Details

analyze1.5s (21.8%)

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
0.4%	99.4%	0.2%	10
4.3%	95.5%	0.2%	11
6.4%	93.3%	0.2%	12
7.9%	91.9%	0.2%	13
13.7%	86%	0.2%	14

Compiler

Compiled 19 to 13 computations (31.6% saved)

sample1.2s (18%)

Results

1.1s	8254×	body	128	valid
75.0ms	484×	body	128	invalid
0.0ms	1×	body	1024	valid
0.0ms	1×	body	256	valid

Compiler

Compiled 38 to 26 computations (31.6% saved)

preprocess48.0ms (0.7%)

Algorithm

2×	egg-herbie

Rules

865×	`div-sub_binary64`
818×	`fma-neg_binary64`
276×	`times-frac_binary64`
245×	`sub-neg_binary64`
228×	`fma-def_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	209
1	174	209
2	495	195
3	1351	187
4	3640	187
0	5	5

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 18 to 12 computations (33.3% saved)

simplify28.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

862×	`fma-neg_binary64`
362×	`div-sub_binary64`
353×	`cancel-sign-sub-inv_binary64`
300×	`sub-neg_binary64`
240×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	13	19
1	28	19
2	67	19
3	166	17
4	423	17
5	1175	17
6	3293	17

Stop Event

1×	node limit

Counts

1 → 2

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

1.9b

Counts

3 → 2

Alt Table

Status	Error	Program
	2.1b	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))
▶	1.9b	(fma.f64 (/.f64 a (-.f64 t (+.f64 z -1))) (-.f64 z y) x)

Compiler

Compiled 100 to 64 computations (36% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 a (-.f64 t (+.f64 z -1)))
✓	1.9b	(fma.f64 (/.f64 a (-.f64 t (+.f64 z -1))) (-.f64 z y) x)

series100.0ms (1.4%)

Counts

2 → 96

Calls

24 calls:

35.0ms	(/.f64 a (-.f64 t (+.f64 z -1)))	a	-inf
5.0ms	(fma.f64 (/.f64 a (-.f64 t (+.f64 z -1))) (-.f64 z y) x)	z	-inf
5.0ms	(fma.f64 (/.f64 a (-.f64 t (+.f64 z -1))) (-.f64 z y) x)	z	inf
5.0ms	(fma.f64 (/.f64 a (-.f64 t (+.f64 z -1))) (-.f64 z y) x)	z	0
4.0ms	(fma.f64 (/.f64 a (-.f64 t (+.f64 z -1))) (-.f64 z y) x)	t	0

rewrite61.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

271×	`fma-neg_binary64`
261×	`expm1-udef_binary64`
261×	`log1p-udef_binary64`
143×	`add-sqr-sqrt_binary64`
136×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	27
1	271	27
2	3974	27

Stop Event

1×	node limit

Counts

2 → 58

simplify78.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

598×	`cancel-sign-sub-inv_binary64`
371×	`times-frac_binary64`
351×	`sub-neg_binary64`
318×	`associate-+r+_binary64`
270×	`+-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	279	3917
1	943	3913
2	3940	3898

Stop Event

1×	node limit

Counts

154 → 133

prune124.0ms (1.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	129	4	133
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	130	5	135

Error

0.0b

Counts

135 → 5

Alt Table

Status	Error	Program
▶	11.3b	(-.f64 (+.f64 (/.f64 (.f64 a z) (-.f64 (+.f64 1 t) z)) x) (/.f64 (.f64 y a) (-.f64 (+.f64 1 t) z)))
✓	1.9b	(fma.f64 (/.f64 a (-.f64 t (+.f64 z -1))) (-.f64 z y) x)
	28.6b	(fma.f64 (.f64 (sqrt.f64 a) (.f64 (sqrt.f64 a) (/.f64 1 (+.f64 (-.f64 t z) 1)))) (-.f64 z y) x)
	33.0b	(pow.f64 (sqrt.f64 (fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)) 2)
	34.4b	(*.f64 a (-.f64 (/.f64 z (-.f64 (+.f64 1 t) z)) (/.f64 y (-.f64 (+.f64 1 t) z))))

Compiler

Compiled 4251 to 2147 computations (49.5% saved)

localize12.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 (/.f64 (.f64 a z) (-.f64 (+.f64 1 t) z)) x) (/.f64 (.f64 y a) (-.f64 (+.f64 1 t) z)))
✓	4.4b	(/.f64 (*.f64 y a) (-.f64 (+.f64 1 t) z))
✓	9.1b	(/.f64 (*.f64 a z) (-.f64 (+.f64 1 t) z))

series138.0ms (2%)

Counts

3 → 105

Calls

36 calls:

