf	(-.f64 x (*.f64 x z))
0.0ms	x	@	inf	(-.f64 x (*.f64 x z))
0.0ms	z	@	inf	(-.f64 x (*.f64 x z))
0.0ms	x	@	-inf	(-.f64 x (*.f64 x z))

rewrite35.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

649×	`pow1_binary64`
604×	`add-log-exp_binary64`
604×	`log1p-expm1-u_binary64`
604×	`expm1-log1p-u_binary64`
591×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	113	7
2	1644	7

Stop Event

1×	node limit

Counts

1 → 38

Calls

Call 1

Inputs
(-.f64 x (*.f64 x z))

Outputs

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

simplify47.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

145×	`fma-def_binary64`
71×	`fma-neg_binary64`
21×	`cancel-sign-sub-inv_binary64`
19×	`sub-neg_binary64`
18×	`associate-r_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	160
1	28	160
2	49	160
3	88	160
4	136	160
5	223	160
6	361	160
7	441	160
8	510	160
9	516	160

Stop Event

1×

saturated

Counts

62 → 45

Calls

Call 1

Inputs
(*.f64 (-.f64 1 z) x)
(*.f64 (-.f64 1 z) x)
(*.f64 (-.f64 1 z) x)
(*.f64 (-.f64 1 z) x)
(*.f64 (-.f64 1 z) x)
(*.f64 (-.f64 1 z) x)
(*.f64 (-.f64 1 z) x)
(*.f64 (-.f64 1 z) x)
(.f64 (+.f64 (.f64 -1 z) 1) x)
(.f64 (+.f64 (.f64 -1 z) 1) x)
(.f64 (+.f64 (.f64 -1 z) 1) x)
(.f64 (+.f64 (.f64 -1 z) 1) x)
x
(+.f64 (.f64 -1 (.f64 z x)) x)
(+.f64 (.f64 -1 (.f64 z x)) x)
(+.f64 (.f64 -1 (.f64 z x)) x)
(.f64 -1 (.f64 z x))
(+.f64 (.f64 -1 (.f64 z x)) x)
(+.f64 (.f64 -1 (.f64 z x)) x)
(+.f64 (.f64 -1 (.f64 z x)) x)
(.f64 -1 (.f64 z x))
(+.f64 (.f64 -1 (.f64 z x)) x)
(+.f64 (.f64 -1 (.f64 z x)) x)
(+.f64 (.f64 -1 (.f64 z x)) x)

Outputs
(*.f64 (-.f64 1 z) x)
(-.f64 x (*.f64 z x))
(*.f64 (-.f64 1 z) x)
(-.f64 x (*.f64 z x))
(*.f64 (-.f64 1 z) x)
(-.f64 x (*.f64 z x))
(*.f64 (-.f64 1 z) x)
(-.f64 x (*.f64 z x))
(*.f64 (-.f64 1 z) x)
(-.f64 x (*.f64 z x))
(*.f64 (-.f64 1 z) x)
(-.f64 x (*.f64 z x))
(*.f64 (-.f64 1 z) x)
(-.f64 x (*.f64 z x))
(*.f64 (-.f64 1 z) x)
(-.f64 x (*.f64 z x))
(.f64 (+.f64 (.f64 -1 z) 1) x)
(*.f64 (-.f64 1 z) x)
(-.f64 x (*.f64 z x))
(.f64 (+.f64 (.f64 -1 z) 1) x)
(*.f64 (-.f64 1 z) x)
(-.f64 x (*.f64 z x))
(.f64 (+.f64 (.f64 -1 z) 1) x)
(*.f64 (-.f64 1 z) x)
(-.f64 x (*.f64 z x))
(.f64 (+.f64 (.f64 -1 z) 1) x)
(*.f64 (-.f64 1 z) x)
(-.f64 x (*.f64 z x))
x
(+.f64 (.f64 -1 (.f64 z x)) x)
(*.f64 (-.f64 1 z) x)
(-.f64 x (*.f64 z x))
(+.f64 (.f64 -1 (.f64 z x)) x)
(*.f64 (-.f64 1 z) x)
(-.f64 x (*.f64 z x))
(+.f64 (.f64 -1 (.f64 z x)) x)
(*.f64 (-.f64 1 z) x)
(-.f64 x (*.f64 z x))
(.f64 -1 (.f64 z x))
(*.f64 (neg.f64 z) x)
(*.f64 z (neg.f64 x))
(*.f64 x (neg.f64 z))
(+.f64 (.f64 -1 (.f64 z x)) x)
(*.f64 (-.f64 1 z) x)
(-.f64 x (*.f64 z x))
(+.f64 (.f64 -1 (.f64 z x)) x)
(*.f64 (-.f64 1 z) x)
(-.f64 x (*.f64 z x))
(+.f64 (.f64 -1 (.f64 z x)) x)
(*.f64 (-.f64 1 z) x)
(-.f64 x (*.f64 z x))
(.f64 -1 (.f64 z x))
(*.f64 (neg.f64 z) x)
(*.f64 z (neg.f64 x))
(*.f64 x (neg.f64 z))
(+.f64 (.f64 -1 (.f64 z x)) x)
(*.f64 (-.f64 1 z) x)
(-.f64 x (*.f64 z x))
(+.f64 (.f64 -1 (.f64 z x)) x)
(*.f64 (-.f64 1 z) x)
(-.f64 x (*.f64 z x))
(+.f64 (.f64 -1 (.f64 z x)) x)
(*.f64 (-.f64 1 z) x)
(-.f64 x (*.f64 z x))

