Details

analyze420.0ms (16.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	50%	25%	4
25%	37.5%	37.5%	5
25%	31.2%	43.8%	6
25%	28.1%	46.9%	7
25%	26.5%	48.5%	8
25%	25.8%	49.2%	9
25%	25.4%	49.6%	10
25%	25.2%	49.8%	11
25%	25.1%	49.9%	12
25%	25%	50%	13
25%	25%	50%	14

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample1.7s (69.4%)

Results

897.0ms	8256×	body	128	valid
801.0ms	8290×	body	128	invalid

Compiler

Compiled 22 to 16 computations (27.3% saved)

preprocess39.0ms (1.6%)

Algorithm

2×	egg-herbie

Rules

868×	`fma-neg_binary64`
396×	`unsub-neg_binary64`
348×	`distribute-neg-in_binary64`
330×	`fma-def_binary64`
262×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	18	12
2	22	12
3	37	12
4	78	12
5	154	12
6	360	12
7	751	12
8	2365	12
9	4284	12
0	1	1

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 10 to 7 computations (30% saved)

simplify29.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

868×	`fma-neg_binary64`
396×	`unsub-neg_binary64`
348×	`distribute-neg-in_binary64`
330×	`fma-def_binary64`
262×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	18	12
2	22	12
3	37	12
4	78	12
5	154	12
6	360	12
7	751	12
8	2365	12
9	4284	12

Stop Event

1×	node limit

Counts

1 → 2

prune2.0ms (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

30.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	30.5b	(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))

Compiler

Compiled 36 to 24 computations (33.3% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (sqrt.f64 (fma.f64 x x -1)))
✓	28.5b	(sqrt.f64 (fma.f64 x x -1))

series6.0ms (0.2%)

Counts

2 → 24

Calls

6 calls:

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

rewrite37.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

654×	`pow1_binary64`
610×	`add-log-exp_binary64`
610×	`log1p-expm1-u_binary64`
610×	`expm1-log1p-u_binary64`
64×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	17
1	125	17
2	1657	17
0	6	17

Stop Event

1×	saturated
1×	node limit

Counts

2 → 55

simplify25.0ms (1%)

Algorithm

1×	egg-herbie

Rules

738×	`associate-/l*_binary64`
658×	`fma-def_binary64`
504×	`associate-/r*_binary64`
265×	`cancel-sign-sub-inv_binary64`
190×	`fma-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	62	396
1	188	377
2	506	375
3	1676	366

Stop Event

1×	node limit

Counts

79 → 97

prune48.0ms (1.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	96	1	97
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	96	2	98

Error

Counts

98 → 2

Alt Table

Status	Error	Program
▶	0.0b	(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))
✓	30.5b	(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))

Compiler

Compiled 1460 to 1059 computations (27.5% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))

series3.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

1.0ms	(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))	x	0
1.0ms	(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))	x	-inf
1.0ms	(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))	x	inf

rewrite33.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

652×	`pow1_binary64`
607×	`add-log-exp_binary64`
606×	`log1p-expm1-u_binary64`
606×	`expm1-log1p-u_binary64`
71×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	146	10
2	1642	10
0	7	10

Stop Event

1×	saturated
1×	node limit

Counts

1 → 18

simplify26.0ms (1%)

Algorithm

1×	egg-herbie

Rules

729×	`fma-def_binary64`
409×	`cancel-sign-sub-inv_binary64`
350×	`sub-neg_binary64`
309×	`fma-neg_binary64`
240×	`associate-l_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	59	272
1	162	258
2	510	258
3	1988	258

Stop Event

1×	node limit

Counts

30 → 40

prune19.0ms (0.8%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	40	0	40
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	40	2	42

Error

Counts

42 → 2

Alt Table

Status	Error	Program
✓	0.0b	(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))
✓	30.5b	(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))

Compiler

Compiled 600 to 467 computations (22.2% saved)

regimes23.0ms (0.9%)

Accuracy

Total 0.3b remaining (82%)

Threshold costs 0.3b (82%)

Counts

6 → 1

Compiler

Compiled 174 to 124 computations (28.7% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10

Stop Event

1×

saturated

end38.0ms (1.5%)

Stop Event

1×

done

Compiler

Compiled 33 to 24 computations (27.3% saved)

Details

analyze420.0ms (16.9%)

sample1.7s (69.4%)

preprocess39.0ms (1.6%)

simplify29.0ms (1.2%)

prune2.0ms (0.1%)

localize6.0ms (0.2%)

series6.0ms (0.2%)

rewrite37.0ms (1.5%)

simplify25.0ms (1%)

prune48.0ms (1.9%)

localize5.0ms (0.2%)

series3.0ms (0.1%)

rewrite33.0ms (1.3%)

simplify26.0ms (1%)

prune19.0ms (0.8%)

regimes23.0ms (0.9%)

simplify2.0ms (0.1%)

end38.0ms (1.5%)

Profiling