Details

analyze156.0ms (13.6%)

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
25%	74.9%	0.1%	5
25%	62.4%	12.6%	6
37.5%	50%	12.6%	7
46.8%	37.5%	15.7%	8
53.1%	30.4%	16.5%	9
58.5%	20.7%	20.8%	10
62%	16.2%	21.8%	11
65%	10.8%	24.2%	12
66.8%	8.3%	24.8%	13
68.3%	5.5%	26.1%	14

Compiler

Compiled 12 to 8 computations (33.3% saved)

sample777.0ms (67.7%)

Results

744.0ms	8256×	body	128	valid
21.0ms	249×	body	128	invalid

Compiler

Compiled 24 to 16 computations (33.3% saved)

preprocess14.0ms (1.2%)

Algorithm

2×	egg-herbie

Rules

30×	`fma-def_binary64`
17×	`*-commutative_binary64`
10×	`distribute-rgt-out_binary64`
8×	`associate-r_binary64`
8×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	20
1	38	20
2	77	20
3	130	20
4	134	20
0	2	2

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0
1

Outputs
0
1

Call 2

Inputs
(.f64 2 (+.f64 (.f64 x x) (*.f64 x y)))
(.f64 2 (+.f64 (.f64 y y) (*.f64 y x)))

Outputs
(.f64 2 (+.f64 (.f64 x x) (*.f64 x y)))
(.f64 2 (.f64 x (+.f64 x y)))
(.f64 (.f64 2 x) (+.f64 x y))
(.f64 (+.f64 x y) (.f64 2 x))
(.f64 2 (+.f64 (.f64 y y) (*.f64 y x)))
(.f64 2 (.f64 y (+.f64 y x)))
(.f64 2 (.f64 y (+.f64 x y)))

Compiler

Compiled 11 to 7 computations (36.4% saved)

simplify7.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

17×	`fma-def_binary64`
13×	`*-commutative_binary64`
6×	`distribute-rgt-out_binary64`
5×	`associate-r_binary64`
5×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	20	10
2	43	10
3	74	10
4	78	10

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

Inputs
(.f64 2 (+.f64 (.f64 x x) (*.f64 x y)))

Outputs
(.f64 2 (+.f64 (.f64 x x) (*.f64 x y)))
(.f64 2 (.f64 x (+.f64 x y)))

prune5.0ms (0.4%)

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

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.0b	(.f64 2 (.f64 x (+.f64 x y)))
	0.0b	(.f64 2 (+.f64 (.f64 x x) (*.f64 x y)))

Compiler

Compiled 58 to 37 computations (36.2% saved)

localize4.0ms (0.3%)

Local error

Found 1 expressions with local error:

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

series3.0ms (0.3%)

Counts

1 → 24

Calls

6 calls:

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

rewrite32.0ms (2.8%)

Algorithm

1×	batch-egg-rewrite

Rules

644×	`pow1_binary64`
601×	`add-log-exp_binary64`
601×	`log1p-expm1-u_binary64`
601×	`expm1-log1p-u_binary64`
60×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	112	7
2	1633	7

Stop Event

1×	node limit

Counts

1 → 24

Calls

Call 1

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

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

Outputs

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

simplify69.0ms (6%)

Algorithm

1×	egg-herbie

Rules

471×	`fma-def_binary64`
466×	`sqr-pow_binary64`
434×	`unswap-sqr_binary64`
281×	`cube-prod_binary64`
272×	`fabs-mul_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	168
1	15	150
2	29	150
3	51	150
4	110	150
5	307	150
6	1033	150
7	2180	150
8	2527	150
9	2719	150
10	2929	150
11	3225	150
12	3632	150
13	4114	150
14	4679	150

Stop Event

1×	node limit

Counts

48 → 29

Calls

Call 1

Inputs
(*.f64 y x)
(+.f64 (*.f64 y x) (pow.f64 x 2))
(+.f64 (*.f64 y x) (pow.f64 x 2))
(+.f64 (*.f64 y x) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 y x) (pow.f64 x 2))
(+.f64 (*.f64 y x) (pow.f64 x 2))
(+.f64 (*.f64 y x) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 y x) (pow.f64 x 2))
(+.f64 (*.f64 y x) (pow.f64 x 2))
(+.f64 (*.f64 y x) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 y x) (pow.f64 x 2))
(+.f64 (*.f64 y x) (pow.f64 x 2))
(+.f64 (*.f64 y x) (pow.f64 x 2))
(*.f64 y x)
(+.f64 (*.f64 y x) (pow.f64 x 2))
(+.f64 (*.f64 y x) (pow.f64 x 2))
(+.f64 (*.f64 y x) (pow.f64 x 2))
(*.f64 y x)
(+.f64 (*.f64 y x) (pow.f64 x 2))
(+.f64 (*.f64 y x) (pow.f64 x 2))
(+.f64 (*.f64 y x) (pow.f64 x 2))

