Details

analyze2.2s (14.6%)

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
0%	99.8%	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
23.5%	76.3%	0.2%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample2.4s (16.3%)

Results

2.1s	8255×	body	128	valid
178.0ms	750×	body	128	invalid
1.0ms	1×	body	2048	valid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify123.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

1894×	`fma-neg_binary64`
843×	`div-sub_binary64`
750×	`fma-def_binary64`
582×	`times-frac_binary64`
397×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	18	16
2	37	14
3	78	14
4	163	14
5	295	14
6	645	14
7	1554	14
8	3040	14
9	3228	14
10	3469	14
11	3370	14
12	3363	14
13	3398	14
14	4949	14

prune13.0ms (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
▶	1.2b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
	12.3b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))

Compiler

Compiled 88 to 50 computations (43.2% saved)

localize16.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series132.0ms (0.9%)

Counts

2 → 96

Calls

2 calls:

85.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
46.0ms	(/.f64 (-.f64 z t) (-.f64 a t))

rewrite111.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

365×	`fma-def_binary64`
222×	`expm1-udef_binary64`
222×	`log1p-udef_binary64`
200×	`fma-neg_binary64`
192×	`log-pow_binary64`

Counts

2 → 77

Calls

2 calls:

107.0ms	(/.f64 (-.f64 z t) (-.f64 a t))
107.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	24
1	226	24
2	3220	24
3	5187	24
0	0	0
1	0	0

simplify235.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

878×	`fma-def_binary64`
678×	`cancel-sign-sub-inv_binary64`
618×	`times-frac_binary64`
513×	`fma-neg_binary64`
322×	`sub-neg_binary64`

Counts

173 → 152

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	172	2919
1	524	2907
2	1879	2271
3	4349	2257
4	5031	2257

prune246.0ms (1.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	148	4	152
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	149	5	154

Error

0.0b

Counts

154 → 5

Alt Table

Status	Error	Program
	28.6b	(-.f64 (+.f64 x (fma.f64 (/.f64 a t) y y)) (.f64 (/.f64 y t) (+.f64 z (/.f64 (.f64 z a) t))))
	12.3b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 a t)) x) (/.f64 (.f64 y t) (-.f64 a t)))
	31.0b	(pow.f64 (sqrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)) 2)
✓	1.2b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
▶	3.7b	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))

Compiler

Compiled 3512 to 1192 computations (66.1% saved)

localize22.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
✓	0.0b	(/.f64 y (-.f64 a t))
✓	10.3b	(*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t))

series182.0ms (1.2%)

Counts

3 → 132

Calls

3 calls:

88.0ms	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
62.0ms	(*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t))
31.0ms	(/.f64 y (-.f64 a t))

rewrite117.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

539×	`fma-def_binary64`
258×	`fma-neg_binary64`
248×	`expm1-udef_binary64`
248×	`log1p-udef_binary64`
135×	`add-sqr-sqrt_binary64`

Counts

3 → 134

Calls

3 calls:

110.0ms	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
110.0ms	(/.f64 y (-.f64 a t))
110.0ms	(*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	36
1	254	34
2	3702	34
3	5260	34
0	0	0
1	0	0

simplify199.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

791×	`fma-neg_binary64`
652×	`times-frac_binary64`
560×	`associate-/l*_binary64`
381×	`sub-neg_binary64`
222×	`associate--l+_binary64`

Counts

266 → 232

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	209	3939
1	608	3612
2	2177	3113
3	4943	3113
4	5559	3113

prune374.0ms (2.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	230	2	232
Fresh	2	1	3
Picked	1	0	1
Done	0	1	1
Total	233	4	237

Error

Counts

237 → 4

Alt Table

Status	Error	Program
	4.1b	(+.f64 x (pow.f64 (cbrt.f64 (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t))) 3))
✓	1.2b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
▶	3.6b	(+.f64 x (/.f64 (-.f64 z t) (/.f64 (-.f64 a t) y)))
	12.3b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 a t)) x) (/.f64 (.f64 y t) (-.f64 a t)))

Compiler

Compiled 5318 to 1691 computations (68.2% saved)

localize15.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 (-.f64 z t) (/.f64 (-.f64 a t) y)))
✓	0.0b	(/.f64 (-.f64 a t) y)
✓	11.2b	(/.f64 (-.f64 z t) (/.f64 (-.f64 a t) y))

series204.0ms (1.4%)

Counts

3 → 136

Calls

3 calls:

109.0ms	(+.f64 x (/.f64 (-.f64 z t) (/.f64 (-.f64 a t) y)))
76.0ms	(/.f64 (-.f64 z t) (/.f64 (-.f64 a t) y))
19.0ms	(/.f64 (-.f64 a t) y)

rewrite126.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

262×	`expm1-udef_binary64`
262×	`log1p-udef_binary64`
143×	`add-sqr-sqrt_binary64`
138×	`log1p-expm1-u_binary64`
138×	`expm1-log1p-u_binary64`

