Details

analyze1.2s (25.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
3.5%	96.2%	0.2%	10
9.5%	90.2%	0.2%	11
14.3%	85.4%	0.2%	12
22.4%	77.4%	0.2%	13
23.5%	76.3%	0.2%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample1.2s (24.4%)

Results

1.1s	8255×	body	128	valid
89.0ms	736×	body	128	invalid
0.0ms	1×	body	1024	valid

Compiler

Compiled 34 to 22 computations (35.3% saved)

preprocess39.0ms (0.8%)

Algorithm

2×	egg-herbie

Rules

921×	`div-sub_binary64`
476×	`fma-def_binary64`
337×	`fma-neg_binary64`
298×	`distribute-rgt-in_binary64`
262×	`times-frac_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	176
1	109	176
2	250	154
3	611	154
4	1505	154
5	4164	154
0	5	5

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 16 to 10 computations (37.5% saved)

simplify22.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

740×	`fma-def_binary64`
579×	`times-frac_binary64`
533×	`div-sub_binary64`
520×	`fma-neg_binary64`
208×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	18	16
2	37	14
3	81	14
4	191	14
5	392	14
6	833	14
7	2397	14

Stop Event

1×	node limit

Counts

1 → 2

prune3.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	1.4b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
	12.8b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))

Compiler

Compiled 88 to 50 computations (43.2% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z t) (-.f64 a t))
✓	1.4b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)

series53.0ms (1.1%)

Counts

2 → 96

Calls

24 calls:

4.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)	t	-inf
3.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)	a	0
3.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)	t	0
3.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)	y	inf
3.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)	x	-inf

rewrite53.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

365×	`fma-def_binary64`
222×	`expm1-udef_binary64`
222×	`log1p-udef_binary64`
200×	`fma-neg_binary64`
192×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	24
1	226	24
2	3371	24

Stop Event

1×	node limit

Counts

2 → 77

simplify59.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

878×	`fma-def_binary64`
678×	`cancel-sign-sub-inv_binary64`
618×	`times-frac_binary64`
322×	`sub-neg_binary64`
175×	`associate--l+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	172	2919
1	553	2907
2	2057	2615

Stop Event

1×	node limit

Counts

173 → 155

prune117.0ms (2.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	150	5	155
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	151	6	157

Error

0.0b

Counts

157 → 6

Alt Table

Status	Error	Program
	14.3b	(fma.f64 y (cbrt.f64 (pow.f64 (/.f64 (-.f64 z t) (-.f64 a t)) 3)) x)
	23.4b	(+.f64 x (-.f64 y (*.f64 (/.f64 y t) z)))
	2.0b	(-.f64 (fma.f64 (/.f64 y (-.f64 a t)) z x) (*.f64 (/.f64 y (-.f64 a t)) t))
	1.6b	(fma.f64 y (pow.f64 (/.f64 (-.f64 a t) (-.f64 z t)) -1) x)
	12.8b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))
▶	1.5b	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))) x)

Compiler

Compiled 3668 to 1237 computations (66.3% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t)))
✓	1.4b	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))) x)

series52.0ms (1.1%)

Counts

2 → 96

Calls

24 calls:

4.0ms	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))) x)	z	-inf
3.0ms	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))) x)	a	0
3.0ms	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))) x)	t	0
3.0ms	(*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t)))	z	0
3.0ms	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))) x)	a	-inf

rewrite63.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

801×	`prod-diff_binary64`
133×	`add-sqr-sqrt_binary64`
125×	`add-cbrt-cube_binary64`
125×	`log1p-expm1-u_binary64`
125×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	24
1	259	24
2	3551	24

Stop Event

1×	node limit

Counts

2 → 64

simplify61.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

878×	`fma-def_binary64`
678×	`cancel-sign-sub-inv_binary64`
618×	`times-frac_binary64`
322×	`sub-neg_binary64`
175×	`associate--l+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	172	2919
1	553	2907
2	2057	2615

Stop Event

1×	node limit

Counts

160 → 142

prune103.0ms (2.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	142	0	142
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	142	6	148

Error

0.0b

Counts

148 → 6

Alt Table

Status	Error	Program
	14.3b	(fma.f64 y (cbrt.f64 (pow.f64 (/.f64 (-.f64 z t) (-.f64 a t)) 3)) x)
	23.4b	(+.f64 x (-.f64 y (*.f64 (/.f64 y t) z)))
	2.0b	(-.f64 (fma.f64 (/.f64 y (-.f64 a t)) z x) (*.f64 (/.f64 y (-.f64 a t)) t))
▶	1.6b	(fma.f64 y (pow.f64 (/.f64 (-.f64 a t) (-.f64 z t)) -1) x)
	12.8b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))
✓	1.5b	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))) x)

Compiler

Compiled 3371 to 1182 computations (64.9% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 a t) (-.f64 z t))
✓	0.4b	(pow.f64 (/.f64 (-.f64 a t) (-.f64 z t)) -1)
✓	1.4b	(fma.f64 y (pow.f64 (/.f64 (-.f64 a t) (-.f64 z t)) -1) x)

series157.0ms (3.2%)

Counts

3 → 132

Calls

33 calls:

19.0ms	(fma.f64 y (pow.f64 (/.f64 (-.f64 a t) (-.f64 z t)) -1) x)	z	inf
19.0ms	(fma.f64 y (pow.f64 (/.f64 (-.f64 a t) (-.f64 z t)) -1) x)	z	-inf
14.0ms	(fma.f64 y (pow.f64 (/.f64 (-.f64 a t) (-.f64 z t)) -1) x)	z	0
12.0ms	(pow.f64 (/.f64 (-.f64 a t) (-.f64 z t)) -1)	z	-inf
10.0ms	(pow.f64 (/.f64 (-.f64 a t) (-.f64 z t)) -1)	z	inf

rewrite71.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

369×	`fma-def_binary64`
249×	`expm1-udef_binary64`
249×	`log1p-udef_binary64`
205×	`fma-neg_binary64`
140×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	40
1	268	34
2	3832	34

