Details

analyze1.4s (24.8%)

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
12.5%	87.3%	0.2%	8
12.5%	87.3%	0.2%	9
18.7%	81.1%	0.2%	10
23.4%	76.4%	0.2%	11
31.6%	68.2%	0.2%	12
34.5%	64.9%	0.6%	13
40.3%	59.2%	0.6%	14

Compiler

Compiled 20 to 14 computations (30% saved)

sample1.8s (31%)

Results

1.2s	8256×	body	128	valid
492.0ms	3100×	body	128	invalid

Compiler

Compiled 59 to 41 computations (30.5% saved)

simplify90.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

871×	`distribute-rgt-in_binary64`
685×	`div-sub_binary64`
652×	`distribute-lft-in_binary64`
409×	`distribute-neg-frac_binary64`
395×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	12	22
1	25	22
2	58	22
3	109	22
4	223	20
5	437	16
6	876	14
7	2098	14
8	2320	14
9	2451	14
10	3042	14
11	3226	14
12	3327	14
13	4913	14

prune4.0ms (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
	3.6b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 t (.f64 (*.f64 z 3) y)))
▶	3.0b	(fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)

Compiler

Compiled 95 to 62 computations (34.7% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 y (/.f64 t y))
✓	0.3b	(/.f64 -1/3 z)
✓	2.8b	(fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)

series26.0ms (0.5%)

Counts

3 → 54

Calls

3 calls:

21.0ms	(fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)
4.0ms	(-.f64 y (/.f64 t y))
1.0ms	(/.f64 -1/3 z)

rewrite76.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

610×	`prod-diff_binary64`
231×	`fma-def_binary64`
210×	`expm1-udef_binary64`
210×	`log1p-udef_binary64`
188×	`egg-rr`

Counts

3 → 188

Calls

3 calls:

72.0ms	(-.f64 y (/.f64 t y))
72.0ms	(/.f64 -1/3 z)
72.0ms	(fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	25
1	223	25
2	2955	25
3	4917	25
0	0	0
1	0	0

simplify141.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

1875×	`fma-neg_binary64`
858×	`distribute-rgt-in_binary64`
782×	`fma-def_binary64`
630×	`div-sub_binary64`
438×	`cancel-sign-sub-inv_binary64`

Counts

242 → 204

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	24	796
1	63	664
2	112	658
3	211	592
4	355	592
5	554	592
6	975	592
7	1507	592
8	2381	592
9	2470	592
10	2908	592
11	3179	592
12	3354	592
13	3356	592
14	5426	592

prune161.0ms (2.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	197	7	204
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	198	8	206

Error

0.0b

Counts

206 → 8

Alt Table

Status	Error	Program
	3.6b	(fma.f64 (pow.f64 (cbrt.f64 (/.f64 -1/3 z)) 3) (-.f64 y (/.f64 t y)) x)
	3.6b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 t (.f64 (*.f64 z 3) y)))
	3.2b	(fma.f64 1/3 (/.f64 (-.f64 (/.f64 t y) y) z) x)
	3.0b	(fma.f64 (*.f64 (/.f64 1 z) -1/3) (-.f64 y (/.f64 t y)) x)
	3.9b	(-.f64 (+.f64 (.f64 1/3 (/.f64 t (.f64 y z))) x) (*.f64 1/3 (/.f64 y z)))
	31.0b	(fma.f64 (pow.f64 (sqrt.f64 (/.f64 -1/3 z)) 2) (-.f64 y (/.f64 t y)) x)
▶	3.0b	(fma.f64 (/.f64 -1/3 z) (fma.f64 t (neg.f64 (/.f64 1 y)) y) x)
	4.0b	(pow.f64 (cbrt.f64 (fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)) 3)

Compiler

Compiled 5314 to 1897 computations (64.3% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 t (neg.f64 (/.f64 1 y)) y)
	0.3b	(/.f64 -1/3 z)
✓	2.8b	(fma.f64 (/.f64 -1/3 z) (fma.f64 t (neg.f64 (/.f64 1 y)) y) x)

series29.0ms (0.5%)

Counts

2 → 72

Calls

2 calls:

23.0ms	(fma.f64 (/.f64 -1/3 z) (fma.f64 t (neg.f64 (/.f64 1 y)) y) x)
6.0ms	(fma.f64 t (neg.f64 (/.f64 1 y)) y)

rewrite59.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

490×	`log-prod_binary64`
199×	`pow1/3_binary64`
199×	`expm1-udef_binary64`
199×	`log1p-udef_binary64`
184×	`pow3_binary64`

Counts

2 → 60

Calls

2 calls:

57.0ms	(fma.f64 t (neg.f64 (/.f64 1 y)) y)
57.0ms	(fma.f64 (/.f64 -1/3 z) (fma.f64 t (neg.f64 (/.f64 1 y)) y) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	23
1	247	23
2	2611	23
3	4912	23
0	0	0
1	0	0

simplify133.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

1785×	`fma-neg_binary64`
1112×	`div-sub_binary64`
629×	`fma-def_binary64`
412×	`sub-neg_binary64`
347×	`distribute-rgt-neg-in_binary64`

Counts

132 → 77

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	25	922
1	65	790
2	115	784
3	219	718
4	368	718
5	627	718
6	1121	718
7	2075	718
8	2707	718
9	3036	718
10	3226	718
11	3332	718
12	3428	718
13	4959	718

prune71.0ms (1.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	100	0	100
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	100	8	108

Error

0.0b

Counts

108 → 8

Alt Table

Status	Error	Program
	3.6b	(fma.f64 (pow.f64 (cbrt.f64 (/.f64 -1/3 z)) 3) (-.f64 y (/.f64 t y)) x)
	3.6b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 t (.f64 (*.f64 z 3) y)))
	3.2b	(fma.f64 1/3 (/.f64 (-.f64 (/.f64 t y) y) z) x)
▶	3.0b	(fma.f64 (*.f64 (/.f64 1 z) -1/3) (-.f64 y (/.f64 t y)) x)
	3.9b	(-.f64 (+.f64 (.f64 1/3 (/.f64 t (.f64 y z))) x) (*.f64 1/3 (/.f64 y z)))
	31.0b	(fma.f64 (pow.f64 (sqrt.f64 (/.f64 -1/3 z)) 2) (-.f64 y (/.f64 t y)) x)
✓	3.0b	(fma.f64 (/.f64 -1/3 z) (fma.f64 t (neg.f64 (/.f64 1 y)) y) x)
	4.0b	(pow.f64 (cbrt.f64 (fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)) 3)

Compiler

Compiled 1815 to 1140 computations (37.2% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(-.f64 y (/.f64 t y))
✓	0.4b	(*.f64 (/.f64 1 z) -1/3)
✓	2.8b	(fma.f64 (*.f64 (/.f64 1 z) -1/3) (-.f64 y (/.f64 t y)) x)

series29.0ms (0.5%)

Counts

2 → 60

Calls

2 calls:

28.0ms	(fma.f64 (*.f64 (/.f64 1 z) -1/3) (-.f64 y (/.f64 t y)) x)
1.0ms	(*.f64 (/.f64 1 z) -1/3)

rewrite62.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

615×	`prod-diff_binary64`
229×	`expm1-udef_binary64`
229×	`log1p-udef_binary64`
129×	`add-sqr-sqrt_binary64`
121×	`log1p-expm1-u_binary64`

Counts

2 → 42

Calls

2 calls:

61.0ms	(*.f64 (/.f64 1 z) -1/3)
61.0ms	(fma.f64 (*.f64 (/.f64 1 z) -1/3) (-.f64 y (/.f64 t y)) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	18
1	256	18
2	3186	18
3	5115	18
0	0	0
1	0	0

simplify148.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

1586×	`fma-neg_binary64`
739×	`distribute-rgt-in_binary64`
580×	`distribute-lft-in_binary64`
517×	`fma-def_binary64`
478×	`div-sub_binary64`

Counts

102 → 55

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	23	823
1	58	691
2	104	685
3	196	619
4	336	619
5	521	619
6	868	619
7	1290	619
8	2156	619
9	2185	619
10	2214	619
11	2694	619
12	2769	619
13	2855	619
14	4000	619
15	5029	619

prune153.0ms (2.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	199	0	199
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	199	8	207

Error

0.0b

Counts

207 → 8

Alt Table

Status	Error	Program
	3.6b	(fma.f64 (pow.f64 (cbrt.f64 (/.f64 -1/3 z)) 3) (-.f64 y (/.f64 t y)) x)
	3.6b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 t (.f64 (*.f64 z 3) y)))
▶	3.2b	(fma.f64 1/3 (/.f64 (-.f64 (/.f64 t y) y) z) x)
✓	3.0b	(fma.f64 (*.f64 (/.f64 1 z) -1/3) (-.f64 y (/.f64 t y)) x)
	3.9b	(-.f64 (+.f64 (.f64 1/3 (/.f64 t (.f64 y z))) x) (*.f64 1/3 (/.f64 y z)))
	31.0b	(fma.f64 (pow.f64 (sqrt.f64 (/.f64 -1/3 z)) 2) (-.f64 y (/.f64 t y)) x)
✓	3.0b	(fma.f64 (/.f64 -1/3 z) (fma.f64 t (neg.f64 (/.f64 1 y)) y) x)
	4.0b	(pow.f64 (cbrt.f64 (fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)) 3)

