Details

analyze1.3s (12.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
3.5%	96.2%	0.2%	10
9.2%	90.6%	0.2%	11
13.7%	86%	0.2%	12
22.1%	77.7%	0.2%	13
23%	76.7%	0.2%	14

Compiler

Compiled 19 to 12 computations (36.8% saved)

sample1.4s (13.7%)

Results

875.0ms	6977×	body	128	valid
143.0ms	481×	body	512	valid
138.0ms	383×	body	1024	valid
103.0ms	790×	body	128	invalid
76.0ms	358×	body	256	valid
26.0ms	57×	body	2048	valid

Compiler

Compiled 56 to 35 computations (37.5% saved)

simplify131.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

1303×	`div-sub_binary64`
658×	`fma-def_binary64`
640×	`sub-neg_binary64`
569×	`unsub-neg_binary64`
393×	`neg-mul-1_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	12	19
1	23	19
2	58	19
3	143	17
4	344	17
5	967	17
6	2282	17
7	3646	17
8	3700	17
9	4097	17
10	4253	17
11	4543	17
12	4719	17
13	5478	17

prune3.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

10.9b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	12.7b	(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))
	16.0b	(-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

Compiler

Compiled 100 to 56 computations (44% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 t z) (-.f64 a t))
✓	4.3b	(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))

series63.0ms (0.6%)

Counts

2 → 96

Calls

2 calls:

42.0ms	(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))
20.0ms	(/.f64 (-.f64 t z) (-.f64 a t))

rewrite74.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

541×	`fma-def_binary64`
271×	`fma-neg_binary64`
254×	`expm1-udef_binary64`
254×	`log1p-udef_binary64`
138×	`add-sqr-sqrt_binary64`

Counts

2 → 76

Calls

2 calls:

72.0ms	(/.f64 (-.f64 t z) (-.f64 a t))
72.0ms	(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	27
1	257	27
2	3781	27
3	5388	27
0	0	0
1	0	0

simplify92.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

901×	`fma-def_binary64`
642×	`times-frac_binary64`
593×	`fma-neg_binary64`
512×	`cancel-sign-sub-inv_binary64`
365×	`sub-neg_binary64`

Counts

172 → 154

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	178	3029
1	521	3008
2	1916	2394
3	4513	2376
4	5051	2376

prune142.0ms (1.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	147	7	154
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	149	7	156

Error

0.0b

Counts

156 → 7

Alt Table

Status	Error	Program
	30.7b	(fma.f64 y (-.f64 (/.f64 t a) (*.f64 (+.f64 (/.f64 t a) 1) (/.f64 z a))) (+.f64 x y))
	29.4b	(-.f64 (+.f64 x (.f64 (+.f64 1 (/.f64 a t)) (/.f64 (.f64 y z) t))) (.f64 y (.f64 (+.f64 1 (/.f64 a t)) (/.f64 a t))))
	25.3b	(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))
	39.6b	(*.f64 (-.f64 (+.f64 1 (/.f64 t (-.f64 a t))) (/.f64 z (-.f64 a t))) y)
▶	13.4b	(+.f64 y (+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 t z))))
	14.8b	(-.f64 (+.f64 y (+.f64 (/.f64 (.f64 y t) (-.f64 a t)) x)) (/.f64 (.f64 y z) (-.f64 a t)))
	13.7b	(*.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 y x))) (pow.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 y x))) 2))

Compiler

Compiled 3916 to 1314 computations (66.4% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 y (-.f64 a t))
✓	4.4b	(+.f64 y (+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 t z))))
✓	12.3b	(*.f64 (/.f64 y (-.f64 a t)) (-.f64 t z))

series97.0ms (0.9%)

Counts

3 → 132

Calls

3 calls:

46.0ms	(+.f64 y (+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 t z))))
34.0ms	(*.f64 (/.f64 y (-.f64 a t)) (-.f64 t z))
16.0ms	(/.f64 y (-.f64 a t))

rewrite85.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

282×	`expm1-udef_binary64`
282×	`log1p-udef_binary64`
153×	`add-sqr-sqrt_binary64`
149×	`log1p-expm1-u_binary64`
149×	`expm1-log1p-u_binary64`

Counts

3 → 113

Calls

3 calls:

82.0ms	(/.f64 y (-.f64 a t))
82.0ms	(+.f64 y (+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 t z))))
82.0ms	(*.f64 (/.f64 y (-.f64 a t)) (-.f64 t z))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	39
1	287	37
2	4341	37
3	5203	37
0	0	0
1	0	0

simplify112.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

711×	`times-frac_binary64`
701×	`cancel-sign-sub-inv_binary64`
462×	`sub-neg_binary64`
390×	`distribute-rgt-neg-in_binary64`
258×	`fma-neg_binary64`

