Details

analyze2.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	56.2%	43.8%	0
0%	56.2%	43.8%	1
28.1%	28.1%	43.8%	2
56.2%	0%	43.8%	3

Compiler

Compiled 22 to 16 computations (27.3% saved)

sample1.4s (54%)

Results

673.0ms	6211×	body	128	valid
386.0ms	1047×	body	1024	valid
167.0ms	620×	body	512	valid
56.0ms	292×	body	256	valid
37.0ms	86×	body	2048	valid

Compiler

Compiled 59 to 43 computations (27.1% saved)

simplify28.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

434×	`cancel-sign-sub-inv_binary64`
372×	`div-sub_binary64`
343×	`sub-neg_binary64`
331×	`fma-neg_binary64`
292×	`fma-def_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	11	19
1	23	19
2	40	19
3	67	19
4	118	19
5	238	17
6	445	17
7	753	17
8	1572	17
9	3643	17

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

18.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	18.0b	(+.f64 1/2 (/.f64 (-.f64 alpha beta) (fma.f64 (+.f64 beta alpha) -2 -4)))

Compiler

Compiled 55 to 39 computations (29.1% saved)

localize7.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 alpha beta) (fma.f64 (+.f64 beta alpha) -2 -4))
✓	1.5b	(+.f64 1/2 (/.f64 (-.f64 alpha beta) (fma.f64 (+.f64 beta alpha) -2 -4)))

series43.0ms (1.7%)

Counts

2 → 48

Calls

2 calls:

28.0ms	(+.f64 1/2 (/.f64 (-.f64 alpha beta) (fma.f64 (+.f64 beta alpha) -2 -4)))
15.0ms	(/.f64 (-.f64 alpha beta) (fma.f64 (+.f64 beta alpha) -2 -4))

rewrite59.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

408×	`fma-def_binary64`
244×	`fma-neg_binary64`
239×	`expm1-udef_binary64`
239×	`log1p-udef_binary64`
133×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	31
1	261	31
2	3736	31

Stop Event

1×	node limit

Counts

2 → 106

Calls

2 calls:

57.0ms	(/.f64 (-.f64 alpha beta) (fma.f64 (+.f64 beta alpha) -2 -4))
57.0ms	(+.f64 1/2 (/.f64 (-.f64 alpha beta) (fma.f64 (+.f64 beta alpha) -2 -4)))

simplify50.0ms (2%)

Algorithm

1×	egg-herbie

Rules

772×	`times-frac_binary64`
643×	`fma-def_binary64`
300×	`sub-neg_binary64`
266×	`cancel-sign-sub-inv_binary64`
156×	`+-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	176	2456
1	569	2372
2	2263	2234

Stop Event

1×	node limit

Counts

154 → 166

prune125.0ms (5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	164	2	166
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	164	3	167

Error

Counts

167 → 3

Alt Table

Status	Error	Program
	48.5b	(-.f64 1 (+.f64 (/.f64 1 beta) (/.f64 alpha beta)))
▶	44.3b	(+.f64 (+.f64 (/.f64 1 alpha) (+.f64 (fma.f64 8 (/.f64 beta (pow.f64 alpha 3)) (/.f64 beta alpha)) (fma.f64 5 (/.f64 beta (/.f64 (pow.f64 alpha 3) beta)) (/.f64 4 (pow.f64 alpha 3))))) (+.f64 (pow.f64 (/.f64 beta alpha) 3) (-.f64 (/.f64 -2 (.f64 alpha alpha)) (.f64 (/.f64 beta alpha) (+.f64 (/.f64 beta alpha) (/.f64 3 alpha))))))
✓	18.0b	(+.f64 1/2 (/.f64 (-.f64 alpha beta) (fma.f64 (+.f64 beta alpha) -2 -4)))

