Details

analyze1.3s (22.5%)

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
13.2%	86.5%	0.2%	10
17%	82.8%	0.2%	11
18.2%	81.5%	0.2%	12
21.7%	78.1%	0.2%	13
32.9%	66.9%	0.2%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample1.2s (20.5%)

Results

1.0s	8256×	body	128	valid
97.0ms	723×	body	128	invalid

Compiler

Compiled 34 to 22 computations (35.3% saved)

preprocess45.0ms (0.8%)

Algorithm

2×	egg-herbie

Rules

878×	`div-sub_binary64`
306×	`fma-def_binary64`
304×	`times-frac_binary64`
248×	`fma-neg_binary64`
219×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	176
1	158	176
2	306	176
3	640	176
4	1557	176
5	3631	176
0	5	5

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 16 to 10 computations (37.5% saved)

simplify25.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

893×	`fma-neg_binary64`
663×	`div-sub_binary64`
241×	`cancel-sign-sub-inv_binary64`
213×	`distribute-neg-frac_binary64`
210×	`associate-/l*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	26	16
2	53	16
3	100	16
4	210	16
5	422	16
6	913	16
7	2616	16

Stop Event

1×	node limit

Counts

1 → 2

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

11.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	11.6b	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))

Compiler

Compiled 59 to 34 computations (42.4% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 t (*.f64 a z))
✓	11.4b	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))

series61.0ms (1.1%)

Counts

2 → 69

Calls

24 calls:

6.0ms	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))	a	0
5.0ms	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))	y	0
4.0ms	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))	t	-inf
4.0ms	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))	t	inf
4.0ms	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))	x	-inf

rewrite68.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

412×	`fma-def_binary64`
244×	`expm1-udef_binary64`
244×	`log1p-udef_binary64`
195×	`fma-neg_binary64`
135×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	23
1	253	23
2	3872	23

Stop Event

1×	node limit

Counts

2 → 134

simplify52.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

608×	`associate-/r*_binary64`
551×	`fma-def_binary64`
458×	`cancel-sign-sub-inv_binary64`
175×	`sub-neg_binary64`
149×	`times-frac_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	118	2839
1	410	2698
2	1884	2491

Stop Event

1×	node limit

Counts

203 → 175

prune138.0ms (2.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	165	10	175
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	166	10	176

Error

2.1b

Counts

176 → 10

Alt Table

Status	Error	Program
	37.2b	(/.f64 (-.f64 x (.f64 y z)) (pow.f64 (sqrt.f64 (-.f64 t (.f64 z a))) 2))
	33.2b	(.f64 (cbrt.f64 (pow.f64 (fma.f64 y (neg.f64 z) x) 2)) (.f64 (cbrt.f64 (fma.f64 y (neg.f64 z) x)) (/.f64 1 (-.f64 t (*.f64 z a)))))
	36.4b	(pow.f64 (sqrt.f64 (/.f64 (fma.f64 y (neg.f64 z) x) (-.f64 t (*.f64 z a)))) 2)
	34.6b	(-.f64 (fma.f64 (/.f64 y (.f64 a a)) (/.f64 t z) (/.f64 y a)) (/.f64 x (.f64 z a)))
▶	8.7b	(-.f64 (/.f64 x (-.f64 t (.f64 z a))) (.f64 (/.f64 z (-.f64 t (*.f64 z a))) y))
	11.7b	(.f64 (fma.f64 y (neg.f64 z) x) (/.f64 1 (-.f64 t (.f64 z a))))
	35.9b	(cbrt.f64 (pow.f64 (/.f64 (fma.f64 y (neg.f64 z) x) (-.f64 t (*.f64 z a))) 3))
	12.0b	(/.f64 (-.f64 x (.f64 y z)) (fma.f64 (.f64 (neg.f64 a) (pow.f64 (cbrt.f64 z) 2)) (cbrt.f64 z) t))
	34.0b	(.f64 (/.f64 (fma.f64 y (neg.f64 z) x) (-.f64 (.f64 t t) (pow.f64 (*.f64 z a) 2))) (fma.f64 z a t))
	33.3b	(.f64 (/.f64 (cbrt.f64 (pow.f64 (fma.f64 y (neg.f64 z) x) 2)) (pow.f64 (cbrt.f64 (-.f64 t (.f64 z a))) 2)) (cbrt.f64 (/.f64 (fma.f64 y (neg.f64 z) x) (-.f64 t (*.f64 z a)))))

