Details

analyze959.0ms (20%)

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
13.3%	86.5%	0.2%	9
17.5%	82.3%	0.2%	10
23.6%	75.2%	1.2%	11
25%	72%	2.9%	12
35.8%	59.6%	4.6%	13
40.3%	54.3%	5.4%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample1.2s (25.4%)

Results

958.0ms	8256×	body	128	valid
241.0ms	2207×	body	128	invalid

Compiler

Compiled 28 to 18 computations (35.7% saved)

preprocess57.0ms (1.2%)

Algorithm

2×	egg-herbie

Rules

505×	`unsub-neg_binary64`
463×	`div-sub_binary64`
427×	`fma-def_binary64`
325×	`sub-neg_binary64`
271×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	77
1	76	77
2	205	77
3	490	77
4	1034	77
5	2211	77
6	4011	77
0	4	4

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 13 to 8 computations (38.5% saved)

simplify51.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

936×	`fma-def_binary64`
721×	`fma-neg_binary64`
220×	`cancel-sign-sub-inv_binary64`
144×	`distribute-rgt-in_binary64`
107×	`div-sub_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	11
1	16	11
2	38	11
3	84	11
4	178	11
5	316	11
6	542	11
7	1015	11
8	1989	11
9	2988	11
10	3630	11
11	3668	11
12	3698	11
13	3703	11
14	3703	11

Stop Event

1×

saturated

Counts

1 → 2

prune3.0ms (0.1%)

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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	6.1b	(fma.f64 x (/.f64 (-.f64 z t) y) t)
▶	2.1b	(+.f64 (*.f64 (/.f64 x y) (-.f64 z t)) t)

Compiler

Compiled 71 to 40 computations (43.7% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (*.f64 (/.f64 x y) (-.f64 z t)) t)
✓	7.6b	(*.f64 (/.f64 x y) (-.f64 z t))

series57.0ms (1.2%)

Counts

2 → 96

Calls

24 calls:

18.0ms	(+.f64 (*.f64 (/.f64 x y) (-.f64 z t)) t)	x	-inf
6.0ms	(+.f64 (*.f64 (/.f64 x y) (-.f64 z t)) t)	t	-inf
2.0ms	(+.f64 (*.f64 (/.f64 x y) (-.f64 z t)) t)	t	inf
2.0ms	(+.f64 (*.f64 (/.f64 x y) (-.f64 z t)) t)	t	0
2.0ms	(+.f64 (*.f64 (/.f64 x y) (-.f64 z t)) t)	z	-inf

rewrite55.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

360×	`fma-def_binary64`
201×	`fma-neg_binary64`
200×	`expm1-udef_binary64`
200×	`log1p-udef_binary64`
173×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	21
1	206	21
2	3117	21

Stop Event

1×	node limit

Counts

2 → 103

simplify97.0ms (2%)

Algorithm

1×	egg-herbie

Rules

855×	`fma-def_binary64`
722×	`fma-neg_binary64`
222×	`cancel-sign-sub-inv_binary64`
151×	`distribute-rgt-in_binary64`
127×	`unsub-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	37	1020
1	95	1020
2	225	948
3	531	948
4	1100	948
5	2085	948
6	3275	948
7	3792	948
8	3819	948
9	3849	948
10	3854	948
11	3854	948

Stop Event

1×

saturated

Counts

199 → 120

prune73.0ms (1.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	114	6	120
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	115	7	122

Error

Counts

122 → 7

Alt Table

Status	Error	Program
	2.6b	(fma.f64 (pow.f64 (cbrt.f64 (-.f64 z t)) 2) (*.f64 (cbrt.f64 (-.f64 z t)) (/.f64 x y)) t)
	7.4b	(+.f64 (/.f64 (-.f64 (.f64 z x) (.f64 t x)) y) t)
	2.5b	(fma.f64 (pow.f64 (cbrt.f64 (/.f64 x y)) 2) (*.f64 (cbrt.f64 (/.f64 x y)) (-.f64 z t)) t)
	3.3b	(pow.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)) 3)
	6.2b	(+.f64 (/.f64 x (/.f64 y (-.f64 z t))) t)
	6.1b	(fma.f64 x (/.f64 (-.f64 z t) y) t)
▶	2.1b	(fma.f64 (-.f64 z t) (/.f64 x y) t)

Compiler

Compiled 1984 to 621 computations (68.7% saved)

localize24.0ms (0.5%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.1b	(fma.f64 (-.f64 z t) (/.f64 x y) t)

series16.0ms (0.3%)

Counts

1 → 48

Calls

12 calls:

2.0ms	(fma.f64 (-.f64 z t) (/.f64 x y) t)	z	-inf
1.0ms	(fma.f64 (-.f64 z t) (/.f64 x y) t)	t	-inf
1.0ms	(fma.f64 (-.f64 z t) (/.f64 x y) t)	t	inf
1.0ms	(fma.f64 (-.f64 z t) (/.f64 x y) t)	z	0
1.0ms	(fma.f64 (-.f64 z t) (/.f64 x y) t)	z	inf

rewrite50.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

455×	`log-prod_binary64`
446×	`prod-diff_binary64`
197×	`fma-def_binary64`
170×	`expm1-udef_binary64`
170×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	175	11
2	2476	11