Counts

245 → 210

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	217	4057
1	606	3961
2	2141	3223
3	4277	3211
4	5315	3211

prune150.0ms (1.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	207	3	210
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	210	7	217

Error

0.0b

Counts

217 → 7

Alt Table

Status	Error	Program
	29.4b	(-.f64 (+.f64 x (.f64 (+.f64 1 (/.f64 a t)) (/.f64 (.f64 y z) t))) (.f64 y (.f64 (+.f64 1 (/.f64 a t)) (/.f64 a t))))
	25.3b	(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))
	13.7b	(+.f64 y (+.f64 x (*.f64 (pow.f64 (cbrt.f64 (/.f64 y (-.f64 a t))) 3) (-.f64 t z))))
	39.6b	(*.f64 (-.f64 (+.f64 1 (/.f64 t (-.f64 a t))) (/.f64 z (-.f64 a t))) y)
	14.8b	(-.f64 (+.f64 y (+.f64 (/.f64 (.f64 y t) (-.f64 a t)) x)) (/.f64 (.f64 y z) (-.f64 a t)))
	13.0b	(+.f64 y (+.f64 x (/.f64 (-.f64 t z) (/.f64 (-.f64 a t) y))))
▶	12.0b	(+.f64 y (+.f64 x (/.f64 y (/.f64 (-.f64 a t) (-.f64 t z)))))

Compiler

Compiled 5543 to 1868 computations (66.3% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 a t) (-.f64 t z))
✓	2.6b	(/.f64 y (/.f64 (-.f64 a t) (-.f64 t z)))
✓	2.7b	(+.f64 y (+.f64 x (/.f64 y (/.f64 (-.f64 a t) (-.f64 t z)))))

series97.0ms (0.9%)

Counts

3 → 144

Calls

3 calls:

46.0ms	(+.f64 y (+.f64 x (/.f64 y (/.f64 (-.f64 a t) (-.f64 t z)))))
31.0ms	(/.f64 y (/.f64 (-.f64 a t) (-.f64 t z)))
19.0ms	(/.f64 (-.f64 a t) (-.f64 t z))

rewrite95.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

292×	`log1p-udef_binary64`
159×	`add-sqr-sqrt_binary64`
155×	`log1p-expm1-u_binary64`
155×	`expm1-log1p-u_binary64`
148×	`add-log-exp_binary64`

Counts

3 → 118

Calls

3 calls:

92.0ms	(/.f64 (-.f64 a t) (-.f64 t z))
92.0ms	(/.f64 y (/.f64 (-.f64 a t) (-.f64 t z)))
90.0ms	(+.f64 y (+.f64 x (/.f64 y (/.f64 (-.f64 a t) (-.f64 t z)))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	42
1	296	40
2	4689	40
3	5183	40
0	0	0
1	0	0

simplify97.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

861×	`times-frac_binary64`
809×	`cancel-sign-sub-inv_binary64`
554×	`sub-neg_binary64`
322×	`fma-neg_binary64`
240×	`associate--r+_binary64`

Counts

262 → 236

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	242	4550
1	700	4400
2	2560	4076
3	5336	4076

prune184.0ms (1.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	235	1	236
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	237	6	243

Error

0.0b

Counts

243 → 6

Alt Table

Status	Error	Program
	29.4b	(-.f64 (+.f64 x (.f64 (+.f64 1 (/.f64 a t)) (/.f64 (.f64 y z) t))) (.f64 y (.f64 (+.f64 1 (/.f64 a t)) (/.f64 a t))))
	25.3b	(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))
	13.7b	(+.f64 y (+.f64 x (*.f64 (pow.f64 (cbrt.f64 (/.f64 y (-.f64 a t))) 3) (-.f64 t z))))
	39.6b	(*.f64 (-.f64 (+.f64 1 (/.f64 t (-.f64 a t))) (/.f64 z (-.f64 a t))) y)
	13.0b	(+.f64 y (+.f64 x (/.f64 (-.f64 t z) (/.f64 (-.f64 a t) y))))
▶	12.0b	(+.f64 y (+.f64 x (/.f64 y (-.f64 (/.f64 a (-.f64 t z)) (/.f64 t (-.f64 t z))))))

Compiler

Compiled 6325 to 2102 computations (66.8% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 t (-.f64 t z))
✓	2.6b	(/.f64 y (-.f64 (/.f64 a (-.f64 t z)) (/.f64 t (-.f64 t z))))
✓	2.7b	(+.f64 y (+.f64 x (/.f64 y (-.f64 (/.f64 a (-.f64 t z)) (/.f64 t (-.f64 t z))))))

series302.0ms (2.9%)

