Details

analyze17.0ms (1.1%)

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
25%	74.9%	0.1%	6
93.7%	6.2%	0.1%	7
96.8%	3.1%	0.1%	8
99.5%	0.4%	0.1%	9
99.7%	0.2%	0.1%	10
99.8%	0.1%	0.1%	11
99.9%	0%	0.1%	12
99.9%	0%	0.1%	13
99.9%	0%	0.1%	14

Compiler

Compiled 22 to 13 computations (40.9% saved)

sample942.0ms (59.3%)

Results

929.0ms

8256×

body

128

valid

Compiler

Compiled 44 to 26 computations (40.9% saved)

preprocess45.0ms (2.8%)

Algorithm

2×	egg-herbie

Rules

968×	`fma-def_binary64`
834×	`fma-neg_binary64`
302×	`cancel-sign-sub-inv_binary64`
287×	`div-sub_binary64`
232×	`associate-/l*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	52
1	44	48
2	102	48
3	217	48
4	462	48
5	889	48
6	1477	48
7	2476	48
8	4351	48
0	2	2

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 21 to 12 computations (42.9% saved)

simplify32.0ms (2%)

Algorithm

1×	egg-herbie

Rules

620×	`fma-def_binary64`
456×	`cancel-sign-sub-inv_binary64`
430×	`times-frac_binary64`
358×	`div-sub_binary64`
252×	`distribute-frac-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	26
1	24	24
2	56	24
3	114	24
4	240	24
5	457	24
6	723	24
7	987	24
8	1607	24
9	3745	24

Stop Event

1×	node limit

Counts

1 → 2

prune3.0ms (0.2%)

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

32.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	32.0b	(/.f64 (fma.f64 x x (.f64 -4 (.f64 y y))) (fma.f64 x x (.f64 y (.f64 y 4))))

Compiler

Compiled 76 to 43 computations (43.4% saved)

localize10.0ms (0.6%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 -4 (.f64 y y))
✓	1.2b	(fma.f64 x x (.f64 -4 (.f64 y y)))
✓	31.4b	(/.f64 (fma.f64 x x (.f64 -4 (.f64 y y))) (fma.f64 x x (.f64 y (.f64 y 4))))

series25.0ms (1.6%)

Counts

3 → 60

Calls

15 calls:

4.0ms	(/.f64 (fma.f64 x x (.f64 -4 (.f64 y y))) (fma.f64 x x (.f64 y (.f64 y 4))))	y	inf
3.0ms	(/.f64 (fma.f64 x x (.f64 -4 (.f64 y y))) (fma.f64 x x (.f64 y (.f64 y 4))))	x	0
2.0ms	(/.f64 (fma.f64 x x (.f64 -4 (.f64 y y))) (fma.f64 x x (.f64 y (.f64 y 4))))	y	0
2.0ms	(/.f64 (fma.f64 x x (.f64 -4 (.f64 y y))) (fma.f64 x x (.f64 y (.f64 y 4))))	x	-inf
2.0ms	(/.f64 (fma.f64 x x (.f64 -4 (.f64 y y))) (fma.f64 x x (.f64 y (.f64 y 4))))	x	inf

rewrite49.0ms (3.1%)

Algorithm

1×	batch-egg-rewrite

Rules

878×	`expm1-log1p-u_binary64`
244×	`prod-diff_binary64`
118×	`add-sqr-sqrt_binary64`
112×	`add-log-exp_binary64`
112×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	42
1	248	36
2	3131	36

Stop Event

1×	node limit

Counts

3 → 71

simplify33.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

499×	`associate-*l/_binary64`
445×	`associate-*r/_binary64`
368×	`fma-def_binary64`
319×	`associate-/r/_binary64`
311×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	46	891
1	121	837
2	346	825
3	1380	807

Stop Event

1×	node limit

Counts

131 → 91

prune51.0ms (3.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	88	3	91
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	88	4	92

Error

0.0b

Counts

92 → 4

Alt Table

Status	Error	Program
	33.4b	1
	31.5b	(fma.f64 (/.f64 1/2 y) (/.f64 (*.f64 x x) y) -1)
▶	30.1b	-1
✓	32.0b	(/.f64 (fma.f64 x x (.f64 -4 (.f64 y y))) (fma.f64 x x (.f64 y (.f64 y 4))))

Compiler

Compiled 1845 to 1243 computations (32.6% saved)

localize0.0ms (0%)

prune2.0ms (0.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

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

Error

0.0b

Counts

4 → 4

Alt Table

Status	Error	Program
	33.4b	1
▶	31.5b	(fma.f64 (/.f64 1/2 y) (/.f64 (*.f64 x x) y) -1)
✓	30.1b	-1
✓	32.0b	(/.f64 (fma.f64 x x (.f64 -4 (.f64 y y))) (fma.f64 x x (.f64 y (.f64 y 4))))

Compiler

Compiled 52 to 36 computations (30.8% saved)

localize7.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	1.7b	(fma.f64 (/.f64 1/2 y) (/.f64 (*.f64 x x) y) -1)
✓	4.8b	(/.f64 (*.f64 x x) y)

series25.0ms (1.5%)