Stop Event

1×	node limit

Counts

1 → 29

simplify69.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

686×	`fma-neg_binary64`
624×	`fma-def_binary64`
169×	`cancel-sign-sub-inv_binary64`
155×	`distribute-rgt-in_binary64`
101×	`associate-/l*_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	29	561
1	70	561
2	166	552
3	386	480
4	840	480
5	1523	480
6	2454	480
7	3087	480
8	3159	480
9	3221	480
10	3352	480
11	3352	480

Stop Event

1×

saturated

Counts

77 → 42

prune30.0ms (0.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	42	0	42
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	42	7	49

Error

Counts

49 → 7

Alt Table

Status	Error	Program
	2.6b	(fma.f64 (pow.f64 (cbrt.f64 (-.f64 z t)) 2) (*.f64 (cbrt.f64 (-.f64 z t)) (/.f64 x y)) t)
	7.4b	(+.f64 (/.f64 (-.f64 (.f64 z x) (.f64 t x)) y) t)
▶	2.5b	(fma.f64 (pow.f64 (cbrt.f64 (/.f64 x y)) 2) (*.f64 (cbrt.f64 (/.f64 x y)) (-.f64 z t)) t)
	3.3b	(pow.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)) 3)
	6.2b	(+.f64 (/.f64 x (/.f64 y (-.f64 z t))) t)
	6.1b	(fma.f64 x (/.f64 (-.f64 z t) y) t)
✓	2.1b	(fma.f64 (-.f64 z t) (/.f64 x y) t)

Compiler

Compiled 734 to 246 computations (66.5% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(fma.f64 (pow.f64 (cbrt.f64 (/.f64 x y)) 2) (*.f64 (cbrt.f64 (/.f64 x y)) (-.f64 z t)) t)
✓	0.2b	(*.f64 (cbrt.f64 (/.f64 x y)) (-.f64 z t))
✓	0.4b	(pow.f64 (cbrt.f64 (/.f64 x y)) 2)
✓	13.4b	(cbrt.f64 (/.f64 x y))

series426.0ms (8.9%)

Counts

4 → 54

Calls

36 calls:

29.0ms	(fma.f64 (pow.f64 (cbrt.f64 (/.f64 x y)) 2) (*.f64 (cbrt.f64 (/.f64 x y)) (-.f64 z t)) t)	t	-inf
29.0ms	(fma.f64 (pow.f64 (cbrt.f64 (/.f64 x y)) 2) (*.f64 (cbrt.f64 (/.f64 x y)) (-.f64 z t)) t)	y	-inf
26.0ms	(fma.f64 (pow.f64 (cbrt.f64 (/.f64 x y)) 2) (*.f64 (cbrt.f64 (/.f64 x y)) (-.f64 z t)) t)	z	0
26.0ms	(pow.f64 (cbrt.f64 (/.f64 x y)) 2)	y	-inf
26.0ms	(fma.f64 (pow.f64 (cbrt.f64 (/.f64 x y)) 2) (*.f64 (cbrt.f64 (/.f64 x y)) (-.f64 z t)) t)	t	0

rewrite64.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

451×	`prod-diff_binary64`
226×	`expm1-udef_binary64`
226×	`log1p-udef_binary64`
128×	`add-sqr-sqrt_binary64`
124×	`fma-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	51
1	257	40
2	3346	40

Stop Event

1×	node limit

Counts

4 → 102

simplify66.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

958×	`fma-def_binary64`
331×	`distribute-rgt-neg-in_binary64`
266×	`fma-neg_binary64`
219×	`distribute-lft-neg-in_binary64`
189×	`unsub-neg_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	26	675
1	68	675
2	153	621
3	374	567
4	970	531
5	2087	531
6	3993	531
7	4939	531

Stop Event

1×	node limit

Counts

156 → 117

prune124.0ms (2.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	148	0	148
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	148	7	155

Error

Counts

155 → 7

Alt Table

Status	Error	Program
▶	2.6b	(fma.f64 (pow.f64 (cbrt.f64 (-.f64 z t)) 2) (*.f64 (cbrt.f64 (-.f64 z t)) (/.f64 x y)) t)
	7.4b	(+.f64 (/.f64 (-.f64 (.f64 z x) (.f64 t x)) y) t)
✓	2.5b	(fma.f64 (pow.f64 (cbrt.f64 (/.f64 x y)) 2) (*.f64 (cbrt.f64 (/.f64 x y)) (-.f64 z t)) t)
	3.3b	(pow.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)) 3)
	6.2b	(+.f64 (/.f64 x (/.f64 y (-.f64 z t))) t)
	6.1b	(fma.f64 x (/.f64 (-.f64 z t) y) t)
✓	2.1b	(fma.f64 (-.f64 z t) (/.f64 x y) t)