Compiler

Compiled 4749 to 1543 computations (67.5% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 x (-.f64 t (.f64 z a))) (.f64 (/.f64 z (-.f64 t (*.f64 z a))) y))
✓	1.8b	(.f64 (/.f64 z (-.f64 t (.f64 z a))) y)
✓	3.4b	(/.f64 x (-.f64 t (*.f64 z a)))
✓	9.5b	(/.f64 z (-.f64 t (*.f64 z a)))

series161.0ms (2.9%)

Counts

4 → 192

Calls

48 calls:

10.0ms	(-.f64 (/.f64 x (-.f64 t (.f64 z a))) (.f64 (/.f64 z (-.f64 t (*.f64 z a))) y))	x	-inf
8.0ms	(-.f64 (/.f64 x (-.f64 t (.f64 z a))) (.f64 (/.f64 z (-.f64 t (*.f64 z a))) y))	y	inf
8.0ms	(-.f64 (/.f64 x (-.f64 t (.f64 z a))) (.f64 (/.f64 z (-.f64 t (*.f64 z a))) y))	z	inf
6.0ms	(.f64 (/.f64 z (-.f64 t (.f64 z a))) y)	a	0
5.0ms	(/.f64 x (-.f64 t (*.f64 z a)))	x	-inf

rewrite81.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

262×	`expm1-udef_binary64`
262×	`log1p-udef_binary64`
145×	`add-sqr-sqrt_binary64`
138×	`log1p-expm1-u_binary64`
138×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	58
1	275	49
2	4207	49

Stop Event

1×	node limit

Counts

4 → 136

simplify102.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

732×	`fma-def_binary64`
498×	`cancel-sign-sub-inv_binary64`
210×	`sub-neg_binary64`
190×	`associate-/l/_binary64`
176×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	157	6597
1	525	6311
2	2290	5827

Stop Event

1×	node limit

Counts

328 → 232

prune175.0ms (3.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	227	5	232
Fresh	5	4	9
Picked	1	0	1
Done	0	0	0
Total	233	9	242

Error

0.0b

Counts

242 → 9

Alt Table

Status	Error	Program
	9.8b	(-.f64 (/.f64 x (-.f64 t (.f64 z a))) (/.f64 z (/.f64 (-.f64 t (.f64 z a)) y)))
	28.2b	(-.f64 (/.f64 x (-.f64 t (.f64 z a))) (.f64 (/.f64 y t) z))
	36.4b	(-.f64 (+.f64 (/.f64 y a) (.f64 (/.f64 t (.f64 a a)) (-.f64 (/.f64 y z) (/.f64 x (*.f64 z z))))) (/.f64 (/.f64 x z) a))
	31.1b	(/.f64 (-.f64 y (/.f64 x z)) a)
	37.2b	(/.f64 (-.f64 x (.f64 y z)) (pow.f64 (sqrt.f64 (-.f64 t (.f64 z a))) 2))
	11.7b	(.f64 (fma.f64 y (neg.f64 z) x) (/.f64 1 (-.f64 t (.f64 z a))))
	35.9b	(cbrt.f64 (pow.f64 (/.f64 (fma.f64 y (neg.f64 z) x) (-.f64 t (*.f64 z a))) 3))
▶	8.8b	(-.f64 (/.f64 x (-.f64 t (.f64 z a))) (.f64 (.f64 z (/.f64 1 (-.f64 t (.f64 z a)))) y))
	34.0b	(.f64 (/.f64 (fma.f64 y (neg.f64 z) x) (-.f64 (.f64 t t) (pow.f64 (*.f64 z a) 2))) (fma.f64 z a t))

Compiler

Compiled 6854 to 2156 computations (68.5% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.8b	(/.f64 1 (-.f64 t (*.f64 z a)))
✓	1.8b	(.f64 (.f64 z (/.f64 1 (-.f64 t (*.f64 z a)))) y)
	3.4b	(/.f64 x (-.f64 t (*.f64 z a)))
✓	8.7b	(.f64 z (/.f64 1 (-.f64 t (.f64 z a))))

series73.0ms (1.3%)

Counts

3 → 120

Calls

30 calls:

7.0ms	(.f64 (.f64 z (/.f64 1 (-.f64 t (*.f64 z a)))) y)	z	0
6.0ms	(.f64 (.f64 z (/.f64 1 (-.f64 t (*.f64 z a)))) y)	y	inf
5.0ms	(.f64 (.f64 z (/.f64 1 (-.f64 t (*.f64 z a)))) y)	y	-inf
4.0ms	(.f64 (.f64 z (/.f64 1 (-.f64 t (*.f64 z a)))) y)	y	0
3.0ms	(.f64 (.f64 z (/.f64 1 (-.f64 t (*.f64 z a)))) y)	z	-inf

rewrite60.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

633×	`prod-diff_binary64`
208×	`expm1-udef_binary64`
208×	`log1p-udef_binary64`
119×	`add-sqr-sqrt_binary64`
111×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	33
1	235	33
2	3155	33

Stop Event

1×	node limit

Counts

3 → 67

simplify64.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

893×	`associate-/l*_binary64`
596×	`associate-/r*_binary64`
458×	`fma-def_binary64`
230×	`associate-*l/_binary64`
162×	`associate-/l/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	116	3505
1	352	3415
2	1434	3137

Stop Event

1×	node limit

Counts

187 → 119

prune134.0ms (2.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	169	1	170
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	171	8	179

Error

0.0b

Counts

179 → 8

Alt Table

Status	Error	Program
	36.4b	(-.f64 (+.f64 (/.f64 y a) (.f64 (/.f64 t (.f64 a a)) (-.f64 (/.f64 y z) (/.f64 x (*.f64 z z))))) (/.f64 (/.f64 x z) a))
	31.1b	(/.f64 (-.f64 y (/.f64 x z)) a)
	37.2b	(/.f64 (-.f64 x (.f64 y z)) (pow.f64 (sqrt.f64 (-.f64 t (.f64 z a))) 2))
	11.7b	(.f64 (fma.f64 y (neg.f64 z) x) (/.f64 1 (-.f64 t (.f64 z a))))
	35.9b	(cbrt.f64 (pow.f64 (/.f64 (fma.f64 y (neg.f64 z) x) (-.f64 t (*.f64 z a))) 3))
	9.8b	(-.f64 (/.f64 x (-.f64 t (.f64 z a))) (/.f64 z (/.f64 (-.f64 t (.f64 z a)) y)))
▶	9.1b	(-.f64 (/.f64 x (-.f64 t (.f64 z a))) (.f64 (.f64 z (pow.f64 (/.f64 1 (cbrt.f64 (-.f64 t (.f64 z a)))) 3)) y))
	34.0b	(.f64 (/.f64 (fma.f64 y (neg.f64 z) x) (-.f64 (.f64 t t) (pow.f64 (*.f64 z a) 2))) (fma.f64 z a t))

Compiler

Compiled 4862 to 1843 computations (62.1% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.8b	(.f64 (.f64 z (pow.f64 (/.f64 1 (cbrt.f64 (-.f64 t (*.f64 z a)))) 3)) y)
	3.4b	(/.f64 x (-.f64 t (*.f64 z a)))
✓	8.7b	(.f64 z (pow.f64 (/.f64 1 (cbrt.f64 (-.f64 t (.f64 z a)))) 3))
✓	10.0b	(cbrt.f64 (-.f64 t (*.f64 z a)))

series109.0ms (1.9%)

Counts

3 → 120

Calls

30 calls:

11.0ms	(cbrt.f64 (-.f64 t (*.f64 z a)))	t	-inf
10.0ms	(.f64 (.f64 z (pow.f64 (/.f64 1 (cbrt.f64 (-.f64 t (*.f64 z a)))) 3)) y)	t	-inf
8.0ms	(.f64 (.f64 z (pow.f64 (/.f64 1 (cbrt.f64 (-.f64 t (*.f64 z a)))) 3)) y)	y	-inf
8.0ms	(.f64 z (pow.f64 (/.f64 1 (cbrt.f64 (-.f64 t (.f64 z a)))) 3))	z	0
4.0ms	(.f64 z (pow.f64 (/.f64 1 (cbrt.f64 (-.f64 t (.f64 z a)))) 3))	t	-inf

rewrite58.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

624×	`prod-diff_binary64`
249×	`log1p-udef_binary64`
144×	`add-sqr-sqrt_binary64`
136×	`add-cbrt-cube_binary64`
136×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	48
1	297	32
2	3740	32

