Details

analyze3.0ms (0.2%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
0%	0%	100%	0%	0%	0%	0%	2
50%	50%	50%	0%	0%	0%	0%	3
66.7%	50%	25%	0%	25%	0%	0%	4
83.3%	62.5%	12.5%	0%	25%	0%	0%	5
91.7%	68.7%	6.2%	0%	25%	0%	0%	6
95.8%	71.8%	3.1%	0%	25%	0%	0%	7
97.9%	73.4%	1.6%	0%	25%	0%	0%	8
99%	74.2%	0.8%	0%	25%	0%	0%	9
99.5%	74.6%	0.4%	0%	25%	0%	0%	10
99.7%	74.8%	0.2%	0%	25%	0%	0%	11
99.9%	74.9%	0.1%	0%	25%	0%	0%	12

Compiler

Compiled 7 to 5 computations (28.6% saved)

sample1.1s (73.8%)

Results

1.1s	8256×	body	256	valid
0.0ms	2×	body	256	infinite

Bogosity

preprocess47.0ms (3%)

Algorithm

2×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`1-exp_binary64`
1×	`fma-def_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	5
1	9	5
0	1	1

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0

Outputs
0

Call 2

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

Outputs
(+.f64 (*.f64 x x) 1)
(fma.f64 x x 1)

Compiler

Compiled 7 to 5 computations (28.6% saved)

simplify8.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`1-exp_binary64`
1×	`fma-def_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	5
1	9	5

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

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

Outputs
(+.f64 (*.f64 x x) 1)
(fma.f64 x x 1)

eval1.0ms (0%)

Compiler: Compiled 10 to 6 computations (40% saved)

prune1.0ms (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

Counts

3 → 2

Alt Table

Click to see full alt table

Status	Error	Program
▶	0b	(fma.f64 x x 1)
▶	0.0b	(+.f64 (*.f64 x x) 1)

Compiler

Compiled 11 to 7 computations (36.4% saved)

localize4.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (*.f64 x x) 1)

Compiler

Compiled 11 to 5 computations (54.5% saved)

series1.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

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

rewrite47.0ms (3.1%)

Algorithm

1×	batch-egg-rewrite

Rules

466×	`pow1_binary64`
456×	`add-sqr-sqrt_binary64`
446×	`*-un-lft-identity_binary64`
437×	`add-log-exp_binary64`
437×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	5
1	104	5
2	1268	5

Stop Event

1×	node limit

Counts

1 → 30

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (fma.f64 x x 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 x 4) (fma.f64 x x -1)) (/.f64 1 (fma.f64 x x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (fma.f64 x x 1))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fma.f64 x x 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (fma.f64 x x 1)) (pow.f64 (cbrt.f64 (fma.f64 x x 1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (fma.f64 x x 1)) 2) (cbrt.f64 (fma.f64 x x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (hypot.f64 1 x) (hypot.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 1 (pow.f64 x 6)) (/.f64 1 (+.f64 (pow.f64 x 4) (-.f64 1 (.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 (pow.f64 x 4) -1) (/.f64 1 (fma.f64 x x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 x 4) (-.f64 1 (.f64 x x))) (+.f64 1 (pow.f64 x 6))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 x x -1) (+.f64 (pow.f64 x 4) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 x 6)) (+.f64 (pow.f64 x 4) (-.f64 1 (.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 x 6)) (+.f64 1 (-.f64 (pow.f64 x 4) (.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 4) -1) (fma.f64 x x -1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 1 (pow.f64 x 6))) (neg.f64 (+.f64 (pow.f64 x 4) (-.f64 1 (.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 x 4) -1)) (neg.f64 (fma.f64 x x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 x 4)) (-.f64 1 (.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 x x 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x x 1) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 x x 1)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 1 x) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 x x 1) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 x x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 x x 1) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 x x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 x x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log1p.f64 (.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x x 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 x x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x 4)) (pow.f64 (cbrt.f64 x) 2) 1)))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (fma.f64 x x 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 x 4) (fma.f64 x x -1)) (/.f64 1 (fma.f64 x x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 x x 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 x x 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 x x 1)) (pow.f64 (cbrt.f64 (fma.f64 x x 1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 x x 1)) 2) (cbrt.f64 (fma.f64 x x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 1 x) (hypot.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (pow.f64 x 6)) (/.f64 1 (+.f64 (pow.f64 x 4) (-.f64 1 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 x 4) -1) (/.f64 1 (fma.f64 x x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 x 4) (-.f64 1 (*.f64 x x))) (+.f64 1 (pow.f64 x 6))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 x x -1) (+.f64 (pow.f64 x 4) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 x 6)) (+.f64 (pow.f64 x 4) (-.f64 1 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 x 6)) (+.f64 1 (-.f64 (pow.f64 x 4) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 4) -1) (fma.f64 x x -1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 1 (pow.f64 x 6))) (neg.f64 (+.f64 (pow.f64 x 4) (-.f64 1 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 x 4) -1)) (neg.f64 (fma.f64 x x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 x 4)) (-.f64 1 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 x x 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x x 1) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 x x 1)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 1 x) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 x x 1) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 x x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 x x 1) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 x x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 x x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log1p.f64 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x x 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 x x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x 4)) (pow.f64 (cbrt.f64 x) 2) 1)))))