localize8.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (.f64 y z) (.f64 z x))
✓	0.0b	(-.f64 (.f64 y z) (.f64 z x))

Compiler

Compiled 28 to 7 computations (75% saved)

series2.0ms (0.1%)

Counts

1 → 36

Calls

9 calls:

Time	Variable		Point	Expression
0.0ms	z	@	inf	(-.f64 (.f64 y z) (.f64 z x))
0.0ms	y	@	0	(-.f64 (.f64 y z) (.f64 z x))
0.0ms	z	@	-inf	(-.f64 (.f64 y z) (.f64 z x))
0.0ms	x	@	-inf	(-.f64 (.f64 y z) (.f64 z x))
0.0ms	y	@	-inf	(-.f64 (.f64 y z) (.f64 z x))

rewrite48.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

877×	`pow1_binary64`
812×	`add-log-exp_binary64`
812×	`log1p-expm1-u_binary64`
812×	`expm1-log1p-u_binary64`
795×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	160	7
2	2221	7

Stop Event

1×	node limit

Counts

1 → 49

Calls

Call 1

Inputs
(-.f64 (.f64 y z) (.f64 z x))

Outputs

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

simplify21.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

118×	`fma-def_binary64`
80×	`fma-neg_binary64`
34×	`unsub-neg_binary64`
28×	`distribute-rgt-in_binary64`
26×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	330
1	43	240
2	97	240
3	240	240
4	399	240
5	520	240
6	589	240
7	594	240

Stop Event

1×

saturated

Counts

85 → 56

Calls

Call 1

Inputs
(.f64 -1 (.f64 z x))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(*.f64 y z)
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(*.f64 y z)
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(*.f64 (-.f64 y x) z)
(*.f64 (-.f64 y x) z)
(*.f64 (-.f64 y x) z)
(*.f64 (-.f64 y x) z)
(*.f64 (-.f64 y x) z)
(*.f64 (-.f64 y x) z)
(*.f64 (-.f64 y x) z)
(*.f64 (-.f64 y x) z)
(.f64 -1 (.f64 z (-.f64 (.f64 -1 y) (.f64 -1 x))))
(.f64 -1 (.f64 z (-.f64 (.f64 -1 y) (.f64 -1 x))))
(.f64 -1 (.f64 z (-.f64 (.f64 -1 y) (.f64 -1 x))))
(.f64 -1 (.f64 z (-.f64 (.f64 -1 y) (.f64 -1 x))))
(*.f64 y z)
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(.f64 -1 (.f64 z x))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(.f64 -1 (.f64 z x))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))

