Details

analyze1.3s (23.4%)

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
2.3%	97.4%	0.2%	9
3.5%	96.2%	0.2%	10
9.5%	90.2%	0.2%	11
14.3%	85.4%	0.2%	12
22.4%	77.4%	0.2%	13
29.7%	70%	0.2%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample1.2s (21.2%)

Results

1.1s	8256×	body	128	valid
88.0ms	718×	body	128	invalid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify119.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

1691×	`fma-neg_binary64`
841×	`div-sub_binary64`
807×	`distribute-rgt-in_binary64`
769×	`fma-def_binary64`
504×	`times-frac_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	19	16
2	40	14
3	82	14
4	166	14
5	297	14
6	643	14
7	1551	14
8	3111	14
9	3064	14
10	3153	14
11	3152	14
12	3170	14
13	3201	14
14	5494	14

prune6.0ms (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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	1.3b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
	10.3b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)))

Compiler

Compiled 88 to 50 computations (43.2% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z t) (-.f64 z a))
✓	1.2b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)

series60.0ms (1%)

Counts

2 → 96

Calls

2 calls:

36.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
24.0ms	(/.f64 (-.f64 z t) (-.f64 z a))

rewrite96.0ms (1.7%)

Algorithm

2×	batch-egg-rewrite

Rules

365×	`fma-def_binary64`
224×	`expm1-udef_binary64`
224×	`log1p-udef_binary64`
200×	`fma-neg_binary64`
193×	`log-pow_binary64`

Counts

2 → 77

Calls

2 calls:

94.0ms	(/.f64 (-.f64 z t) (-.f64 z a))
94.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	24
1	227	24
2	3258	24
3	4982	24
4	4996	24
0	0	0
1	0	0

simplify94.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

774×	`fma-def_binary64`
656×	`times-frac_binary64`
497×	`fma-neg_binary64`
494×	`cancel-sign-sub-inv_binary64`
324×	`sub-neg_binary64`

Counts

173 → 152

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	176	2936
1	482	2936
2	1844	2292
3	4561	2286
4	4998	2286

prune122.0ms (2.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	148	4	152
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	148	6	154

Error

0.0b

Counts

154 → 6

Alt Table

Status	Error	Program
▶	1.3b	(fma.f64 y (pow.f64 (/.f64 (-.f64 z a) (-.f64 z t)) -1) x)
	1.4b	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 z a))) x)
	2.6b	(+.f64 x (*.f64 (/.f64 y (-.f64 z a)) (-.f64 z t)))
✓	1.3b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
	10.3b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)))
	10.9b	(fma.f64 y (cbrt.f64 (pow.f64 (/.f64 (-.f64 z t) (-.f64 z a)) 3)) x)

Compiler

Compiled 3491 to 1205 computations (65.5% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z a) (-.f64 z t))
✓	0.3b	(pow.f64 (/.f64 (-.f64 z a) (-.f64 z t)) -1)
✓	1.2b	(fma.f64 y (pow.f64 (/.f64 (-.f64 z a) (-.f64 z t)) -1) x)

series236.0ms (4.1%)

Counts

3 → 132

Calls

3 calls:

137.0ms	(fma.f64 y (pow.f64 (/.f64 (-.f64 z a) (-.f64 z t)) -1) x)
80.0ms	(pow.f64 (/.f64 (-.f64 z a) (-.f64 z t)) -1)
18.0ms	(/.f64 (-.f64 z a) (-.f64 z t))

rewrite81.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

369×	`fma-def_binary64`
251×	`expm1-udef_binary64`
251×	`log1p-udef_binary64`
205×	`fma-neg_binary64`
141×	`add-sqr-sqrt_binary64`

Counts

3 → 122

Calls

3 calls:

78.0ms	(/.f64 (-.f64 z a) (-.f64 z t))
78.0ms	(pow.f64 (/.f64 (-.f64 z a) (-.f64 z t)) -1)
78.0ms	(fma.f64 y (pow.f64 (/.f64 (-.f64 z a) (-.f64 z t)) -1) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	40
1	269	34
2	3641	34
3	4940	34
0	0	0
1	0	0

simplify123.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

610×	`associate-/l*_binary64`
490×	`associate-/r*_binary64`
308×	`associate--l+_binary64`
261×	`associate-r_binary64`
192×	`+-commutative_binary64`

Counts

254 → 254

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	514	7109
1	1673	6956
2	5109	6956

prune273.0ms (4.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	253	1	254
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	255	5	260

Error

Counts

260 → 5

Alt Table

Status	Error	Program
▶	2.6b	(+.f64 x (*.f64 (/.f64 y (-.f64 z a)) (-.f64 z t)))
	22.8b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 z a)) (+.f64 (/.f64 (.f64 y (.f64 a t)) (pow.f64 (-.f64 z a) 2)) x)) (/.f64 (.f64 y (*.f64 t z)) (pow.f64 (-.f64 z a) 2)))
✓	1.3b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
	10.3b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)))
	10.9b	(fma.f64 y (cbrt.f64 (pow.f64 (/.f64 (-.f64 z t) (-.f64 z a)) 3)) x)

Compiler

Compiled 9000 to 3754 computations (58.3% saved)

localize15.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (*.f64 (/.f64 y (-.f64 z a)) (-.f64 z t)))
✓	0.0b	(/.f64 y (-.f64 z a))
✓	12.5b	(*.f64 (/.f64 y (-.f64 z a)) (-.f64 z t))

series101.0ms (1.8%)

