Details

analyze878.0ms (13.8%)

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
18.7%	81.1%	0.2%	9
22.6%	77.2%	0.2%	10
25%	74.9%	0.2%	11
39.4%	60.4%	0.2%	12
46.5%	53.2%	0.3%	13
48%	51.4%	0.6%	14

Compiler

Compiled 16 to 11 computations (31.3% saved)

sample1.4s (21.4%)

Results

1.1s	8256×	body	128	valid
94.0ms	712×	body	128	invalid

Compiler

Compiled 47 to 32 computations (31.9% saved)

simplify153.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

1028×	`fma-neg_binary64`
470×	`fma-def_binary64`
271×	`associate-/l*_binary64`
255×	`cancel-sign-sub-inv_binary64`
255×	`div-sub_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	13
1	24	13
2	53	13
3	109	13
4	185	13
5	336	13
6	549	13
7	870	13
8	1606	13
9	1757	13
10	1912	13
11	1986	13
12	1980	13
13	1985	13
14	1993	13
15	1993	13
16	1872	13

prune8.0ms (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

5.7b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	6.0b	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))
	7.4b	(/.f64 (.f64 x 2) (-.f64 (.f64 y z) (*.f64 t z)))

Compiler

Compiled 80 to 53 computations (33.8% saved)

localize13.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 2 (-.f64 y t))
✓	0.2b	(/.f64 (/.f64 2 (-.f64 y t)) z)
✓	5.9b	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))

series206.0ms (3.2%)

Counts

3 → 108

Calls

3 calls:

142.0ms	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))
43.0ms	(/.f64 (/.f64 2 (-.f64 y t)) z)
21.0ms	(/.f64 2 (-.f64 y t))

rewrite114.0ms (1.8%)

Algorithm

2×	batch-egg-rewrite

Rules

473×	`prod-diff_binary64`
212×	`expm1-udef_binary64`
212×	`log1p-udef_binary64`
193×	`fma-def_binary64`
182×	`log-pow_binary64`

Counts

3 → 88

Calls

3 calls:

112.0ms	(/.f64 2 (-.f64 y t))
112.0ms	(/.f64 (/.f64 2 (-.f64 y t)) z)
112.0ms	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	30
1	226	30
2	3094	30
3	4978	30
4	5124	30
0	0	0
1	0	0

simplify73.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

811×	`fma-def_binary64`
705×	`associate-/l*_binary64`
480×	`associate-/r*_binary64`
159×	`distribute-lft-out_binary64`
117×	`distribute-rgt-out_binary64`

Counts

196 → 133

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	132	2577
1	446	2445
2	1620	2229
3	4985	2229

prune107.0ms (1.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	123	10	133
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	125	10	135

Error

0.0b

Counts

135 → 10

Alt Table

Status	Error	Program
	36.0b	(/.f64 (/.f64 (*.f64 x (/.f64 2 (-.f64 y t))) (sqrt.f64 z)) (sqrt.f64 z))
	32.2b	(.f64 (/.f64 x z) (fma.f64 2 (/.f64 t (.f64 y y)) (/.f64 2 y)))
	28.9b	(*.f64 x (/.f64 (cbrt.f64 (pow.f64 (/.f64 2 (-.f64 y t)) 3)) z))
	6.0b	(.f64 x (.f64 (/.f64 2 (-.f64 y t)) (/.f64 1 z)))
	6.0b	(/.f64 (.f64 2 x) (.f64 (-.f64 y t) z))
	5.6b	(/.f64 (/.f64 (*.f64 x (/.f64 2 (-.f64 y t))) (pow.f64 (cbrt.f64 z) 2)) (cbrt.f64 z))
▶	5.0b	(/.f64 (*.f64 x (/.f64 2 (-.f64 y t))) z)
	5.3b	(/.f64 1 (/.f64 z (*.f64 x (/.f64 2 (-.f64 y t)))))
	28.2b	(cbrt.f64 (pow.f64 (*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z)) 3))
	6.6b	(pow.f64 (cbrt.f64 (*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))) 3)

Compiler

Compiled 2537 to 1482 computations (41.6% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(/.f64 2 (-.f64 y t))
✓	0.2b	(*.f64 x (/.f64 2 (-.f64 y t)))
✓	4.8b	(/.f64 (*.f64 x (/.f64 2 (-.f64 y t))) z)

series101.0ms (1.6%)

Counts

2 → 84

Calls

2 calls:

64.0ms	(/.f64 (*.f64 x (/.f64 2 (-.f64 y t))) z)
37.0ms	(*.f64 x (/.f64 2 (-.f64 y t)))

rewrite118.0ms (1.9%)