Outputs
(.f64 -1 (.f64 z x))
(neg.f64 (*.f64 z x))
(*.f64 x (neg.f64 z))
(*.f64 z (neg.f64 x))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(fma.f64 y z (neg.f64 (*.f64 z x)))
(*.f64 z (-.f64 y x))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(fma.f64 y z (neg.f64 (*.f64 z x)))
(*.f64 z (-.f64 y x))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(fma.f64 y z (neg.f64 (*.f64 z x)))
(*.f64 z (-.f64 y x))
(*.f64 y z)
(*.f64 z y)
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(fma.f64 y z (neg.f64 (*.f64 z x)))
(*.f64 z (-.f64 y x))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(fma.f64 y z (neg.f64 (*.f64 z x)))
(*.f64 z (-.f64 y x))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(fma.f64 y z (neg.f64 (*.f64 z x)))
(*.f64 z (-.f64 y x))
(*.f64 y z)
(*.f64 z y)
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(fma.f64 y z (neg.f64 (*.f64 z x)))
(*.f64 z (-.f64 y x))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(fma.f64 y z (neg.f64 (*.f64 z x)))
(*.f64 z (-.f64 y x))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(fma.f64 y z (neg.f64 (*.f64 z x)))
(*.f64 z (-.f64 y x))
(*.f64 (-.f64 y x) z)
(fma.f64 y z (neg.f64 (*.f64 z x)))
(*.f64 z (-.f64 y x))
(*.f64 (-.f64 y x) z)
(fma.f64 y z (neg.f64 (*.f64 z x)))
(*.f64 z (-.f64 y x))
(*.f64 (-.f64 y x) z)
(fma.f64 y z (neg.f64 (*.f64 z x)))
(*.f64 z (-.f64 y x))
(*.f64 (-.f64 y x) z)
(fma.f64 y z (neg.f64 (*.f64 z x)))
(*.f64 z (-.f64 y x))
(*.f64 (-.f64 y x) z)
(fma.f64 y z (neg.f64 (*.f64 z x)))
(*.f64 z (-.f64 y x))
(*.f64 (-.f64 y x) z)
(fma.f64 y z (neg.f64 (*.f64 z x)))
(*.f64 z (-.f64 y x))
(*.f64 (-.f64 y x) z)
(fma.f64 y z (neg.f64 (*.f64 z x)))
(*.f64 z (-.f64 y x))
(*.f64 (-.f64 y x) z)
(fma.f64 y z (neg.f64 (*.f64 z x)))
(*.f64 z (-.f64 y x))
(.f64 -1 (.f64 z (-.f64 (.f64 -1 y) (.f64 -1 x))))
(fma.f64 y z (neg.f64 (*.f64 z x)))
(*.f64 z (-.f64 y x))
(.f64 -1 (.f64 z (-.f64 (.f64 -1 y) (.f64 -1 x))))
(fma.f64 y z (neg.f64 (*.f64 z x)))
(*.f64 z (-.f64 y x))
(.f64 -1 (.f64 z (-.f64 (.f64 -1 y) (.f64 -1 x))))
(fma.f64 y z (neg.f64 (*.f64 z x)))
(*.f64 z (-.f64 y x))
(.f64 -1 (.f64 z (-.f64 (.f64 -1 y) (.f64 -1 x))))
(fma.f64 y z (neg.f64 (*.f64 z x)))
(*.f64 z (-.f64 y x))
(*.f64 y z)
(*.f64 z y)
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(fma.f64 y z (neg.f64 (*.f64 z x)))
(*.f64 z (-.f64 y x))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(fma.f64 y z (neg.f64 (*.f64 z x)))
(*.f64 z (-.f64 y x))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(fma.f64 y z (neg.f64 (*.f64 z x)))
(*.f64 z (-.f64 y x))
(.f64 -1 (.f64 z x))
(neg.f64 (*.f64 z x))
(*.f64 x (neg.f64 z))
(*.f64 z (neg.f64 x))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(fma.f64 y z (neg.f64 (*.f64 z x)))
(*.f64 z (-.f64 y x))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(fma.f64 y z (neg.f64 (*.f64 z x)))
(*.f64 z (-.f64 y x))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(fma.f64 y z (neg.f64 (*.f64 z x)))
(*.f64 z (-.f64 y x))
(.f64 -1 (.f64 z x))
(neg.f64 (*.f64 z x))
(*.f64 x (neg.f64 z))
(*.f64 z (neg.f64 x))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(fma.f64 y z (neg.f64 (*.f64 z x)))
(*.f64 z (-.f64 y x))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(fma.f64 y z (neg.f64 (*.f64 z x)))
(*.f64 z (-.f64 y x))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(fma.f64 y z (neg.f64 (*.f64 z x)))
(*.f64 z (-.f64 y x))