Outputs
(*.f64 y x)
(+.f64 (*.f64 y x) (pow.f64 x 2))
(fma.f64 y x (*.f64 x x))
(*.f64 x (+.f64 y x))
(+.f64 (*.f64 y x) (pow.f64 x 2))
(fma.f64 y x (*.f64 x x))
(*.f64 x (+.f64 y x))
(+.f64 (*.f64 y x) (pow.f64 x 2))
(fma.f64 y x (*.f64 x x))
(*.f64 x (+.f64 y x))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 y x) (pow.f64 x 2))
(fma.f64 y x (*.f64 x x))
(*.f64 x (+.f64 y x))
(+.f64 (*.f64 y x) (pow.f64 x 2))
(fma.f64 y x (*.f64 x x))
(*.f64 x (+.f64 y x))
(+.f64 (*.f64 y x) (pow.f64 x 2))
(fma.f64 y x (*.f64 x x))
(*.f64 x (+.f64 y x))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 y x) (pow.f64 x 2))
(fma.f64 y x (*.f64 x x))
(*.f64 x (+.f64 y x))
(+.f64 (*.f64 y x) (pow.f64 x 2))
(fma.f64 y x (*.f64 x x))
(*.f64 x (+.f64 y x))
(+.f64 (*.f64 y x) (pow.f64 x 2))
(fma.f64 y x (*.f64 x x))
(*.f64 x (+.f64 y x))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 y x) (pow.f64 x 2))
(fma.f64 y x (*.f64 x x))
(*.f64 x (+.f64 y x))
(+.f64 (*.f64 y x) (pow.f64 x 2))
(fma.f64 y x (*.f64 x x))
(*.f64 x (+.f64 y x))
(+.f64 (*.f64 y x) (pow.f64 x 2))
(fma.f64 y x (*.f64 x x))
(*.f64 x (+.f64 y x))
(*.f64 y x)
(+.f64 (*.f64 y x) (pow.f64 x 2))
(fma.f64 y x (*.f64 x x))
(*.f64 x (+.f64 y x))
(+.f64 (*.f64 y x) (pow.f64 x 2))
(fma.f64 y x (*.f64 x x))
(*.f64 x (+.f64 y x))
(+.f64 (*.f64 y x) (pow.f64 x 2))
(fma.f64 y x (*.f64 x x))
(*.f64 x (+.f64 y x))
(*.f64 y x)
(+.f64 (*.f64 y x) (pow.f64 x 2))
(fma.f64 y x (*.f64 x x))
(*.f64 x (+.f64 y x))
(+.f64 (*.f64 y x) (pow.f64 x 2))
(fma.f64 y x (*.f64 x x))
(*.f64 x (+.f64 y x))
(+.f64 (*.f64 y x) (pow.f64 x 2))
(fma.f64 y x (*.f64 x x))
(*.f64 x (+.f64 y x))

prune14.0ms (1.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	28	1	29
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	30	1	31

Error

Counts

31 → 1

Alt Table

Status	Error	Program
▶	0b	(.f64 2 (fma.f64 x x (.f64 x y)))

Compiler

Compiled 366 to 175 computations (52.2% saved)

localize5.0ms (0.4%)

prune1.0ms (0.1%)

Pruning

1 alts after pruning (0 fresh and 1 done)

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

Error

Counts

1 → 1

Alt Table

Status	Error	Program
✓	0b	(.f64 2 (fma.f64 x x (.f64 x y)))

Compiler

Compiled 10 to 6 computations (40% saved)

regimes26.0ms (2.3%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0.0b (0%)

Counts

6 → 1

Compiler

Compiled 67 to 39 computations (41.8% saved)

simplify2.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	9	11

Stop Event

1×

saturated

Calls

Call 1

Inputs
(.f64 2 (fma.f64 x x (.f64 x y)))

Outputs
(.f64 2 (fma.f64 x x (.f64 x y)))

end34.0ms (3%)

Stop Event

1×

done

Compiler

Compiled 30 to 18 computations (40% saved)

Details

analyze156.0ms (13.6%)

sample777.0ms (67.7%)

preprocess14.0ms (1.2%)

simplify7.0ms (0.6%)

prune5.0ms (0.4%)

localize4.0ms (0.3%)

series3.0ms (0.3%)

rewrite32.0ms (2.8%)

simplify69.0ms (6%)

prune14.0ms (1.2%)

localize5.0ms (0.4%)

prune1.0ms (0.1%)

regimes26.0ms (2.3%)

simplify2.0ms (0.2%)

end34.0ms (3%)

Profiling