Compiler

Compiled 5499 to 2129 computations (61.3% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 t y) y)
✓	0.4b	(fma.f64 1/3 (/.f64 (-.f64 (/.f64 t y) y) z) x)
✓	2.7b	(/.f64 (-.f64 (/.f64 t y) y) z)

series44.0ms (0.8%)

Counts

3 → 82

Calls

3 calls:

23.0ms	(fma.f64 1/3 (/.f64 (-.f64 (/.f64 t y) y) z) x)
15.0ms	(/.f64 (-.f64 (/.f64 t y) y) z)
6.0ms	(-.f64 (/.f64 t y) y)

rewrite115.0ms (2%)

Algorithm

2×	batch-egg-rewrite

Rules

872×	`prod-diff_binary64`
346×	`egg-rr`
213×	`log1p-udef_binary64`
117×	`add-sqr-sqrt_binary64`
111×	`log1p-expm1-u_binary64`

Counts

3 → 346

Calls

3 calls:

104.0ms	(-.f64 (/.f64 t y) y)
104.0ms	(fma.f64 1/3 (/.f64 (-.f64 (/.f64 t y) y) z) x)
104.0ms	(/.f64 (-.f64 (/.f64 t y) y) z)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	31
1	224	31
2	3112	31
3	5184	31
0	0	0
1	0	0

simplify151.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

1733×	`fma-neg_binary64`
929×	`div-sub_binary64`
662×	`fma-def_binary64`
583×	`times-frac_binary64`
386×	`neg-mul-1_binary64`

Counts

428 → 368

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	29	1121
1	76	989
2	140	961
3	278	851
4	484	851
5	937	851
6	1934	851
7	2873	851
8	2934	851
9	3186	851
10	3138	851
11	3365	851
12	4940	851

prune246.0ms (4.3%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	368	0	368
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	368	8	376

Error

0.0b

Counts

376 → 8

Alt Table

Status	Error	Program
	3.6b	(fma.f64 (pow.f64 (cbrt.f64 (/.f64 -1/3 z)) 3) (-.f64 y (/.f64 t y)) x)
	3.6b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 t (.f64 (*.f64 z 3) y)))
✓	3.2b	(fma.f64 1/3 (/.f64 (-.f64 (/.f64 t y) y) z) x)
✓	3.0b	(fma.f64 (*.f64 (/.f64 1 z) -1/3) (-.f64 y (/.f64 t y)) x)
	3.9b	(-.f64 (+.f64 (.f64 1/3 (/.f64 t (.f64 y z))) x) (*.f64 1/3 (/.f64 y z)))
	31.0b	(fma.f64 (pow.f64 (sqrt.f64 (/.f64 -1/3 z)) 2) (-.f64 y (/.f64 t y)) x)
✓	3.0b	(fma.f64 (/.f64 -1/3 z) (fma.f64 t (neg.f64 (/.f64 1 y)) y) x)
	4.0b	(pow.f64 (cbrt.f64 (fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)) 3)

Compiler

Compiled 12273 to 3266 computations (73.4% saved)

regimes627.0ms (10.9%)

Accuracy

Total 0.5b remaining (93.8%)

Threshold costs 0.5b (93.8%)

Counts

71 → 3

Compiler

Compiled 6598 to 4557 computations (30.9% saved)

bsearch28.0ms (0.5%)

Steps

Iters	Range		Point
8	2.5757515159561172e-25	1.473655488592338e-22	1.533233474346769e-23
1	-2.0443101595776655e-63	-8.142863412040852e-71	-4.1631542270516714e-67

Compiler

Compiled 5 to 4 computations (20% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

7×	`*-commutative_binary64`
6×	`+-commutative_binary64`
5×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	74
1	44	74
2	52	74
3	59	74
4	64	74
5	67	74
6	68	74
7	65	74

end121.0ms (2.1%)

Compiler: Compiled 245 to 159 computations (35.1% saved)

Details

analyze1.4s (24.8%)

sample1.8s (31%)

simplify90.0ms (1.6%)

prune4.0ms (0.1%)

localize7.0ms (0.1%)

series26.0ms (0.5%)

rewrite76.0ms (1.3%)

simplify141.0ms (2.4%)

prune161.0ms (2.8%)

localize9.0ms (0.2%)

series29.0ms (0.5%)

rewrite59.0ms (1%)

simplify133.0ms (2.3%)

prune71.0ms (1.2%)

localize8.0ms (0.1%)

series29.0ms (0.5%)

rewrite62.0ms (1.1%)

simplify148.0ms (2.6%)

prune153.0ms (2.6%)

localize7.0ms (0.1%)

series44.0ms (0.8%)

rewrite115.0ms (2%)

simplify151.0ms (2.6%)

prune246.0ms (4.3%)

regimes627.0ms (10.9%)

bsearch28.0ms (0.5%)

simplify4.0ms (0.1%)

end121.0ms (2.1%)

Profiling