eval48.0ms (1.5%)

Compiler: Compiled 1458 to 415 computations (71.5% saved)

prune17.0ms (0.5%)

Pruning

7 alts after pruning (2 fresh and 5 done)

	Pruned	Kept	Total
New	100	1	101
Fresh	0	1	1
Picked	0	1	1
Done	0	4	4
Total	100	7	107

Error

Counts

107 → 7

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.0b	(+.f64 x (*.f64 (-.f64 y x) z))
▶	0.1b	(+.f64 x (+.f64 (.f64 z (-.f64 y x)) (+.f64 (fma.f64 (neg.f64 x) z (.f64 z x)) (fma.f64 (neg.f64 x) z (*.f64 z x)))))
✓	0.0b	(+.f64 x (-.f64 (.f64 y z) (.f64 z x)))
✓	15.0b	(+.f64 x (*.f64 y z))
✓	21.1b	(-.f64 x (*.f64 x z))
✓	48.1b	(*.f64 z (neg.f64 x))
	35.4b	x

Compiler

Compiled 75 to 42 computations (44% saved)

localize16.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	51.3b	(fma.f64 (neg.f64 x) z (*.f64 z x))
	0.0b	(*.f64 z (-.f64 y x))
✓	0.0b	(*.f64 z (-.f64 y x))
✓	51.3b	(fma.f64 (neg.f64 x) z (*.f64 z x))

Compiler

Compiled 85 to 11 computations (87.1% saved)

series6.0ms (0.2%)

Counts

2 → 60

Calls

15 calls:

Time	Variable		Point	Expression
1.0ms	z	@	inf	(fma.f64 (neg.f64 x) z (*.f64 z x))
1.0ms	z	@	-inf	(fma.f64 (neg.f64 x) z (*.f64 z x))
1.0ms	x	@	0	(fma.f64 (neg.f64 x) z (*.f64 z x))
0.0ms	z	@	0	(fma.f64 (neg.f64 x) z (*.f64 z x))
0.0ms	x	@	-inf	(fma.f64 (neg.f64 x) z (*.f64 z x))

rewrite154.0ms (4.9%)

Algorithm

1×	batch-egg-rewrite

Rules

901×	`pow1_binary64`
831×	`add-log-exp_binary64`
830×	`log1p-expm1-u_binary64`
830×	`expm1-log1p-u_binary64`
812×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	192	14
2	2666	14

Stop Event

1×	node limit

Counts

2 → 39

Calls

Call 1

Inputs
(fma.f64 (neg.f64 x) z (*.f64 z x))
(*.f64 z (-.f64 y x))

Outputs

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

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

simplify21.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

109×	`fma-def_binary64`
102×	`fma-neg_binary64`
34×	`associate-r_binary64`
32×	`distribute-rgt-in_binary64`
26×	`associate-l_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	408
1	56	264
2	111	264
3	146	264
4	223	264
5	377	264
6	627	264
7	673	264

