Details

analyze2.6s (12.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.6%	0.4%	0
0%	99.6%	0.4%	1
0%	99.6%	0.4%	2
0%	99.6%	0.4%	3
0%	99.6%	0.4%	4
0%	99.6%	0.4%	5
0%	99.6%	0.4%	6
0%	99.6%	0.4%	7
0%	74.7%	25.3%	8
0%	74.7%	25.3%	9
0%	65.4%	34.6%	10
0%	51.4%	48.6%	11
0%	51.4%	48.6%	12
0%	51.4%	48.6%	13
0%	51.4%	48.6%	14

Compiler

Compiled 30 to 21 computations (30% saved)

sample8.0s (37%)

Symmetry

(sort z t a)

Results

4.3s	11341×	body	128	invalid
3.4s	8253×	body	128	valid
2.0ms	2×	body	512	valid
1.0ms	1×	body	1024	valid

Compiler

Compiled 89 to 62 computations (30.3% saved)

simplify92.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

2664×	`associate-+l+_binary64`
1041×	`associate-+r+_binary64`
923×	`+-commutative_binary64`
750×	`fma-def_binary64`
5×	`*-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	30
1	41	26
2	109	26
3	376	26
4	1118	26
5	1592	26
6	1698	26
7	1698	26
8	1698	26
9	1698	26
10	2706	26
11	2958	26
12	2958	26
13	2910	26
14	2910	26
15	2540	26
16	2524	26

prune7.0ms (0%)

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

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 y i (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a)))

Compiler

Compiled 99 to 61 computations (38.4% saved)

localize32.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a)
✓	0.1b	(fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a))
✓	0.1b	(fma.f64 x (log.f64 y) z)

series2.0s (9.1%)

Counts

3 → 180

Calls

3 calls:

1.4s	(fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a))
313.0ms	(+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a)
215.0ms	(fma.f64 x (log.f64 y) z)

rewrite108.0ms (0.5%)

Algorithm

2×	batch-egg-rewrite

Rules

322×	`expm1-udef_binary64`
322×	`log1p-udef_binary64`
178×	`add-sqr-sqrt_binary64`
169×	`log1p-expm1-u_binary64`
169×	`expm1-log1p-u_binary64`

Counts

3 → 89

Calls

3 calls:

103.0ms	(+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a)
103.0ms	(fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a))
103.0ms	(fma.f64 x (log.f64 y) z)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	42
1	343	42
2	4381	42
3	5295	42
0	0	0
1	0	0

simplify224.0ms (1%)

Algorithm

1×	egg-herbie

Rules

523×	`associate--r+_binary64`
502×	`fma-neg_binary64`
464×	`unsub-neg_binary64`
445×	`distribute-neg-in_binary64`
405×	`sub-neg_binary64`

Counts

269 → 127

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	85	2921
1	243	2919
2	671	2696
3	2141	2696
4	4038	2696
5	4912	2696
6	5138	2696

prune227.0ms (1.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	123	4	127
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	123	5	128

Error

0.1b

Counts

128 → 5

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 y i (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a)))
	56.0b	(fma.f64 y i (/.f64 (+.f64 (pow.f64 (.f64 (-.f64 b 1/2) (log.f64 c)) 3) (pow.f64 (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a) 3)) (+.f64 (.f64 (.f64 (-.f64 b 1/2) (log.f64 c)) (.f64 (-.f64 b 1/2) (log.f64 c))) (-.f64 (pow.f64 (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a) 2) (.f64 (.f64 (-.f64 b 1/2) (log.f64 c)) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a))))))
	49.3b	(fma.f64 y i (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (pow.f64 (sqrt.f64 (fma.f64 x (log.f64 y) z)) 2) t) a)))
▶	0.5b	(fma.f64 y i (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (pow.f64 (cbrt.f64 (fma.f64 x (log.f64 y) z)) 3) t) a)))
	0.6b	(fma.f64 y i (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (*.f64 (cbrt.f64 (fma.f64 x (log.f64 y) z)) (pow.f64 (cbrt.f64 (fma.f64 x (log.f64 y) z)) 2)) t) a)))