Compiler

Compiled 5030 to 3282 computations (34.8% saved)

localize30.0ms (1.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	5.9b	(+.f64 (+.f64 (/.f64 1 alpha) (+.f64 (fma.f64 8 (/.f64 beta (pow.f64 alpha 3)) (/.f64 beta alpha)) (fma.f64 5 (/.f64 beta (/.f64 (pow.f64 alpha 3) beta)) (/.f64 4 (pow.f64 alpha 3))))) (+.f64 (pow.f64 (/.f64 beta alpha) 3) (-.f64 (/.f64 -2 (.f64 alpha alpha)) (.f64 (/.f64 beta alpha) (+.f64 (/.f64 beta alpha) (/.f64 3 alpha))))))
✓	6.4b	(+.f64 (pow.f64 (/.f64 beta alpha) 3) (-.f64 (/.f64 -2 (.f64 alpha alpha)) (.f64 (/.f64 beta alpha) (+.f64 (/.f64 beta alpha) (/.f64 3 alpha)))))
✓	7.9b	(/.f64 (pow.f64 alpha 3) beta)
✓	7.9b	(/.f64 beta (pow.f64 alpha 3))

series98.0ms (3.9%)

Counts

4 → 48

Calls

4 calls:

36.0ms	(+.f64 (+.f64 (/.f64 1 alpha) (+.f64 (fma.f64 8 (/.f64 beta (pow.f64 alpha 3)) (/.f64 beta alpha)) (fma.f64 5 (/.f64 beta (/.f64 (pow.f64 alpha 3) beta)) (/.f64 4 (pow.f64 alpha 3))))) (+.f64 (pow.f64 (/.f64 beta alpha) 3) (-.f64 (/.f64 -2 (.f64 alpha alpha)) (.f64 (/.f64 beta alpha) (+.f64 (/.f64 beta alpha) (/.f64 3 alpha))))))
27.0ms	(/.f64 beta (pow.f64 alpha 3))
22.0ms	(+.f64 (pow.f64 (/.f64 beta alpha) 3) (-.f64 (/.f64 -2 (.f64 alpha alpha)) (.f64 (/.f64 beta alpha) (+.f64 (/.f64 beta alpha) (/.f64 3 alpha)))))
13.0ms	(/.f64 (pow.f64 alpha 3) beta)

rewrite52.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

332×	`log1p-expm1-u_binary64`
332×	`expm1-log1p-u_binary64`
328×	`add-cbrt-cube_binary64`
313×	`add-log-exp_binary64`
312×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	126
1	702	126

Stop Event

1×	node limit

Counts

4 → 86

Calls

4 calls:

50.0ms	(+.f64 (+.f64 (/.f64 1 alpha) (+.f64 (fma.f64 8 (/.f64 beta (pow.f64 alpha 3)) (/.f64 beta alpha)) (fma.f64 5 (/.f64 beta (/.f64 (pow.f64 alpha 3) beta)) (/.f64 4 (pow.f64 alpha 3))))) (+.f64 (pow.f64 (/.f64 beta alpha) 3) (-.f64 (/.f64 -2 (.f64 alpha alpha)) (.f64 (/.f64 beta alpha) (+.f64 (/.f64 beta alpha) (/.f64 3 alpha))))))
50.0ms	(+.f64 (pow.f64 (/.f64 beta alpha) 3) (-.f64 (/.f64 -2 (.f64 alpha alpha)) (.f64 (/.f64 beta alpha) (+.f64 (/.f64 beta alpha) (/.f64 3 alpha)))))
50.0ms	(/.f64 (pow.f64 alpha 3) beta)
50.0ms	(/.f64 beta (pow.f64 alpha 3))

simplify55.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

687×	`fma-neg_binary64`
517×	`associate-+l+_binary64`
454×	`fma-def_binary64`
431×	`sub-neg_binary64`
410×	`associate--l+_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	76	2068
1	232	2035
2	861	1794
3	4284	1792

Stop Event

1×	node limit

Counts

134 → 122

prune149.0ms (5.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	122	0	122
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	122	3	125