Stop Event

1×

saturated

Counts

99 → 51

Calls

Call 1

Inputs
(.f64 (+.f64 (.f64 -1 z) z) x)
(.f64 (+.f64 (.f64 -1 z) z) x)
(.f64 (+.f64 (.f64 -1 z) z) x)
(.f64 (+.f64 (.f64 -1 z) z) x)
(.f64 (+.f64 (.f64 -1 z) z) x)
(.f64 (+.f64 (.f64 -1 z) z) x)
(.f64 (+.f64 (.f64 -1 z) z) x)
(.f64 (+.f64 (.f64 -1 z) z) x)
(.f64 -1 (.f64 (+.f64 (*.f64 -1 z) z) x))
(.f64 -1 (.f64 (+.f64 (*.f64 -1 z) z) x))
(.f64 -1 (.f64 (+.f64 (*.f64 -1 z) z) x))
(.f64 -1 (.f64 (+.f64 (*.f64 -1 z) z) x))
(.f64 z (+.f64 (.f64 -1 x) x))
(.f64 z (+.f64 (.f64 -1 x) x))
(.f64 z (+.f64 (.f64 -1 x) x))
(.f64 z (+.f64 (.f64 -1 x) x))
(.f64 z (+.f64 (.f64 -1 x) x))
(.f64 z (+.f64 (.f64 -1 x) x))
(.f64 z (+.f64 (.f64 -1 x) x))
(.f64 z (+.f64 (.f64 -1 x) x))
(.f64 -1 (.f64 z (+.f64 (*.f64 -1 x) x)))
(.f64 -1 (.f64 z (+.f64 (*.f64 -1 x) x)))
(.f64 -1 (.f64 z (+.f64 (*.f64 -1 x) x)))
(.f64 -1 (.f64 z (+.f64 (*.f64 -1 x) x)))
(*.f64 (-.f64 y x) z)
(*.f64 (-.f64 y x) z)
(*.f64 (-.f64 y x) z)
(*.f64 (-.f64 y x) z)
(*.f64 (-.f64 y x) z)
(*.f64 (-.f64 y x) z)
(*.f64 (-.f64 y x) z)
(*.f64 (-.f64 y x) z)
(*.f64 (-.f64 y x) z)
(*.f64 (-.f64 y x) z)
(*.f64 (-.f64 y x) z)
(*.f64 (-.f64 y x) z)
(.f64 -1 (.f64 z x))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(*.f64 y z)
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(*.f64 y z)
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(*.f64 y z)
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(.f64 -1 (.f64 z x))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(.f64 -1 (.f64 z x))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))

