Details

analyze1.0s (12.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
12.5%	87.2%	0.3%	7
12.5%	87.2%	0.3%	8
12.5%	87.2%	0.3%	9
12.5%	87.2%	0.3%	10
18.7%	81%	0.3%	11
28%	71.7%	0.3%	12
31.2%	68.5%	0.3%	13
31.2%	68.5%	0.3%	14

Compiler

Compiled 24 to 16 computations (33.3% saved)

sample1.3s (16.1%)

Infinites

3.2% of outputs are infinite.

Results

1.2s

8256×

body

128

valid

Compiler

Compiled 71 to 47 computations (33.8% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

16×	`fma-def_binary64`
6×	`+-commutative_binary64`
6×	`*-commutative_binary64`
4×	`associate-/l*_binary64`
4×	`associate-/r/_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	16	25
1	29	25
2	41	21
3	51	21
4	61	21
5	65	21
6	64	21

prune4.0ms (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

13.6b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	18.0b	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
	18.5b	(/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)))

Compiler

Compiled 126 to 78 computations (38.1% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (fma.f64 b (/.f64 y t) a))
✓	3.5b	(fma.f64 y (/.f64 z t) x)
✓	3.6b	(fma.f64 b (/.f64 y t) a)
✓	13.5b	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))

series263.0ms (3.3%)

Counts

4 → 216

Calls

4 calls:

216.0ms	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
17.0ms	(fma.f64 b (/.f64 y t) a)
14.0ms	(fma.f64 y (/.f64 z t) x)
14.0ms	(+.f64 1 (fma.f64 b (/.f64 y t) a))

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64`
14×	`add-sqr-sqrt_binary64`
14×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`
6×	`add-cbrt-cube_binary64`

Counts

4 → 73

Calls

4 calls:

4.0ms	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
2.0ms	(+.f64 1 (fma.f64 b (/.f64 y t) a))
0.0ms	(fma.f64 b (/.f64 y t) a)
0.0ms	(fma.f64 y (/.f64 z t) x)

simplify149.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

741×	`times-frac_binary64`
527×	`associate-/l*_binary64`
403×	`associate-/r*_binary64`
235×	`fma-def_binary64`
208×	`associate-l_binary64`

Counts

289 → 158

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	440	9932
1	1379	9371
2	5036	9371

prune202.0ms (2.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	150	8	158
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	151	9	160

Error

0.3b

Counts

160 → 9

Alt Table

Status	Error	Program
	41.7b	(/.f64 z b)
	37.9b	(-.f64 (fma.f64 (/.f64 y t) (/.f64 z (fma.f64 b (/.f64 y t) 1)) (/.f64 x (fma.f64 b (/.f64 y t) 1))) (fma.f64 (/.f64 a t) (/.f64 (.f64 y z) (pow.f64 (fma.f64 b (/.f64 y t) 1) 2)) (/.f64 (.f64 x a) (pow.f64 (fma.f64 b (/.f64 y t) 1) 2))))
	45.3b	(/.f64 (.f64 (+.f64 (/.f64 (.f64 y z) t) x) t) (*.f64 y b))
	38.1b	(/.f64 (sqrt.f64 (fma.f64 y (/.f64 z t) x)) (/.f64 (+.f64 1 (fma.f64 b (/.f64 y t) a)) (sqrt.f64 (fma.f64 y (/.f64 z t) x))))
✓	18.0b	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
▶	16.7b	(fma.f64 (/.f64 y (+.f64 1 (fma.f64 b (/.f64 y t) a))) (/.f64 z t) (/.f64 x (+.f64 1 (fma.f64 b (/.f64 y t) a))))
	16.8b	(+.f64 (/.f64 (.f64 y z) (.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t)) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))))
	18.1b	(/.f64 (+.f64 (/.f64 (*.f64 y z) t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
	42.3b	(-.f64 (fma.f64 (/.f64 t y) (/.f64 x b) (/.f64 z b)) (fma.f64 (/.f64 t y) (/.f64 z (.f64 b b)) (/.f64 (.f64 a (.f64 z t)) (.f64 y (*.f64 b b)))))

