Details

analyze1.5s (29.3%)

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
10.1%	89.6%	0.2%	11
15.2%	84.6%	0.2%	12
20.5%	79.3%	0.2%	13
21.6%	77.1%	1.3%	14

Compiler

Compiled 15 to 10 computations (33.3% saved)

sample1.5s (29.7%)

Results

1.1s	8256×	body	128	valid
333.0ms	2544×	body	128	invalid

Compiler

Compiled 44 to 29 computations (34.1% saved)

simplify65.0ms (1.3%)

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

prune3.0ms (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
	7.4b	(fma.f64 y (/.f64 (-.f64 t z) a) x)
▶	4.4b	(-.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 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
✓	0.0b	(*.f64 y (-.f64 z t))
✓	5.5b	(/.f64 (*.f64 y (-.f64 z t)) a)

series54.0ms (1.1%)

Counts

3 → 144

Calls

3 calls:

28.0ms	(-.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
19.0ms	(/.f64 (*.f64 y (-.f64 z t)) a)
7.0ms	(*.f64 y (-.f64 z t))

rewrite26.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`add-sqr-sqrt_binary64`
41×	`*-un-lft-identity_binary64`
39×	`prod-diff_binary64`
37×	`add-cube-cbrt_binary64`
15×	`times-frac_binary64`

Counts

3 → 121

Calls

3 calls:

7.0ms	(/.f64 (*.f64 y (-.f64 z t)) a)
6.0ms	(*.f64 y (-.f64 z t))
5.0ms	(-.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))

simplify138.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

753×	`fma-def_binary64`
746×	`times-frac_binary64`
299×	`exp-prod_binary64`
213×	`cancel-sign-sub-inv_binary64`
208×	`fma-neg_binary64`

Counts

265 → 195

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	268	3653
1	555	3282
2	2075	2974
3	4562	2896
4	4877	2896

prune219.0ms (4.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	190	5	195
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	190	7	197

Error

Counts

197 → 7

Alt Table

Status	Error	Program
	4.5b	(-.f64 x (/.f64 1 (/.f64 a (*.f64 y (-.f64 z t)))))
	7.4b	(fma.f64 y (/.f64 (-.f64 t z) a) x)
✓	4.4b	(-.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
▶	1.5b	(fma.f64 (/.f64 y a) (fma.f64 -1 z t) x)
	35.7b	(/.f64 y (/.f64 a (-.f64 t z)))
	4.9b	(-.f64 x (/.f64 (/.f64 (.f64 y (-.f64 z t)) (.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 a)))
	4.5b	(-.f64 x (.f64 (.f64 y (-.f64 z t)) (/.f64 1 a)))

Compiler

Compiled 4017 to 1030 computations (74.4% saved)

localize9.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	1.5b	(fma.f64 (/.f64 y a) (fma.f64 -1 z t) x)

series24.0ms (0.5%)

Counts

1 → 60

Calls

1 calls:

24.0ms

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

simplify73.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

402×	`distribute-rgt-neg-out_binary64`
399×	`distribute-lft-neg-out_binary64`
377×	`distribute-rgt-in_binary64`
373×	`distribute-lft-in_binary64`
227×	`distribute-rgt-out_binary64`

Counts

70 → 33

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	40	875
1	79	750
2	165	733
3	440	733
4	2134	733
5	4825	733
6	5128	733

prune24.0ms (0.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	33	0	33
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	33	7	40

Error

Counts

40 → 7

Alt Table

Status	Error	Program
▶	4.5b	(-.f64 x (/.f64 1 (/.f64 a (*.f64 y (-.f64 z t)))))
	7.4b	(fma.f64 y (/.f64 (-.f64 t z) a) x)
✓	4.4b	(-.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
✓	1.5b	(fma.f64 (/.f64 y a) (fma.f64 -1 z t) x)
	35.7b	(/.f64 y (/.f64 a (-.f64 t z)))
	4.9b	(-.f64 x (/.f64 (/.f64 (.f64 y (-.f64 z t)) (.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 a)))
	4.5b	(-.f64 x (.f64 (.f64 y (-.f64 z t)) (/.f64 1 a)))

Compiler

Compiled 576 to 238 computations (58.7% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (/.f64 1 (/.f64 a (*.f64 y (-.f64 z t)))))
	0.0b	(*.f64 y (-.f64 z t))
✓	0.4b	(/.f64 1 (/.f64 a (*.f64 y (-.f64 z t))))
✓	5.5b	(/.f64 a (*.f64 y (-.f64 z t)))

series87.0ms (1.7%)

Counts

3 → 156

Calls

3 calls:

39.0ms	(/.f64 a (*.f64 y (-.f64 z t)))
28.0ms	(-.f64 x (/.f64 1 (/.f64 a (*.f64 y (-.f64 z t)))))
19.0ms	(/.f64 1 (/.f64 a (*.f64 y (-.f64 z t))))

rewrite62.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

188×	`times-frac_binary64`
127×	`add-sqr-sqrt_binary64`
124×	`*-un-lft-identity_binary64`
120×	`add-cube-cbrt_binary64`
96×	`prod-diff_binary64`

Counts

3 → 240

Calls

3 calls:

