Details

analyze932.0ms (1.3%)

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
19.9%	79.9%	0.2%	10
22.8%	77%	0.2%	11
25.4%	72.7%	1.9%	12
35.8%	59.6%	4.6%	13
42%	52.3%	5.8%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample1.7s (2.4%)

Results

1.2s	8256×	body	128	valid
327.0ms	2140×	body	128	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify68.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

775×	`fma-def_binary64`
730×	`fma-neg_binary64`
228×	`cancel-sign-sub-inv_binary64`
138×	`distribute-rgt-in_binary64`
97×	`unsub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	15	11
2	31	11
3	72	11
4	146	11
5	255	11
6	409	11
7	668	11
8	1099	11
9	1352	11
10	1478	11
11	1525	11
12	1531	11
13	1536	11
14	1536	11
15	1451	11

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

1.4b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	1.4b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
	1.4b	(+.f64 x (*.f64 (-.f64 y x) (/.f64 z t)))

Compiler

Compiled 71 to 39 computations (45.1% saved)

localize6.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	1.4b	(fma.f64 (-.f64 y x) (/.f64 z t) x)

series17.0ms (0%)

Counts

1 → 48

Calls

1 calls:

17.0ms

(fma.f64 (-.f64 y x) (/.f64 z t) x)

rewrite52.0ms (0.1%)

Algorithm

2×	batch-egg-rewrite

Rules

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

Counts

1 → 29

Calls

1 calls:

51.0ms

(fma.f64 (-.f64 y x) (/.f64 z t) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	175	11
2	2368	11
3	5028	11
0	0	0
1	0	0

simplify89.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

733×	`fma-neg_binary64`
716×	`fma-def_binary64`
244×	`cancel-sign-sub-inv_binary64`
159×	`distribute-rgt-in_binary64`
109×	`distribute-lft-in_binary64`

Counts

77 → 42

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	29	777
1	69	561
2	152	552
3	273	552
4	527	480
5	936	480
6	1333	480
7	1453	480
8	1489	480
9	1533	480
10	1543	480
11	1543	480
12	1458	480

prune32.0ms (0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	38	4	42
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	39	5	44

Error

0.0b

Counts

44 → 5

Alt Table

Status	Error	Program
	34.2b	(*.f64 z (/.f64 (-.f64 y x) t))
✓	1.4b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
	4.9b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 z x) t))
▶	2.5b	(pow.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) 3)
	30.0b	(/.f64 (-.f64 (.f64 (.f64 (-.f64 y x) (/.f64 z t)) (.f64 (-.f64 y x) (/.f64 z t))) (.f64 x x)) (-.f64 (*.f64 (-.f64 y x) (/.f64 z t)) x))

Compiler

Compiled 696 to 214 computations (69.3% saved)

localize8.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.6b	(cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))
✓	0.7b	(pow.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) 3)
	1.4b	(fma.f64 (-.f64 y x) (/.f64 z t) x)

series1.1min (92.5%)

Counts

2 → 96

Calls

2 calls:

1.1min	(pow.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) 3)
229.0ms	(cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))

rewrite113.0ms (0.2%)

Algorithm

2×	batch-egg-rewrite

Rules

537×	`prod-diff_binary64`
207×	`fma-def_binary64`
199×	`expm1-udef_binary64`
199×	`log1p-udef_binary64`
177×	`log-pow_binary64`

Counts

2 → 68

Calls

2 calls:

110.0ms	(cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))
110.0ms	(pow.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) 3)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	24
1	222	24
2	2791	24
3	4862	24
4	5025	24
0	0	0
1	0	0

simplify346.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

651×	`times-frac_binary64`
423×	`associate-/l*_binary64`
398×	`associate-/r*_binary64`
317×	`fma-def_binary64`
179×	`*-commutative_binary64`

Counts

164 → 179

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	468	7305
1	1660	7001
2	5026	7001

prune257.0ms (0.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	219	2	221
Fresh	2	1	3
Picked	0	1	1
Done	0	1	1
Total	221	5	226

Error

0.0b

Counts

226 → 5

Alt Table

Status	Error	Program
	31.4b	(fma.f64 (*.f64 (-.f64 y x) (sqrt.f64 (/.f64 z t))) (sqrt.f64 (/.f64 z t)) x)
▶	4.9b	(fma.f64 (*.f64 (-.f64 y x) z) (/.f64 1 t) x)
	34.2b	(*.f64 z (/.f64 (-.f64 y x) t))
✓	1.4b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
✓	2.5b	(pow.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) 3)

Compiler

Compiled 8713 to 4172 computations (52.1% saved)

localize12.0ms (0%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (-.f64 y x) z)
✓	4.7b	(fma.f64 (*.f64 (-.f64 y x) z) (/.f64 1 t) x)

series66.0ms (0.1%)

Counts

2 → 84

Calls

2 calls:

55.0ms	(fma.f64 (*.f64 (-.f64 y x) z) (/.f64 1 t) x)
10.0ms	(*.f64 (-.f64 y x) z)

rewrite74.0ms (0.1%)

Algorithm

2×	batch-egg-rewrite

Rules

491×	`log-prod_binary64`
433×	`prod-diff_binary64`
207×	`fma-def_binary64`
188×	`expm1-udef_binary64`
188×	`log1p-udef_binary64`

