Details

analyze1.9s (11.2%)

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
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
0%	99.7%	0.3%	9
0%	99.7%	0.3%	10
0.6%	99.1%	0.3%	11
1.8%	98%	0.3%	12
2.6%	97.1%	0.3%	13
4%	95.7%	0.3%	14

Compiler

Compiled 24 to 15 computations (37.5% saved)

sample1.4s (8%)

Results

1.2s	8256×	body	128	valid
65.0ms	431×	body	128	invalid

Compiler

Compiled 71 to 44 computations (38% saved)

simplify72.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

920×	`times-frac_binary64`
593×	`fma-def_binary64`
507×	`div-sub_binary64`
484×	`sub-neg_binary64`
470×	`neg-mul-1_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	23
1	25	21
2	50	21
3	93	21
4	157	21
5	270	21
6	423	21
7	724	21
8	1341	21
9	3898	21
10	4400	21
11	4952	21

prune3.0ms (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

21.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	21.7b	(/.f64 (fma.f64 x y (*.f64 z (-.f64 t a))) (fma.f64 z (-.f64 b y) y))

Compiler

Compiled 80 to 41 computations (48.8% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 z (-.f64 b y) y)
✓	0.0b	(*.f64 z (-.f64 t a))
✓	20.9b	(/.f64 (fma.f64 x y (*.f64 z (-.f64 t a))) (fma.f64 z (-.f64 b y) y))

series153.0ms (0.9%)

Counts

3 → 144

Calls

3 calls:

141.0ms	(/.f64 (fma.f64 x y (*.f64 z (-.f64 t a))) (fma.f64 z (-.f64 b y) y))
6.0ms	(fma.f64 z (-.f64 b y) y)
6.0ms	(*.f64 z (-.f64 t a))

rewrite69.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

976×	`prod-diff_binary64`
151×	`add-sqr-sqrt_binary64`
143×	`log1p-expm1-u_binary64`
143×	`expm1-log1p-u_binary64`
139×	`add-log-exp_binary64`

Counts

3 → 77

Calls

3 calls:

67.0ms	(fma.f64 z (-.f64 b y) y)
67.0ms	(*.f64 z (-.f64 t a))
67.0ms	(/.f64 (fma.f64 x y (*.f64 z (-.f64 t a))) (fma.f64 z (-.f64 b y) y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	36
1	285	36
2	3837	36
3	5805	36

simplify105.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

768×	`times-frac_binary64`
647×	`associate-/l*_binary64`
486×	`fma-def_binary64`
258×	`+-commutative_binary64`
206×	`associate-+r+_binary64`

Counts

221 → 175

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	609	7563
1	2082	6977
2	5107	6977

prune686.0ms (4.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	166	9	175
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	166	10	176

Error

0.1b

Counts

176 → 10

Alt Table

Status	Error	Program
	44.5b	(-.f64 (fma.f64 (/.f64 a y) (/.f64 z (+.f64 z -1)) (/.f64 (.f64 a (.f64 b (.f64 z z))) (.f64 (.f64 y y) (pow.f64 (+.f64 z -1) 2)))) (fma.f64 (/.f64 z y) (/.f64 (.f64 b x) (pow.f64 (+.f64 z -1) 2)) (fma.f64 (/.f64 t y) (/.f64 z (+.f64 z -1)) (fma.f64 (/.f64 (.f64 b b) (.f64 y y)) (/.f64 (.f64 x (.f64 z z)) (pow.f64 (+.f64 z -1) 3)) (fma.f64 (/.f64 t (.f64 y y)) (/.f64 (.f64 b (*.f64 z z)) (pow.f64 (+.f64 z -1) 2)) (/.f64 x (+.f64 z -1)))))))
	43.1b	(/.f64 x (-.f64 1 z))
▶	21.8b	(.f64 (fma.f64 x y (.f64 z (-.f64 t a))) (/.f64 1 (fma.f64 z (-.f64 b y) y)))
	27.7b	(-.f64 (fma.f64 (/.f64 y z) (/.f64 a (pow.f64 (-.f64 y b) 2)) (/.f64 a (-.f64 y b))) (fma.f64 (/.f64 y z) (/.f64 x (-.f64 y b)) (fma.f64 (/.f64 y z) (/.f64 t (pow.f64 (-.f64 y b) 2)) (/.f64 t (-.f64 y b)))))
	27.0b	(-.f64 (fma.f64 (/.f64 y (-.f64 b y)) (/.f64 x z) (fma.f64 (/.f64 a (pow.f64 (-.f64 b y) 2)) (/.f64 y z) (/.f64 t (-.f64 b y)))) (fma.f64 (/.f64 y (pow.f64 (-.f64 b y) 2)) (/.f64 t z) (/.f64 a (-.f64 b y))))
	37.4b	(/.f64 (-.f64 (.f64 t z) (.f64 a z)) (-.f64 (+.f64 y (.f64 z b)) (.f64 y z)))
	29.8b	(/.f64 (-.f64 t a) (-.f64 b y))
✓	21.7b	(/.f64 (fma.f64 x y (*.f64 z (-.f64 t a))) (fma.f64 z (-.f64 b y) y))
	43.8b	(/.f64 (fma.f64 x y (*.f64 z (-.f64 t a))) (pow.f64 (sqrt.f64 (fma.f64 z (-.f64 b y) y)) 2))
	22.4b	(/.f64 (fma.f64 x y (*.f64 z (-.f64 t a))) (pow.f64 (cbrt.f64 (fma.f64 z (-.f64 b y) y)) 3))

