Details

analyze2.0ms (0%)

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)

sample1.8s (36.6%)

Results

738.0ms	6202×	body	128	valid
443.0ms	1041×	body	1024	valid
204.0ms	607×	body	512	valid
59.0ms	319×	body	256	valid
40.0ms	87×	body	2048	valid

Compiler

Compiled 59 to 43 computations (27.1% saved)

simplify206.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

890×	`sub-neg_binary64`
434×	`cancel-sign-sub-inv_binary64`
422×	`associate-/l*_binary64`
388×	`distribute-rgt-neg-in_binary64`
379×	`neg-mul-1_binary64`

Counts

1 → 2

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	11	19
1	23	19
2	39	19
3	64	19
4	108	19
5	215	17
6	353	17
7	603	17
8	1141	17
9	2484	17
10	3195	17
11	3981	17
12	4235	17
13	4399	17
14	4503	17
15	4531	17
16	4533	17
17	4768	17
18	4708	17
19	4930	17
20	4826	17

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

13.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	13.7b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)

Compiler

Compiled 55 to 39 computations (29.1% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))
✓	2.1b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)

series40.0ms (0.8%)

Counts

2 → 48

Calls

2 calls:

25.0ms	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)
15.0ms	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))

rewrite83.0ms (1.7%)

Algorithm

2×	batch-egg-rewrite

Rules

472×	`fma-def_binary64`
257×	`fma-neg_binary64`
236×	`expm1-udef_binary64`
236×	`log1p-udef_binary64`
132×	`add-sqr-sqrt_binary64`

Counts

2 → 74

Calls

2 calls:

81.0ms	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))
81.0ms	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	30
1	261	30
2	3563	30
3	4908	30
0	0	0
1	0	0

simplify99.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

935×	`times-frac_binary64`
498×	`cancel-sign-sub-inv_binary64`
367×	`sub-neg_binary64`
205×	`+-commutative_binary64`
189×	`associate-+r+_binary64`

Counts

122 → 128

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	221	2358
1	749	2323
2	2913	2279
3	5252	2279

prune137.0ms (2.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	125	3	128
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	125	4	129

Error

0.0b

Counts

129 → 4

Alt Table

Status	Error	Program
▶	43.6b	(-.f64 1 (+.f64 (/.f64 1 beta) (/.f64 alpha beta)))
	47.9b	(/.f64 (+.f64 beta 1) alpha)
	50.9b	(-.f64 (+.f64 (pow.f64 (/.f64 beta alpha) 3) (+.f64 (/.f64 1 alpha) (+.f64 (/.f64 4 (pow.f64 alpha 3)) (+.f64 (/.f64 beta alpha) (fma.f64 8 (/.f64 beta (pow.f64 alpha 3)) (.f64 5 (/.f64 (.f64 beta beta) (pow.f64 alpha 3)))))))) (+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 7 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 4)) (+.f64 (/.f64 8 (pow.f64 alpha 4)) (+.f64 (/.f64 (pow.f64 beta 4) (pow.f64 alpha 4)) (fma.f64 18 (/.f64 (.f64 beta beta) (pow.f64 alpha 4)) (fma.f64 20 (/.f64 beta (pow.f64 alpha 4)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (.f64 (/.f64 beta alpha) (/.f64 beta alpha))))))))))
✓	13.7b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)

Compiler

Compiled 4035 to 2584 computations (36% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series8.0ms (0.2%)

Counts

1 → 15

Calls

1 calls:

8.0ms

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

rewrite56.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

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

Counts

1 → 54

Calls

1 calls:

54.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	155	10
2	2141	10
3	5503	10
0	0	0
1	0	0

simplify12.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Counts

69 → 57

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	96
1	11	96
2	10	96

prune37.0ms (0.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	57	0	57
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	57	4	61