Outputs
(.f64 (+.f64 (.f64 -1 z) z) x)
(.f64 (.f64 0 z) x)
0
(.f64 (+.f64 (.f64 -1 z) z) x)
(.f64 (.f64 0 z) x)
0
(.f64 (+.f64 (.f64 -1 z) z) x)
(.f64 (.f64 0 z) x)
0
(.f64 (+.f64 (.f64 -1 z) z) x)
(.f64 (.f64 0 z) x)
0
(.f64 (+.f64 (.f64 -1 z) z) x)
(.f64 (.f64 0 z) x)
0
(.f64 (+.f64 (.f64 -1 z) z) x)
(.f64 (.f64 0 z) x)
0
(.f64 (+.f64 (.f64 -1 z) z) x)
(.f64 (.f64 0 z) x)
0
(.f64 (+.f64 (.f64 -1 z) z) x)
(.f64 (.f64 0 z) x)
0
(.f64 -1 (.f64 (+.f64 (*.f64 -1 z) z) x))
(.f64 (.f64 0 z) x)
0
(.f64 -1 (.f64 (+.f64 (*.f64 -1 z) z) x))
(.f64 (.f64 0 z) x)
0
(.f64 -1 (.f64 (+.f64 (*.f64 -1 z) z) x))
(.f64 (.f64 0 z) x)
0
(.f64 -1 (.f64 (+.f64 (*.f64 -1 z) z) x))
(.f64 (.f64 0 z) x)
0
(.f64 z (+.f64 (.f64 -1 x) x))
(.f64 (.f64 0 z) x)
0
(.f64 z (+.f64 (.f64 -1 x) x))
(.f64 (.f64 0 z) x)
0
(.f64 z (+.f64 (.f64 -1 x) x))
(.f64 (.f64 0 z) x)
0
(.f64 z (+.f64 (.f64 -1 x) x))
(.f64 (.f64 0 z) x)
0
(.f64 z (+.f64 (.f64 -1 x) x))
(.f64 (.f64 0 z) x)
0
(.f64 z (+.f64 (.f64 -1 x) x))
(.f64 (.f64 0 z) x)
0
(.f64 z (+.f64 (.f64 -1 x) x))
(.f64 (.f64 0 z) x)
0
(.f64 z (+.f64 (.f64 -1 x) x))
(.f64 (.f64 0 z) x)
0
(.f64 -1 (.f64 z (+.f64 (*.f64 -1 x) x)))
(.f64 (.f64 0 z) x)
0
(.f64 -1 (.f64 z (+.f64 (*.f64 -1 x) x)))
(.f64 (.f64 0 z) x)
0
(.f64 -1 (.f64 z (+.f64 (*.f64 -1 x) x)))
(.f64 (.f64 0 z) x)
0
(.f64 -1 (.f64 z (+.f64 (*.f64 -1 x) x)))
(.f64 (.f64 0 z) x)
0
(*.f64 (-.f64 y x) z)
(*.f64 z (-.f64 y x))
(*.f64 (-.f64 y x) z)
(*.f64 z (-.f64 y x))
(*.f64 (-.f64 y x) z)
(*.f64 z (-.f64 y x))
(*.f64 (-.f64 y x) z)
(*.f64 z (-.f64 y x))
(*.f64 (-.f64 y x) z)
(*.f64 z (-.f64 y x))
(*.f64 (-.f64 y x) z)
(*.f64 z (-.f64 y x))
(*.f64 (-.f64 y x) z)
(*.f64 z (-.f64 y x))
(*.f64 (-.f64 y x) z)
(*.f64 z (-.f64 y x))
(*.f64 (-.f64 y x) z)
(*.f64 z (-.f64 y x))
(*.f64 (-.f64 y x) z)
(*.f64 z (-.f64 y x))
(*.f64 (-.f64 y x) z)
(*.f64 z (-.f64 y x))
(*.f64 (-.f64 y x) z)
(*.f64 z (-.f64 y x))
(.f64 -1 (.f64 z x))
(*.f64 (neg.f64 z) x)
(*.f64 z (neg.f64 x))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(*.f64 z (-.f64 y x))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(*.f64 z (-.f64 y x))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(*.f64 z (-.f64 y x))
(*.f64 y z)
(*.f64 z y)
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(*.f64 z (-.f64 y x))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(*.f64 z (-.f64 y x))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(*.f64 z (-.f64 y x))
(*.f64 y z)
(*.f64 z y)
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(*.f64 z (-.f64 y x))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(*.f64 z (-.f64 y x))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(*.f64 z (-.f64 y x))
(*.f64 y z)
(*.f64 z y)
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(*.f64 z (-.f64 y x))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(*.f64 z (-.f64 y x))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(*.f64 z (-.f64 y x))
(.f64 -1 (.f64 z x))
(*.f64 (neg.f64 z) x)
(*.f64 z (neg.f64 x))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(*.f64 z (-.f64 y x))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(*.f64 z (-.f64 y x))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(*.f64 z (-.f64 y x))
(.f64 -1 (.f64 z x))
(*.f64 (neg.f64 z) x)
(*.f64 z (neg.f64 x))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(*.f64 z (-.f64 y x))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(*.f64 z (-.f64 y x))
(+.f64 (.f64 y z) (.f64 -1 (*.f64 z x)))
(*.f64 z (-.f64 y x))

eval15.0ms (0.5%)

Compiler: Compiled 1952 to 449 computations (77% saved)

prune14.0ms (0.4%)

Pruning

7 alts after pruning (1 fresh and 6 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	1	1
Picked	0	1	1
Done	0	5	5
Total	76	7	83