Counts

2 → 48

Calls

12 calls:

4.0ms	(fma.f64 (/.f64 1/2 y) (/.f64 (*.f64 x x) y) -1)	y	-inf
3.0ms	(fma.f64 (/.f64 1/2 y) (/.f64 (*.f64 x x) y) -1)	y	0
2.0ms	(fma.f64 (/.f64 1/2 y) (/.f64 (*.f64 x x) y) -1)	x	-inf
2.0ms	(fma.f64 (/.f64 1/2 y) (/.f64 (*.f64 x x) y) -1)	x	inf
2.0ms	(/.f64 (*.f64 x x) y)	y	-inf

rewrite44.0ms (2.8%)

Algorithm

1×	batch-egg-rewrite

Rules

870×	`log1p-expm1-u_binary64`
870×	`expm1-log1p-u_binary64`
92×	`add-sqr-sqrt_binary64`
86×	`add-cbrt-cube_binary64`
86×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	21
1	188	21
2	2376	21

Stop Event

1×	node limit

Counts

2 → 58

simplify38.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

706×	`associate-/l*_binary64`
426×	`associate-/l/_binary64`
424×	`associate-/r*_binary64`
399×	`unswap-sqr_binary64`
328×	`associate-*l/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	462
1	28	462
2	53	462
3	148	462
4	759	462
5	4781	462

Stop Event

1×	node limit

Counts

106 → 65

prune35.0ms (2.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	65	0	65
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	65	4	69

Error

0.0b

Counts

69 → 4

Alt Table

Status	Error	Program
▶	33.4b	1
✓	31.5b	(fma.f64 (/.f64 1/2 y) (/.f64 (*.f64 x x) y) -1)
✓	30.1b	-1
✓	32.0b	(/.f64 (fma.f64 x x (.f64 -4 (.f64 y y))) (fma.f64 x x (.f64 y (.f64 y 4))))

Compiler

Compiled 976 to 541 computations (44.6% saved)

localize0.0ms (0%)

prune3.0ms (0.2%)

Pruning

4 alts after pruning (0 fresh and 4 done)

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

Error

0.0b

Counts

4 → 4

Alt Table

Status	Error	Program
✓	33.4b	1
✓	31.5b	(fma.f64 (/.f64 1/2 y) (/.f64 (*.f64 x x) y) -1)
✓	30.1b	-1
✓	32.0b	(/.f64 (fma.f64 x x (.f64 -4 (.f64 y y))) (fma.f64 x x (.f64 y (.f64 y 4))))

Compiler

Compiled 37 to 25 computations (32.4% saved)

regimes133.0ms (8.4%)

Accuracy

Total 13.3b remaining (97.7%)

Threshold costs 0b (0%)

Counts

6 → 9

Compiler

Compiled 592 to 390 computations (34.1% saved)

bsearch1.0ms (0%)

Algorithm

8×	left-value

Calls

8 calls:

0.0ms	(*.f64 x x)
0.0ms	(*.f64 x x)
0.0ms	(*.f64 x x)
0.0ms	(*.f64 x x)
0.0ms	(*.f64 x x)

Steps

Iters	Point		Range
3.9401376541324113e+307	∈ [	3.9401376541324113e+307	,	#hash((type . real) (value . +inf))	]
6.606821305716693e+68	∈ [	6.606821305716693e+68	,	1.0677125580981696e+76	]
9.636435449841436e+56	∈ [	9.636435449841436e+56	,	4.69607753393049e+57	]
22106031556944.254	∈ [	22106031556944.254	,	1697127538385023.3	]
3.256700432886185e-112	∈ [	3.256700432886185e-112	,	1.2051341551929727e-110	]
1.1087674357060143e-172	∈ [	1.1087674357060143e-172	,	1.5960497097893924e-172	]
2.499038807843666e-253	∈ [	2.499038807843666e-253	,	7.175154733885467e-247	]
7.594980201689878e-293	∈ [	7.594980201689878e-293	,	2.492628971526032e-292	]

Compiler

Compiled 5 to 3 computations (40% saved)

simplify6.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	225
1	49	225

Stop Event

1×

saturated

end90.0ms (5.6%)

Stop Event

1×

done

Compiler

Compiled 355 to 181 computations (49% saved)

Details

analyze17.0ms (1.1%)

sample942.0ms (59.3%)

preprocess45.0ms (2.8%)

simplify32.0ms (2%)

prune3.0ms (0.2%)

localize10.0ms (0.6%)

series25.0ms (1.6%)

rewrite49.0ms (3.1%)

simplify33.0ms (2.1%)

prune51.0ms (3.2%)

localize0.0ms (0%)

prune2.0ms (0.2%)

localize7.0ms (0.4%)

series25.0ms (1.5%)

rewrite44.0ms (2.8%)

simplify38.0ms (2.4%)

prune35.0ms (2.2%)

localize0.0ms (0%)

prune3.0ms (0.2%)

regimes133.0ms (8.4%)

bsearch1.0ms (0%)

simplify6.0ms (0.4%)

end90.0ms (5.6%)

Profiling