Counts

3 → 118

Calls

3 calls:

121.0ms	(+.f64 x (/.f64 (-.f64 z t) (/.f64 (-.f64 a t) y)))
121.0ms	(/.f64 (-.f64 a t) y)
121.0ms	(/.f64 (-.f64 z t) (/.f64 (-.f64 a t) y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	36
1	266	34
2	4203	34
3	5001	34
0	0	0
1	0	0

simplify189.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

990×	`cancel-sign-sub-inv_binary64`
904×	`fma-def_binary64`
521×	`times-frac_binary64`
374×	`sub-neg_binary64`
322×	`fma-neg_binary64`

Counts

254 → 199

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	178	3786
1	529	3198
2	1904	2956
3	4930	2956
4	5088	2956

prune307.0ms (2.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	199	0	199
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	199	4	203

Error

Counts

203 → 4

Alt Table

Status	Error	Program
▶	4.1b	(+.f64 x (pow.f64 (cbrt.f64 (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t))) 3))
✓	1.2b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
✓	3.6b	(+.f64 x (/.f64 (-.f64 z t) (/.f64 (-.f64 a t) y)))
	12.3b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 a t)) x) (/.f64 (.f64 y t) (-.f64 a t)))

Compiler

Compiled 4636 to 1435 computations (69% saved)

localize27.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 y (-.f64 a t))
✓	0.6b	(pow.f64 (cbrt.f64 (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t))) 3)
✓	7.3b	(cbrt.f64 (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
	10.3b	(*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t))

series4.8s (32.8%)

Counts

2 → 96

Calls

2 calls:

3.7s	(pow.f64 (cbrt.f64 (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t))) 3)
1.2s	(cbrt.f64 (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))

rewrite100.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

736×	`prod-diff_binary64`
229×	`log1p-udef_binary64`
127×	`add-sqr-sqrt_binary64`
124×	`log1p-expm1-u_binary64`
124×	`expm1-log1p-u_binary64`

Counts

2 → 95

Calls

2 calls:

96.0ms	(pow.f64 (cbrt.f64 (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t))) 3)
96.0ms	(cbrt.f64 (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	28
1	253	28
2	3397	28
3	5150	28
0	0	0
1	0	0

simplify279.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

869×	`fma-def_binary64`
364×	`*-commutative_binary64`
203×	`+-commutative_binary64`
147×	`sub-neg_binary64`
146×	`associate-+r+_binary64`

Counts

191 → 219

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	877	9683
1	3223	9491
2	4969	9491

prune702.0ms (4.8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	355	0	355
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	355	4	359

Error

Counts

359 → 4

Alt Table

Status	Error	Program
✓	4.1b	(+.f64 x (pow.f64 (cbrt.f64 (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t))) 3))
✓	1.2b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
✓	3.6b	(+.f64 x (/.f64 (-.f64 z t) (/.f64 (-.f64 a t) y)))
	12.3b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 a t)) x) (/.f64 (.f64 y t) (-.f64 a t)))

Compiler

Compiled 17094 to 8282 computations (51.6% saved)

regimes1.5s (10.3%)

Accuracy

Total 1.3b remaining (98.9%)

Threshold costs 0b (0%)

Counts

129 → 1

Compiler

Compiled 15584 to 10068 computations (35.4% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
3×	`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	11	16
1	15	16
2	21	16
3	23	16
4	24	16
5	24	16

end132.0ms (0.9%)

Compiler: Compiled 104 to 64 computations (38.5% saved)

Details

analyze2.2s (14.6%)

sample2.4s (16.3%)

simplify123.0ms (0.8%)

prune13.0ms (0.1%)

localize16.0ms (0.1%)

series132.0ms (0.9%)

rewrite111.0ms (0.8%)

simplify235.0ms (1.6%)

prune246.0ms (1.7%)

localize22.0ms (0.1%)

series182.0ms (1.2%)

rewrite117.0ms (0.8%)

simplify199.0ms (1.3%)

prune374.0ms (2.5%)

localize15.0ms (0.1%)

series204.0ms (1.4%)

rewrite126.0ms (0.9%)

simplify189.0ms (1.3%)

prune307.0ms (2.1%)

localize27.0ms (0.2%)

series4.8s (32.8%)

rewrite100.0ms (0.7%)

simplify279.0ms (1.9%)

prune702.0ms (4.8%)

regimes1.5s (10.3%)

simplify5.0ms (0%)

end132.0ms (0.9%)

Profiling