Compiler

Compiled 8599 to 3880 computations (54.9% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	3.6b	(fma.f64 b (/.f64 y t) a)
✓	4.6b	(/.f64 x (+.f64 1 (fma.f64 b (/.f64 y t) a)))
✓	5.3b	(/.f64 y (+.f64 1 (fma.f64 b (/.f64 y t) a)))
✓	9.3b	(fma.f64 (/.f64 y (+.f64 1 (fma.f64 b (/.f64 y t) a))) (/.f64 z t) (/.f64 x (+.f64 1 (fma.f64 b (/.f64 y t) a))))

series534.0ms (6.8%)

Counts

3 → 180

Calls

3 calls:

336.0ms

(fma.f64 (/.f64 y (+.f64 1 (fma.f64 b (/.f64 y t) a))) (/.f64 z t) (/.f64 x (+.f64 1 (fma.f64 b (/.f64 y t) a))))

115.0ms

(/.f64 x (+.f64 1 (fma.f64 b (/.f64 y t) a)))

83.0ms

(/.f64 y (+.f64 1 (fma.f64 b (/.f64 y t) a)))

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`*-un-lft-identity_binary64`
24×	`times-frac_binary64`
21×	`add-sqr-sqrt_binary64`
21×	`add-cube-cbrt_binary64`
8×	`associate-/r*_binary64`

Counts

3 → 80

Calls

3 calls:

4.0ms

(/.f64 y (+.f64 1 (fma.f64 b (/.f64 y t) a)))

3.0ms

(/.f64 x (+.f64 1 (fma.f64 b (/.f64 y t) a)))

0.0ms

(fma.f64 (/.f64 y (+.f64 1 (fma.f64 b (/.f64 y t) a))) (/.f64 z t) (/.f64 x (+.f64 1 (fma.f64 b (/.f64 y t) a))))

simplify202.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

678×	`associate-/l*_binary64`
534×	`associate-/r*_binary64`
290×	`fma-def_binary64`
175×	`+-commutative_binary64`
162×	`associate-*l/_binary64`

Counts

260 → 202

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	560	16227
1	1790	15272
2	5036	15272

prune284.0ms (3.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	230	4	234
Fresh	2	5	7
Picked	0	1	1
Done	1	0	1
Total	233	10	243

Error

0.0b

Counts

243 → 10

Alt Table

Status	Error	Program
	35.3b	(/.f64 (+.f64 (/.f64 (*.f64 t x) y) z) b)
	41.7b	(/.f64 z b)
	18.1b	(/.f64 (+.f64 (/.f64 (*.f64 y z) t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
	41.2b	(fma.f64 (/.f64 (sqrt.f64 y) (/.f64 (+.f64 1 (fma.f64 b (/.f64 y t) a)) (sqrt.f64 y))) (/.f64 z t) (/.f64 x (+.f64 1 (fma.f64 b (/.f64 y t) a))))
	33.5b	(fma.f64 (/.f64 y t) (/.f64 z (+.f64 1 (/.f64 (.f64 y b) t))) (/.f64 x (+.f64 1 (/.f64 (.f64 y b) t))))
	42.3b	(-.f64 (fma.f64 (/.f64 t y) (/.f64 x b) (/.f64 z b)) (fma.f64 (/.f64 t y) (/.f64 z (.f64 b b)) (/.f64 (.f64 a (.f64 z t)) (.f64 y (*.f64 b b)))))
	16.9b	(fma.f64 (.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 1 (fma.f64 b (/.f64 y t) a))) (cbrt.f64 (+.f64 1 (fma.f64 b (/.f64 y t) a))))) (/.f64 y (cbrt.f64 (+.f64 1 (fma.f64 b (/.f64 y t) a))))) (/.f64 z t) (/.f64 x (+.f64 1 (fma.f64 b (/.f64 y t) a))))
	38.1b	(/.f64 (sqrt.f64 (fma.f64 y (/.f64 z t) x)) (/.f64 (+.f64 1 (fma.f64 b (/.f64 y t) a)) (sqrt.f64 (fma.f64 y (/.f64 z t) x))))
✓	16.7b	(fma.f64 (/.f64 y (+.f64 1 (fma.f64 b (/.f64 y t) a))) (/.f64 z t) (/.f64 x (+.f64 1 (fma.f64 b (/.f64 y t) a))))
▶	16.8b	(+.f64 (/.f64 (.f64 y z) (.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t)) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))))