Compiler

Compiled 2926 to 931 computations (68.2% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(pow.f64 (cbrt.f64 (-.f64 z t)) 2)
✓	0.6b	(cbrt.f64 (-.f64 z t))
✓	0.9b	(fma.f64 (pow.f64 (cbrt.f64 (-.f64 z t)) 2) (*.f64 (cbrt.f64 (-.f64 z t)) (/.f64 x y)) t)
✓	4.2b	(*.f64 (cbrt.f64 (-.f64 z t)) (/.f64 x y))

series694.0ms (14.5%)

Counts

4 → 84

Calls

36 calls:

207.0ms	(fma.f64 (pow.f64 (cbrt.f64 (-.f64 z t)) 2) (*.f64 (cbrt.f64 (-.f64 z t)) (/.f64 x y)) t)	t	0
97.0ms	(fma.f64 (pow.f64 (cbrt.f64 (-.f64 z t)) 2) (*.f64 (cbrt.f64 (-.f64 z t)) (/.f64 x y)) t)	z	0
25.0ms	(*.f64 (cbrt.f64 (-.f64 z t)) (/.f64 x y))	z	0
23.0ms	(fma.f64 (pow.f64 (cbrt.f64 (-.f64 z t)) 2) (*.f64 (cbrt.f64 (-.f64 z t)) (/.f64 x y)) t)	z	-inf
23.0ms	(pow.f64 (cbrt.f64 (-.f64 z t)) 2)	z	0

rewrite57.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

451×	`prod-diff_binary64`
228×	`expm1-udef_binary64`
228×	`log1p-udef_binary64`
129×	`add-sqr-sqrt_binary64`
124×	`fma-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	51
1	258	40
2	3375	40

Stop Event

1×	node limit

Counts

4 → 90

simplify61.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

548×	`cancel-sign-sub-inv_binary64`
357×	`times-frac_binary64`
261×	`distribute-rgt-neg-in_binary64`
253×	`associate-r_binary64`
247×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	222	2595
1	731	2579
2	2722	2567

Stop Event

1×	node limit

Counts

174 → 160

prune181.0ms (3.8%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	201	0	201
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	201	7	208

Error

Counts

208 → 7

Alt Table

Status	Error	Program
✓	2.6b	(fma.f64 (pow.f64 (cbrt.f64 (-.f64 z t)) 2) (*.f64 (cbrt.f64 (-.f64 z t)) (/.f64 x y)) t)
	7.4b	(+.f64 (/.f64 (-.f64 (.f64 z x) (.f64 t x)) y) t)
✓	2.5b	(fma.f64 (pow.f64 (cbrt.f64 (/.f64 x y)) 2) (*.f64 (cbrt.f64 (/.f64 x y)) (-.f64 z t)) t)
	3.3b	(pow.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)) 3)
	6.2b	(+.f64 (/.f64 x (/.f64 y (-.f64 z t))) t)
	6.1b	(fma.f64 x (/.f64 (-.f64 z t) y) t)
✓	2.1b	(fma.f64 (-.f64 z t) (/.f64 x y) t)

Compiler

Compiled 5996 to 3069 computations (48.8% saved)

regimes233.0ms (4.9%)

Accuracy

Total 1.6b remaining (99.4%)

Threshold costs 0b (0%)

Counts

32 → 3

Compiler

Compiled 2737 to 1682 computations (38.5% saved)

bsearch1.0ms (0%)

Algorithm

2×	left-value

Calls

2 calls:

0.0ms	(/.f64 x y)
0.0ms	(/.f64 x y)

Steps

Iters	Point		Range
2.63608031016327e-310	∈ [	2.63608031016327e-310	,	1.3162610907863735e-303	]
-5.822884373689189e-101	∈ [	-5.822884373689189e-101	,	-2.8422503593170577e-111	]

Compiler

Compiled 7 to 5 computations (28.6% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
2×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	54
1	25	54
2	30	54
3	32	54
4	33	54

Stop Event

1×

saturated

end90.0ms (1.9%)

Stop Event

1×

fuel

Compiler

Compiled 189 to 99 computations (47.6% saved)

Details

analyze959.0ms (20%)

sample1.2s (25.4%)

preprocess57.0ms (1.2%)

simplify51.0ms (1.1%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

series57.0ms (1.2%)

rewrite55.0ms (1.1%)

simplify97.0ms (2%)

prune73.0ms (1.5%)

localize24.0ms (0.5%)

series16.0ms (0.3%)

rewrite50.0ms (1%)

simplify69.0ms (1.4%)

prune30.0ms (0.6%)

localize11.0ms (0.2%)

series426.0ms (8.9%)

rewrite64.0ms (1.3%)

simplify66.0ms (1.4%)

prune124.0ms (2.6%)

localize10.0ms (0.2%)

series694.0ms (14.5%)

rewrite57.0ms (1.2%)

simplify61.0ms (1.3%)

prune181.0ms (3.8%)

regimes233.0ms (4.9%)

bsearch1.0ms (0%)

simplify4.0ms (0.1%)

end90.0ms (1.9%)

Profiling