Compiler

Compiled 9865 to 4181 computations (57.6% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 z (-.f64 b y) y)
	0.0b	(*.f64 z (-.f64 t a))
✓	0.4b	(/.f64 1 (fma.f64 z (-.f64 b y) y))
✓	20.6b	(.f64 (fma.f64 x y (.f64 z (-.f64 t a))) (/.f64 1 (fma.f64 z (-.f64 b y) y)))

series297.0ms (1.8%)

Counts

2 → 108

Calls

2 calls:

268.0ms	(.f64 (fma.f64 x y (.f64 z (-.f64 t a))) (/.f64 1 (fma.f64 z (-.f64 b y) y)))
29.0ms	(/.f64 1 (fma.f64 z (-.f64 b y) y))

rewrite69.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

967×	`prod-diff_binary64`
165×	`add-sqr-sqrt_binary64`
155×	`log1p-expm1-u_binary64`
155×	`expm1-log1p-u_binary64`
151×	`add-cbrt-cube_binary64`

Counts

2 → 51

Calls

2 calls:

68.0ms	(/.f64 1 (fma.f64 z (-.f64 b y) y))
68.0ms	(.f64 (fma.f64 x y (.f64 z (-.f64 t a))) (/.f64 1 (fma.f64 z (-.f64 b y) y)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	32
1	321	32
2	4062	32
3	5979	32

simplify161.0ms (1%)

Algorithm

1×	egg-herbie

Rules

767×	`associate-/l*_binary64`
518×	`fma-def_binary64`
315×	`+-commutative_binary64`
239×	`associate-+r+_binary64`
175×	`sub-neg_binary64`

Counts

159 → 188

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	749	8864
1	2494	8329
2	4988	8329

prune245.0ms (1.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	252	0	252
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	252	10	262

