Details

analyze1.7s (17.7%)

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
3.9%	95.8%	0.3%	11
7.4%	92.3%	0.3%	12
8.8%	90.9%	0.3%	13
10.2%	89.5%	0.3%	14

Compiler

Compiled 24 to 16 computations (33.3% saved)

sample1.5s (15%)

Results

1.4s	8256×	body	128	valid
43.0ms	304×	body	128	invalid

Compiler

Compiled 48 to 32 computations (33.3% saved)

preprocess31.0ms (0.3%)

Algorithm

2×	egg-herbie

Rules

208×	`fma-def_binary64`
68×	`+-commutative_binary64`
50×	`*-commutative_binary64`
41×	`associate-+l+_binary64`
40×	`associate-+r+_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	97	400
1	213	400
2	352	336
3	486	336
4	606	336
5	642	336
0	6	6

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 23 to 15 computations (34.8% saved)

simplify14.0ms (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`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	16	25
1	29	25
2	42	21
3	54	21
4	64	21
5	68	21

Stop Event

1×

saturated

Counts

1 → 2

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

10.8b

Counts

3 → 2

Alt Table

Status	Error	Program
	16.0b	(/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)))
▶	14.6b	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 a (fma.f64 y (/.f64 b t) 1)))

Compiler

Compiled 126 to 78 computations (38.1% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 a (fma.f64 y (/.f64 b t) 1))
✓	1.9b	(fma.f64 y (/.f64 b t) 1)
✓	2.3b	(fma.f64 y (/.f64 z t) x)
✓	10.6b	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 a (fma.f64 y (/.f64 b t) 1)))

series211.0ms (2.2%)

Counts

4 → 204

Calls

51 calls:

20.0ms	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 a (fma.f64 y (/.f64 b t) 1)))	t	0
19.0ms	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 a (fma.f64 y (/.f64 b t) 1)))	b	-inf
18.0ms	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 a (fma.f64 y (/.f64 b t) 1)))	b	inf
13.0ms	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 a (fma.f64 y (/.f64 b t) 1)))	a	inf
12.0ms	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 a (fma.f64 y (/.f64 b t) 1)))	a	-inf

rewrite70.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

633×	`prod-diff_binary64`
153×	`add-sqr-sqrt_binary64`
142×	`add-cbrt-cube_binary64`
142×	`log1p-expm1-u_binary64`
142×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	48
1	296	48
2	4113	48

Stop Event

1×	node limit

Counts

4 → 116

simplify101.0ms (1%)

Algorithm

1×	egg-herbie

Rules

733×	`times-frac_binary64`
509×	`associate-/l*_binary64`
394×	`associate-/r*_binary64`
229×	`associate-r_binary64`
220×	`fma-def_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	356	8483
1	1438	8094

Stop Event

1×	node limit

Counts

320 → 191

prune231.0ms (2.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	184	7	191
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	186	7	193

Error

0.0b

Counts

193 → 7

Alt Table

Status	Error	Program
	47.1b	(.f64 (/.f64 t y) (/.f64 (+.f64 x (.f64 (/.f64 y t) z)) b))
	41.4b	(/.f64 z b)
	14.7b	(*.f64 (fma.f64 y (/.f64 z t) x) (/.f64 1 (+.f64 a (fma.f64 y (/.f64 b t) 1))))
	14.8b	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 a (pow.f64 (cbrt.f64 (fma.f64 y (/.f64 b t) 1)) 3)))
	40.6b	(.f64 (/.f64 y t) (/.f64 z (+.f64 (+.f64 1 a) (.f64 (/.f64 y t) b))))
▶	13.7b	(fma.f64 (/.f64 y (+.f64 (+.f64 1 a) (.f64 (/.f64 y t) b))) (/.f64 z t) (/.f64 x (+.f64 (+.f64 1 a) (.f64 (/.f64 y t) b))))
	15.1b	(+.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 9020 to 4272 computations (52.6% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	2.2b	(/.f64 x (+.f64 (+.f64 1 a) (*.f64 (/.f64 y t) b)))
✓	5.1b	(*.f64 (/.f64 y t) b)
✓	5.2b	(/.f64 y (+.f64 (+.f64 1 a) (*.f64 (/.f64 y t) b)))
✓	7.3b	(fma.f64 (/.f64 y (+.f64 (+.f64 1 a) (.f64 (/.f64 y t) b))) (/.f64 z t) (/.f64 x (+.f64 (+.f64 1 a) (.f64 (/.f64 y t) b))))

series389.0ms (4%)