Counts

3 → 120

Calls

3 calls:

163.0ms	(+.f64 y (+.f64 x (/.f64 y (-.f64 (/.f64 a (-.f64 t z)) (/.f64 t (-.f64 t z))))))
129.0ms	(/.f64 y (-.f64 (/.f64 a (-.f64 t z)) (/.f64 t (-.f64 t z))))
9.0ms	(/.f64 t (-.f64 t z))

rewrite95.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

318×	`log1p-udef_binary64`
172×	`add-sqr-sqrt_binary64`
168×	`log1p-expm1-u_binary64`
168×	`expm1-log1p-u_binary64`
160×	`add-log-exp_binary64`

Counts

3 → 97

Calls

3 calls:

90.0ms	(/.f64 t (-.f64 t z))
90.0ms	(/.f64 y (-.f64 (/.f64 a (-.f64 t z)) (/.f64 t (-.f64 t z))))
90.0ms	(+.f64 y (+.f64 x (/.f64 y (-.f64 (/.f64 a (-.f64 t z)) (/.f64 t (-.f64 t z))))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	39
1	322	39
2	4886	39
3	5429	39
0	0	0
1	0	0

simplify140.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

631×	`associate-/l*_binary64`
515×	`associate-/r*_binary64`
271×	`associate-r_binary64`
266×	`fma-def_binary64`
216×	`+-commutative_binary64`

Counts

217 → 229

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	529	7684
1	1803	7292
2	5237	7292

prune1.7s (16.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	229	0	229
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	229	6	235

Error

0.0b

Counts

235 → 6

Alt Table

Status	Error	Program
	29.4b	(-.f64 (+.f64 x (.f64 (+.f64 1 (/.f64 a t)) (/.f64 (.f64 y z) t))) (.f64 y (.f64 (+.f64 1 (/.f64 a t)) (/.f64 a t))))
	25.3b	(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))
	13.7b	(+.f64 y (+.f64 x (*.f64 (pow.f64 (cbrt.f64 (/.f64 y (-.f64 a t))) 3) (-.f64 t z))))
	39.6b	(*.f64 (-.f64 (+.f64 1 (/.f64 t (-.f64 a t))) (/.f64 z (-.f64 a t))) y)
	13.0b	(+.f64 y (+.f64 x (/.f64 (-.f64 t z) (/.f64 (-.f64 a t) y))))
✓	12.0b	(+.f64 y (+.f64 x (/.f64 y (-.f64 (/.f64 a (-.f64 t z)) (/.f64 t (-.f64 t z))))))

Compiler

Compiled 11148 to 4753 computations (57.4% saved)

regimes3.9s (37.2%)

Accuracy

Total 6.7b remaining (99.3%)

Threshold costs 0b (0%)

Counts

176 → 4

Compiler

Compiled 19932 to 12558 computations (37% saved)

bsearch60.0ms (0.6%)

Steps

Iters	Range		Point
10	468074494.78407884	1.1563927298062573e+22	2.424014653994123e+20
1	7.506161008111892e-260	7.585925672274598e-257	2.3862866475908086e-258
8	-1.8397419076820124e+99	-1.0105297313624401e+95	-1.294458439019683e+97

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

10×	`+-commutative_binary64`
6×	`sub-neg_binary64`
4×	`*-commutative_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	80
1	40	80
2	51	80
3	57	80
4	60	80
5	60	80

end92.0ms (0.9%)

Compiler: Compiled 245 to 129 computations (47.3% saved)

Details

analyze1.3s (12.2%)

sample1.4s (13.7%)

simplify131.0ms (1.3%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series63.0ms (0.6%)

rewrite74.0ms (0.7%)

simplify92.0ms (0.9%)

prune142.0ms (1.4%)

localize8.0ms (0.1%)

series97.0ms (0.9%)

rewrite85.0ms (0.8%)

simplify112.0ms (1.1%)

prune150.0ms (1.4%)

localize9.0ms (0.1%)

series97.0ms (0.9%)

rewrite95.0ms (0.9%)

simplify97.0ms (0.9%)

prune184.0ms (1.8%)

localize11.0ms (0.1%)

series302.0ms (2.9%)

rewrite95.0ms (0.9%)

simplify140.0ms (1.3%)

prune1.7s (16.3%)

regimes3.9s (37.2%)

bsearch60.0ms (0.6%)

simplify4.0ms (0%)

end92.0ms (0.9%)

Profiling