Error

Counts

125 → 3

Alt Table

Status	Error	Program
▶	48.5b	(-.f64 1 (+.f64 (/.f64 1 beta) (/.f64 alpha beta)))
✓	44.3b	(+.f64 (+.f64 (/.f64 1 alpha) (+.f64 (fma.f64 8 (/.f64 beta (pow.f64 alpha 3)) (/.f64 beta alpha)) (fma.f64 5 (/.f64 beta (/.f64 (pow.f64 alpha 3) beta)) (/.f64 4 (pow.f64 alpha 3))))) (+.f64 (pow.f64 (/.f64 beta alpha) 3) (-.f64 (/.f64 -2 (.f64 alpha alpha)) (.f64 (/.f64 beta alpha) (+.f64 (/.f64 beta alpha) (/.f64 3 alpha))))))
✓	18.0b	(+.f64 1/2 (/.f64 (-.f64 alpha beta) (fma.f64 (+.f64 beta alpha) -2 -4)))

Compiler

Compiled 6827 to 4086 computations (40.1% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 1 beta) (/.f64 alpha beta))

series7.0ms (0.3%)

Counts

1 → 15

Calls

1 calls:

7.0ms

(+.f64 (/.f64 1 beta) (/.f64 alpha beta))

rewrite40.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

959×	`prod-diff_binary64`
858×	`expm1-log1p-u_binary64`
78×	`add-sqr-sqrt_binary64`
74×	`add-cbrt-cube_binary64`
74×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	156	10
2	2324	10

Stop Event

1×	node limit

Counts

1 → 54

Calls

1 calls:

39.0ms

(+.f64 (/.f64 1 beta) (/.f64 alpha beta))

simplify7.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	96
1	11	96

Stop Event

1×

saturated

Counts

69 → 57

prune27.0ms (1.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	57	0	57
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	57	3	60

Error

Counts

60 → 3

Alt Table

Status	Error	Program
✓	48.5b	(-.f64 1 (+.f64 (/.f64 1 beta) (/.f64 alpha beta)))
✓	44.3b	(+.f64 (+.f64 (/.f64 1 alpha) (+.f64 (fma.f64 8 (/.f64 beta (pow.f64 alpha 3)) (/.f64 beta alpha)) (fma.f64 5 (/.f64 beta (/.f64 (pow.f64 alpha 3) beta)) (/.f64 4 (pow.f64 alpha 3))))) (+.f64 (pow.f64 (/.f64 beta alpha) 3) (-.f64 (/.f64 -2 (.f64 alpha alpha)) (.f64 (/.f64 beta alpha) (+.f64 (/.f64 beta alpha) (/.f64 3 alpha))))))
✓	18.0b	(+.f64 1/2 (/.f64 (-.f64 alpha beta) (fma.f64 (+.f64 beta alpha) -2 -4)))

Compiler

Compiled 925 to 530 computations (42.7% saved)

regimes266.0ms (10.5%)

Accuracy

Total 0.1b remaining (73.3%)

Threshold costs 0.1b (73.3%)

Counts

39 → 2

Compiler

Compiled 5557 to 3883 computations (30.1% saved)

bsearch2.0ms (0.1%)

Compiler: Compiled 11 to 7 computations (36.4% saved)

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

17×	`+-commutative_binary64`
9×	`sub-neg_binary64`
7×	`*-commutative_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	113
1	65	113
2	83	113
3	96	113
4	109	113
5	112	113
6	113	113

Stop Event

1×

saturated

end100.0ms (4%)

Compiler: Compiled 238 to 150 computations (37% saved)

Details

analyze2.0ms (0.1%)

sample1.4s (54%)

simplify28.0ms (1.1%)

prune3.0ms (0.1%)

localize7.0ms (0.3%)

series43.0ms (1.7%)

rewrite59.0ms (2.3%)

simplify50.0ms (2%)

prune125.0ms (5%)

localize30.0ms (1.2%)

series98.0ms (3.9%)

rewrite52.0ms (2.1%)

simplify55.0ms (2.2%)

prune149.0ms (5.9%)

localize5.0ms (0.2%)

series7.0ms (0.3%)

rewrite40.0ms (1.6%)

simplify7.0ms (0.3%)

prune27.0ms (1.1%)

regimes266.0ms (10.5%)

bsearch2.0ms (0.1%)

simplify5.0ms (0.2%)

end100.0ms (4%)

Profiling