Counts

4 → 216

Calls

54 calls:

21.0ms	(fma.f64 (/.f64 y (+.f64 (+.f64 1 a) (.f64 (/.f64 y t) b))) (/.f64 z t) (/.f64 x (+.f64 (+.f64 1 a) (.f64 (/.f64 y t) b))))	b	-inf
20.0ms	(fma.f64 (/.f64 y (+.f64 (+.f64 1 a) (.f64 (/.f64 y t) b))) (/.f64 z t) (/.f64 x (+.f64 (+.f64 1 a) (.f64 (/.f64 y t) b))))	b	inf
17.0ms	(fma.f64 (/.f64 y (+.f64 (+.f64 1 a) (.f64 (/.f64 y t) b))) (/.f64 z t) (/.f64 x (+.f64 (+.f64 1 a) (.f64 (/.f64 y t) b))))	a	-inf
16.0ms	(fma.f64 (/.f64 y (+.f64 (+.f64 1 a) (.f64 (/.f64 y t) b))) (/.f64 z t) (/.f64 x (+.f64 (+.f64 1 a) (.f64 (/.f64 y t) b))))	z	-inf
16.0ms	(fma.f64 (/.f64 y (+.f64 (+.f64 1 a) (.f64 (/.f64 y t) b))) (/.f64 z t) (/.f64 x (+.f64 (+.f64 1 a) (.f64 (/.f64 y t) b))))	a	inf

rewrite51.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

179×	`add-sqr-sqrt_binary64`
168×	`log1p-expm1-u_binary64`
168×	`expm1-log1p-u_binary64`
167×	`add-cbrt-cube_binary64`
164×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	77
1	352	69

Stop Event

1×	node limit

Counts

4 → 114

simplify151.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

642×	`associate-/l*_binary64`
519×	`associate-/r*_binary64`
282×	`fma-def_binary64`
258×	`associate-r_binary64`
225×	`associate-l_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	450	14399
1	1753	13747

Stop Event

1×	node limit

Counts

330 → 232

prune356.0ms (3.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	255	3	258
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	259	6	265

Error

0.0b

Counts

265 → 6

Alt Table

Status	Error	Program
	37.4b	(/.f64 (+.f64 z (/.f64 x (/.f64 y t))) b)
▶	13.9b	(fma.f64 (.f64 (pow.f64 (cbrt.f64 y) 2) (.f64 (cbrt.f64 y) (/.f64 1 (fma.f64 (/.f64 y t) b (+.f64 1 a))))) (/.f64 z t) (/.f64 x (+.f64 (+.f64 1 a) (*.f64 (/.f64 y t) b))))
	44.3b	(fma.f64 (/.f64 y (+.f64 (+.f64 1 a) (.f64 (/.f64 y t) b))) (/.f64 z t) (.f64 (/.f64 t y) (/.f64 x b)))
	14.8b	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 a (pow.f64 (cbrt.f64 (fma.f64 y (/.f64 b t) 1)) 3)))
	40.6b	(.f64 (/.f64 y t) (/.f64 z (+.f64 (+.f64 1 a) (.f64 (/.f64 y t) b))))
	15.1b	(+.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 13853 to 6639 computations (52.1% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	2.2b	(/.f64 x (+.f64 (+.f64 1 a) (*.f64 (/.f64 y t) b)))
✓	3.0b	(.f64 (pow.f64 (cbrt.f64 y) 2) (.f64 (cbrt.f64 y) (/.f64 1 (fma.f64 (/.f64 y t) b (+.f64 1 a)))))
	5.1b	(*.f64 (/.f64 y t) b)
✓	7.3b	(fma.f64 (.f64 (pow.f64 (cbrt.f64 y) 2) (.f64 (cbrt.f64 y) (/.f64 1 (fma.f64 (/.f64 y t) b (+.f64 1 a))))) (/.f64 z t) (/.f64 x (+.f64 (+.f64 1 a) (*.f64 (/.f64 y t) b))))

series288.0ms (2.9%)

Counts

2 → 120

Calls

30 calls:

26.0ms	(fma.f64 (.f64 (pow.f64 (cbrt.f64 y) 2) (.f64 (cbrt.f64 y) (/.f64 1 (fma.f64 (/.f64 y t) b (+.f64 1 a))))) (/.f64 z t) (/.f64 x (+.f64 (+.f64 1 a) (*.f64 (/.f64 y t) b))))	b	-inf
19.0ms	(fma.f64 (.f64 (pow.f64 (cbrt.f64 y) 2) (.f64 (cbrt.f64 y) (/.f64 1 (fma.f64 (/.f64 y t) b (+.f64 1 a))))) (/.f64 z t) (/.f64 x (+.f64 (+.f64 1 a) (*.f64 (/.f64 y t) b))))	b	inf
18.0ms	(fma.f64 (.f64 (pow.f64 (cbrt.f64 y) 2) (.f64 (cbrt.f64 y) (/.f64 1 (fma.f64 (/.f64 y t) b (+.f64 1 a))))) (/.f64 z t) (/.f64 x (+.f64 (+.f64 1 a) (*.f64 (/.f64 y t) b))))	y	-inf
17.0ms	(fma.f64 (.f64 (pow.f64 (cbrt.f64 y) 2) (.f64 (cbrt.f64 y) (/.f64 1 (fma.f64 (/.f64 y t) b (+.f64 1 a))))) (/.f64 z t) (/.f64 x (+.f64 (+.f64 1 a) (*.f64 (/.f64 y t) b))))	a	inf
15.0ms	(fma.f64 (.f64 (pow.f64 (cbrt.f64 y) 2) (.f64 (cbrt.f64 y) (/.f64 1 (fma.f64 (/.f64 y t) b (+.f64 1 a))))) (/.f64 z t) (/.f64 x (+.f64 (+.f64 1 a) (*.f64 (/.f64 y t) b))))	a	-inf

rewrite35.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

225×	`add-sqr-sqrt_binary64`
213×	`log1p-expm1-u_binary64`
213×	`expm1-log1p-u_binary64`
211×	`add-cbrt-cube_binary64`
207×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	54
1	485	54

Stop Event

1×	node limit

Counts

2 → 33

simplify119.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

642×	`associate-/l*_binary64`
519×	`associate-/r*_binary64`
258×	`associate-r_binary64`
236×	`fma-def_binary64`
225×	`associate-l_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	412	10340
1	1613	9840

Stop Event

1×	node limit

Counts

153 → 121

prune263.0ms (2.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	210	0	210
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	210	6	216

Error

0.0b

Counts

216 → 6

Alt Table

Status	Error	Program
	37.4b	(/.f64 (+.f64 z (/.f64 x (/.f64 y t))) b)
✓	13.9b	(fma.f64 (.f64 (pow.f64 (cbrt.f64 y) 2) (.f64 (cbrt.f64 y) (/.f64 1 (fma.f64 (/.f64 y t) b (+.f64 1 a))))) (/.f64 z t) (/.f64 x (+.f64 (+.f64 1 a) (*.f64 (/.f64 y t) b))))
	44.3b	(fma.f64 (/.f64 y (+.f64 (+.f64 1 a) (.f64 (/.f64 y t) b))) (/.f64 z t) (.f64 (/.f64 t y) (/.f64 x b)))
▶	14.8b	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 a (pow.f64 (cbrt.f64 (fma.f64 y (/.f64 b t) 1)) 3)))
	40.6b	(.f64 (/.f64 y t) (/.f64 z (+.f64 (+.f64 1 a) (.f64 (/.f64 y t) b))))
	15.1b	(+.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 12876 to 6458 computations (49.8% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	1.9b	(fma.f64 y (/.f64 b t) 1)
	2.3b	(fma.f64 y (/.f64 z t) x)
✓	10.6b	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 a (pow.f64 (cbrt.f64 (fma.f64 y (/.f64 b t) 1)) 3)))
✓	11.2b	(cbrt.f64 (fma.f64 y (/.f64 b t) 1))

series205.0ms (2.1%)

Counts

2 → 108

Calls

27 calls:

22.0ms	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 a (pow.f64 (cbrt.f64 (fma.f64 y (/.f64 b t) 1)) 3)))	b	inf
18.0ms	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 a (pow.f64 (cbrt.f64 (fma.f64 y (/.f64 b t) 1)) 3)))	b	-inf
17.0ms	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 a (pow.f64 (cbrt.f64 (fma.f64 y (/.f64 b t) 1)) 3)))	y	-inf
16.0ms	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 a (pow.f64 (cbrt.f64 (fma.f64 y (/.f64 b t) 1)) 3)))	a	inf
12.0ms	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 a (pow.f64 (cbrt.f64 (fma.f64 y (/.f64 b t) 1)) 3)))	a	-inf

rewrite67.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

811×	`prod-diff_binary64`
171×	`add-sqr-sqrt_binary64`
162×	`log1p-expm1-u_binary64`
162×	`expm1-log1p-u_binary64`
160×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	31
1	357	31
2	4612	31