simplify162.0ms (10.5%)

Algorithm

1×	egg-herbie

Rules

1366×	`sqr-pow_binary64`
695×	`pow-sqr_binary64`
617×	`cube-prod_binary64`
611×	`fabs-mul_binary64`
434×	`unswap-sqr_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	72
1	13	54
2	20	54
3	31	54
4	60	54
5	162	54
6	581	54
7	1447	54
8	1631	54
9	1815	54
10	2023	54
11	2318	54
12	2709	54
13	3188	54
14	3754	54
15	4444	54
16	5281	54
17	5677	54
18	5967	54
19	6243	54
20	6317	54
21	6351	54
22	7292	54

Stop Event

1×	node limit

Counts

42 → 34

Calls

Call 1

Inputs
1
(+.f64 1 (pow.f64 x 2))
(+.f64 1 (pow.f64 x 2))
(+.f64 1 (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 1 (pow.f64 x 2))
(+.f64 1 (pow.f64 x 2))
(+.f64 1 (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 1 (pow.f64 x 2))
(+.f64 1 (pow.f64 x 2))
(+.f64 1 (pow.f64 x 2))

Outputs
1
(+.f64 1 (pow.f64 x 2))
(+.f64 1 (*.f64 x x))
(fma.f64 x x 1)
(+.f64 1 (pow.f64 x 2))
(+.f64 1 (*.f64 x x))
(fma.f64 x x 1)
(+.f64 1 (pow.f64 x 2))
(+.f64 1 (*.f64 x x))
(fma.f64 x x 1)
(pow.f64 x 2)
(*.f64 x x)
(+.f64 1 (pow.f64 x 2))
(+.f64 1 (*.f64 x x))
(fma.f64 x x 1)
(+.f64 1 (pow.f64 x 2))
(+.f64 1 (*.f64 x x))
(fma.f64 x x 1)
(+.f64 1 (pow.f64 x 2))
(+.f64 1 (*.f64 x x))
(fma.f64 x x 1)
(pow.f64 x 2)
(*.f64 x x)
(+.f64 1 (pow.f64 x 2))
(+.f64 1 (*.f64 x x))
(fma.f64 x x 1)
(+.f64 1 (pow.f64 x 2))
(+.f64 1 (*.f64 x x))
(fma.f64 x x 1)
(+.f64 1 (pow.f64 x 2))
(+.f64 1 (*.f64 x x))
(fma.f64 x x 1)

localize3.0ms (0.2%)

Compiler: Compiled 7 to 4 computations (42.9% saved)

eval17.0ms (1.1%)

Compiler: Compiled 302 to 209 computations (30.8% saved)

prune5.0ms (0.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	32	2	34
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	32	4	36

Error

Counts

36 → 4

Alt Table

Click to see full alt table

Status	Error	Program
	22.3b	1
✓	0b	(fma.f64 x x 1)
✓	0.0b	(+.f64 (*.f64 x x) 1)
▶	38.9b	(*.f64 x x)

Compiler

Compiled 17 to 11 computations (35.3% saved)

localize2.0ms (0.2%)

Compiler: Compiled 5 to 2 computations (60% saved)

eval0.0ms (0%)

Compiler: Compiled 1 to 1 computations (0% saved)

prune3.0ms (0.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	1	1
Done	2	2
Total	4	4

Error

Counts

4 → 4

Alt Table

Click to see full alt table

Status	Error	Program
	22.3b	1
✓	0b	(fma.f64 x x 1)
✓	0.0b	(+.f64 (*.f64 x x) 1)
✓	38.9b	(*.f64 x x)

Compiler

Compiled 17 to 11 computations (35.3% saved)

eval0.0ms (0%)

Compiler: Compiled 1 to 1 computations (0% saved)

prune2.0ms (0.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	3	3
Total	4	4

