Details

analyze1.2s (26.3%)

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
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
13.2%	86.5%	0.2%	11
16.8%	83%	0.2%	12
22.7%	77.1%	0.2%	13
24.1%	74.7%	1.3%	14

Compiler

Compiled 15 to 10 computations (33.3% saved)

sample127.0ms (2.7%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
3.0ms	83×	body	128	invalid

Compiler

Compiled 34 to 24 computations (29.4% saved)

simplify67.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

783×	`fma-neg_binary64`
721×	`fma-def_binary64`
244×	`cancel-sign-sub-inv_binary64`
187×	`distribute-rgt-in_binary64`
138×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	17	13
2	39	13
3	98	13
4	258	11
5	542	11
6	1019	11
7	1302	11
8	1414	11
9	1470	11
10	1476	11
11	1481	11
12	1481	11
13	1408	11

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
▶	6.4b	(fma.f64 y (/.f64 (-.f64 t z) a) x)
	7.4b	(-.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))

Compiler

Compiled 76 to 46 computations (39.5% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 t z) a)
✓	6.1b	(fma.f64 y (/.f64 (-.f64 t z) a) x)

series45.0ms (0.9%)

Counts

2 → 88

Calls

2 calls:

29.0ms	(fma.f64 y (/.f64 (-.f64 t z) a) x)
15.0ms	(/.f64 (-.f64 t z) a)

rewrite8.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`*-un-lft-identity_binary64`
20×	`add-sqr-sqrt_binary64`
15×	`times-frac_binary64`
12×	`add-cube-cbrt_binary64`
5×	`associate-/l*_binary64`

Counts

2 → 50

Calls

2 calls:

5.0ms	(/.f64 (-.f64 t z) a)
0.0ms	(fma.f64 y (/.f64 (-.f64 t z) a) x)

simplify91.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

696×	`distribute-rgt-in_binary64`
684×	`distribute-lft-in_binary64`
583×	`times-frac_binary64`
453×	`fma-def_binary64`
215×	`div-sub_binary64`

Counts

138 → 78

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	111	1607
1	238	1462
2	525	1460
3	1333	1460
4	4886	1460
5	4983	1460

prune54.0ms (1.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	74	4	78
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	75	5	80

Error

0.0b

Counts

80 → 5

Alt Table

Status	Error	Program
	6.4b	(fma.f64 y (/.f64 1 (/.f64 a (-.f64 t z))) x)
▶	2.8b	(fma.f64 (/.f64 y a) (-.f64 t z) x)
	38.2b	(fma.f64 y (*.f64 (sqrt.f64 (-.f64 t z)) (/.f64 (sqrt.f64 (-.f64 t z)) a)) x)
	7.4b	(-.f64 (+.f64 (/.f64 (.f64 y t) a) x) (/.f64 (.f64 y z) a))
✓	6.4b	(fma.f64 y (/.f64 (-.f64 t z) a) x)

Compiler

Compiled 1187 to 343 computations (71.1% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.7b	(fma.f64 (/.f64 y a) (-.f64 t z) x)

series26.0ms (0.5%)

Counts

1 → 60

Calls

1 calls:

26.0ms

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

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

0.0ms

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

simplify73.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

426×	`distribute-lft-neg-out_binary64`
425×	`distribute-rgt-neg-out_binary64`
378×	`distribute-rgt-in_binary64`
375×	`distribute-lft-in_binary64`
225×	`distribute-rgt-out_binary64`

Counts

70 → 27

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	40	863
1	76	750
2	164	733
3	450	733
4	2142	733
5	4579	733
6	5069	733

prune18.0ms (0.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	27	0	27
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	27	5	32

Error

0.0b

Counts

32 → 5

Alt Table

Status	Error	Program
▶	6.4b	(fma.f64 y (/.f64 1 (/.f64 a (-.f64 t z))) x)
✓	2.8b	(fma.f64 (/.f64 y a) (-.f64 t z) x)
	38.2b	(fma.f64 y (*.f64 (sqrt.f64 (-.f64 t z)) (/.f64 (sqrt.f64 (-.f64 t z)) a)) x)
	7.4b	(-.f64 (+.f64 (/.f64 (.f64 y t) a) x) (/.f64 (.f64 y z) a))
✓	6.4b	(fma.f64 y (/.f64 (-.f64 t z) a) x)

Compiler

Compiled 419 to 138 computations (67.1% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 a (-.f64 t z))
✓	0.5b	(/.f64 1 (/.f64 a (-.f64 t z)))
✓	6.1b	(fma.f64 y (/.f64 1 (/.f64 a (-.f64 t z))) x)

series74.0ms (1.6%)

Counts

3 → 120

Calls

3 calls:

30.0ms	(fma.f64 y (/.f64 1 (/.f64 a (-.f64 t z))) x)
23.0ms	(/.f64 a (-.f64 t z))
21.0ms	(/.f64 1 (/.f64 a (-.f64 t z)))

rewrite31.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

138×	`times-frac_binary64`
103×	`*-un-lft-identity_binary64`
103×	`add-sqr-sqrt_binary64`
71×	`add-cube-cbrt_binary64`
26×	`associate-/r*_binary64`

Counts

3 → 159

Calls

3 calls:

7.0ms	(/.f64 1 (/.f64 a (-.f64 t z)))
4.0ms	(/.f64 a (-.f64 t z))
0.0ms	(fma.f64 y (/.f64 1 (/.f64 a (-.f64 t z))) x)

simplify180.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

382×	`fma-neg_binary64`
340×	`times-frac_binary64`
325×	`associate-/l*_binary64`
268×	`fma-def_binary64`
223×	`associate-/r*_binary64`