Stop Event

1×	node limit

Counts

2 → 57

simplify109.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

885×	`times-frac_binary64`
624×	`associate-/l*_binary64`
529×	`associate-/r*_binary64`
262×	`fma-def_binary64`
155×	`+-commutative_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	478	9112
1	1873	8655

Stop Event

1×	node limit

Counts

165 → 166

prune240.0ms (2.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	221	0	221
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	221	6	227

Error

0.0b

Counts

227 → 6

Alt Table

Status	Error	Program
	37.4b	(/.f64 (+.f64 z (/.f64 x (/.f64 y t))) b)
✓	13.9b	(fma.f64 (.f64 (pow.f64 (cbrt.f64 y) 2) (.f64 (cbrt.f64 y) (/.f64 1 (fma.f64 (/.f64 y t) b (+.f64 1 a))))) (/.f64 z t) (/.f64 x (+.f64 (+.f64 1 a) (*.f64 (/.f64 y t) b))))
	44.3b	(fma.f64 (/.f64 y (+.f64 (+.f64 1 a) (.f64 (/.f64 y t) b))) (/.f64 z t) (.f64 (/.f64 t y) (/.f64 x b)))
✓	14.8b	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 a (pow.f64 (cbrt.f64 (fma.f64 y (/.f64 b t) 1)) 3)))
	40.6b	(.f64 (/.f64 y t) (/.f64 z (+.f64 (+.f64 1 a) (.f64 (/.f64 y t) b))))
	15.1b	(+.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 11151 to 5482 computations (50.8% saved)

regimes3.4s (35%)

Accuracy

Total 5.4b remaining (95.2%)

Threshold costs 0b (0%)

Counts

199 → 6

Compiler

Compiled 45748 to 29232 computations (36.1% saved)

bsearch8.0ms (0.1%)

Algorithm

5×	left-value

Calls

5 calls:

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

Steps

Iters	Point		Range
#hash((type . real) (value . +inf))	∈ [	#hash((type . real) (value . +inf))	,	#hash((type . real) (value . NaN))	]
1.7642758988097463e+126	∈ [	1.7642758988097463e+126	,	9.522429229578847e+129	]
-0.0	∈ [	-0.0	,	6.76677e-318	]
-4.472539530856903e-289	∈ [	-4.472539530856903e-289	,	-0.0	]
#hash((type . real) (value . -inf))	∈ [	#hash((type . real) (value . -inf))	,	-1.0780738215685349e+306	]

Compiler

Compiled 23 to 15 computations (34.8% saved)

simplify12.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

12×	`+-commutative_binary64`
10×	`*-commutative_binary64`
5×	`sub-neg_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	52	310
1	72	310
2	83	306
3	92	306
4	97	306
5	99	306

Stop Event

1×

saturated

end144.0ms (1.5%)

Stop Event

1×

fuel

Compiler

Compiled 584 to 266 computations (54.5% saved)

Details

analyze1.7s (17.7%)

sample1.5s (15%)

preprocess31.0ms (0.3%)

simplify14.0ms (0.1%)

prune4.0ms (0%)

localize14.0ms (0.1%)

series211.0ms (2.2%)

rewrite70.0ms (0.7%)

simplify101.0ms (1%)

prune231.0ms (2.4%)

localize12.0ms (0.1%)

series389.0ms (4%)

rewrite51.0ms (0.5%)

simplify151.0ms (1.5%)

prune356.0ms (3.6%)

localize19.0ms (0.2%)

series288.0ms (2.9%)

rewrite35.0ms (0.4%)

simplify119.0ms (1.2%)

prune263.0ms (2.7%)

localize13.0ms (0.1%)

series205.0ms (2.1%)

rewrite67.0ms (0.7%)

simplify109.0ms (1.1%)

prune240.0ms (2.5%)

regimes3.4s (35%)

bsearch8.0ms (0.1%)

simplify12.0ms (0.1%)

end144.0ms (1.5%)

Profiling