Algorithm

2×	batch-egg-rewrite

Rules

395×	`prod-diff_binary64`
318×	`fma-udef_binary64`
220×	`fma-def_binary64`
212×	`expm1-udef_binary64`
212×	`log1p-udef_binary64`

Counts

2 → 67

Calls

2 calls:

117.0ms	(*.f64 x (/.f64 2 (-.f64 y t)))
117.0ms	(/.f64 (*.f64 x (/.f64 2 (-.f64 y t))) z)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	23
1	226	23
2	3112	23
3	4847	23
4	4849	23
5	5031	23
0	0	0
1	0	0

simplify54.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

932×	`times-frac_binary64`
599×	`associate-/l*_binary64`
577×	`fma-def_binary64`
400×	`associate-/r*_binary64`
136×	`associate-/r/_binary64`

Counts

151 → 98

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	97	1992
1	332	1902
2	1231	1698
3	5080	1698

prune142.0ms (2.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	131	5	136
Fresh	5	4	9
Picked	1	0	1
Done	0	0	0
Total	137	9	146

Error

Counts

146 → 9

Alt Table

Status	Error	Program
	6.0b	(.f64 x (.f64 (/.f64 2 (-.f64 y t)) (/.f64 1 z)))
	5.1b	(.f64 (/.f64 2 (-.f64 y t)) (.f64 x (/.f64 1 z)))
	5.3b	(/.f64 1 (/.f64 z (*.f64 x (/.f64 2 (-.f64 y t)))))
	29.7b	(neg.f64 (.f64 (/.f64 2 z) (.f64 (+.f64 (/.f64 y t) 1) (/.f64 x t))))
	28.9b	(*.f64 x (/.f64 (cbrt.f64 (pow.f64 (/.f64 2 (-.f64 y t)) 3)) z))
	6.0b	(/.f64 (.f64 2 x) (.f64 (-.f64 y t) z))
▶	4.9b	(/.f64 (*.f64 2 (/.f64 x (-.f64 y t))) z)
	4.9b	(/.f64 (/.f64 1 (/.f64 (-.f64 y t) (*.f64 x 2))) z)
	5.1b	(*.f64 (/.f64 x z) (/.f64 2 (-.f64 y t)))

Compiler

Compiled 2523 to 1452 computations (42.4% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 x (-.f64 y t))
✓	0.0b	(*.f64 2 (/.f64 x (-.f64 y t)))
✓	4.8b	(/.f64 (*.f64 2 (/.f64 x (-.f64 y t))) z)

series78.0ms (1.2%)

Counts

3 → 96

Calls

3 calls:

39.0ms	(/.f64 (*.f64 2 (/.f64 x (-.f64 y t))) z)
22.0ms	(*.f64 2 (/.f64 x (-.f64 y t)))
18.0ms	(/.f64 x (-.f64 y t))

rewrite134.0ms (2.1%)

Algorithm

2×	batch-egg-rewrite

Rules

404×	`prod-diff_binary64`
328×	`fma-udef_binary64`
220×	`fma-def_binary64`
213×	`expm1-udef_binary64`
213×	`log1p-udef_binary64`

Counts

3 → 100

Calls

3 calls:

132.0ms	(/.f64 x (-.f64 y t))
132.0ms	(*.f64 2 (/.f64 x (-.f64 y t)))
132.0ms	(/.f64 (*.f64 2 (/.f64 x (-.f64 y t))) z)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	30
1	225	30
2	3162	30
3	4881	30
4	4888	30
5	4953	30
0	0	0
1	0	0

simplify94.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

934×	`times-frac_binary64`
676×	`fma-def_binary64`
601×	`associate-/l*_binary64`
285×	`fma-neg_binary64`
138×	`associate-/r/_binary64`

Counts

196 → 145

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	111	2478
1	375	2388
2	1352	2073
3	4993	2070
4	5191	2070

prune113.0ms (1.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	143	2	145
Fresh	4	4	8
Picked	0	1	1
Done	0	0	0
Total	147	7	154

Error

Counts

154 → 7

Alt Table

Status	Error	Program
	6.0b	(.f64 x (.f64 (/.f64 2 (-.f64 y t)) (/.f64 1 z)))
	5.1b	(.f64 (/.f64 2 (-.f64 y t)) (.f64 x (/.f64 1 z)))
	6.0b	(/.f64 (.f64 2 x) (.f64 (-.f64 y t) z))
▶	5.0b	(.f64 2 (/.f64 1 (.f64 z (/.f64 (-.f64 y t) x))))
✓	4.9b	(/.f64 (*.f64 2 (/.f64 x (-.f64 y t))) z)
	29.7b	(neg.f64 (.f64 (/.f64 2 z) (.f64 (+.f64 (/.f64 y t) 1) (/.f64 x t))))
	25.3b	(/.f64 (cbrt.f64 (pow.f64 (*.f64 2 (/.f64 x (-.f64 y t))) 3)) z)