Counts

2 → 55

Calls

2 calls:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	21
1	208	20
2	2530	20
3	5173	20
0	0	0
1	0	0

simplify145.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

778×	`fma-def_binary64`
667×	`fma-neg_binary64`
156×	`distribute-rgt-in_binary64`
151×	`cancel-sign-sub-inv_binary64`
95×	`associate-/l*_binary64`

Counts

139 → 75

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	32	1107
1	78	801
2	156	792
3	288	792
4	554	720
5	964	720
6	1327	720
7	1455	720
8	1508	720
9	1536	720
10	1537	720
11	1537	720
12	1452	720

prune61.0ms (0.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	75	0	75
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	75	5	80

Error

0.0b

Counts

80 → 5

Alt Table

Status	Error	Program
▶	31.4b	(fma.f64 (*.f64 (-.f64 y x) (sqrt.f64 (/.f64 z t))) (sqrt.f64 (/.f64 z t)) x)
✓	4.9b	(fma.f64 (*.f64 (-.f64 y x) z) (/.f64 1 t) x)
	34.2b	(*.f64 z (/.f64 (-.f64 y x) t))
✓	1.4b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
✓	2.5b	(pow.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) 3)

Compiler

Compiled 1121 to 379 computations (66.2% saved)

localize13.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (*.f64 (-.f64 y x) (sqrt.f64 (/.f64 z t))) (sqrt.f64 (/.f64 z t)) x)
✓	0.1b	(*.f64 (-.f64 y x) (sqrt.f64 (/.f64 z t)))
✓	7.3b	(sqrt.f64 (/.f64 z t))

series385.0ms (0.5%)

Counts

3 → 51

Calls

3 calls:

252.0ms	(fma.f64 (*.f64 (-.f64 y x) (sqrt.f64 (/.f64 z t))) (sqrt.f64 (/.f64 z t)) x)
98.0ms	(*.f64 (-.f64 y x) (sqrt.f64 (/.f64 z t)))
34.0ms	(sqrt.f64 (/.f64 z t))

rewrite126.0ms (0.2%)

Algorithm

2×	batch-egg-rewrite

Rules

539×	`prod-diff_binary64`
216×	`fma-def_binary64`
201×	`expm1-udef_binary64`
201×	`log1p-udef_binary64`
183×	`log-pow_binary64`

Counts

3 → 86

Calls

3 calls:

124.0ms	(fma.f64 (*.f64 (-.f64 y x) (sqrt.f64 (/.f64 z t))) (sqrt.f64 (/.f64 z t)) x)
124.0ms	(*.f64 (-.f64 y x) (sqrt.f64 (/.f64 z t)))
123.0ms	(sqrt.f64 (/.f64 z t))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	39
1	215	31
2	2838	29
3	4963	29
4	5187	29
0	0	0
1	0	0

simplify139.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

908×	`fma-neg_binary64`
733×	`fma-def_binary64`
234×	`cancel-sign-sub-inv_binary64`
177×	`distribute-rgt-in_binary64`
116×	`unsub-neg_binary64`

Counts

137 → 101

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	25	816
1	59	672
2	114	636
3	181	564
4	389	528
5	731	528
6	1204	528
7	1544	528
8	1625	528
9	1702	528
10	1698	528
11	1708	528
12	1708	528
13	1619	528

prune102.0ms (0.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	130	2	132
Fresh	1	0	1
Picked	1	0	1
Done	0	3	3
Total	132	5	137

Error

Counts

137 → 5

Alt Table

Status	Error	Program
✓	4.9b	(fma.f64 (*.f64 (-.f64 y x) z) (/.f64 1 t) x)
✓	1.4b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
	32.8b	(fma.f64 (*.f64 (-.f64 y x) (sqrt.f64 (/.f64 z t))) (cbrt.f64 (pow.f64 (/.f64 z t) 3/2)) x)
	7.0b	(fma.f64 z (/.f64 (-.f64 y x) t) x)
✓	2.5b	(pow.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) 3)

Compiler

Compiled 2231 to 559 computations (74.9% saved)

regimes441.0ms (0.6%)

Accuracy

Total 1.9b remaining (98.8%)

Threshold costs 0b (0%)

Counts

43 → 1

Compiler

Compiled 3962 to 2296 computations (42% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	10	11
2	15	11
3	17	11
4	18	11
5	18	11

end131.0ms (0.2%)

Compiler: Compiled 97 to 59 computations (39.2% saved)

Details

analyze932.0ms (1.3%)

sample1.7s (2.4%)

simplify68.0ms (0.1%)

prune4.0ms (0%)

localize6.0ms (0%)

series17.0ms (0%)

rewrite52.0ms (0.1%)

simplify89.0ms (0.1%)

prune32.0ms (0%)

localize8.0ms (0%)

series1.1min (92.5%)

rewrite113.0ms (0.2%)

simplify346.0ms (0.5%)

prune257.0ms (0.4%)

localize12.0ms (0%)

series66.0ms (0.1%)

rewrite74.0ms (0.1%)

simplify145.0ms (0.2%)

prune61.0ms (0.1%)

localize13.0ms (0%)

series385.0ms (0.5%)

rewrite126.0ms (0.2%)

simplify139.0ms (0.2%)

prune102.0ms (0.1%)

regimes441.0ms (0.6%)

simplify4.0ms (0%)

end131.0ms (0.2%)

Profiling