Details

analyze122.0ms (3%)

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
37.5%	62.4%	0.1%	6
50%	46.8%	3.2%	7
59.3%	34.3%	6.3%	8
67.1%	24.2%	8.7%	9
72.6%	18%	9.5%	10
76.9%	12.3%	10.8%	11
79.8%	9.2%	11%	12
82%	6.2%	11.8%	13
84.3%	3.9%	11.8%	14

Compiler

Compiled 12 to 9 computations (25% saved)

sample1.2s (30%)

Results

733.0ms	6226×	body	128	valid
208.0ms	691×	body	1024	valid
184.0ms	804×	body	512	valid
89.0ms	525×	body	256	valid
8.0ms	71×	body	128	invalid
4.0ms	10×	body	2048	valid

Compiler

Compiled 24 to 18 computations (25% saved)

preprocess15.0ms (0.4%)

Algorithm

2×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	26
1	12	26
0	2	2

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 11 to 8 computations (27.3% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	10	13

Stop Event

1×

saturated

Counts

1 → 1

prune3.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

14.7b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	14.7b	(+.f64 x (*.f64 (-.f64 1 x) (-.f64 1 y)))

Compiler

Compiled 33 to 24 computations (27.3% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (-.f64 1 x) (-.f64 1 y))
✓	2.1b	(+.f64 x (*.f64 (-.f64 1 x) (-.f64 1 y)))

series10.0ms (0.2%)

Counts

2 → 48

Calls

12 calls:

3.0ms	(*.f64 (-.f64 1 x) (-.f64 1 y))	y	-inf
1.0ms	(*.f64 (-.f64 1 x) (-.f64 1 y))	y	inf
1.0ms	(*.f64 (-.f64 1 x) (-.f64 1 y))	x	-inf
1.0ms	(*.f64 (-.f64 1 x) (-.f64 1 y))	x	inf
1.0ms	(+.f64 x (*.f64 (-.f64 1 x) (-.f64 1 y)))	y	-inf

rewrite35.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

724×	`log1p-expm1-u_binary64`
724×	`expm1-log1p-u_binary64`
157×	`expm1-udef_binary64`
157×	`log1p-udef_binary64`
148×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	23
1	160	23
2	1766	23

Stop Event

1×	node limit

Counts

2 → 36

simplify14.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`
1×	`fma-def_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	420
1	21	420

Stop Event

1×

saturated

Counts

84 → 47

prune29.0ms (0.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	46	1	47
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	46	2	48

Error

0.0b

Counts

48 → 2

Alt Table

Status	Error	Program
▶	0.0b	(-.f64 (fma.f64 y x 1) y)
✓	14.7b	(+.f64 x (*.f64 (-.f64 1 x) (-.f64 1 y)))

Compiler

Compiled 590 to 421 computations (28.6% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (fma.f64 y x 1) y)

series6.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

1.0ms	(-.f64 (fma.f64 y x 1) y)	y	-inf
1.0ms	(-.f64 (fma.f64 y x 1) y)	y	inf
1.0ms	(-.f64 (fma.f64 y x 1) y)	x	-inf
1.0ms	(-.f64 (fma.f64 y x 1) y)	y	0
1.0ms	(-.f64 (fma.f64 y x 1) y)	x	inf

rewrite30.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

492×	`log1p-expm1-u_binary64`
492×	`expm1-log1p-u_binary64`
194×	`unpow-prod-down_binary64`
154×	`pow2_binary64`
143×	`log-prod_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	114	8
2	1217	8

Stop Event

1×	node limit

Counts

1 → 36

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`
1×	`fma-def_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	174
1	17	174

Stop Event

1×

saturated

Counts

60 → 43

prune25.0ms (0.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	42	1	43
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	42	3	45

Error

Counts

45 → 3

Alt Table

Status	Error	Program
✓	0.0b	(-.f64 (fma.f64 y x 1) y)
▶	38.4b	(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (-.f64 (fma.f64 y x 1) y))) 2)) (log.f64 (cbrt.f64 (exp.f64 (-.f64 (fma.f64 y x 1) y)))))
✓	14.7b	(+.f64 x (*.f64 (-.f64 1 x) (-.f64 1 y)))