Stop Event

1×	node limit

Counts

3 → 122

simplify96.0ms (2%)

Algorithm

1×	egg-herbie

Rules

601×	`associate-/l*_binary64`
479×	`associate-/r*_binary64`
331×	`associate--l+_binary64`
264×	`associate-r_binary64`
183×	`sub-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	484	7079
1	1766	6953

Stop Event

1×	node limit

Counts

254 → 258

prune239.0ms (4.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	256	2	258
Fresh	2	2	4
Picked	1	0	1
Done	0	1	1
Total	259	5	264

Error

Counts

264 → 5

Alt Table

Status	Error	Program
	1.4b	(fma.f64 y (-.f64 (/.f64 z (-.f64 a t)) (/.f64 t (-.f64 a t))) x)
	2.0b	(-.f64 (fma.f64 (/.f64 y (-.f64 a t)) z x) (*.f64 (/.f64 y (-.f64 a t)) t))
▶	1.3b	(+.f64 x (/.f64 y (/.f64 (-.f64 a t) (-.f64 z t))))
	12.8b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))
✓	1.5b	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))) x)

Compiler

Compiled 8746 to 3597 computations (58.9% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 y (/.f64 (-.f64 a t) (-.f64 z t))))
	0.0b	(/.f64 (-.f64 a t) (-.f64 z t))
✓	2.8b	(/.f64 y (/.f64 (-.f64 a t) (-.f64 z t)))

series75.0ms (1.5%)

Counts

2 → 108

Calls

27 calls:

6.0ms	(/.f64 y (/.f64 (-.f64 a t) (-.f64 z t)))	y	inf
4.0ms	(/.f64 y (/.f64 (-.f64 a t) (-.f64 z t)))	t	0
4.0ms	(+.f64 x (/.f64 y (/.f64 (-.f64 a t) (-.f64 z t))))	t	inf
4.0ms	(+.f64 x (/.f64 y (/.f64 (-.f64 a t) (-.f64 z t))))	y	0
3.0ms	(+.f64 x (/.f64 y (/.f64 (-.f64 a t) (-.f64 z t))))	a	0

rewrite66.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

258×	`expm1-udef_binary64`
258×	`log1p-udef_binary64`
141×	`add-sqr-sqrt_binary64`
136×	`log1p-expm1-u_binary64`
136×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	29
1	263	27
2	4303	27

Stop Event

1×	node limit

Counts

2 → 81

simplify66.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

988×	`cancel-sign-sub-inv_binary64`
894×	`fma-def_binary64`
521×	`times-frac_binary64`
369×	`sub-neg_binary64`
222×	`associate--l+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	171	3333
1	602	3006
2	2072	2764

Stop Event

1×	node limit

Counts

189 → 160

prune172.0ms (3.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	241	1	242
Fresh	2	1	3
Picked	0	1	1
Done	0	1	1
Total	243	4	247

Error

Counts

247 → 4

Alt Table

Status	Error	Program
	2.0b	(fma.f64 (/.f64 y (-.f64 a t)) (-.f64 z t) x)
✓	1.3b	(+.f64 x (/.f64 y (/.f64 (-.f64 a t) (-.f64 z t))))
	12.8b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))
✓	1.5b	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))) x)

Compiler

Compiled 5881 to 1942 computations (67% saved)

regimes765.0ms (15.7%)

Accuracy

Total 0.8b remaining (98.8%)

Threshold costs 0.8b (98.8%)

Counts

88 → 3

Compiler

Compiled 9879 to 6281 computations (36.4% saved)

bsearch2.0ms (0%)

Algorithm

2×	left-value

Calls

2 calls:

0.0ms	(/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t))
0.0ms	(/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t))

Steps

Iters	Point		Range
3.3293842485947703e+274	∈ [	3.3293842485947703e+274	,	#hash((type . real) (value . +inf))	]
-4.7126067703191754e+24	∈ [	-4.7126067703191754e+24	,	-1.330174752204497e+24	]

Compiler

Compiled 14 to 9 computations (35.7% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	82
1	29	82
2	35	82
3	37	82
4	38	82

Stop Event

1×

saturated

end67.0ms (1.4%)

Stop Event

1×

fuel

Compiler

Compiled 186 to 82 computations (55.9% saved)

Details

analyze1.2s (25.6%)

sample1.2s (24.4%)

preprocess39.0ms (0.8%)

simplify22.0ms (0.4%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

series53.0ms (1.1%)

rewrite53.0ms (1.1%)

simplify59.0ms (1.2%)

prune117.0ms (2.4%)

localize8.0ms (0.2%)

series52.0ms (1.1%)

rewrite63.0ms (1.3%)

simplify61.0ms (1.2%)

prune103.0ms (2.1%)

localize10.0ms (0.2%)

series157.0ms (3.2%)

rewrite71.0ms (1.4%)

simplify96.0ms (2%)

prune239.0ms (4.9%)

localize7.0ms (0.2%)

series75.0ms (1.5%)

rewrite66.0ms (1.4%)

simplify66.0ms (1.4%)

prune172.0ms (3.5%)

regimes765.0ms (15.7%)

bsearch2.0ms (0%)

simplify4.0ms (0.1%)

end67.0ms (1.4%)

Profiling