Stop Event

1×	node limit

Counts

3 → 59

simplify87.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

595×	`cancel-sign-sub-inv_binary64`
244×	`associate-r_binary64`
227×	`unswap-sqr_binary64`
227×	`times-frac_binary64`
190×	`associate-/r*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	253	4303
1	850	4191
2	3466	4041

Stop Event

1×	node limit

Counts

179 → 149

prune177.0ms (3.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	199	1	200
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	200	8	208

Error

0.0b

Counts

208 → 8

Alt Table

Status	Error	Program
	36.4b	(-.f64 (+.f64 (/.f64 y a) (.f64 (/.f64 t (.f64 a a)) (-.f64 (/.f64 y z) (/.f64 x (*.f64 z z))))) (/.f64 (/.f64 x z) a))
	31.1b	(/.f64 (-.f64 y (/.f64 x z)) a)
	37.2b	(/.f64 (-.f64 x (.f64 y z)) (pow.f64 (sqrt.f64 (-.f64 t (.f64 z a))) 2))
	11.7b	(.f64 (fma.f64 y (neg.f64 z) x) (/.f64 1 (-.f64 t (.f64 z a))))
	9.8b	(-.f64 (/.f64 x (-.f64 t (.f64 z a))) (/.f64 z (/.f64 (-.f64 t (.f64 z a)) y)))
✓	9.1b	(-.f64 (/.f64 x (-.f64 t (.f64 z a))) (.f64 (.f64 z (pow.f64 (/.f64 1 (cbrt.f64 (-.f64 t (.f64 z a)))) 3)) y))
	34.0b	(.f64 (/.f64 (fma.f64 y (neg.f64 z) x) (-.f64 (.f64 t t) (pow.f64 (*.f64 z a) 2))) (fma.f64 z a t))
	22.1b	(-.f64 (/.f64 x (-.f64 t (.f64 z a))) (cbrt.f64 (pow.f64 (.f64 z (/.f64 y (-.f64 t (*.f64 z a)))) 3)))

Compiler

Compiled 7142 to 3269 computations (54.2% saved)

regimes1.4s (24.2%)

Accuracy

Total 4.4b remaining (99.2%)

Threshold costs 0b (0%)

Counts

123 → 4

Compiler

Compiled 15650 to 9544 computations (39% saved)

bsearch4.0ms (0.1%)

Algorithm

3×	left-value

Calls

3 calls:

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

Steps

Iters	Point		Range
#hash((type . real) (value . +inf))	∈ [	#hash((type . real) (value . +inf))	,	#hash((type . real) (value . NaN))	]
0.0	∈ [	0.0	,	1.47e-321	]
-1.3626397029500643e-289	∈ [	-1.3626397029500643e-289	,	-2.4595e-320	]

Compiler

Compiled 16 to 10 computations (37.5% saved)

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

17×	`sub-neg_binary64`
15×	`+-commutative_binary64`
13×	`*-commutative_binary64`
11×	`cancel-sign-sub-inv_binary64`
11×	`neg-sub0_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	39	154
1	71	152
2	113	152
3	143	152
4	157	152
5	158	152

Stop Event

1×

saturated

end118.0ms (2.1%)

Stop Event

1×

fuel

Compiler

Compiled 394 to 170 computations (56.9% saved)

Details

analyze1.3s (22.5%)

sample1.2s (20.5%)

preprocess45.0ms (0.8%)

simplify25.0ms (0.4%)

prune2.0ms (0%)

localize8.0ms (0.1%)

series61.0ms (1.1%)

rewrite68.0ms (1.2%)

simplify52.0ms (0.9%)

prune138.0ms (2.5%)

localize8.0ms (0.1%)

series161.0ms (2.9%)

rewrite81.0ms (1.4%)

simplify102.0ms (1.8%)

prune175.0ms (3.1%)

localize14.0ms (0.2%)

series73.0ms (1.3%)

rewrite60.0ms (1.1%)

simplify64.0ms (1.1%)

prune134.0ms (2.4%)

localize15.0ms (0.3%)

series109.0ms (1.9%)

rewrite58.0ms (1%)

simplify87.0ms (1.5%)

prune177.0ms (3.1%)

regimes1.4s (24.2%)

bsearch4.0ms (0.1%)

simplify9.0ms (0.2%)

end118.0ms (2.1%)

Profiling