Counts

3 → 132

Calls

3 calls:

47.0ms	(+.f64 x (*.f64 (/.f64 y (-.f64 z a)) (-.f64 z t)))
35.0ms	(*.f64 (/.f64 y (-.f64 z a)) (-.f64 z t))
19.0ms	(/.f64 y (-.f64 z a))

rewrite84.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

539×	`fma-def_binary64`
258×	`fma-neg_binary64`
250×	`expm1-udef_binary64`
250×	`log1p-udef_binary64`
136×	`add-sqr-sqrt_binary64`

Counts

3 → 134

Calls

3 calls:

81.0ms	(+.f64 x (*.f64 (/.f64 y (-.f64 z a)) (-.f64 z t)))
81.0ms	(/.f64 y (-.f64 z a))
81.0ms	(*.f64 (/.f64 y (-.f64 z a)) (-.f64 z t))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	36
1	255	34
2	3741	34
3	5315	34
0	0	0
1	0	0

simplify112.0ms (2%)

Algorithm

1×	egg-herbie

Rules

830×	`fma-def_binary64`
679×	`times-frac_binary64`
554×	`fma-neg_binary64`
528×	`cancel-sign-sub-inv_binary64`
277×	`sub-neg_binary64`

Counts

266 → 231

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	179	3947
1	496	3704
2	1773	3086
3	4584	3086
4	5019	3086

prune170.0ms (3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	230	1	231
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	232	4	236

Error

Counts

236 → 4

Alt Table

Status	Error	Program
▶	1.2b	(+.f64 x (/.f64 y (/.f64 (-.f64 z a) (-.f64 z t))))
	22.8b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 z a)) (+.f64 (/.f64 (.f64 y (.f64 a t)) (pow.f64 (-.f64 z a) 2)) x)) (/.f64 (.f64 y (*.f64 t z)) (pow.f64 (-.f64 z a) 2)))
✓	1.3b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
	10.3b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)))

Compiler

Compiled 5319 to 1688 computations (68.3% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 y (/.f64 (-.f64 z a) (-.f64 z t))))
	0.0b	(/.f64 (-.f64 z a) (-.f64 z t))
✓	1.9b	(/.f64 y (/.f64 (-.f64 z a) (-.f64 z t)))

series82.0ms (1.4%)

Counts

2 → 108

Calls

2 calls:

48.0ms	(+.f64 x (/.f64 y (/.f64 (-.f64 z a) (-.f64 z t))))
34.0ms	(/.f64 y (/.f64 (-.f64 z a) (-.f64 z t)))

rewrite87.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

294×	`fma-neg_binary64`
260×	`expm1-udef_binary64`
260×	`log1p-udef_binary64`
142×	`add-sqr-sqrt_binary64`
137×	`log1p-expm1-u_binary64`

Counts

2 → 81

Calls

2 calls:

84.0ms	(+.f64 x (/.f64 y (/.f64 (-.f64 z a) (-.f64 z t))))
84.0ms	(/.f64 y (/.f64 (-.f64 z a) (-.f64 z t)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	29
1	264	27
2	4092	27
3	5219	27
0	0	0
1	0	0

simplify139.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

669×	`fma-def_binary64`
539×	`times-frac_binary64`
519×	`cancel-sign-sub-inv_binary64`
469×	`associate-/l*_binary64`
444×	`fma-neg_binary64`

Counts

189 → 158

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	145	3341
1	420	3098
2	1517	2588
3	4527	2586
4	4979	2586
5	5000	2586
6	4982	2586

prune177.0ms (3.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	241	0	241
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	241	4	245

Error

Counts

245 → 4

Alt Table

Status	Error	Program
✓	1.2b	(+.f64 x (/.f64 y (/.f64 (-.f64 z a) (-.f64 z t))))
	22.8b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 z a)) (+.f64 (/.f64 (.f64 y (.f64 a t)) (pow.f64 (-.f64 z a) 2)) x)) (/.f64 (.f64 y (*.f64 t z)) (pow.f64 (-.f64 z a) 2)))
✓	1.3b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
	10.3b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)))

Compiler

Compiled 5800 to 1902 computations (67.2% saved)

regimes911.0ms (15.9%)

Accuracy

Total 1.1b remaining (98.5%)

Threshold costs 0b (0%)

Counts

125 → 1

Compiler

Compiled 18083 to 11104 computations (38.6% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	16	16
2	24	16
3	28	16
4	30	16
5	30	16

end66.0ms (1.1%)

Compiler: Compiled 117 to 70 computations (40.2% saved)

Details

analyze1.3s (23.4%)

sample1.2s (21.2%)

simplify119.0ms (2.1%)

prune6.0ms (0.1%)

localize9.0ms (0.2%)

series60.0ms (1%)

rewrite96.0ms (1.7%)

simplify94.0ms (1.6%)

prune122.0ms (2.1%)

localize8.0ms (0.1%)

series236.0ms (4.1%)

rewrite81.0ms (1.4%)

simplify123.0ms (2.1%)

prune273.0ms (4.7%)

localize15.0ms (0.3%)

series101.0ms (1.8%)

rewrite84.0ms (1.5%)

simplify112.0ms (2%)

prune170.0ms (3%)

localize7.0ms (0.1%)

series82.0ms (1.4%)

rewrite87.0ms (1.5%)

simplify139.0ms (2.4%)

prune177.0ms (3.1%)

regimes911.0ms (15.9%)

simplify2.0ms (0%)

end66.0ms (1.1%)

Profiling