Compiler

Compiled 583 to 377 computations (35.3% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(pow.f64 (cbrt.f64 (exp.f64 (-.f64 (fma.f64 y x 1) y))) 2)
✓	0.6b	(cbrt.f64 (exp.f64 (-.f64 (fma.f64 y x 1) y)))
✓	1.0b	(log.f64 (cbrt.f64 (exp.f64 (-.f64 (fma.f64 y x 1) y))))
✓	1.3b	(log.f64 (pow.f64 (cbrt.f64 (exp.f64 (-.f64 (fma.f64 y x 1) y))) 2))

series1.7s (41%)

Counts

4 → 96

Calls

24 calls:

184.0ms	(log.f64 (pow.f64 (cbrt.f64 (exp.f64 (-.f64 (fma.f64 y x 1) y))) 2))	y	inf
176.0ms	(log.f64 (pow.f64 (cbrt.f64 (exp.f64 (-.f64 (fma.f64 y x 1) y))) 2))	y	-inf
161.0ms	(log.f64 (pow.f64 (cbrt.f64 (exp.f64 (-.f64 (fma.f64 y x 1) y))) 2))	x	-inf
158.0ms	(log.f64 (pow.f64 (cbrt.f64 (exp.f64 (-.f64 (fma.f64 y x 1) y))) 2))	x	inf
148.0ms	(log.f64 (cbrt.f64 (exp.f64 (-.f64 (fma.f64 y x 1) y))))	y	-inf

rewrite44.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

824×	`log1p-expm1-u_binary64`
824×	`expm1-log1p-u_binary64`
108×	`add-sqr-sqrt_binary64`
102×	`add-cbrt-cube_binary64`
102×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	58
1	221	52
2	2201	52

Stop Event

1×	node limit

Counts

4 → 68

simplify346.0ms (8.4%)

Algorithm

1×	egg-herbie

Rules

860×	`sqr-pow_binary64`
384×	`fma-def_binary64`
298×	`pow-sqr_binary64`
296×	`log-pow_binary64`
255×	`log-prod_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	756	9435
1	1228	8887
2	1426	8341
3	1619	8083
4	1845	7971
5	2100	7931
6	2436	7931
7	2959	7931
8	3852	7931

Stop Event

1×	node limit

Counts

164 → 138

prune345.0ms (8.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	177	0	177
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	177	3	180

Error

Counts

180 → 3

Alt Table

Status	Error	Program
✓	0.0b	(-.f64 (fma.f64 y x 1) y)
✓	38.4b	(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (-.f64 (fma.f64 y x 1) y))) 2)) (log.f64 (cbrt.f64 (exp.f64 (-.f64 (fma.f64 y x 1) y)))))
✓	14.7b	(+.f64 x (*.f64 (-.f64 1 x) (-.f64 1 y)))

Compiler

Compiled 14350 to 11350 computations (20.9% saved)

regimes85.0ms (2%)

Accuracy

Total 0.0b remaining (78.3%)

Threshold costs 0.0b (78.3%)

Counts

12 → 1

Compiler

Compiled 624 to 467 computations (25.2% saved)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	8	8

Stop Event

1×

saturated

end53.0ms (1.3%)

Stop Event

1×

done

Compiler

Compiled 58 to 40 computations (31% saved)

Details

analyze122.0ms (3%)

sample1.2s (30%)

preprocess15.0ms (0.4%)

simplify5.0ms (0.1%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series10.0ms (0.2%)

rewrite35.0ms (0.8%)

simplify14.0ms (0.3%)

prune29.0ms (0.7%)

localize4.0ms (0.1%)

series6.0ms (0.1%)

rewrite30.0ms (0.7%)

simplify8.0ms (0.2%)

prune25.0ms (0.6%)

localize12.0ms (0.3%)

series1.7s (41%)

rewrite44.0ms (1.1%)

simplify346.0ms (8.4%)

prune345.0ms (8.3%)

regimes85.0ms (2%)

simplify1.0ms (0%)

end53.0ms (1.3%)

Profiling