Error

0.0b

Counts

61 → 4

Alt Table

Status	Error	Program
✓	43.6b	(-.f64 1 (+.f64 (/.f64 1 beta) (/.f64 alpha beta)))
▶	47.9b	(/.f64 (+.f64 beta 1) alpha)
	50.9b	(-.f64 (+.f64 (pow.f64 (/.f64 beta alpha) 3) (+.f64 (/.f64 1 alpha) (+.f64 (/.f64 4 (pow.f64 alpha 3)) (+.f64 (/.f64 beta alpha) (fma.f64 8 (/.f64 beta (pow.f64 alpha 3)) (.f64 5 (/.f64 (.f64 beta beta) (pow.f64 alpha 3)))))))) (+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 7 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 4)) (+.f64 (/.f64 8 (pow.f64 alpha 4)) (+.f64 (/.f64 (pow.f64 beta 4) (pow.f64 alpha 4)) (fma.f64 18 (/.f64 (.f64 beta beta) (pow.f64 alpha 4)) (fma.f64 20 (/.f64 beta (pow.f64 alpha 4)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (.f64 (/.f64 beta alpha) (/.f64 beta alpha))))))))))
✓	13.7b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)

Compiler

Compiled 1080 to 642 computations (40.6% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series6.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

6.0ms

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

rewrite49.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

645×	`log1p-expm1-u_binary64`
645×	`expm1-log1p-u_binary64`
298×	`log-prod_binary64`
112×	`log1p-udef_binary64`
111×	`expm1-udef_binary64`

Counts

1 → 36

Calls

1 calls:

48.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	128	7
2	1621	7
3	5298	7
0	0	0
1	0	0

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Counts

48 → 39

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	102
1	10	102
2	9	102

prune27.0ms (0.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	39	0	39
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	39	4	43

Error

0.0b

Counts

43 → 4

Alt Table

Status	Error	Program
✓	43.6b	(-.f64 1 (+.f64 (/.f64 1 beta) (/.f64 alpha beta)))
✓	47.9b	(/.f64 (+.f64 beta 1) alpha)
▶	50.9b	(-.f64 (+.f64 (pow.f64 (/.f64 beta alpha) 3) (+.f64 (/.f64 1 alpha) (+.f64 (/.f64 4 (pow.f64 alpha 3)) (+.f64 (/.f64 beta alpha) (fma.f64 8 (/.f64 beta (pow.f64 alpha 3)) (.f64 5 (/.f64 (.f64 beta beta) (pow.f64 alpha 3)))))))) (+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 7 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 4)) (+.f64 (/.f64 8 (pow.f64 alpha 4)) (+.f64 (/.f64 (pow.f64 beta 4) (pow.f64 alpha 4)) (fma.f64 18 (/.f64 (.f64 beta beta) (pow.f64 alpha 4)) (fma.f64 20 (/.f64 beta (pow.f64 alpha 4)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (.f64 (/.f64 beta alpha) (/.f64 beta alpha))))))))))
✓	13.7b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)

Compiler

Compiled 629 to 432 computations (31.3% saved)

localize48.0ms (1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	16.1b	(/.f64 (*.f64 beta beta) (pow.f64 alpha 3))
✓	18.0b	(-.f64 (+.f64 (pow.f64 (/.f64 beta alpha) 3) (+.f64 (/.f64 1 alpha) (+.f64 (/.f64 4 (pow.f64 alpha 3)) (+.f64 (/.f64 beta alpha) (fma.f64 8 (/.f64 beta (pow.f64 alpha 3)) (.f64 5 (/.f64 (.f64 beta beta) (pow.f64 alpha 3)))))))) (+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 7 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 4)) (+.f64 (/.f64 8 (pow.f64 alpha 4)) (+.f64 (/.f64 (pow.f64 beta 4) (pow.f64 alpha 4)) (fma.f64 18 (/.f64 (.f64 beta beta) (pow.f64 alpha 4)) (fma.f64 20 (/.f64 beta (pow.f64 alpha 4)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (.f64 (/.f64 beta alpha) (/.f64 beta alpha))))))))))
✓	19.1b	(/.f64 (pow.f64 beta 3) (pow.f64 alpha 4))
✓	19.8b	(/.f64 (pow.f64 beta 4) (pow.f64 alpha 4))

series156.0ms (3.2%)

Counts

4 → 48

Calls

4 calls:

53.0ms	(-.f64 (+.f64 (pow.f64 (/.f64 beta alpha) 3) (+.f64 (/.f64 1 alpha) (+.f64 (/.f64 4 (pow.f64 alpha 3)) (+.f64 (/.f64 beta alpha) (fma.f64 8 (/.f64 beta (pow.f64 alpha 3)) (.f64 5 (/.f64 (.f64 beta beta) (pow.f64 alpha 3)))))))) (+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 7 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 4)) (+.f64 (/.f64 8 (pow.f64 alpha 4)) (+.f64 (/.f64 (pow.f64 beta 4) (pow.f64 alpha 4)) (fma.f64 18 (/.f64 (.f64 beta beta) (pow.f64 alpha 4)) (fma.f64 20 (/.f64 beta (pow.f64 alpha 4)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (.f64 (/.f64 beta alpha) (/.f64 beta alpha))))))))))
36.0ms	(/.f64 (pow.f64 beta 3) (pow.f64 alpha 4))
36.0ms	(/.f64 (pow.f64 beta 4) (pow.f64 alpha 4))
31.0ms	(/.f64 (*.f64 beta beta) (pow.f64 alpha 3))

rewrite125.0ms (2.6%)

Algorithm

2×	batch-egg-rewrite

Rules

504×	`log1p-expm1-u_binary64`
504×	`expm1-log1p-u_binary64`
374×	`prod-diff_binary64`
162×	`unpow-prod-down_binary64`
135×	`log-prod_binary64`

Counts

4 → 110

Calls

4 calls:

118.0ms	(/.f64 (*.f64 beta beta) (pow.f64 alpha 3))
118.0ms	(-.f64 (+.f64 (pow.f64 (/.f64 beta alpha) 3) (+.f64 (/.f64 1 alpha) (+.f64 (/.f64 4 (pow.f64 alpha 3)) (+.f64 (/.f64 beta alpha) (fma.f64 8 (/.f64 beta (pow.f64 alpha 3)) (.f64 5 (/.f64 (.f64 beta beta) (pow.f64 alpha 3)))))))) (+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 7 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 4)) (+.f64 (/.f64 8 (pow.f64 alpha 4)) (+.f64 (/.f64 (pow.f64 beta 4) (pow.f64 alpha 4)) (fma.f64 18 (/.f64 (.f64 beta beta) (pow.f64 alpha 4)) (fma.f64 20 (/.f64 beta (pow.f64 alpha 4)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (.f64 (/.f64 beta alpha) (/.f64 beta alpha))))))))))
117.0ms	(/.f64 (pow.f64 beta 3) (pow.f64 alpha 4))
117.0ms	(/.f64 (pow.f64 beta 4) (pow.f64 alpha 4))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	168
1	1082	160
2	4920	160
3	5278	160
0	0	0
1	0	0

simplify55.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

766×	`associate--l+_binary64`
732×	`fma-def_binary64`
235×	`sub-neg_binary64`
208×	`times-frac_binary64`
204×	`distribute-neg-in_binary64`

Counts

158 → 142

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	105	2015
1	349	2007
2	1424	1891
3	5230	1891

prune465.0ms (9.6%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	139	3	142
Fresh	0	0	0
Picked	1	0	1
Done	0	3	3
Total	140	6	146