Compiler

Compiled 3390 to 1244 computations (63.3% saved)

localize37.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (pow.f64 (cbrt.f64 (fma.f64 x (log.f64 y) z)) 3) t) a))
	0.1b	(fma.f64 x (log.f64 y) z)
✓	0.6b	(cbrt.f64 (fma.f64 x (log.f64 y) z))
✓	0.7b	(pow.f64 (cbrt.f64 (fma.f64 x (log.f64 y) z)) 3)

series3.6s (16.9%)

Counts

3 → 156

Calls

3 calls:

2.5s	(pow.f64 (cbrt.f64 (fma.f64 x (log.f64 y) z)) 3)
743.0ms	(fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (pow.f64 (cbrt.f64 (fma.f64 x (log.f64 y) z)) 3) t) a))
422.0ms	(cbrt.f64 (fma.f64 x (log.f64 y) z))

rewrite72.0ms (0.3%)

Algorithm

2×	batch-egg-rewrite

Rules

351×	`log1p-udef_binary64`
196×	`add-sqr-sqrt_binary64`
189×	`log1p-expm1-u_binary64`
189×	`expm1-log1p-u_binary64`
184×	`add-log-exp_binary64`

Counts

3 → 67

Calls

3 calls:

71.0ms	(fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (pow.f64 (cbrt.f64 (fma.f64 x (log.f64 y) z)) 3) t) a))
71.0ms	(cbrt.f64 (fma.f64 x (log.f64 y) z))
71.0ms	(pow.f64 (cbrt.f64 (fma.f64 x (log.f64 y) z)) 3)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	38
1	390	38
2	4818	38
3	5273	38
0	0	0
1	0	0

simplify167.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

699×	`fma-def_binary64`
265×	`cancel-sign-sub-inv_binary64`
200×	`associate-/r/_binary64`
197×	`fma-neg_binary64`
178×	`unswap-sqr_binary64`

Counts

223 → 153

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	213	4427
1	699	4343
2	2410	3868
3	4811	3834
4	4998	3834
5	4958	3834

prune468.0ms (2.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	182	0	182
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	182	5	187

Error

0.1b

Counts

187 → 5

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 y i (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a)))
	56.0b	(fma.f64 y i (/.f64 (+.f64 (pow.f64 (.f64 (-.f64 b 1/2) (log.f64 c)) 3) (pow.f64 (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a) 3)) (+.f64 (.f64 (.f64 (-.f64 b 1/2) (log.f64 c)) (.f64 (-.f64 b 1/2) (log.f64 c))) (-.f64 (pow.f64 (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a) 2) (.f64 (.f64 (-.f64 b 1/2) (log.f64 c)) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a))))))
	49.3b	(fma.f64 y i (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (pow.f64 (sqrt.f64 (fma.f64 x (log.f64 y) z)) 2) t) a)))
✓	0.5b	(fma.f64 y i (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (pow.f64 (cbrt.f64 (fma.f64 x (log.f64 y) z)) 3) t) a)))
▶	0.6b	(fma.f64 y i (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (*.f64 (cbrt.f64 (fma.f64 x (log.f64 y) z)) (pow.f64 (cbrt.f64 (fma.f64 x (log.f64 y) z)) 2)) t) a)))

Compiler

Compiled 6019 to 2975 computations (50.6% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 x (log.f64 y) z)
✓	0.4b	(*.f64 (cbrt.f64 (fma.f64 x (log.f64 y) z)) (pow.f64 (cbrt.f64 (fma.f64 x (log.f64 y) z)) 2))
✓	0.5b	(pow.f64 (cbrt.f64 (fma.f64 x (log.f64 y) z)) 2)
	0.6b	(cbrt.f64 (fma.f64 x (log.f64 y) z))

series750.0ms (3.5%)

Counts

2 → 72

Calls

2 calls:

652.0ms	(pow.f64 (cbrt.f64 (fma.f64 x (log.f64 y) z)) 2)
97.0ms	(*.f64 (cbrt.f64 (fma.f64 x (log.f64 y) z)) (pow.f64 (cbrt.f64 (fma.f64 x (log.f64 y) z)) 2))

rewrite72.0ms (0.3%)

Algorithm

2×	batch-egg-rewrite

Rules

681×	`log1p-expm1-u_binary64`
681×	`expm1-log1p-u_binary64`
145×	`expm1-udef_binary64`
145×	`log1p-udef_binary64`
136×	`log-pow_binary64`

Counts

2 → 55

Calls

2 calls:

70.0ms	(*.f64 (cbrt.f64 (fma.f64 x (log.f64 y) z)) (pow.f64 (cbrt.f64 (fma.f64 x (log.f64 y) z)) 2))
70.0ms	(pow.f64 (cbrt.f64 (fma.f64 x (log.f64 y) z)) 2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	19
1	177	17
2	1803	17
3	4924	17
4	4921	17
0	0	0
1	0	0

simplify58.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

893×	`associate-/r*_binary64`
458×	`fma-def_binary64`
277×	`unswap-sqr_binary64`
196×	`associate-/r/_binary64`
196×	`cancel-sign-sub-inv_binary64`

Counts

127 → 106

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	150	1973
1	495	1909
2	1847	1714
3	5535	1714

prune286.0ms (1.3%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	293	3	296
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	293	8	301

Error

0.0b

Counts

301 → 8

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 y i (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a)))
	56.0b	(fma.f64 y i (/.f64 (+.f64 (pow.f64 (.f64 (-.f64 b 1/2) (log.f64 c)) 3) (pow.f64 (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a) 3)) (+.f64 (.f64 (.f64 (-.f64 b 1/2) (log.f64 c)) (.f64 (-.f64 b 1/2) (log.f64 c))) (-.f64 (pow.f64 (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a) 2) (.f64 (.f64 (-.f64 b 1/2) (log.f64 c)) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a))))))
	49.3b	(fma.f64 y i (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (pow.f64 (sqrt.f64 (fma.f64 x (log.f64 y) z)) 2) t) a)))
✓	0.5b	(fma.f64 y i (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (pow.f64 (cbrt.f64 (fma.f64 x (log.f64 y) z)) 3) t) a)))
✓	0.6b	(fma.f64 y i (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (*.f64 (cbrt.f64 (fma.f64 x (log.f64 y) z)) (pow.f64 (cbrt.f64 (fma.f64 x (log.f64 y) z)) 2)) t) a)))
	49.4b	(fma.f64 y i (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (*.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (fma.f64 x (log.f64 y) z)) 2)) (pow.f64 (cbrt.f64 (fma.f64 x (log.f64 y) z)) 2)) t) a)))
▶	0.7b	(fma.f64 y i (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x (log.f64 y) z))) 3) (pow.f64 (cbrt.f64 (fma.f64 x (log.f64 y) z)) 2)) t) a)))
	35.3b	(fma.f64 y i (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (log.f64 y)) z) t) a)))

Compiler

Compiled 12912 to 6120 computations (52.6% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.5b	(pow.f64 (cbrt.f64 (fma.f64 x (log.f64 y) z)) 2)
	0.6b	(cbrt.f64 (fma.f64 x (log.f64 y) z))
✓	0.6b	(cbrt.f64 (cbrt.f64 (fma.f64 x (log.f64 y) z)))
✓	0.7b	(pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x (log.f64 y) z))) 3)

series930.0ms (4.3%)

Counts

2 → 72

Calls

2 calls:

488.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x (log.f64 y) z))) 3)
441.0ms	(cbrt.f64 (cbrt.f64 (fma.f64 x (log.f64 y) z)))

rewrite116.0ms (0.5%)

Algorithm

2×	batch-egg-rewrite

Rules

714×	`log1p-expm1-u_binary64`
714×	`expm1-log1p-u_binary64`
149×	`expm1-udef_binary64`
149×	`log1p-udef_binary64`
91×	`fma-neg_binary64`