Compiler

Compiled 2604 to 1342 computations (48.5% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 y t) x)
✓	0.0b	(.f64 2 (/.f64 1 (.f64 z (/.f64 (-.f64 y t) x))))
✓	0.7b	(/.f64 1 (*.f64 z (/.f64 (-.f64 y t) x)))
✓	4.3b	(*.f64 z (/.f64 (-.f64 y t) x))

series113.0ms (1.8%)

Counts

4 → 172

Calls

4 calls:

42.0ms	(.f64 2 (/.f64 1 (.f64 z (/.f64 (-.f64 y t) x))))
38.0ms	(/.f64 1 (*.f64 z (/.f64 (-.f64 y t) x)))
22.0ms	(*.f64 z (/.f64 (-.f64 y t) x))
9.0ms	(/.f64 (-.f64 y t) x)

rewrite113.0ms (1.8%)

Algorithm

2×	batch-egg-rewrite

Rules

550×	`prod-diff_binary64`
261×	`egg-rr`
233×	`log1p-udef_binary64`
131×	`add-sqr-sqrt_binary64`
124×	`log1p-expm1-u_binary64`

Counts

4 → 261

Calls

4 calls:

104.0ms	(/.f64 (-.f64 y t) x)
104.0ms	(.f64 2 (/.f64 1 (.f64 z (/.f64 (-.f64 y t) x))))
104.0ms	(/.f64 1 (*.f64 z (/.f64 (-.f64 y t) x)))
104.0ms	(*.f64 z (/.f64 (-.f64 y t) x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	43
1	263	40
2	3423	40
3	4923	40
0	0	0
1	0	0

simplify111.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

812×	`times-frac_binary64`
525×	`associate-/l*_binary64`
490×	`fma-def_binary64`
362×	`associate-/r*_binary64`
274×	`associate-*l/_binary64`

Counts

433 → 310

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	93	2930
1	310	2732
2	1170	2507
3	4887	2507
4	5009	2507

prune375.0ms (5.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	309	1	310
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	311	6	317

Error

Counts

317 → 6

Alt Table

Status	Error	Program
	6.0b	(/.f64 (.f64 2 x) (.f64 (-.f64 y t) z))
	6.0b	(.f64 2 (.f64 (/.f64 (/.f64 1 z) (-.f64 y t)) x))
	5.1b	(.f64 (/.f64 2 (-.f64 y t)) (.f64 x (/.f64 1 z)))
✓	5.0b	(.f64 2 (/.f64 1 (.f64 z (/.f64 (-.f64 y t) x))))
✓	4.9b	(/.f64 (*.f64 2 (/.f64 x (-.f64 y t))) z)
	25.3b	(/.f64 (cbrt.f64 (pow.f64 (*.f64 2 (/.f64 x (-.f64 y t))) 3)) z)

Compiler

Compiled 9632 to 3995 computations (58.5% saved)

regimes1.5s (23.1%)

Accuracy

Total 0.4b remaining (96.2%)

Threshold costs 0.4b (96.2%)

Counts

72 → 5

Compiler

Compiled 7493 to 5452 computations (27.2% saved)

bsearch4.0ms (0.1%)

Compiler: Compiled 11 to 7 computations (36.4% saved)

simplify13.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

11×	`*-commutative_binary64`
5×	`+-commutative_binary64`
5×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	131
1	53	131
2	63	131
3	69	131
4	73	131
5	74	131
6	73	131

end399.0ms (6.3%)

Compiler: Compiled 273 to 149 computations (45.4% saved)

Details

analyze878.0ms (13.8%)

sample1.4s (21.4%)

simplify153.0ms (2.4%)

prune8.0ms (0.1%)

localize13.0ms (0.2%)

series206.0ms (3.2%)

rewrite114.0ms (1.8%)

simplify73.0ms (1.1%)

prune107.0ms (1.7%)

localize6.0ms (0.1%)

series101.0ms (1.6%)

rewrite118.0ms (1.9%)

simplify54.0ms (0.9%)

prune142.0ms (2.2%)

localize8.0ms (0.1%)

series78.0ms (1.2%)

rewrite134.0ms (2.1%)

simplify94.0ms (1.5%)

prune113.0ms (1.8%)

localize9.0ms (0.1%)

series113.0ms (1.8%)

rewrite113.0ms (1.8%)

simplify111.0ms (1.7%)

prune375.0ms (5.9%)

regimes1.5s (23.1%)

bsearch4.0ms (0.1%)

simplify13.0ms (0.2%)

end399.0ms (6.3%)

Profiling