Error

Counts

83 → 7

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.0b	(+.f64 x (*.f64 (-.f64 y x) z))
✓	0.1b	(+.f64 x (+.f64 (.f64 z (-.f64 y x)) (+.f64 (fma.f64 (neg.f64 x) z (.f64 z x)) (fma.f64 (neg.f64 x) z (*.f64 z x)))))
✓	0.0b	(+.f64 x (-.f64 (.f64 y z) (.f64 z x)))
✓	15.0b	(+.f64 x (*.f64 y z))
✓	21.1b	(-.f64 x (*.f64 x z))
✓	48.1b	(*.f64 z (neg.f64 x))
	35.4b	x

Compiler

Compiled 75 to 42 computations (44% saved)

regimes22.0ms (0.7%)

Counts

7 → 1

Calls

Call 1

Inputs
x
(*.f64 z (neg.f64 x))
(-.f64 x (*.f64 x z))
(+.f64 x (*.f64 y z))
(+.f64 x (*.f64 (-.f64 y x) z))
(+.f64 x (-.f64 (.f64 y z) (.f64 z x)))
(+.f64 x (+.f64 (.f64 z (-.f64 y x)) (+.f64 (fma.f64 (neg.f64 x) z (.f64 z x)) (fma.f64 (neg.f64 x) z (*.f64 z x)))))

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

Calls

4 calls:

6.0ms	x
5.0ms	z
5.0ms	(+.f64 x (*.f64 (-.f64 y x) z))
5.0ms	y

Results

Error	Segments	Branch
0.0b	1	`x`
0.0b	1	`y`
0.0b	1	`z`
0.0b	1	`(+.f64 x (*.f64 (-.f64 y x) z))`

Compiler

Compiled 79 to 35 computations (55.7% saved)

regimes52.0ms (1.7%)

Counts

4 → 3

Calls

Call 1

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

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

Calls

3 calls:

28.0ms	z
12.0ms	x
10.0ms	y

Results

Error	Segments	Branch
8.6b	3	`x`
7.9b	3	`y`
10.7b	3	`z`

Compiler

Compiled 30 to 18 computations (40% saved)

bsearch35.0ms (1.1%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
20.0ms	3.794316329055393e+24	6.656267659888089e+27
15.0ms	-1.149756232658117e+26	-2.8193327722020287e+23

Compiler

Compiled 16 to 11 computations (31.3% saved)

regimes138.0ms (4.4%)

Counts

3 → 1

Calls

Call 1

Inputs
x
(*.f64 z (neg.f64 x))
(-.f64 x (*.f64 x z))

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

Calls

3 calls:

130.0ms	y
3.0ms	z
3.0ms	x

Results

Error	Segments	Branch
21.1b	1	`x`
21.1b	1	`y`
21.1b	1	`z`

Compiler

Compiled 25 to 16 computations (36% saved)

regimes28.0ms (0.9%)

Accuracy

Total -40.2b remaining (-184.7%)

Threshold costs -40.2b (-184.7%)

Counts

2 → 3

Calls

Call 1

Inputs
x
(*.f64 z (neg.f64 x))

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

Calls

3 calls:

11.0ms	x
9.0ms	z
8.0ms	y

Results

Error	Segments	Branch
32.5b	3	`x`
34.4b	3	`y`
21.7b	3	`z`

Compiler

Compiled 20 to 14 computations (30% saved)

bsearch37.0ms (1.2%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
22.0ms	1.0137383709752594e-11	2.445416525238844e-6
15.0ms	-4266169.684303526	-4.783005926315238e-12

Compiler

Compiled 16 to 11 computations (31.3% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

7×	`+-commutative_binary64`
7×	`*-commutative_binary64`
5×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	76
1	42	76
2	52	76
3	57	76
4	60	76
5	61	76

Stop Event

1×

saturated

Calls

Call 1

Inputs
(+.f64 x (*.f64 (-.f64 y x) z))
(if (<=.f64 y -114975623265811707962851328) (+.f64 x (.f64 y z)) (if (<=.f64 y 3794316329055393236910080) (-.f64 x (.f64 x z)) (+.f64 x (*.f64 y z))))
(-.f64 x (*.f64 x z))
(if (<=.f64 z -1145191204579393/268435456) (.f64 z (neg.f64 x)) (if (<=.f64 z 3137368296975525/309485009821345068724781056) x (.f64 z (neg.f64 x))))
x