24.0ms	(-.f64 (+.f64 (/.f64 (.f64 a z) (-.f64 (+.f64 1 t) z)) x) (/.f64 (.f64 y a) (-.f64 (+.f64 1 t) z)))	z	inf
5.0ms	(-.f64 (+.f64 (/.f64 (.f64 a z) (-.f64 (+.f64 1 t) z)) x) (/.f64 (.f64 y a) (-.f64 (+.f64 1 t) z)))	z	-inf
5.0ms	(-.f64 (+.f64 (/.f64 (.f64 a z) (-.f64 (+.f64 1 t) z)) x) (/.f64 (.f64 y a) (-.f64 (+.f64 1 t) z)))	t	-inf
5.0ms	(-.f64 (+.f64 (/.f64 (.f64 a z) (-.f64 (+.f64 1 t) z)) x) (/.f64 (.f64 y a) (-.f64 (+.f64 1 t) z)))	y	-inf
4.0ms	(-.f64 (+.f64 (/.f64 (.f64 a z) (-.f64 (+.f64 1 t) z)) x) (/.f64 (.f64 y a) (-.f64 (+.f64 1 t) z)))	t	0

rewrite52.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

179×	`add-sqr-sqrt_binary64`
173×	`log1p-expm1-u_binary64`
173×	`expm1-log1p-u_binary64`
172×	`add-cbrt-cube_binary64`
165×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	57
1	349	57

Stop Event

1×	node limit

Counts

3 → 131

simplify69.0ms (1%)

Algorithm

1×	egg-herbie

Rules

515×	`associate-+r+_binary64`
417×	`times-frac_binary64`
373×	`associate-+l+_binary64`
283×	`associate-/l*_binary64`
203×	`associate--l+_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	388	4977
1	1497	4965

Stop Event

1×	node limit

Counts

236 → 251

prune276.0ms (4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	250	1	251
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	251	5	256

Error

Counts

256 → 5

Alt Table

Status	Error	Program
✓	11.3b	(-.f64 (+.f64 (/.f64 (.f64 a z) (-.f64 (+.f64 1 t) z)) x) (/.f64 (.f64 y a) (-.f64 (+.f64 1 t) z)))
✓	1.9b	(fma.f64 (/.f64 a (-.f64 t (+.f64 z -1))) (-.f64 z y) x)
▶	27.3b	(-.f64 (+.f64 (/.f64 (*.f64 a z) (-.f64 (+.f64 1 t) z)) x) (/.f64 a (/.f64 t y)))
	33.0b	(pow.f64 (sqrt.f64 (fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)) 2)
	34.4b	(*.f64 a (-.f64 (/.f64 z (-.f64 (+.f64 1 t) z)) (/.f64 y (-.f64 (+.f64 1 t) z))))

Compiler

Compiled 10546 to 5399 computations (48.8% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 (/.f64 (*.f64 a z) (-.f64 (+.f64 1 t) z)) x) (/.f64 a (/.f64 t y)))
✓	6.1b	(/.f64 a (/.f64 t y))
	9.1b	(/.f64 (*.f64 a z) (-.f64 (+.f64 1 t) z))

series54.0ms (0.8%)

Counts

2 → 96

Calls

24 calls:

4.0ms	(-.f64 (+.f64 (/.f64 (*.f64 a z) (-.f64 (+.f64 1 t) z)) x) (/.f64 a (/.f64 t y)))	a	-inf
4.0ms	(-.f64 (+.f64 (/.f64 (*.f64 a z) (-.f64 (+.f64 1 t) z)) x) (/.f64 a (/.f64 t y)))	z	-inf
3.0ms	(-.f64 (+.f64 (/.f64 (*.f64 a z) (-.f64 (+.f64 1 t) z)) x) (/.f64 a (/.f64 t y)))	z	inf
3.0ms	(-.f64 (+.f64 (/.f64 (*.f64 a z) (-.f64 (+.f64 1 t) z)) x) (/.f64 a (/.f64 t y)))	y	inf
3.0ms	(-.f64 (+.f64 (/.f64 (*.f64 a z) (-.f64 (+.f64 1 t) z)) x) (/.f64 a (/.f64 t y)))	t	inf

rewrite42.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

185×	`add-sqr-sqrt_binary64`
179×	`log1p-expm1-u_binary64`
179×	`expm1-log1p-u_binary64`
178×	`add-cbrt-cube_binary64`
171×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	32
1	357	32

Stop Event

1×	node limit

Counts

2 → 90

simplify46.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

588×	`times-frac_binary64`
521×	`fma-def_binary64`
498×	`associate-/l*_binary64`
316×	`associate-/r*_binary64`
177×	`associate-*l/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	128	2047
1	411	2043
2	1496	1805

Stop Event

1×	node limit

Counts

186 → 138

prune147.0ms (2.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	208	0	208
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	208	5	213