Compiler

Compiled 13454 to 6034 computations (55.2% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	3.8b	(/.f64 (*.f64 y b) t)
✓	4.6b	(/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))
✓	5.5b	(.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t)
✓	13.3b	(/.f64 (.f64 y z) (.f64 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))) t))

series297.0ms (3.8%)

Counts

4 → 152

Calls

4 calls:

142.0ms	(/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))
124.0ms	(/.f64 (.f64 y z) (.f64 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))) t))
19.0ms	(.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t)
11.0ms	(/.f64 (*.f64 y b) t)

rewrite35.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`*-un-lft-identity_binary64`
25×	`add-cbrt-cube_binary64`
25×	`add-exp-log_binary64`
20×	`add-sqr-sqrt_binary64`
19×	`times-frac_binary64`

Counts

4 → 111

Calls

4 calls:

10.0ms	(/.f64 (.f64 y z) (.f64 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))) t))
8.0ms	(.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t)
7.0ms	(/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))
4.0ms	(/.f64 (*.f64 y b) t)

simplify182.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

687×	`associate-/l*_binary64`
522×	`associate-/r*_binary64`
472×	`fma-def_binary64`
298×	`associate-l_binary64`
156×	`associate-*l/_binary64`

Counts

263 → 241

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	430	10630
1	1368	9571
2	4935	9243
3	5254	9243

prune322.0ms (4.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	267	2	269
Fresh	2	6	8
Picked	0	1	1
Done	0	1	1
Total	269	10	279

Error

Counts

279 → 10

Alt Table

Status	Error	Program
	35.3b	(/.f64 (+.f64 (/.f64 (*.f64 t x) y) z) b)
	28.1b	(+.f64 (/.f64 z b) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
	33.5b	(fma.f64 (/.f64 y t) (/.f64 z (+.f64 1 (/.f64 (.f64 y b) t))) (/.f64 x (+.f64 1 (/.f64 (.f64 y b) t))))
	42.3b	(-.f64 (fma.f64 (/.f64 t y) (/.f64 x b) (/.f64 z b)) (fma.f64 (/.f64 t y) (/.f64 z (.f64 b b)) (/.f64 (.f64 a (.f64 z t)) (.f64 y (*.f64 b b)))))
	16.9b	(fma.f64 (.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 1 (fma.f64 b (/.f64 y t) a))) (cbrt.f64 (+.f64 1 (fma.f64 b (/.f64 y t) a))))) (/.f64 y (cbrt.f64 (+.f64 1 (fma.f64 b (/.f64 y t) a))))) (/.f64 z t) (/.f64 x (+.f64 1 (fma.f64 b (/.f64 y t) a))))
▶	15.3b	(+.f64 (/.f64 y (/.f64 (.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t) z)) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
	38.1b	(/.f64 (sqrt.f64 (fma.f64 y (/.f64 z t) x)) (/.f64 (+.f64 1 (fma.f64 b (/.f64 y t) a)) (sqrt.f64 (fma.f64 y (/.f64 z t) x))))
✓	16.7b	(fma.f64 (/.f64 y (+.f64 1 (fma.f64 b (/.f64 y t) a))) (/.f64 z t) (/.f64 x (+.f64 1 (fma.f64 b (/.f64 y t) a))))
✓	16.8b	(+.f64 (/.f64 (.f64 y z) (.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t)) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))))
	18.1b	(/.f64 (+.f64 (/.f64 (*.f64 y z) t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))

Compiler

Compiled 11896 to 4542 computations (61.8% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	4.6b	(/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))
✓	5.5b	(/.f64 (.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t) z)
	5.5b	(.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t)
✓	6.9b	(/.f64 y (/.f64 (.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t) z))

series179.0ms (2.3%)

Counts

2 → 116

Calls

2 calls:

139.0ms	(/.f64 y (/.f64 (.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t) z))
40.0ms	(/.f64 (.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t) z)

rewrite22.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`times-frac_binary64`
20×	`*-un-lft-identity_binary64`
20×	`add-sqr-sqrt_binary64`
20×	`add-cube-cbrt_binary64`
16×	`add-cbrt-cube_binary64`

Counts

2 → 75

Calls

2 calls:

8.0ms	(/.f64 y (/.f64 (.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t) z))
8.0ms	(/.f64 (.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t) z)

simplify145.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

522×	`times-frac_binary64`
404×	`associate-/l*_binary64`
275×	`associate-/r*_binary64`
198×	`fma-neg_binary64`
179×	`associate-r_binary64`

Counts

191 → 170

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	310	7427
1	945	6768
2	4538	6692
3	5064	6692

prune317.0ms (4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	301	1	302
Fresh	1	6	7
Picked	0	1	1
Done	2	0	2
Total	304	8	312

Error

Counts

312 → 8

Alt Table

Status	Error	Program
	35.3b	(/.f64 (+.f64 (/.f64 (*.f64 t x) y) z) b)
	28.1b	(+.f64 (/.f64 z b) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
	33.5b	(fma.f64 (/.f64 y t) (/.f64 z (+.f64 1 (/.f64 (.f64 y b) t))) (/.f64 x (+.f64 1 (/.f64 (.f64 y b) t))))
	42.3b	(-.f64 (fma.f64 (/.f64 t y) (/.f64 x b) (/.f64 z b)) (fma.f64 (/.f64 t y) (/.f64 z (.f64 b b)) (/.f64 (.f64 a (.f64 z t)) (.f64 y (*.f64 b b)))))
✓	15.3b	(+.f64 (/.f64 y (/.f64 (.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t) z)) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
	38.1b	(/.f64 (sqrt.f64 (fma.f64 y (/.f64 z t) x)) (/.f64 (+.f64 1 (fma.f64 b (/.f64 y t) a)) (sqrt.f64 (fma.f64 y (/.f64 z t) x))))
	16.5b	(+.f64 (/.f64 (/.f64 y (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))) (/.f64 t z)) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))))
	18.1b	(/.f64 (+.f64 (/.f64 (*.f64 y z) t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))

Compiler

Compiled 12984 to 5082 computations (60.9% saved)

regimes2.2s (27.4%)

Accuracy

Total 9.7b remaining (98.2%)

Threshold costs 0b (0%)

Counts

112 → 5

Compiler

Compiled 26351 to 15621 computations (40.7% saved)

bsearch72.0ms (0.9%)

Steps

Iters	Range		Point
6	31121227.71858336	260700112.10782298	31525899.08026222
5	3.2114091689890327e-32	1.073628127456031e-31	1.046109116160516e-31
7	1.3634234745545974e-263	8.552594892858096e-262	6.2810140716487435e-263
7	-2.673743879145309e-83	-2.0703170876931712e-85	-2.1055779123004298e-85

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
4×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	154
1	56	154
2	55	154

end132.0ms (1.7%)

Compiler: Compiled 445 to 227 computations (49% saved)

Details

analyze1.0s (12.9%)

sample1.3s (16.1%)

simplify9.0ms (0.1%)

prune4.0ms (0%)

localize10.0ms (0.1%)

series263.0ms (3.3%)

rewrite10.0ms (0.1%)

simplify149.0ms (1.9%)

prune202.0ms (2.6%)

localize11.0ms (0.1%)

series534.0ms (6.8%)

rewrite13.0ms (0.2%)

simplify202.0ms (2.6%)

prune284.0ms (3.6%)

localize14.0ms (0.2%)

series297.0ms (3.8%)

rewrite35.0ms (0.4%)

simplify182.0ms (2.3%)

prune322.0ms (4.1%)

localize12.0ms (0.2%)

series179.0ms (2.3%)

rewrite22.0ms (0.3%)

simplify145.0ms (1.8%)

prune317.0ms (4%)

regimes2.2s (27.4%)

bsearch72.0ms (0.9%)

simplify4.0ms (0.1%)

end132.0ms (1.7%)

Profiling