Counts

279 → 229

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	204	4381
1	421	3949
2	1210	3759
3	3983	3759
4	4992	3759
5	4962	3759

prune153.0ms (3.2%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	229	0	229
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	229	5	234

Error

0.0b

Counts

234 → 5

Alt Table

Status	Error	Program
✓	6.4b	(fma.f64 y (/.f64 1 (/.f64 a (-.f64 t z))) x)
✓	2.8b	(fma.f64 (/.f64 y a) (-.f64 t z) x)
	38.2b	(fma.f64 y (*.f64 (sqrt.f64 (-.f64 t z)) (/.f64 (sqrt.f64 (-.f64 t z)) a)) x)
▶	7.4b	(-.f64 (+.f64 (/.f64 (.f64 y t) a) x) (/.f64 (.f64 y z) a))
✓	6.4b	(fma.f64 y (/.f64 (-.f64 t z) a) x)

Compiler

Compiled 4299 to 1493 computations (65.3% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 (/.f64 (.f64 y t) a) x) (/.f64 (.f64 y z) a))
✓	0.0b	(+.f64 (/.f64 (*.f64 y t) a) x)
✓	6.4b	(/.f64 (*.f64 y z) a)
✓	6.4b	(/.f64 (*.f64 y t) a)

series89.0ms (1.9%)

Counts

4 → 72

Calls

4 calls:

40.0ms	(-.f64 (+.f64 (/.f64 (.f64 y t) a) x) (/.f64 (.f64 y z) a))
18.0ms	(+.f64 (/.f64 (*.f64 y t) a) x)
18.0ms	(/.f64 (*.f64 y t) a)
13.0ms	(/.f64 (*.f64 y z) a)

rewrite38.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`*-un-lft-identity_binary64`
30×	`add-sqr-sqrt_binary64`
28×	`prod-diff_binary64`
28×	`add-cube-cbrt_binary64`
24×	`times-frac_binary64`

Counts

4 → 126

Calls

4 calls:

10.0ms	(+.f64 (/.f64 (*.f64 y t) a) x)
9.0ms	(-.f64 (+.f64 (/.f64 (.f64 y t) a) x) (/.f64 (.f64 y z) a))
4.0ms	(/.f64 (*.f64 y z) a)
4.0ms	(/.f64 (*.f64 y t) a)

simplify135.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

900×	`times-frac_binary64`
670×	`fma-def_binary64`
192×	`cancel-sign-sub-inv_binary64`
173×	`neg-mul-1_binary64`
161×	`fma-neg_binary64`

Counts

198 → 179

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	210	3211
1	531	2770
2	1879	2409
3	4417	2409
4	4914	2409
5	4887	2409

prune240.0ms (5.1%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	177	2	179
Fresh	0	1	1
Picked	0	1	1
Done	1	2	3
Total	178	6	184

Error

0.0b

Counts

184 → 6

Alt Table

Status	Error	Program
	38.2b	(fma.f64 y (*.f64 (sqrt.f64 (-.f64 t z)) (/.f64 (sqrt.f64 (-.f64 t z)) a)) x)
✓	7.4b	(-.f64 (+.f64 (/.f64 (.f64 y t) a) x) (/.f64 (.f64 y z) a))
	7.4b	(-.f64 (+.f64 (/.f64 (.f64 y t) a) x) (.f64 (*.f64 y z) (/.f64 1 a)))
	34.8b	(-.f64 (+.f64 (/.f64 (.f64 y t) a) x) (.f64 (/.f64 y (sqrt.f64 a)) (/.f64 z (sqrt.f64 a))))
✓	2.8b	(fma.f64 (/.f64 y a) (-.f64 t z) x)
✓	6.4b	(fma.f64 y (/.f64 (-.f64 t z) a) x)

Compiler

Compiled 4255 to 753 computations (82.3% saved)

regimes892.0ms (18.9%)

Accuracy

Total 0.3b remaining (93.9%)

Threshold costs 0.3b (93.9%)

Counts

41 → 3

Compiler

Compiled 6046 to 3830 computations (36.7% saved)

bsearch1.0ms (0%)

Compiler: Compiled 10 to 7 computations (30% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

9×	`+-commutative_binary64`
8×	`*-commutative_binary64`
8×	`sub-neg_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	56
1	37	56
2	50	56
3	63	56
4	70	56
5	73	56
6	74	56
7	74	56

end1.0ms (0%)

Compiler: Compiled 43 to 23 computations (46.5% saved)

sample1.1s (23.2%)

Algorithm

1×

intervals

Results

366.0ms	8000×	body	128	valid
127.0ms	2565×	body	128	invalid

Compiler

Compiled 168 to 101 computations (39.9% saved)

Details

analyze1.2s (26.3%)

sample127.0ms (2.7%)

simplify67.0ms (1.4%)

prune4.0ms (0.1%)

localize7.0ms (0.1%)

series45.0ms (0.9%)

rewrite8.0ms (0.2%)

simplify91.0ms (1.9%)

prune54.0ms (1.1%)

localize6.0ms (0.1%)

series26.0ms (0.5%)

rewrite1.0ms (0%)

simplify73.0ms (1.6%)

prune18.0ms (0.4%)

localize8.0ms (0.2%)

series74.0ms (1.6%)

rewrite31.0ms (0.7%)

simplify180.0ms (3.8%)

prune153.0ms (3.2%)

localize9.0ms (0.2%)

series89.0ms (1.9%)

rewrite38.0ms (0.8%)

simplify135.0ms (2.9%)

prune240.0ms (5.1%)

regimes892.0ms (18.9%)

bsearch1.0ms (0%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample1.1s (23.2%)

Profiling