Error

Counts

213 → 5

Alt Table

Status	Error	Program
✓	11.3b	(-.f64 (+.f64 (/.f64 (.f64 a z) (-.f64 (+.f64 1 t) z)) x) (/.f64 (.f64 y a) (-.f64 (+.f64 1 t) z)))
✓	1.9b	(fma.f64 (/.f64 a (-.f64 t (+.f64 z -1))) (-.f64 z y) x)
✓	27.3b	(-.f64 (+.f64 (/.f64 (*.f64 a z) (-.f64 (+.f64 1 t) z)) x) (/.f64 a (/.f64 t y)))
▶	33.0b	(pow.f64 (sqrt.f64 (fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)) 2)
	34.4b	(*.f64 a (-.f64 (/.f64 z (-.f64 (+.f64 1 t) z)) (/.f64 y (-.f64 (+.f64 1 t) z))))

Compiler

Compiled 6420 to 2694 computations (58% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 a (+.f64 (-.f64 t z) 1))
✓	0.0b	(sqrt.f64 (fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x))
✓	0.2b	(pow.f64 (sqrt.f64 (fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)) 2)
✓	1.9b	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)

series1.3s (18.5%)

Counts

4 → 168

Calls

54 calls:

431.0ms	(pow.f64 (sqrt.f64 (fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)) 2)	a	0
60.0ms	(pow.f64 (sqrt.f64 (fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)) 2)	a	inf
59.0ms	(pow.f64 (sqrt.f64 (fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)) 2)	a	-inf
53.0ms	(pow.f64 (sqrt.f64 (fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)) 2)	z	inf
49.0ms	(sqrt.f64 (fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x))	z	-inf

rewrite77.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

923×	`prod-diff_binary64`
157×	`add-sqr-sqrt_binary64`
153×	`log1p-expm1-u_binary64`
153×	`expm1-log1p-u_binary64`
150×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	63
1	333	63
2	4294	63

Stop Event

1×	node limit

Counts

4 → 110

simplify185.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

428×	`+-commutative_binary64`
386×	`*-commutative_binary64`
352×	`associate-+r+_binary64`
243×	`fma-def_binary64`
199×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1165	15825
1	4440	15825

Stop Event

1×	node limit

Counts

278 → 245

prune341.0ms (4.9%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	245	0	245
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	245	5	250

Error

Counts

250 → 5

Alt Table

Status	Error	Program
✓	11.3b	(-.f64 (+.f64 (/.f64 (.f64 a z) (-.f64 (+.f64 1 t) z)) x) (/.f64 (.f64 y a) (-.f64 (+.f64 1 t) z)))
✓	1.9b	(fma.f64 (/.f64 a (-.f64 t (+.f64 z -1))) (-.f64 z y) x)
✓	27.3b	(-.f64 (+.f64 (/.f64 (*.f64 a z) (-.f64 (+.f64 1 t) z)) x) (/.f64 a (/.f64 t y)))
✓	33.0b	(pow.f64 (sqrt.f64 (fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)) 2)
	34.4b	(*.f64 a (-.f64 (/.f64 z (-.f64 (+.f64 1 t) z)) (/.f64 y (-.f64 (+.f64 1 t) z))))

Compiler

Compiled 20456 to 11803 computations (42.3% saved)

regimes862.0ms (12.5%)

Accuracy

Total 0.1b remaining (83.1%)

Threshold costs 0.1b (83.1%)

Counts

88 → 3

Compiler

Compiled 11575 to 7766 computations (32.9% saved)

bsearch3.0ms (0%)

Algorithm

2×	left-value

Calls

2 calls:

0.0ms	(/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a))
0.0ms	(/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a))

Steps

Iters	Point		Range
-0.0	∈ [	-0.0	,	1.250987873e-314	]
-2.768622796203182e-119	∈ [	-2.768622796203182e-119	,	-1.4631364563877067e-121	]

Compiler

Compiled 16 to 11 computations (31.3% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

16×	`+-commutative_binary64`
12×	`sub-neg_binary64`
8×	`*-commutative_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	107
1	50	107
2	69	107
3	85	107
4	93	107
5	96	107
6	97	107

Stop Event

1×

saturated

end94.0ms (1.4%)

Stop Event

1×

fuel

Compiler

Compiled 263 to 159 computations (39.5% saved)

Details

analyze1.5s (21.8%)

sample1.2s (18%)

preprocess48.0ms (0.7%)

simplify28.0ms (0.4%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series100.0ms (1.4%)

rewrite61.0ms (0.9%)

simplify78.0ms (1.1%)

prune124.0ms (1.8%)

localize12.0ms (0.2%)

series138.0ms (2%)

rewrite52.0ms (0.8%)

simplify69.0ms (1%)

prune276.0ms (4%)

localize11.0ms (0.2%)

series54.0ms (0.8%)

rewrite42.0ms (0.6%)

simplify46.0ms (0.7%)

prune147.0ms (2.1%)

localize12.0ms (0.2%)

series1.3s (18.5%)

rewrite77.0ms (1.1%)

simplify185.0ms (2.7%)

prune341.0ms (4.9%)

regimes862.0ms (12.5%)

bsearch3.0ms (0%)

simplify5.0ms (0.1%)

end94.0ms (1.4%)

Profiling