Error

Counts

4 → 4

Alt Table

Click to see full alt table

Status	Error	Program
	22.3b	1
✓	0b	(fma.f64 x x 1)
✓	0.0b	(+.f64 (*.f64 x x) 1)
✓	38.9b	(*.f64 x x)

Compiler

Compiled 17 to 11 computations (35.3% saved)

eval0.0ms (0%)

Compiler: Compiled 1 to 1 computations (0% saved)

prune2.0ms (0.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	3	3
Total	4	4

Error

Counts

4 → 4

Alt Table

Click to see full alt table

Status	Error	Program
	22.3b	1
✓	0b	(fma.f64 x x 1)
✓	0.0b	(+.f64 (*.f64 x x) 1)
✓	38.9b	(*.f64 x x)

Compiler

Compiled 17 to 11 computations (35.3% saved)

regimes17.0ms (1.1%)

Counts

4 → 1

Calls

Call 1

Inputs
1
(*.f64 x x)
(+.f64 (*.f64 x x) 1)
(fma.f64 x x 1)

Outputs
(fma.f64 x x 1)

Calls

5 calls:

4.0ms	x
3.0ms	(+.f64 (*.f64 x x) 1)
3.0ms	(*.f64 x x)
3.0ms	(*.f64 x x)
2.0ms	(+.f64 (*.f64 x x) 1)

Results

Error	Segments	Branch
0b	1	`x`
0b	1	`(+.f64 (*.f64 x x) 1)`
0b	1	`(+.f64 (*.f64 x x) 1)`
0b	1	`(*.f64 x x)`
0b	1	`(*.f64 x x)`

Compiler

Compiled 36 to 20 computations (44.4% saved)

regimes10.0ms (0.7%)

Counts

3 → 1

Calls

Call 1

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

Outputs
(+.f64 (*.f64 x x) 1)

Calls

3 calls:

4.0ms	x
3.0ms	(+.f64 (*.f64 x x) 1)
3.0ms	(*.f64 x x)

Results

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

Compiler

Compiled 22 to 12 computations (45.5% saved)

regimes16.0ms (1%)

Accuracy

Total -61.0b remaining (-124155.9%)

Threshold costs -61.0b (-124155.9%)

Counts

2 → 2

Calls

Call 1

Inputs
1
(*.f64 x x)

Outputs
1
(*.f64 x x)

Calls

2 calls:

11.0ms	x
4.0ms	(*.f64 x x)

Results

Error	Segments	Branch
0.0b	3	`x`
0.0b	2	`(*.f64 x x)`

Compiler

Compiled 11 to 6 computations (45.5% saved)

bsearch11.0ms (0.7%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
11.0ms	4.874764784896079e-18	7253660980743.06

Compiler

Compiled 10 to 7 computations (30% saved)

simplify6.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	27
1	13	27

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(fma.f64 x x 1)
(+.f64 (*.f64 x x) 1)
(if (<=.f64 (.f64 x x) 6327806469678029/1298074214633706907132624082305024) 1 (.f64 x x))
1

Outputs
(fma.f64 x x 1)
(+.f64 (*.f64 x x) 1)
(+.f64 1 (*.f64 x x))
(if (<=.f64 (.f64 x x) 6327806469678029/1298074214633706907132624082305024) 1 (.f64 x x))
1

Compiler

Compiled 24 to 15 computations (37.5% saved)

soundness7.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`1-exp_binary64`
1×	`fma-def_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	5
1	9	5

Stop Event

1×

saturated

Compiler

Compiled 11 to 7 computations (36.4% saved)

end27.0ms (1.7%)

Compiler: Compiled 21 to 11 computations (47.6% saved)

Details

analyze3.0ms (0.2%)

sample1.1s (73.8%)

preprocess47.0ms (3%)

simplify8.0ms (0.5%)

eval1.0ms (0%)

prune1.0ms (0.1%)

localize4.0ms (0.3%)

series1.0ms (0.1%)

rewrite47.0ms (3.1%)

simplify162.0ms (10.5%)

localize3.0ms (0.2%)

eval17.0ms (1.1%)

prune5.0ms (0.4%)

localize2.0ms (0.2%)

eval0.0ms (0%)

prune3.0ms (0.2%)

eval0.0ms (0%)

prune2.0ms (0.1%)

eval0.0ms (0%)

prune2.0ms (0.1%)

regimes17.0ms (1.1%)

regimes10.0ms (0.7%)

regimes16.0ms (1%)

bsearch11.0ms (0.7%)

simplify6.0ms (0.4%)

soundness7.0ms (0.5%)

end27.0ms (1.7%)

Profiling