19.0ms	(-.f64 x (/.f64 1 (/.f64 a (*.f64 y (-.f64 z t)))))
7.0ms	(/.f64 1 (/.f64 a (*.f64 y (-.f64 z t))))
5.0ms	(/.f64 a (*.f64 y (-.f64 z t)))

simplify241.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

862×	`fma-def_binary64`
274×	`cancel-sign-sub-inv_binary64`
172×	`exp-prod_binary64`
169×	`fma-neg_binary64`
162×	`associate-l_binary64`

Counts

396 → 343

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	311	10611
1	754	7936
2	2669	6479
3	4539	6479
4	4767	6479

prune334.0ms (6.6%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	410	0	410
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	410	7	417

Error

Counts

417 → 7

Alt Table

Status	Error	Program
✓	4.5b	(-.f64 x (/.f64 1 (/.f64 a (*.f64 y (-.f64 z t)))))
	7.4b	(fma.f64 y (/.f64 (-.f64 t z) a) x)
✓	4.4b	(-.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
✓	1.5b	(fma.f64 (/.f64 y a) (fma.f64 -1 z t) x)
	35.7b	(/.f64 y (/.f64 a (-.f64 t z)))
	4.9b	(-.f64 x (/.f64 (/.f64 (.f64 y (-.f64 z t)) (.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 a)))
▶	4.5b	(-.f64 x (.f64 (.f64 y (-.f64 z t)) (/.f64 1 a)))

Compiler

Compiled 12773 to 4955 computations (61.2% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (.f64 (.f64 y (-.f64 z t)) (/.f64 1 a)))
	0.0b	(*.f64 y (-.f64 z t))
✓	5.6b	(.f64 (.f64 y (-.f64 z t)) (/.f64 1 a))

series62.0ms (1.2%)

Counts

2 → 108

Calls

2 calls:

40.0ms	(-.f64 x (.f64 (.f64 y (-.f64 z t)) (/.f64 1 a)))
21.0ms	(.f64 (.f64 y (-.f64 z t)) (/.f64 1 a))

rewrite19.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-exp-log_binary64`
14×	`add-cbrt-cube_binary64`
13×	`associate-r_binary64`
12×	`prod-exp_binary64`
11×	`*-un-lft-identity_binary64`

Counts

2 → 64

Calls

2 calls:

8.0ms	(.f64 (.f64 y (-.f64 z t)) (/.f64 1 a))
3.0ms	(-.f64 x (.f64 (.f64 y (-.f64 z t)) (/.f64 1 a)))

simplify70.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

640×	`distribute-rgt-in_binary64`
634×	`distribute-lft-in_binary64`
446×	`fma-def_binary64`
168×	`distribute-rgt-neg-in_binary64`
153×	`cancel-sign-sub-inv_binary64`

Counts

172 → 124

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	151	2142
1	384	2076
2	1335	1918
3	5314	1918

prune122.0ms (2.4%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	191	0	191
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	191	7	198

Error

Counts

198 → 7

Alt Table

Status	Error	Program
✓	4.5b	(-.f64 x (/.f64 1 (/.f64 a (*.f64 y (-.f64 z t)))))
	7.4b	(fma.f64 y (/.f64 (-.f64 t z) a) x)
✓	4.4b	(-.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
✓	1.5b	(fma.f64 (/.f64 y a) (fma.f64 -1 z t) x)
	35.7b	(/.f64 y (/.f64 a (-.f64 t z)))
	4.9b	(-.f64 x (/.f64 (/.f64 (.f64 y (-.f64 z t)) (.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 a)))
✓	4.5b	(-.f64 x (.f64 (.f64 y (-.f64 z t)) (/.f64 1 a)))

Compiler

Compiled 3546 to 1313 computations (63% saved)

regimes330.0ms (6.5%)

Accuracy

Total 1.5b remaining (99.4%)

Threshold costs 0b (0%)

Counts

28 → 3

Compiler

Compiled 3721 to 2526 computations (32.1% saved)

bsearch1.0ms (0%)

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

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	51
1	29	51
2	38	51
3	50	51
4	62	51
5	81	51
6	89	51
7	90	51
8	86	51

end88.0ms (1.7%)

Compiler: Compiled 186 to 108 computations (41.9% saved)

Details

analyze1.5s (29.3%)

sample1.5s (29.7%)

simplify65.0ms (1.3%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

series54.0ms (1.1%)

rewrite26.0ms (0.5%)

simplify138.0ms (2.7%)

prune219.0ms (4.3%)

localize9.0ms (0.2%)

series24.0ms (0.5%)

rewrite1.0ms (0%)

simplify73.0ms (1.4%)

prune24.0ms (0.5%)

localize12.0ms (0.2%)

series87.0ms (1.7%)

rewrite62.0ms (1.2%)

simplify241.0ms (4.7%)

prune334.0ms (6.6%)

localize8.0ms (0.2%)

series62.0ms (1.2%)

rewrite19.0ms (0.4%)

simplify70.0ms (1.4%)

prune122.0ms (2.4%)

regimes330.0ms (6.5%)

bsearch1.0ms (0%)

simplify5.0ms (0.1%)

end88.0ms (1.7%)

Profiling