Counts

2 → 47

Calls

2 calls:

114.0ms	(cbrt.f64 (cbrt.f64 (fma.f64 x (log.f64 y) z)))
114.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x (log.f64 y) z))) 3)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	178	19
2	1894	19
3	4988	19
4	4972	19
5	4930	19
0	0	0
1	0	0

simplify89.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

892×	`fma-def_binary64`
351×	`unswap-sqr_binary64`
266×	`associate-r_binary64`
214×	`times-frac_binary64`
164×	`associate-/r*_binary64`

Counts

119 → 133

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	234	3216
1	818	3128
2	3233	2938
3	4971	2938

prune349.0ms (1.6%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	328	0	328
Fresh	0	4	4
Picked	0	1	1
Done	0	3	3
Total	328	8	336

Error

0.0b

Counts

336 → 8

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 y i (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a)))
	56.0b	(fma.f64 y i (/.f64 (+.f64 (pow.f64 (.f64 (-.f64 b 1/2) (log.f64 c)) 3) (pow.f64 (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a) 3)) (+.f64 (.f64 (.f64 (-.f64 b 1/2) (log.f64 c)) (.f64 (-.f64 b 1/2) (log.f64 c))) (-.f64 (pow.f64 (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a) 2) (.f64 (.f64 (-.f64 b 1/2) (log.f64 c)) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a))))))
	49.3b	(fma.f64 y i (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (pow.f64 (sqrt.f64 (fma.f64 x (log.f64 y) z)) 2) t) a)))
✓	0.5b	(fma.f64 y i (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (pow.f64 (cbrt.f64 (fma.f64 x (log.f64 y) z)) 3) t) a)))
✓	0.6b	(fma.f64 y i (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (*.f64 (cbrt.f64 (fma.f64 x (log.f64 y) z)) (pow.f64 (cbrt.f64 (fma.f64 x (log.f64 y) z)) 2)) t) a)))
	49.4b	(fma.f64 y i (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (*.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (fma.f64 x (log.f64 y) z)) 2)) (pow.f64 (cbrt.f64 (fma.f64 x (log.f64 y) z)) 2)) t) a)))
✓	0.7b	(fma.f64 y i (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x (log.f64 y) z))) 3) (pow.f64 (cbrt.f64 (fma.f64 x (log.f64 y) z)) 2)) t) a)))
	35.3b	(fma.f64 y i (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (log.f64 y)) z) t) a)))

Compiler

Compiled 17357 to 8973 computations (48.3% saved)

regimes744.0ms (3.5%)

Accuracy

Total 0.0b remaining (26.8%)

Threshold costs 0.0b (26.8%)

Counts

40 → 1

Compiler

Compiled 13867 to 9150 computations (34% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
1×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	26
1	23	26
2	24	26
3	23	26

end495.0ms (2.3%)

Remove: (sort z t a)
Compiler: Compiled 406 to 252 computations (37.9% saved)

Details

analyze2.6s (12.1%)

sample8.0s (37%)

simplify92.0ms (0.4%)

prune7.0ms (0%)

localize32.0ms (0.1%)

series2.0s (9.1%)

rewrite108.0ms (0.5%)

simplify224.0ms (1%)

prune227.0ms (1.1%)

localize37.0ms (0.2%)

series3.6s (16.9%)

rewrite72.0ms (0.3%)

simplify167.0ms (0.8%)

prune468.0ms (2.2%)

localize20.0ms (0.1%)

series750.0ms (3.5%)

rewrite72.0ms (0.3%)

simplify58.0ms (0.3%)

prune286.0ms (1.3%)

localize23.0ms (0.1%)

series930.0ms (4.3%)

rewrite116.0ms (0.5%)

simplify89.0ms (0.4%)

prune349.0ms (1.6%)

regimes744.0ms (3.5%)

simplify2.0ms (0%)

end495.0ms (2.3%)

Profiling