Error

0.1b

Counts

262 → 10

Alt Table

Status	Error	Program
	44.5b	(-.f64 (fma.f64 (/.f64 a y) (/.f64 z (+.f64 z -1)) (/.f64 (.f64 a (.f64 b (.f64 z z))) (.f64 (.f64 y y) (pow.f64 (+.f64 z -1) 2)))) (fma.f64 (/.f64 z y) (/.f64 (.f64 b x) (pow.f64 (+.f64 z -1) 2)) (fma.f64 (/.f64 t y) (/.f64 z (+.f64 z -1)) (fma.f64 (/.f64 (.f64 b b) (.f64 y y)) (/.f64 (.f64 x (.f64 z z)) (pow.f64 (+.f64 z -1) 3)) (fma.f64 (/.f64 t (.f64 y y)) (/.f64 (.f64 b (*.f64 z z)) (pow.f64 (+.f64 z -1) 2)) (/.f64 x (+.f64 z -1)))))))
	43.1b	(/.f64 x (-.f64 1 z))
✓	21.8b	(.f64 (fma.f64 x y (.f64 z (-.f64 t a))) (/.f64 1 (fma.f64 z (-.f64 b y) y)))
	27.7b	(-.f64 (fma.f64 (/.f64 y z) (/.f64 a (pow.f64 (-.f64 y b) 2)) (/.f64 a (-.f64 y b))) (fma.f64 (/.f64 y z) (/.f64 x (-.f64 y b)) (fma.f64 (/.f64 y z) (/.f64 t (pow.f64 (-.f64 y b) 2)) (/.f64 t (-.f64 y b)))))
	27.0b	(-.f64 (fma.f64 (/.f64 y (-.f64 b y)) (/.f64 x z) (fma.f64 (/.f64 a (pow.f64 (-.f64 b y) 2)) (/.f64 y z) (/.f64 t (-.f64 b y)))) (fma.f64 (/.f64 y (pow.f64 (-.f64 b y) 2)) (/.f64 t z) (/.f64 a (-.f64 b y))))
	37.4b	(/.f64 (-.f64 (.f64 t z) (.f64 a z)) (-.f64 (+.f64 y (.f64 z b)) (.f64 y z)))
	29.8b	(/.f64 (-.f64 t a) (-.f64 b y))
✓	21.7b	(/.f64 (fma.f64 x y (*.f64 z (-.f64 t a))) (fma.f64 z (-.f64 b y) y))
	43.8b	(/.f64 (fma.f64 x y (*.f64 z (-.f64 t a))) (pow.f64 (sqrt.f64 (fma.f64 z (-.f64 b y) y)) 2))
▶	22.4b	(/.f64 (fma.f64 x y (*.f64 z (-.f64 t a))) (pow.f64 (cbrt.f64 (fma.f64 z (-.f64 b y) y)) 3))

Compiler

Compiled 13071 to 5770 computations (55.9% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 z (-.f64 t a))
✓	0.5b	(pow.f64 (cbrt.f64 (fma.f64 z (-.f64 b y) y)) 3)
✓	12.2b	(cbrt.f64 (fma.f64 z (-.f64 b y) y))
✓	20.9b	(/.f64 (fma.f64 x y (*.f64 z (-.f64 t a))) (pow.f64 (cbrt.f64 (fma.f64 z (-.f64 b y) y)) 3))

series6.9s (40.8%)

Counts

3 → 144

Calls

3 calls:

6.7s	(pow.f64 (cbrt.f64 (fma.f64 z (-.f64 b y) y)) 3)
143.0ms	(/.f64 (fma.f64 x y (*.f64 z (-.f64 t a))) (pow.f64 (cbrt.f64 (fma.f64 z (-.f64 b y) y)) 3))
55.0ms	(cbrt.f64 (fma.f64 z (-.f64 b y) y))

rewrite84.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

988×	`prod-diff_binary64`
169×	`add-sqr-sqrt_binary64`
163×	`log1p-expm1-u_binary64`
163×	`expm1-log1p-u_binary64`
157×	`add-cbrt-cube_binary64`

Counts

3 → 85

Calls

3 calls:

82.0ms	(pow.f64 (cbrt.f64 (fma.f64 z (-.f64 b y) y)) 3)
82.0ms	(cbrt.f64 (fma.f64 z (-.f64 b y) y))
82.0ms	(/.f64 (fma.f64 x y (*.f64 z (-.f64 t a))) (pow.f64 (cbrt.f64 (fma.f64 z (-.f64 b y) y)) 3))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	39
1	332	39
2	4281	39
3	6198	39

simplify182.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

935×	`fma-def_binary64`
366×	`+-commutative_binary64`
297×	`*-commutative_binary64`
265×	`associate-+r+_binary64`
236×	`sub-neg_binary64`

Counts

229 → 273

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1111	13085
1	3704	12438
2	5055	12438

prune315.0ms (1.9%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	300	0	300
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	300	10	310

