Details

analyze2.0s (33.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
0%	99.7%	0.3%	9
0%	99.7%	0.3%	10
0%	99.7%	0.3%	11
0%	99.7%	0.3%	12
1.6%	98.1%	0.3%	13
2.3%	97.4%	0.3%	14

Compiler

Compiled 28 to 20 computations (28.6% saved)

sample2.0s (32.6%)

Results

1.2s	8253×	body	128	valid
688.0ms	4599×	body	128	invalid
1.0ms	3×	body	512	valid

Compiler

Compiled 56 to 40 computations (28.6% saved)

preprocess33.0ms (0.5%)

Algorithm

2×	egg-herbie

Rules

567×	`fma-def_binary64`
428×	`associate-+l+_binary64`
390×	`associate--r+_binary64`
321×	`distribute-rgt-in_binary64`
291×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	111	496
1	369	432
2	1332	400
0	6	6

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 27 to 19 computations (29.6% saved)

simplify20.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

494×	`fma-neg_binary64`
457×	`associate--l-_binary64`
357×	`associate--r-_binary64`
300×	`sub-neg_binary64`
274×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	19	31
1	49	27
2	145	25
3	591	25
4	2190	25

Stop Event

1×	node limit

Counts

1 → 2

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(fma.f64 (+.f64 y (+.f64 t -2)) b (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x)))

Compiler

Compiled 93 to 61 computations (34.4% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 y (+.f64 t -2))
✓	0.0b	(fma.f64 (+.f64 y (+.f64 t -2)) b (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x)))
✓	0.0b	(fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x))
✓	0.0b	(fma.f64 a (-.f64 1 t) x)

series56.0ms (0.9%)

Counts

4 → 192

Calls

48 calls:

3.0ms	(fma.f64 (+.f64 y (+.f64 t -2)) b (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x)))	z	0
3.0ms	(fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x))	z	0
2.0ms	(fma.f64 (+.f64 y (+.f64 t -2)) b (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x)))	x	0
2.0ms	(fma.f64 (+.f64 y (+.f64 t -2)) b (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x)))	x	-inf
2.0ms	(fma.f64 (+.f64 y (+.f64 t -2)) b (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x)))	z	-inf

rewrite66.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

326×	`log1p-udef_binary64`
182×	`add-sqr-sqrt_binary64`
171×	`add-cbrt-cube_binary64`
171×	`log1p-expm1-u_binary64`
171×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	55
1	353	55
2	4716	55

Stop Event

1×	node limit

Counts

4 → 108

simplify90.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

493×	`unsub-neg_binary64`
471×	`associate--l+_binary64`
466×	`associate--r+_binary64`
437×	`sub-neg_binary64`
388×	`associate-+l+_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	81	3102
1	268	3100
2	837	3043
3	3039	3041
4	4696	3041

Stop Event

1×	node limit

Counts

300 → 161

prune144.0ms (2.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	159	2	161
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	160	2	162

Error

Counts

162 → 2

Alt Table

Status	Error	Program
	0.0b	(+.f64 a (-.f64 (+.f64 x (fma.f64 b (+.f64 t y) z)) (fma.f64 a t (fma.f64 z y (*.f64 b 2)))))
▶	0.0b	(fma.f64 (+.f64 y (+.f64 t -2)) b (-.f64 (+.f64 a (+.f64 z x)) (+.f64 (.f64 y z) (.f64 a t))))

Compiler

Compiled 3618 to 2086 computations (42.3% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 y (+.f64 t -2))
✓	0.0b	(+.f64 (.f64 y z) (.f64 a t))
✓	0.0b	(fma.f64 (+.f64 y (+.f64 t -2)) b (-.f64 (+.f64 a (+.f64 z x)) (+.f64 (.f64 y z) (.f64 a t))))
✓	0.0b	(-.f64 (+.f64 a (+.f64 z x)) (+.f64 (.f64 y z) (.f64 a t)))

series57.0ms (1%)

Counts

3 → 99

Calls

45 calls:

6.0ms	(fma.f64 (+.f64 y (+.f64 t -2)) b (-.f64 (+.f64 a (+.f64 z x)) (+.f64 (.f64 y z) (.f64 a t))))	x	inf
3.0ms	(-.f64 (+.f64 a (+.f64 z x)) (+.f64 (.f64 y z) (.f64 a t)))	x	-inf
2.0ms	(fma.f64 (+.f64 y (+.f64 t -2)) b (-.f64 (+.f64 a (+.f64 z x)) (+.f64 (.f64 y z) (.f64 a t))))	x	-inf
2.0ms	(fma.f64 (+.f64 y (+.f64 t -2)) b (-.f64 (+.f64 a (+.f64 z x)) (+.f64 (.f64 y z) (.f64 a t))))	x	0
2.0ms	(fma.f64 (+.f64 y (+.f64 t -2)) b (-.f64 (+.f64 a (+.f64 z x)) (+.f64 (.f64 y z) (.f64 a t))))	z	-inf

rewrite39.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

212×	`add-sqr-sqrt_binary64`
208×	`log1p-expm1-u_binary64`
208×	`expm1-log1p-u_binary64`
207×	`add-cbrt-cube_binary64`
197×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	52
1	407	52