Error

0.0b

Counts

146 → 6

Alt Table

Status	Error	Program
	51.1b	(pow.f64 (sqrt.f64 (-.f64 (+.f64 (pow.f64 (/.f64 beta alpha) 3) (+.f64 (/.f64 1 alpha) (+.f64 (fma.f64 4 (pow.f64 alpha -3) (/.f64 beta alpha)) (fma.f64 8 (/.f64 beta (pow.f64 alpha 3)) (.f64 5 (/.f64 (.f64 beta beta) (pow.f64 alpha 3))))))) (fma.f64 2 (pow.f64 alpha -2) (fma.f64 7 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 4)) (fma.f64 8 (pow.f64 alpha -4) (fma.f64 (pow.f64 beta 4) (pow.f64 alpha -4) (fma.f64 18 (/.f64 (.f64 beta beta) (pow.f64 alpha 4)) (fma.f64 20 (/.f64 beta (pow.f64 alpha 4)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (pow.f64 (/.f64 beta alpha) 2)))))))))) 2)
	51.1b	(fma.f64 (sqrt.f64 (+.f64 (pow.f64 (/.f64 beta alpha) 3) (+.f64 (/.f64 1 alpha) (+.f64 (fma.f64 4 (pow.f64 alpha -3) (/.f64 beta alpha)) (fma.f64 8 (/.f64 beta (pow.f64 alpha 3)) (.f64 5 (/.f64 (.f64 beta beta) (pow.f64 alpha 3)))))))) (sqrt.f64 (+.f64 (pow.f64 (/.f64 beta alpha) 3) (+.f64 (/.f64 1 alpha) (+.f64 (fma.f64 4 (pow.f64 alpha -3) (/.f64 beta alpha)) (fma.f64 8 (/.f64 beta (pow.f64 alpha 3)) (.f64 5 (/.f64 (.f64 beta beta) (pow.f64 alpha 3)))))))) (neg.f64 (fma.f64 2 (pow.f64 alpha -2) (fma.f64 7 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 4)) (fma.f64 8 (pow.f64 alpha -4) (fma.f64 (pow.f64 beta 4) (pow.f64 alpha -4) (fma.f64 18 (/.f64 (.f64 beta beta) (pow.f64 alpha 4)) (fma.f64 20 (/.f64 beta (pow.f64 alpha 4)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (pow.f64 (/.f64 beta alpha) 2))))))))))
✓	43.6b	(-.f64 1 (+.f64 (/.f64 1 beta) (/.f64 alpha beta)))
✓	47.9b	(/.f64 (+.f64 beta 1) alpha)
	51.2b	(pow.f64 (cbrt.f64 (-.f64 (+.f64 (pow.f64 (/.f64 beta alpha) 3) (+.f64 (/.f64 1 alpha) (+.f64 (fma.f64 4 (pow.f64 alpha -3) (/.f64 beta alpha)) (fma.f64 8 (/.f64 beta (pow.f64 alpha 3)) (.f64 5 (/.f64 (.f64 beta beta) (pow.f64 alpha 3))))))) (fma.f64 2 (pow.f64 alpha -2) (fma.f64 7 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 4)) (fma.f64 8 (pow.f64 alpha -4) (fma.f64 (pow.f64 beta 4) (pow.f64 alpha -4) (fma.f64 18 (/.f64 (.f64 beta beta) (pow.f64 alpha 4)) (fma.f64 20 (/.f64 beta (pow.f64 alpha 4)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (pow.f64 (/.f64 beta alpha) 2)))))))))) 3)
✓	13.7b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)

Compiler

Compiled 18648 to 11813 computations (36.7% saved)

regimes1.1s (22.9%)

Accuracy

Total -0.0b remaining (-12.6%)

Threshold costs -0.0b (-12.6%)

Counts

73 → 2

Compiler

Compiled 27925 to 18746 computations (32.9% saved)

bsearch9.0ms (0.2%)

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

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

18×	`+-commutative_binary64`
10×	`*-commutative_binary64`
10×	`sub-neg_binary64`
7×	`neg-sub0_binary64`
7×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	136
1	66	136
2	80	136
3	99	136
4	115	136
5	121	136
6	123	136
7	120	136

end297.0ms (6.2%)

Compiler: Compiled 542 to 363 computations (33% saved)

Details

analyze2.0ms (0%)

sample1.8s (36.6%)

simplify206.0ms (4.3%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series40.0ms (0.8%)

rewrite83.0ms (1.7%)

simplify99.0ms (2.1%)

prune137.0ms (2.8%)

localize5.0ms (0.1%)

series8.0ms (0.2%)

rewrite56.0ms (1.2%)

simplify12.0ms (0.2%)

prune37.0ms (0.8%)

localize3.0ms (0.1%)

series6.0ms (0.1%)

rewrite49.0ms (1%)

simplify9.0ms (0.2%)

prune27.0ms (0.6%)

localize48.0ms (1%)

series156.0ms (3.2%)

rewrite125.0ms (2.6%)

simplify55.0ms (1.2%)

prune465.0ms (9.6%)

regimes1.1s (22.9%)

bsearch9.0ms (0.2%)

simplify7.0ms (0.1%)

end297.0ms (6.2%)

Profiling