Error

0.1b

Counts

310 → 10

Alt Table

Status	Error	Program
	44.5b	(-.f64 (fma.f64 (/.f64 a y) (/.f64 z (+.f64 z -1)) (/.f64 (.f64 a (.f64 b (.f64 z z))) (.f64 (.f64 y y) (pow.f64 (+.f64 z -1) 2)))) (fma.f64 (/.f64 z y) (/.f64 (.f64 b x) (pow.f64 (+.f64 z -1) 2)) (fma.f64 (/.f64 t y) (/.f64 z (+.f64 z -1)) (fma.f64 (/.f64 (.f64 b b) (.f64 y y)) (/.f64 (.f64 x (.f64 z z)) (pow.f64 (+.f64 z -1) 3)) (fma.f64 (/.f64 t (.f64 y y)) (/.f64 (.f64 b (*.f64 z z)) (pow.f64 (+.f64 z -1) 2)) (/.f64 x (+.f64 z -1)))))))
	43.1b	(/.f64 x (-.f64 1 z))
✓	21.8b	(.f64 (fma.f64 x y (.f64 z (-.f64 t a))) (/.f64 1 (fma.f64 z (-.f64 b y) y)))
	27.7b	(-.f64 (fma.f64 (/.f64 y z) (/.f64 a (pow.f64 (-.f64 y b) 2)) (/.f64 a (-.f64 y b))) (fma.f64 (/.f64 y z) (/.f64 x (-.f64 y b)) (fma.f64 (/.f64 y z) (/.f64 t (pow.f64 (-.f64 y b) 2)) (/.f64 t (-.f64 y b)))))
▶	27.0b	(-.f64 (fma.f64 (/.f64 y (-.f64 b y)) (/.f64 x z) (fma.f64 (/.f64 a (pow.f64 (-.f64 b y) 2)) (/.f64 y z) (/.f64 t (-.f64 b y)))) (fma.f64 (/.f64 y (pow.f64 (-.f64 b y) 2)) (/.f64 t z) (/.f64 a (-.f64 b y))))
	37.4b	(/.f64 (-.f64 (.f64 t z) (.f64 a z)) (-.f64 (+.f64 y (.f64 z b)) (.f64 y z)))
	29.8b	(/.f64 (-.f64 t a) (-.f64 b y))
✓	21.7b	(/.f64 (fma.f64 x y (*.f64 z (-.f64 t a))) (fma.f64 z (-.f64 b y) y))
	43.8b	(/.f64 (fma.f64 x y (*.f64 z (-.f64 t a))) (pow.f64 (sqrt.f64 (fma.f64 z (-.f64 b y) y)) 2))
✓	22.4b	(/.f64 (fma.f64 x y (*.f64 z (-.f64 t a))) (pow.f64 (cbrt.f64 (fma.f64 z (-.f64 b y) y)) 3))

Compiler

Compiled 18819 to 9264 computations (50.8% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	7.2b	(fma.f64 (/.f64 y (pow.f64 (-.f64 b y) 2)) (/.f64 t z) (/.f64 a (-.f64 b y)))
✓	7.7b	(/.f64 a (pow.f64 (-.f64 b y) 2))
✓	11.8b	(fma.f64 (/.f64 a (pow.f64 (-.f64 b y) 2)) (/.f64 y z) (/.f64 t (-.f64 b y)))
✓	16.7b	(/.f64 y (pow.f64 (-.f64 b y) 2))

series237.0ms (1.4%)

Counts

4 → 176

Calls

4 calls:

94.0ms	(fma.f64 (/.f64 a (pow.f64 (-.f64 b y) 2)) (/.f64 y z) (/.f64 t (-.f64 b y)))
80.0ms	(fma.f64 (/.f64 y (pow.f64 (-.f64 b y) 2)) (/.f64 t z) (/.f64 a (-.f64 b y)))
54.0ms	(/.f64 a (pow.f64 (-.f64 b y) 2))
10.0ms	(/.f64 y (pow.f64 (-.f64 b y) 2))

rewrite87.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

457×	`prod-diff_binary64`
191×	`add-sqr-sqrt_binary64`
180×	`log1p-expm1-u_binary64`
180×	`expm1-log1p-u_binary64`
177×	`add-log-exp_binary64`

Counts

4 → 98

Calls

4 calls:

85.0ms	(fma.f64 (/.f64 y (pow.f64 (-.f64 b y) 2)) (/.f64 t z) (/.f64 a (-.f64 b y)))
85.0ms	(/.f64 a (pow.f64 (-.f64 b y) 2))
85.0ms	(fma.f64 (/.f64 a (pow.f64 (-.f64 b y) 2)) (/.f64 y z) (/.f64 t (-.f64 b y)))
85.0ms	(/.f64 y (pow.f64 (-.f64 b y) 2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	66
1	378	66
2	4846	66
3	5858	66

simplify115.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

964×	`associate-/r*_binary64`
419×	`associate-/r/_binary64`
228×	`associate-+r+_binary64`
209×	`times-frac_binary64`
197×	`+-commutative_binary64`

Counts

274 → 194

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	265	5811
1	783	5515
2	2841	5137
3	5751	5137

prune186.0ms (1.1%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	193	1	194
Fresh	1	5	6
Picked	1	0	1
Done	0	3	3
Total	195	9	204