Stop Event

1×	node limit

Counts

3 → 91

simplify69.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

490×	`unsub-neg_binary64`
471×	`associate--l+_binary64`
463×	`associate--r+_binary64`
436×	`sub-neg_binary64`
392×	`associate-+l+_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	78	1937
1	262	1935
2	835	1878
3	3041	1876
4	4696	1876

Stop Event

1×	node limit

Counts

190 → 138

prune129.0ms (2.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	183	0	183
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	183	2	185

Error

Counts

185 → 2

Alt Table

Status	Error	Program
▶	0.0b	(+.f64 a (-.f64 (+.f64 x (fma.f64 b (+.f64 t y) z)) (fma.f64 a t (fma.f64 z y (*.f64 b 2)))))
✓	0.0b	(fma.f64 (+.f64 y (+.f64 t -2)) b (-.f64 (+.f64 a (+.f64 z x)) (+.f64 (.f64 y z) (.f64 a t))))

Compiler

Compiled 4827 to 1570 computations (67.5% saved)

localize12.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a t (fma.f64 z y (*.f64 b 2)))
✓	0.0b	(fma.f64 b (+.f64 t y) z)
✓	0.0b	(-.f64 (+.f64 x (fma.f64 b (+.f64 t y) z)) (fma.f64 a t (fma.f64 z y (*.f64 b 2))))

series61.0ms (1%)

Counts

3 → 180

Calls

45 calls:

6.0ms	(-.f64 (+.f64 x (fma.f64 b (+.f64 t y) z)) (fma.f64 a t (fma.f64 z y (*.f64 b 2))))	z	inf
4.0ms	(fma.f64 a t (fma.f64 z y (*.f64 b 2)))	a	-inf
3.0ms	(-.f64 (+.f64 x (fma.f64 b (+.f64 t y) z)) (fma.f64 a t (fma.f64 z y (*.f64 b 2))))	x	0
2.0ms	(-.f64 (+.f64 x (fma.f64 b (+.f64 t y) z)) (fma.f64 a t (fma.f64 z y (*.f64 b 2))))	x	-inf
2.0ms	(-.f64 (+.f64 x (fma.f64 b (+.f64 t y) z)) (fma.f64 a t (fma.f64 z y (*.f64 b 2))))	y	inf

rewrite72.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

315×	`log1p-udef_binary64`
173×	`add-sqr-sqrt_binary64`
166×	`log1p-expm1-u_binary64`
166×	`expm1-log1p-u_binary64`
165×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	45
1	332	45
2	4670	45

Stop Event

1×	node limit

Counts

3 → 94

simplify78.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

629×	`associate-+l-_binary64`
534×	`+-commutative_binary64`
442×	`unsub-neg_binary64`
310×	`sub-neg_binary64`
264×	`associate--r+_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	64	2588
1	204	2495
2	629	2495
3	2043	2493
4	4315	2493

Stop Event

1×	node limit

Counts

274 → 150

prune126.0ms (2.1%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	150	0	150
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	150	2	152

Error

Counts

152 → 2

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 a (-.f64 (+.f64 x (fma.f64 b (+.f64 t y) z)) (fma.f64 a t (fma.f64 z y (*.f64 b 2)))))
✓	0.0b	(fma.f64 (+.f64 y (+.f64 t -2)) b (-.f64 (+.f64 a (+.f64 z x)) (+.f64 (.f64 y z) (.f64 a t))))

Compiler

Compiled 3791 to 1483 computations (60.9% saved)

regimes922.0ms (15.3%)

Accuracy

Total 0.0b remaining (27.1%)

Threshold costs 0.0b (27.1%)

Counts

135 → 1

Compiler

Compiled 19633 to 12829 computations (34.7% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
2×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	27
1	23	27
2	28	27
3	30	27
4	31	27

Stop Event

1×

saturated

end53.0ms (0.9%)

Stop Event

1×

done

Compiler

Compiled 102 to 61 computations (40.2% saved)

Details

analyze2.0s (33.2%)

sample2.0s (32.6%)

preprocess33.0ms (0.5%)

simplify20.0ms (0.3%)

prune3.0ms (0.1%)

localize11.0ms (0.2%)

series56.0ms (0.9%)

rewrite66.0ms (1.1%)

simplify90.0ms (1.5%)

prune144.0ms (2.4%)

localize13.0ms (0.2%)

series57.0ms (1%)

rewrite39.0ms (0.7%)

simplify69.0ms (1.1%)

prune129.0ms (2.1%)

localize12.0ms (0.2%)

series61.0ms (1%)

rewrite72.0ms (1.2%)

simplify78.0ms (1.3%)

prune126.0ms (2.1%)

regimes922.0ms (15.3%)

simplify3.0ms (0%)

end53.0ms (0.9%)

Profiling