Outputs
(+.f64 x (*.f64 (-.f64 y x) z))
(if (<=.f64 y -114975623265811707962851328) (+.f64 x (.f64 y z)) (if (<=.f64 y 3794316329055393236910080) (-.f64 x (.f64 x z)) (+.f64 x (*.f64 y z))))
(-.f64 x (*.f64 x z))
(if (<=.f64 z -1145191204579393/268435456) (.f64 z (neg.f64 x)) (if (<=.f64 z 3137368296975525/309485009821345068724781056) x (.f64 z (neg.f64 x))))
(if (<=.f64 z -1145191204579393/268435456) (.f64 x (neg.f64 z)) (if (<=.f64 z 3137368296975525/309485009821345068724781056) x (.f64 x (neg.f64 z))))
x

end118.0ms (3.8%)

Stop Event

1×

fuel

Compiler

Compiled 124 to 62 computations (50% saved)

Iter	Nodes	Cost
0	9	210
1	17	210
2	35	156
3	58	156
4	86	156
5	138	156
6	254	156
7	410	156
8	576	156
9	730	156
10	744	156

Iter	Nodes	Cost
0	13	160
1	28	160
2	49	160
3	88	160
4	136	160
5	223	160
6	361	160
7	441	160
8	510	160
9	516	160

Iter	Nodes	Cost
0	9	210
1	17	210
2	35	156
3	58	156
4	86	156
5	138	156
6	254	156
7	410	156
8	576	156
9	730	156
10	744	156

Iter	Nodes	Cost
0	13	160
1	28	160
2	49	160
3	88	160
4	136	160
5	223	160
6	361	160
7	441	160
8	510	160
9	516	160

Details

analyze178.0ms (5.7%)

sample1.4s (44.2%)

preprocess104.0ms (3.3%)

simplify20.0ms (0.6%)

eval0.0ms (0%)

prune1.0ms (0%)

localize6.0ms (0.2%)

series4.0ms (0.1%)

rewrite91.0ms (2.9%)

simplify32.0ms (1%)

eval4.0ms (0.1%)

prune10.0ms (0.3%)

localize6.0ms (0.2%)

series3.0ms (0.1%)

rewrite37.0ms (1.2%)

simplify15.0ms (0.5%)

localize5.0ms (0.2%)

localize114.0ms (3.6%)

series4.0ms (0.1%)

rewrite45.0ms (1.4%)

simplify121.0ms (3.9%)

eval16.0ms (0.5%)

prune18.0ms (0.6%)

localize5.0ms (0.1%)

localize19.0ms (0.6%)

series2.0ms (0.1%)

rewrite35.0ms (1.1%)

simplify47.0ms (1.5%)

localize8.0ms (0.3%)

series2.0ms (0.1%)

rewrite48.0ms (1.5%)

simplify21.0ms (0.7%)

eval48.0ms (1.5%)

prune17.0ms (0.5%)

localize16.0ms (0.5%)

series6.0ms (0.2%)

rewrite154.0ms (4.9%)

simplify21.0ms (0.7%)

eval15.0ms (0.5%)

prune14.0ms (0.4%)

regimes22.0ms (0.7%)

regimes52.0ms (1.7%)

bsearch35.0ms (1.1%)

regimes138.0ms (4.4%)

regimes28.0ms (0.9%)

bsearch37.0ms (1.2%)

simplify4.0ms (0.1%)

end118.0ms (3.8%)

Profiling

Iter	Nodes	Cost
0	9	210
1	17	210
2	35	156
3	58	156
4	86	156
5	138	156
6	254	156
7	410	156
8	576	156
9	730	156
10	744	156

Iter	Nodes	Cost
0	13	160
1	28	160
2	49	160
3	88	160
4	136	160
5	223	160
6	361	160
7	441	160
8	510	160
9	516	160