Error

0.1b

Counts

204 → 9

Alt Table

Status	Error	Program
	44.5b	(-.f64 (fma.f64 (/.f64 a y) (/.f64 z (+.f64 z -1)) (/.f64 (.f64 a (.f64 b (.f64 z z))) (.f64 (.f64 y y) (pow.f64 (+.f64 z -1) 2)))) (fma.f64 (/.f64 z y) (/.f64 (.f64 b x) (pow.f64 (+.f64 z -1) 2)) (fma.f64 (/.f64 t y) (/.f64 z (+.f64 z -1)) (fma.f64 (/.f64 (.f64 b b) (.f64 y y)) (/.f64 (.f64 x (.f64 z z)) (pow.f64 (+.f64 z -1) 3)) (fma.f64 (/.f64 t (.f64 y y)) (/.f64 (.f64 b (*.f64 z z)) (pow.f64 (+.f64 z -1) 2)) (/.f64 x (+.f64 z -1)))))))
	43.1b	(/.f64 x (-.f64 1 z))
✓	21.8b	(.f64 (fma.f64 x y (.f64 z (-.f64 t a))) (/.f64 1 (fma.f64 z (-.f64 b y) y)))
	27.7b	(-.f64 (fma.f64 (/.f64 y z) (/.f64 a (pow.f64 (-.f64 y b) 2)) (/.f64 a (-.f64 y b))) (fma.f64 (/.f64 y z) (/.f64 x (-.f64 y b)) (fma.f64 (/.f64 y z) (/.f64 t (pow.f64 (-.f64 y b) 2)) (/.f64 t (-.f64 y b)))))
	37.4b	(/.f64 (-.f64 (.f64 t z) (.f64 a z)) (-.f64 (+.f64 y (.f64 z b)) (.f64 y z)))
✓	21.7b	(/.f64 (fma.f64 x y (*.f64 z (-.f64 t a))) (fma.f64 z (-.f64 b y) y))
	25.4b	(-.f64 (fma.f64 (/.f64 y (-.f64 b y)) (/.f64 x z) (/.f64 t (-.f64 b y))) (fma.f64 (/.f64 y (pow.f64 (-.f64 b y) 2)) (/.f64 t z) (/.f64 a (-.f64 b y))))
	43.8b	(/.f64 (fma.f64 x y (*.f64 z (-.f64 t a))) (pow.f64 (sqrt.f64 (fma.f64 z (-.f64 b y) y)) 2))
✓	22.4b	(/.f64 (fma.f64 x y (*.f64 z (-.f64 t a))) (pow.f64 (cbrt.f64 (fma.f64 z (-.f64 b y) y)) 3))

Compiler

Compiled 10518 to 3531 computations (66.4% saved)

regimes3.4s (20.3%)

Accuracy

Total 5.1b remaining (96.3%)

Threshold costs 0b (0%)

Counts

113 → 5

Compiler

Compiled 34444 to 19872 computations (42.3% saved)

bsearch10.0ms (0.1%)

Compiler: Compiled 23 to 14 computations (39.1% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

11×	`+-commutative_binary64`
10×	`*-commutative_binary64`
8×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	306
1	74	306
2	86	306
3	94	306
4	98	306
5	98	306

end176.0ms (1%)

Compiler: Compiled 737 to 306 computations (58.5% saved)

Details

analyze1.9s (11.2%)

sample1.4s (8%)

simplify72.0ms (0.4%)

prune3.0ms (0%)

localize10.0ms (0.1%)

series153.0ms (0.9%)

rewrite69.0ms (0.4%)

simplify105.0ms (0.6%)

prune686.0ms (4.1%)

localize11.0ms (0.1%)

series297.0ms (1.8%)

rewrite69.0ms (0.4%)

simplify161.0ms (1%)

prune245.0ms (1.5%)

localize14.0ms (0.1%)

series6.9s (40.8%)

rewrite84.0ms (0.5%)

simplify182.0ms (1.1%)

prune315.0ms (1.9%)

localize22.0ms (0.1%)

series237.0ms (1.4%)

rewrite87.0ms (0.5%)

simplify115.0ms (0.7%)

prune186.0ms (1.1%)

regimes3.4s (20.3%)

bsearch10.0ms (0.1%)

simplify9.0ms (0.1%)

end176.0ms (1%)

Profiling